String Theory
for Kids, Teens, even Adults
Henry Bernatowicz
Chapters
1. What Is String Theory?
2. Classical Physics
6. Cosmology – Mom, Where’d You Put My Universe
What Is String Theory?
Strings are all around you. Your clothes are made of strings woven into cloth. Spider webs are string. To physicists, who study energy and matter, a string is anything much longer than it is wide. The cables that hold up suspension bridges are strings even though they are six inches thick. Some people collect string and wind it in a ball. No one knows why. A scientist would even call your DNA a string, though it curls up and those curls curl up and so on. Your DNA stretched out like a string would be a few meters long. To a mathematician a string has no width, only length. Scientists are beginning to believe that absolutely everything, from stars to cotton candy, may be made of string, very tiny mathematician’s string. This is string theory.
String theory is very weird, more than you can imagine. It involves higher dimensions and other universes. Vibrating strings make up everything. Everything is chunky and fuzzy when you look at it close enough. You can still hear and see the Big Bang that started the universe. Black holes are hairy. Is dark energy making you lose weight? Is dark chocolate matter making you gain weight? Instead of using the dog-ate-my-homework excuse, try this one. “I left it in the eighth dimension.”
String theory is the first theory of physics that tries to explain everything. What does it mean to explain everything? We would know how the universe began and where it is going. A theory of everything would explain everything we feel, see, or measure. We would understand all the forces and all types of matter. We would know what is most basic and how everything else is composed of these basic parts. Could the universe have been different? Are there other universes? A theory of everything should answer these questions. Every big scientific discovery changes how we think about our purpose and ourselves. String theory is the biggest, most exciting change that ever happened in science.
As you read, you will find this symbol ξ looking like a wiggly string. It means, pause here and answer a question or think about what you just read. “I don’t know or understand,” can be your answer, but it is more fun to guess. Answers will come as you read more. You will also sometimes find a String Break!
This is a way to relax before plunging further into string theory. String breaks contain forgettable facts about strings. Finally, there are quotes from Albert Einstein. He was the world’s most famous scientist, recognized as the most important man of the 20th century. All his life he had trouble with his hair. This led him to discover several hairdos: the afro, the cotton ball, and spiked hair. Here he is in wilting spiked hair with the first quote.
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“The important thing is not to stop questioning. |
Curiosity has its own reason for existing.” A. Einstein
To understand string theory we have to know about some of the discoveries of the last century. Science almost never says that an old theory is wrong. Scientists test a theory every way they can imagine. If it passes the tests, the theory is true for all the stuff tested. If it does not pass, then you modify the theory. The old theories were carefully tested. That means string theory has to give the same results. It may not replace many theories. It will mostly add to them or pull together different looking parts into a whole. That is why we have to know what was happening in physics before string theory. String theory depends on the theories of the 20th century.
Big Numbers and Small Numbers
To understand physics, it helps to be comfortable with big and small numbers. Science gives most of its results as numbers. We are going to discuss everything from strings, much smaller than an atomic nucleus, to the whole universe. Scientists have a way to give an estimate of the sizes of things. They round the number to the nearest power of ten and just keep track of the number of zeros in an exponent, a little number to the upper right of the ten. For example, in this notation, 822 to the nearest power of ten is 1000 or 10+3 in the shorthand. There are three zeros in 1000. The number 147 is closer to 100 than 1000 so it is 10+2.
There is a similar trick for small numbers. A proton is about 0.000000000000001 meters. That is 14 zeros and a 1 after the decimal point. If you wrote it as a fraction, it would be 1/1,000,000,000,000,000. One divided by a one followed by 15 zeros. That is small. It is one quadrillionth. In shorthand, it is 10-15 meters, our small number. The minus sign tells us the number is less than one and the number zeros you would need to write it as a fraction.
A billion is one followed by nine zeros. A trillion is one followed by twelve zeros. A quadrillion is one followed by fifteen zeros. Other Western languages use trillion and quadrillion but they have different values. Our quadrillion is the British trillion. In exponential notation, everyone agrees. The table shows that the exponential notation is neat, simple, and easy to read.
Three Ways to Write Large and Small Numbers
10-30 0.0000000000000000000000000000001 One quadrillionth of a quadrillionth
10-8 0.00000001 Ten trillionths
100 1.0 One
10+10 10,000,000,000 Ten billions
10+41 100,000,000,000,000,000,000,000, 100 billion quadrillion quadrillions
000, 000,000,000,000,000
Big things are very big and small things are very small. The number of bacteria end-to-end it would take to cross the universe is almost the same as the number of strings it would take to be as long as a bacterium. ξ The biggest things are huge. Humans and our piece of the universe are insignificant judging by size alone.
We are only aware of the things that are near our size, about a meter. Bacteria, 10-5
meters long cause strep throat. Your fingertip can just barely detect an edge that size. One of the biggest things in our environment is a skyscraper, 10+3 meters. That gives a range of sizes in our piece of the universe of about eight powers of ten. A skyscraper is 10+8, or 100,000,000 times bigger than a bacterium. This is just a tiny slice of the universe that covers 61 powers of 10. The universe is 10+61 times bigger than the smallest thing, a string. String theory aims to explain it all.
The number to the upper right of the ten, the exponent, tells the story. Negative exponents mean small numbers. Positive exponents mean big numbers. The larger the number in the exponent, the bigger the number is if it is a positive exponent. The larger a negative exponent is, smaller the number is. The range of sizes of parts of the universe is amazing.
How BIG and How Small Things Are
String Proton Atom Bacteria Kid Earth Solar System Milky Way Universe
10-35 10-15
10-11 10-5 1 10+8
10+13
10+21 10+26 meters
Science explores the wonders of the universe we cannot directly see. To study the very large we have telescopes, satellites, and space probes. For the very small there are microscopes. The electron microscope can detect individual atoms. Is there anything smaller? ξ There sure is. Atoms are made of elementary particles. To see that small we need a different tool, particle accelerators, once called atom smashers. Elementary particles contain strings. The strings of string theory are the smallest things that can exist in the universe. We will never see them, but they explain all there is. String theory is a theory of everything, but it is not the first. We will look next at some of the oldest theories of everything.
Myths and Creation Stories
Men and women have always been curious. We want to know who we are, where we came from, how the world began, and why the world is the way it is. We do not know what life was like for cave dwellers. They could not write. They left behind little more than their bones. Therefore, this is just a guess. For cave dwellers, these questions were answered by the strongest one in the tribe, later by the holiest, and then by the smartest. The questioning led first to myths, then religions, and to science. The first idea was that gods and other supernatural beings lived in everything: trees, animals, stars, water, and sky. This idea is still found in the most isolated and primitive tribes.
Cave dwellers had a hard life, with little time for thinking. They were constantly searching for their next meal and hiding from saber tooth tigers and other nasty animals. Eventually, they learned how to hunt, protect themselves, and grow some food. Then a new thing happened, spare time. They had spare time but no video games. What should they do? What would you do? ξ Cavemen began to play, explore, observe, think, ask questions about the world, and make art. This happened about 40,000 years ago. Their biggest questions were the same as ours. Why am I here? Why is the world as it is? About 10,000 years ago, men started developing complex myths and the first religions. We are going to learn about some of these before we tackle science.
Even before we got smart enough to carefully observe nature, we wanted an explanation of how humans and the world began. Here are the stories of some ancient peoples. While you are reading, try to notice errors or holes, something not explained, in these stories. Is the story more complicated than what it tries to explain?
Australian Aborigines
– The ancient people of Australia believe that the Earth started bare and flat but many things slept under the Earth including their ancestors. The ancestors woke up and wandered around the Earth in strange forms, sometimes animal, sometimes plant, and often all mixed up and missing parts. Two beings popped into existence out of nothing, they were the Ungambikula. Wandering the world, they found half-made human beings everywhere. They took great stone knives and carved all the badly formed part humans into real humans.
What do you think of this story? Does it leave a lot not explained? What are some holes? ξ Where did those ancestors in the ground come from? Can things pop into existence out of nothing? ξ Surprise! Modern physics found that strings could pop into existence out of nothing.
Chinese
– Phan Ku hatched from a giant cosmic egg. He pushed half the shell above him as the sky, the other half below him was the Earth. He grew taller each day for 18,000 years, gradually pushing the pieces apart until they reached the correct places. After all this effort, Phan Ku fell apart. His limbs become the mountains, his blood the rivers, his breath the wind and his voice the thunder. His eyes are the sun and the moon. The fleas in his hair became human beings. Ugh!
Greek
– This myth is more recent than the others are and is more complex. All is emptiness, except for two things, Nyx, a bird with black wings, and the wind. Nyx laid a golden egg, and for ages she sat on it. Finally, life began to stir in the egg and out came Eros, god of love. One-half of the shell rose into the air and became the sky. Eros made Nyx and the wind fall in love. They had many children who were giant gods, the Titans. The Titans had children and grandchildren, who were normal sized. They were afraid of the grandchildren. Cronus decided to protect himself. He swallowed his grandchildren when they were still infants. Ugh! Zeus hid and was not swallowed. He made Cronus barf up his brothers and sisters. Double ugh! They battled the Titans and took over. Soon the Earth was looking good but without humans and animals. Zeus told his sons to go to Earth, make them, and give each a gift like speed, the ability to swim, or camouflage. One son used up all the gifts making the animals. The other, Prometheus, had nothing to give to humans, so he gave them fire. This made Zeus mad. Earth was like the Garden of Eden, and fire gave man too much power. Zeus got even by giving Pandora a pretty box she was never to open. Of course she did, releasing wars, sickness, skinned knees, and playground bullies.
Are you glad we got fire even though we got all the troubles in Pandora’s Box? ξ Notice how much you have to accept to believe this story. Do you have to accept more than it explains?
Iroquois Indians
– They believed that at first there was only an island in the sky, where the sky people lived. Maybe it was a flying saucer. No one died and no one was born. Then a sky woman discovered she was going to have twin sons. Her husband got mad and threw her out of the sky. Kids would change things. She fell down to the water covering the Earth where animals caught her and made her a place by spreading mud on a giant turtle’s back. The mud grew big as North America. One son was good and one evil. They created the rest of the Earth. They made animals and humans. The bad son made all the bad things like bones in fish, thorns around roses, winter without snow, and poison ivy.
Where did the sky people come from? ξ Many other creation myths have the world created by opposites such as good/bad, man/woman, creative/destructive.
Hindu
– According to the story, an elephant supports the world. But, someone asked what holds up the elephant? A turtle. What supports the turtle? A bigger turtle. Well, what supports that turtle? After that, it’s turtles all the way down. This story illustrates how an explanation may not explain anything but just puts off having to answer the real question.
Bible
– God took seven days. He created light and separated it from darkness. A separation of light and darkness happens in the Big Bang. Then he made the rest of the world. Man was last. He started with just Adam and Eve, in the Garden of Eden. God said do not eat the fruit of a certain tree, but of course, they did. That was like Pandora’s Box, and since then we have had a hard time. They had to leave paradise and populate the Earth.
Which creation story do you like best? What story seems most true to you? ξ Imagine that science never happened. You might believe the world is on an elephant on a stack of turtles and that your ancestors were fleas in a giant’s hair. ξ The story of string theory is going to seem even stranger to you.
Physics Begins with Astronomy
Science started about 2000 years ago with the first tries at biology, astronomy, and medicine. Physical science, study of non-living things, started 500 years later. There were reasons for the slow start. Science was confused with magic and witchcraft and religion opposed it. In addition, science demands concentration, time, and record keeping. All were in short supply several thousand years ago. The first physical science was astronomy. Astronomy was important because it could predict the seasons and tell when to start planting. Many civilizations built monuments like Stonehenge to tell the seasons.
The Greeks and later the Christians thought the Earth was imperfect. There was hunger, disease, and death. However, the stars looked perfect. They were little twinkling points of light that moved smoothly across the heavens with the seasons. Anyone looking up on a dark night could see that the stars circled the Earth. The Greeks decided the sun and stars hung on a moving glass sphere with the flat Earth at the center. The sphere was the Greek ideal of perfection. This model of the universe was beautiful and simple. Then someone noticed that a few stars moved at different speeds. The Greeks called them planets, meaning wanderers. They decided they could still keep the heavens neat if the each planet moved on a different glass sphere. The spheres moved in perfect circles around the Earth. They even had a phrase to describe this perfection, “the music of the spheres.” Not the kind of music you hear with your ears.
As observations got more accurate and covered more years, the Greeks found that this did not work. The planets sometimes moved backwards and then went forwards again. Ptolemy, a mathematician, developed the most sophisticated model of the motions of the Earth-centered solar system. He was great at algebra and geometry. That was all the math Greeks knew.
In order to follow the details of planetary motions, his model was very complex. He could fix things up if the planets stuck to smaller glass spheres that rolled around outside the original planetary spheres. The original glass spheres also had to shift off center from the Earth. Even that did not quite work so he ended up with 39 spheres. The sun still circled the Earth. The glass sphere approach was beginning to look cracked. Why didn’t someone ask where all that glass came from? What is holding up the flat Earth? Those are two holes in that theory. You know much more science than all the ancient Greeks combined.
Copernicus finally got it right. He put the sun at the center and the model simplified. Religion, however, favored Ptolemy’s view of the heavens and did not want to hear anything else. What do you think of religions trying to block the facts of astronomy? ξ Which is the better theory Ptolemy, or Copernicus? ξ If they both accurately fit observations, which is the better theory? ξ Hurray, if you chose Copernicus. Scientists have a profound faith in the beauty and simplicity of the world. They believe that the world’s beauty should show in the beauty and simplicity of their theories. They also have faith in math. Some Greeks thought mathematics was abstract perfection.
This look at early astronomy shows how science works. Make a theory from the first available data—stars and planets move smoothly across the sky. Test it by more observations. Planets move differently. Use math, the language of science. If it fits the theory, that is great. If not, try for a better theory. The Greeks added more glass spheres resulting in a very complex theory. Copernicus moved the sun to the center. Copernicus’s theory was more accurate and much simpler than the Greek’s model. Sometimes the new data is something we missed; sometimes a new piece of equipment gives data never imagined. Galileo made the telescope. With it, he could see moons of Jupiter, and the phases of Venus. This made him certain that the Earth circled the sun. New data and striving for simplicity makes a better theory.
Classical Physics
At the start of science, the basic stuff of the universe was the four ancient elements – Earth, wind, fire, and water. Different mixes of these four elements made everything. We still describe people by the properties of these four elements. He has a fiery temper. Nice people go with the flow. Classical physics began with machines and mechanics, the science of motion. This included the motions of the planets and stars. Classical physics is the period 1700-1900. Before classical physics, there was not a good theory of matter.
Classical science discovered the 92 modern elements and their atoms. If you started dividing a little bit of gold smaller and smaller, you could not get a piece of gold smaller than a gold atom. Atoms made everything. Atoms were the smallest things that could exist. They were hard little balls, a different ball for each of the elements.
The greatest classical physicist was Newton. Around 1700, he discovered three laws of motion. The first is the law of inertia; objects do not change speed or direction unless acted on by a force. The second law says that if there is a force on an object, it changes the speed, causing a constant acceleration. The third says every action has an equal but opposite reaction. The laws of motion applied to every moving thing. Other scientists were beginning to understand parts of this but Newton put it all together. Newton’s laws helped the industrial revolution happen. Gravity and the electromagnetic force are two of the fundamental forces string theory unifies.
Newton’s Law of Gravitation
His other big accomplishment was the law of gravitation. It says there is an attractive force between any two objects that have mass. It also tells us how to calculate the gravitational force. Before Newton, there was not even a word for gravity. Newton had to invent it. We walked around on the Earth because that is how it is. We stand on the ground. If there were, something holding us down, no one could imagine it could also hold the Earth around the sun, no one except Newton. The Greeks and Copernicus made models that duplicated the movements of the stars and planets. They did not know why they moved. Newton provided that answer. There was not another scientist as great as Newton until Darwin in the 1800’s. Darwin’s work with evolution provided the framework for the study of living things like Newton did for non-living.
Newton had to develop a new math, calculus, to describe the motions of machines, falling objects, planets, and clocks. Calculus is about position, speed, time, and acceleration. If you know some of these, calculus lets you figure out the others. It is even more powerful. If you know physics and the starting positions and velocities of the planets, for example, then with calculus and Newton’s laws you can calculate their positions and velocities for any time in the distant future or in the past. When Newton applied mechanics, the study of motion, to the planets, he found that their orbits never were circles. They travel in an ellipse, a squashed circle.
He came up with an equation to describe the force of gravity between two masses. Objects feel this force even when they do not touch, even when they are all the way across the solar system, even all the way across the universe. Fields are forces that work without contact. Every mass surrounds itself with a gravitational field of force. Iron filings and a magnet show the magnetic field.
[Figure force field, illustration] Nobody understood forces until Newton. He also determined how bodies responded to force. This defined inertia and acceleration. Then with a simple equation and calculus, Newton could predict the orbits of planets. A mathematician in Newton’s time was studying curves, looking at position, slope, and change of slope, which are similar to position, velocity, and acceleration that Newton was studying. Frequently science and math develop together. Sometimes math is ahead, sometimes science.
Newton wrote this equation for the force of gravity between two masses:
F = GmM / R2
F is the force of gravity; m is the light mass; M is the heavy mass; R is the distance apart; G is a constant, the gravitational field strength.
Do not be afraid of equations. They just say that the left side equals the right side. They are just shorthand for how to calculate something. Scientists usually leave out the, multiplication signs between two variables. If variables are next to each other, like mM, it means multiply these two masses. This equation says to calculate the force of attraction between a mass m (you for example) and a larger mass M (the Earth), multiply the masses, divide by the separation squared R2, or R times R. The separation is the distance between you and the center of the Earth. Then multiply the result by the gravitational force constant G, a number. If you do that, then you have figured out the numerical force of gravity, F, on you. If you put in the actual numbers for the symbols G, m, M, and R, you would find that the force on you, F, is your weight. It is interesting that you pull on the Earth as hard as it pulls on you. That is Newton’s law of action-reaction. The Earth is too heavy to notice.
The equation tells us gravity gets stronger if the masses are heavier. What happens if the masses get closer? R gets smaller; the force is stronger. The closer the masses are, the stronger the attraction. In fact, if R = 0, the force is infinite. That can only happen if the masses have zero radiuses.
In 20th century physics, theoretical physicists treated elementary particles, protons and neutrons, as if they are points. Their radius is zero, but they have mass. Zero radius means they can get so close that their separation is zero so R = 0. No matter what the numerator GmM is, divide it by zero and the result is ∞, infinite. Is the gravitational force between elementary particles infinite? Do you believe it? ξ In the real world, values of measurements can equal zero but they cannot be infinite. Only string theory solves this problem. It took three paragraphs to explain Newton’s equation for gravity. This is why physicists like math and equations. With a glance, they can understand all the above and more.
How big is infinity? Think of the biggest number you can. Then multiply it by itself. Do that ten times and you are still nowhere near infinity. Subtract the biggest number you can think of from infinity and the result is still infinity. All you can say about infinity is that it’s bigger than that. Here is another example. If you throw dice, there is a chance that the dice will stop with snake eyes, both sides with one dot up. On average, snake eyes turn up one time in 24. If everyone on earth rolled dice, what is the chance of all rolling snake eyes? ξ It is impossibly small—never in a billion years. What if everyone rolled an infinite number of times? How many times would all snake eyes appear? All snake eyes would occur an infinite number of times. No, that does not mean it happens every time. This is like a bunch of monkeys typing at random for a long enough time. One of them would type a whole Shakespeare play at random. Another would type the whole play but misspell “The End” as “The E%$##”. One would start it off by typing “a Play by YOUR NAME.” There is a lot of room in infinity for nearly everything you can imagine. Things get strange when you are dealing with infinity. xxstopped
Infinity was not a problem for Newton. He did not know and could not imagine anything with a zero radius. For him everything had a size, from a speck of dust to Jupiter, all non-zero. Therefore, for him the separation between the centers of two objects could never be zero. We will soon look at some physics that sometimes gives infinity for exactly this reason. To a physicist infinity usually means he did not just make a mistake, he made a BIG mistake.
| String Break! Native people in Asia, Australia, Africa, the Arctic, the Americas, and the Pacific discovered the fun of playing with a loop of string to make designs. This one is flock of birds, from the South Pacific. Some designs are ancient. There are over 2000 designs. Why did people do this? |
They didn’t have entertainment so they had a lot of time on their hands, which turned into string on their hands. Cat’s Cradle is a game, played with a loop of string, where one person makes a pattern. Then another lifts the string into a new pattern. String theorists do this while waiting for their computer to finish a calculation. You can find out more about string loop patterns at http://www.isfa.org/.
Electricity and Magnetism
Newton pretty much settled the study of motion. Later, other scientists tried to understand electricity and magnetism. Classical physics discovered electricity and also discovered magnetism but at first did not understand them. Physics knew of three forces. They were gravity, electricity, and magnetism. At first, electricity and magnetism were only good for impressing your friends by making their hair stand on end.
In the late 19th century, James Clerk Maxwell found equations that explained electricity and magnetism and showed that they are different views of the same thing. There are four Maxwell’s equations. They are complex, relating currents and charges to electric and magnetic fields and how they vary with distance and with time. The equations say that moving electricity, a current, generates a magnetic field. That is how loudspeakers work. A moving magnetic field generates a current of electricity. That is how a car alternator works.
Maxwell discovered that one solution of his equations was a wave that could travel through empty space. This was something that popped out of the math, but was totally unknown and unexpected. What do you think physicists did? ξ Did they send him to remedial math? Try for a theory that did not predict silly things? Use the equations for everything else? Physicists did not do anything like that. They started looking for those waves. They believed the equations more than experience or common sense. They were right. Experimenters made radio waves and showed that they moved through empty space. Not only that, light is also a wave of electricity and magnetism.
The Missing Paper Caper
Physics is the most complex science. It is the study of matter and energy. Matter can range from the particles inside an atom to all the matter in the universe. How do physics and the other sciences work? Is it different from myth? ξ Science relies on observation, experiments, and confirming predictions. Myths rely on faith in people’s thought, feelings, and imagination.
Sometimes there are two or more explanations when something happens. For example, your teacher wants you to take a book to the library. When you come back, your book report is gone (observation one). Courtney tells you that three crows flew into the room, shredded your paper, and flew away with it to make a nest (theory one). James tells you that Courtney took it (theory two). You remember that the window was closed (observation two), but Courtney says the teacher opened it because it was hot. This explanation added to theory one to explain contradictory observation two.
What do you think of Courtney’s explanation? ξ Courtney’s story is complicated. Like a scientist, you think about predictions of Courtney’s story and observe if the predictions are true. If the window was open, it should still be open (prediction one). It is not. If crows were in the room, there should be feathers or paper shreds on the floor (prediction two). None are visible. Courtney says someone cleaned up and closed the window. This is theory three which improves theory two by adding cleanup. Looking around, you see that no one has a book report. Since no one else has their report, you decide that the teacher took yours too (theory four). Later the teacher asks you for your paper and you now have data that contradicts theory four. You decide Courtney took it (theory two). If she took your paper, it should be nearby (prediction three). Looking at her desk, you see the corner of your paper sticking out of her books. Case solved, theory two is correct.
In science, there are often several theories as there were for the missing paper. A theory must match current data. It should make good predictions and there should be a way to show it is wrong. Theory one made bad predictions, no feathers, or paper shreds. That was fixed by making the theory more complicated, adding the clean up. What if two theories make good predictions and fit the current information, like theories two, three, and four did for a while? What should you do then? ξ Pick the simple one. The simplest theory is the one that has the fewest assumptions, and depends on the least number of unproven facts. If you picked the simplest, you would have correctly decided on theory two.
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Everything should be made as simple as possible, but not simpler.” |
A. Einstein
Courtney took the paper. Why pick the simple one? ξ Let Courtney convince you why. She still wants you to believe her crow theory. She says she followed the crows and climbed up a tree to get the paper back. She glued it neatly together and put it between her books to squash it flat. Now do you believe her? ξ Courtney’s story gets more and more complex. Explanations often become more complex in order to try to save a broken theory.
Which Came First? Chicken or Egg, Math or Science
Math is important to science because science often begins with measurements and numbers, as the most important information. More importantly, the universe seems to follows mathematical rules. Isn’t that amazing? ξ We could live in a universe where one day the sky is clear blue and the next day it has purple polka dots. One day you go outside and you are taller than the trees, and your dog turned into a blue hippo. Our world is very orderly. [Figure James’ tall see sneakers house from elevated point of view and blue hippo dog, drawing] Things do not change without reason. Things are so normal that measurements agree day-to-day, century-to-century all over the Earth and the universe, done by different scientists. When measurements do change, the change is orderly and predictable using math. This is the reason math and science need each other.
Newton came up with the theory of gravitation. Without math his theory would have been: “Planets attract each other.” That is not a theory that could get a man to the moon. Newton needed to develop calculus, which could deal with speed, position, and acceleration. Mathematicians discovered the math Einstein needed for general relativity, math for warped space, before he even started work. The same thing happened with string theory. Mathematicians developed much of the math before the physicists got going.
Math is abstract. You start with a set of objects, operations, and rules. The objects do not have to be numbers, they can be spaces, geometrical forms, any idea mathematicians can imagine. The most familiar set of objects are the numbers and the operations of add, subtract, multiply and divide. All of mathematics follows from a small set of rules called axioms.
Mathematicians care about math and are not concerned that their work corresponds to reality. For example, they consider objects where a + b does not equal b + a. They also invented imaginary numbers. Complex variable math deals with imaginary numbers. Imaginary numbers come from taking the square root of negative numbers. Mathematicians worked out how they should add, subtract, multiply, and divide, and how to handle numbers that are part normal and part imaginary. Some equations have solutions that are imaginary or part imaginary, part real. Mathematicians did this work for the pure joy of solving an interesting problem. Most mathematicians do not care whether their work applies to the real world or not. Some do not even leave their office for a week. Complex variables turned out to be necessary to analyze periodic motion like waves. Again, math turns out to describe how the universe works. This is true many, many times even though mathematicians were not heading in that direction. Even Einstein could not figure it out. What do you think? ξ Just how can ideas that start in a mathematician’s imagination lead to detailed explanations of the world?
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“How can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to the objects of reality?” A. Einstein |
Science is public. Results are public. Anyone can find the latest research on the Internet. Scientists check results, reproduce, and reinterpret. Significant things get hundreds of checkers. Predictions are very important because a clever scientist or Courtney could bend or invent a theory to fit old data. No one can fudge data that does not yet exist. Philosophers and scientists agree that a theory needs to have a way to prove it is true. This could be as dramatic as setting off the first atomic bomb to prove that nuclear physics was correct. Many philosophers and scientists also believe every theory should also have a way to prove that it is wrong.
That brings up an embarrassing subject. There is a nasty duck on your head! It is angry and it is stomping on your head. It is invisible so no one can see it. There is no way to detect it. It is like magic. It is weightless, invisible, not affected by any force, silent, and it is on your head. You know what ducks do besides quack. Can you prove the duck is not there? There is no way to prove it is there or not there because of the magic way it affects nothing, but it’s there. You may think I am lying or joking. Can you prove there is not an invisible duck on your head right now? Yes, your head. ξ No, you cannot.
Scientists would say the duck is nonsense. Existence of the duck is impossible to prove. To a scientist, something that cannot be proven true or false is not part of science. The duck idea does not lead to any predictions, because it does not affect anything. There is no way to prove that the duck isn’t there. People have made up millions of such beliefs and many more will follow. Science deals only with ideas that can be proven one way or the other. This is important for string theory. So far, there is no way to prove it is true or false.
In this information age, many other sources of information: politicians, advertisers, preachers, songs, videos, the Internet, cults, and blogs constantly bombard us. Are they as reliable as science? ξ Should we apply to these sources of information some of the rules of science? ξ
The Mechanical Universe
At the end of the 1800’s Maxwell discovered that electricity and magnetism were one force, the electromagnetic force. Physicists then knew of only two forces, electromagnetic and gravity. Newton’s laws were marvelous in understanding the motion of everything from pendulums to planets. Physicists began to feel confident that they knew just about everything. Men built fine clocks and large complex machines. The universe was neat and tidy. Everything in it moved like clockwork. Some physicists thought they were near the end of the exciting physics. The patent offices could close. Physicists would need new jobs. Some wondered if they could get on American Idol. It turns out there was more than enough to keep them working through the 20th century.
Classical theory was close to a theory of everything. Newton could calculate the positions, velocities, and accelerations of the planets for any time in the future or any time in the past. He did not even have a laptop. The model of the universe was the clock. People could imagine that everything moved in an orderly and predictable way. Forces happened and calculus let us determine the result. Classical physics let men build and understand machines, pumps, pipes, pressure, steam engines, autos, airplanes, levers, pulleys, gases, ships and much more. Success made scientists optimistic and confident. To predict the planets’ paths all you had to know was their initial velocity and position. The model for atoms was tiny hard balls. Therefore, the atomic world was just like a game of pool. Classical mechanics worked for pool so why not for atoms. According to classical physics, the past and future could be determined if we knew where all the atoms or pool balls were now and their velocities. It was as if the universe were a clock; wind it up and away it goes in a neat predictable way.
Even living things like bacteria are complicated tiny machines, containing smaller, complex machines. The machines inside are just too tiny to see. Recent work in molecular biology agrees that a cell is a combination of many molecule-sized machines. Genes are the control system turning on cell-sized machines when needed. If bacteria are machines, then maybe animals are machines. Animals are just a large number of cells. Newton’s laws apply to all parts from the atoms on up. Biological processes were due to the interactions of hard little atom balls that joined up to make molecules, that joined to make cells, and all exerted forces on each other. That sounds mechanical. The internal molecular machines had to follow the same Newton’s laws. Can you see where we are going with this? ξ Animals would be mechanical devices just like a clock only more complicated. We are animals so we also are very complicated mechanical devices. This made many uneasy because there was no room for soul or mind. Worse, the future of mechanical devices is determined by their past. There is no sin, no free will. The ultimate statement of classical physics was that given the initial velocity and positions of everything, you could calculate the fate of the universe. What do you think of this idea? Why? ξ Do you feel like a robot with your life determined by physics? ξ
Physicists now know that the above series of generalizations from planets to pool balls to people goes too far. A thing can be greater than the sum of its parts. We are made of a few chemicals and a lot of water but you would not expect a few gallons of water and some chemicals to drive a car or write a symphony. Complexity theory studies how some simple things and simple rules can lead to things as complex as living things. Chaos theory studies how complex things like the global weather changes and how even a small event, a butterfly flying, can change the course of a storm.
Space and time were simple, an unchanging framework where everything happened. Physicists took them for granted. Everyone could agree on the meaning of time and space. Newton’s laws of motion and gravity applied to everything in the universe. There were only two forces, gravity and electromagnetic. After classical physics, the most interesting research was of parts of the universe that we do not experience every day. They were things that were either huge or very small.
In 1900, there were just two problems handled incorrectly by classical physics. These were a small part of physics, and someone would figure it out. The first problem was that physicists could not measure the speed of the Earth through space. They got zero. That meant the Earth was standing still. Therefore, it had to be at the center of the universe since all the stars were moving. Were Copernicus and Galileo wrong? The solution to this problem changed our understanding of the large things in the universe and the universe itself. Second, when physicists calculated the color of hot objects, it came out wrong. That did not seem to be a big problem. This problem changed understanding of the atomic world and reality to its roots. The solution of both these problems profoundly changed our view of reality and of measurement. This, of course, had a large impact on string theory which was to follow..
Relativity
Einstein was a clerk at a patent office, but he followed the latest news in physics. He knew about the speed of the Earth experiment. He knew we were not at the center of the universe. He started thinking about it. That got him to thinking about how different observers see the same thing. This began the theory of relativity.
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“When you sit with a nice girl [boy] for two hours, it seems like two minutes. That’s relativity.” A. Einstein |
It is true that your point of view, your surroundings, who you are, who you are with and what you are doing all affect how you see and interpret things. This is the relativity that psychology studies. Einstein thought most about how observers moving at high speed past each other on rockets would see things. This was one of his famous thought experiments. Let us do our own thought experiment about relativity.
Relativity Baseball
You are in a softball game against the Blue Meanies. They always play dirty. For this game, their pitcher is riding on a four-wheeler. [Figure 4-wheeler baseball, drawing] Coach Nozair says, “There’s nothing in the rules against pitching from a four-wheeler. If it’s not forbidden, it’s allowed.”
Your coach, Mr. Whimper, agrees! The game is for the championship. Their pitcher does not have a fastball. In the game, he drives the four-wheeler out near second base and guns it toward home. As the four-wheeler crosses the mound, he throws the ball. It has wicked fast. He then puts the four-wheeler in reverse and drives backward back to second base.
Between innings, you hear their pitcher telling Nozair, “My pitch is still slow coach. It doesn’t look any faster to me.”
Nozair replies, “Do you have a banana for a brain? Of course, it looks the same to you. Relative to you the ball always has the speed you throw it. Relative to the batter, the speed of the four-wheeler adds to the speed you throw. That way, all your pitches are fast.”
The score is tied. You are at bat. Bases loaded. The count is three and two. Their pitcher decides to be cute and surprise you by throwing the ball early. He has to pitch from the mound, but he does it while he crosses the mound speeding backwards to second. He throws and the pitch rolls slowly toward second. It never reaches home plate. Your team wins. What happened? ξ The vehicle speed was opposite to the direction of the pitch speed. To get the speed relative to the batter, subtract the vehicle speed from the pitch speed. Since the four-wheeler was going faster than he could pitch, the ball rolls away from the plate. You walk and that pushes in a run so your team wins.
Einstein became the world’s most famous scientist by doing thought experiments about relativity like the one we did. Our analysis of the softball game is correct. The speed of the four-wheeler adds to the speed of the ball. When the four-wheeler is moving opposite to the direction of the ball, it subtracts from the speed of the ball.
How Fast Is the Earth Moving?
Since it worked for baseball, it was natural to assume that a light pulse fired in different directions from a moving body would travel at different speeds. At the start of the twentieth century, several physicists decided to determine the speed of the Earth through the universe. Mirrors split a light beam and sent it along two perpendicular directions. Mirrors reflected it back to a point to a compare their speeds. The apparatus could very accurately determine the time to travel the identical arms. [Figure Earth speed measurement, illustration]
The earth was moving so they expected that the time along one arm would not equal the time on the other. In the ball game, this is like comparing the speed of a pitch to the speed of a pick-off throw to first base. The four-wheeler speed speeds up pitches to the plate. The speed of a pitch to first is just the normal slow speed because the four-wheeler is not moving toward or away from first base. The pitch to the plate is faster than the throw to first by the speed of the four-wheeler. They predicted that the light going in the direction of the Earth’s motion would take a different time than that aimed perpendicular to the motion.
The experimenters did not know exactly in which direction the Earth was moving but expected a difference. One arm would point more in the direction of travel of the Earth than the other would. The result of the experiment was that the velocity of light along each arm was equal. The arms were long and the detector looked for interference between the two light beams. This made the measurement very sensitive. They waited a few hours for the Earth to turn and the arms to point in different directions. The velocities were still equal. They did it dozens of times with the same result. In the four-wheeler and ball example, this was like the ball coming to the batter at the same speed whether the four-wheeler was coming or going away. This was an astounding result. What is the explanation? ξ
The great thinkers first pay attention to the details, but don’t stay there. They next make their point of view bigger. They think about everything connected to the details. Einstein didn’t just think about the experiment. He asked how we should change our thinking to make it agree with the experiment. It did not matter if the change was silly or weird. This lead Einstein to ask himself the question what is reality? You cannot get much bigger than that.
He worked through the thought experiments and decided that high-speed rockets moving by each other could not change reality. The pilots should agree about most of their observations. Don’t you think that makes sense? ξ He decided that there was no way for them to know their real speed. In fact, both could be moving or either one could be stopped and only the other moving. Looking out a window does not help. You would not know if what you see is moving or you are moving. Have you ever been in a vehicle stopped with others? You look out the window and the vehicle next to you moves backward. For a second you can’t decide if it moved backwards or you went forwards. The pilots could only agree on the relative speed, the difference in speed, between them.
Einstein decided that reality not changing meant that scientists on board would come up with the same laws of physics. It does not matter which rocket you are on, or whether you are still or moving. If the rocket pilots cannot tell if they are moving or not, then we on Earth also cannot tell and that is why the experiment failed to measure the speed of the Earth. From thinking like this, Einstein came up with a powerful, simple theory called special relativity. Special relativity is required when speeds are very fast, near the speed of light. He accepted that the velocity of light is a universal constant. The velocity of light was the same no matter how fast the source or observer was moving, even if they were moving nearly at the speed of light toward each other. What Einstein did was simply restate the experimental results. Light travels at a constant speed no matter how fast the source or receiver is moving. The constant velocity of light is one of the major results of relativity.
Lightball Game
The announcer breaks into the program you are viewing and says, “We switch now to live coverage of the finish of the 22nd Century Lightball Championship. [Figure Lightball, drawing] It looks suspiciously like the Blue Meanies game about 150 years ago. Their pitcher does not have a fastball and the count is two balls and two strikes in the bottom of the ninth with bases loaded and the Blue Meanies ahead. Coach Nozarino rolls in his secret weapon, the light speed rocket pack. “It’s not forbidden so it’s allowed,” he says defiantly. The pitcher puts on the rocket pack at second base and we have ignition. The pitcher flies over the mound at 98% of the speed of light. He fires his lightball laser gun. Will the batter be able to see it? He does. To the batter it appears to travel at the speed of light like a standard Lightball and it is high and inside. Ball three. The pitcher is desperate he turns up the power, and he and decides to trick the batter by firing his lightball backwards while crossing the mound heading back to second. He tucks the lightball laser under his arm, powers up his rocket, and fires while moving backward over the mound. Game over.
Coach Nozairino is all excited. “Why did you fire backwards?
Pitcher replies, “I know I can’t throw faster than the speed of light. That is the speed limit for everything in our universe, but I thought I could throw slower. You know a change-up.”
Nozairino asks, “Do you have a banana for a brain? The speed of light is a constant no matter if you go toward or away from the batter so you cannot throw slower. I thought the rocket pack noise might confuse their batter, and the batter would expect an extra fast pitch, but they all know relativity better than you do. You, however, were brilliant to pitch backwards. Light from a source that is moving away shifts toward the red. The rocket pack goes so fast that the lightball shifted past red into the infrared, a color the batter could not see. Instead of a pulse of light, the lightball became a pulse of heat. He could not see it; he could not hit it. He struck out.”
The pitcher cheers, “The Blue Meanies finally won! ”
Einstein’s Solution
Experiments showed the speed of light is constant. To keep the speed of light constant and reality the same for moving observers, space and time had to mix. The result of this mixing is that objects moving near the speed of light squash in the direction of motion, get heavier, and their clocks run slower. If two rockets, moving near the speed of light, pass each other, one observer would see the other rocket looking shorter and with its clock running in slow motion compared to his own. Do you know which one? ξ Trick question. Both are doing exactly the same thing. The problem is unchanged by switching the two rockets. The problem is symmetric to changing rockets. Whatever the pilot of one rocket sees, the other has to see the same. They each would think the other passed them looking squashed and with their clock running slow. Symmetry is a powerful tool. Since symmetry is common in nature, it is common in physics.
Mathematically these changes behaved as if time were another dimension, just like the three dimensions we know. Everyone called it spacetime. The real difference between the two observers is that their spacetime coordinates are rotated. Rotating coordinates in spacetime means any coordinate, x for example, would become a combination of x, y, z, and time. The speed of light is the absolute speed limit for anything in our universe. Muons are unstable elementary particles that decay in two millionths of a second, 2 x 10-6 seconds. If a muon could move at the speed of light, its time would have stopped (it would never decay). It would have zero thickness in the direction of motion, and its mass would be infinite. That sounds very non-physical and it is. The infinite mass means would require infinite force to get to light speed. Therefore, we never can accelerate a particle with mass to the speed of light. Only massless particles, like light itself, can move at the speed of light, but current accelerators can move muons fast enough to lengthen their lifetime to a millisecond, one thousandth of a second, 10-3 seconds. That is 500 times longer than their lifetime if they are not moving.
The time and length changes are precise and happen in a mathematical way called a rotation of coordinates. This just means tilting the coordinates of a graph. What if Monaco, a European country smaller than some parking lots, conquered the world? They wanted to be more popular and decided that the North Pole should be in Monaco. That would be a rotation and movement of coordinates. All of the maps would have to be redrawn. Every place on Earth would be south of Monaco. The old latitude and longitude lines would be wrong. The new latitude and longitude would be a combination of the old ones. Not everything would change. Would the distance from Rome to Paris have to be changed? ξ Would the shape of Florida have changed? If you walked up a creek to get to your friend’s house, would that change? ξ If you said no to these questions, you are right. Einstein knew that if the coordinate system moves to a train traveling in a straight line at high velocity, the distances in four-dimensional spacetime do not change. Monaco’s rotating and moving the coordinate system on the Earth leaves the Earth unchanged. Rotating the directions in spacetime mixes space and time. From this, all of relativity follows.
We know Einstein was right when even though we do not have enough energy to move a rocket anywhere near to the speed of light. Physicists have built accelerators that can move sub-atomic particles faster than 99.999% of the speed of light. Unstable particles moving that fast take much longer to decay. We do have enough energy to move a clock fast enough to see relativity effects. Atomic clocks now orbit Earth. They are very accurate and tick billions of times per second. They run exactly the way predicted by relativity. With these hiflying clocks, there are two relativistic effects a slow down from their speed, and a quickening from being in a since gravity is weaker up there. The latter comes from special relativity. Global positioning satellite systems needs correction for relativity. Another property changes, the mass of the particles increase. Einstein found the famous equation E = mc2 .This says that matter, m, can convert into energy, E, and vice versa. The speed of light is c.
Messiness
Even though relativity mixes time with spatial coordinates, time remains special. One question that has bothered scientists and philosophers for a long time is – What is time? Can time go backward? We think time moves in only one direction. We remember the past, but not the future. However, physics equations work fine if you put in a negative time. That is exactly how to calculate where a planet was three years ago. Relativity also allows negative time. Nevertheless, the universe seems to know which way time is going. It goes from neat to messy just like your room. The universe began neatly. Everything was in a point at the Big Bang. After, things got messy.
It is a law of classical physics that randomness, messiness, or information increases in all processes in the universe. Physicists call it entropy. Information seems very different from messiness, but it is not. Think about writing a long list of all the stuff in your room. You list what it is and where it is. It is a shorter list if your room is neat. It takes more words to describe a mess.
Try this out if your Mom says you have to vacuum. “I can’t vacuum because it makes things messier.” When you vacuum, you are making the universe messier. The vacuum runs on electricity. The power plant that makes the electricity burns coal with all the mess that comes from mining, shipping, burning, CO2, and ashes. You have to eat food for the energy to push the vacuum around. You make waste. The walking and vacuuming shreds up the rugs a little more, making more dust to clean up. When she knows all that, your mother will forbid you to vacuum ever again.
If we are looking at a video of a system, we can determine if the movie is running forwards or backward by seeing if the mess increases. Broken cups do not fly back onto a table and reassemble themselves. Positive time goes in the direction of increased messiness. These concepts of entropy are very important in analysis of the Big Bang.
Maxwell’s Equations
Maxwell’s equations were the greatest achievement of classical physics so we have to look at them. The four equations for the magnetic field, M, and electric field, E, in free space are:
You may have seen magnetic field lines by holding a paper with iron filings over a magnet.
The equations are just for looking at. They are college level. How do they look to you? ξ They are a powerful set of equations and not bad looking as equations go. Physicists call them elegant, even beautiful. The E and M, electric and magnetic fields, behave in the same way. Put more elegantly, the equations are symmetric in E and M. If you switch M and E, you get back the same equations.
The triangle symbol with the dot and the triangle with an x after it are shorthand for two different ways of calculating how a field changes in space. These two Maxwell’s equations say that the way one electromagnetic field changes in space equals the way the other field changes with time. The two equations that equal zero say the field is zero unless a charge or magnet is present.
If an electric field varies in time, it causes a perpendicular magnetic field varying in space, and vice versa. A magnetic field varying in space causes an electric field varying with time. This action of causing each other causes electromagnetic waves. A changing magnetic field produces a changing electric field, which produces a changing magnetic field, which produces a changing electric field, and so on through space. This makes waves like light, x-rays, and radio.
These equations are the basis for woofers, alternators, and computers. Physicists consider these equations beautiful because the pack so much information into a compact form and they explain so much of the world. Can spacetime simplify them even more? Einstein redid the equations in four-dimensional spacetime. A change in spacetime covers changes in space and in time. The magnetic and electric fields combine into one four-dimensional thing, F, filled with the parts of E and M in the different directions of spacetime. This had an amazing result – the four equations become one beautifully simple equation.
Maxwell’s Equation in Spacetime for F – the Electromagnetic Field
ε F = 0
F is the four-dimensional electromagnetic field. The ε is a four-dimensional grid made up of 1’s, 0’s, and -1’s. Four complex Maxwell’s equations became this one simple one when expressed in spacetime. Most physics students spend a semester battling with the original Maxwell’s equations. Then this equation appears, and they know once more, why they want to be physicists. The beauty of a theory often shows in the math.
| Einstein all dressed up in his Nehru jacket and cotton ball hair. |
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“An equation is something for eternity.” A. Einstein |
Einstein’s theory of special relativity mixed together things that classical physics thought completely separate – space with time and energy with mass.
Gravity by Einstein
Einstein was not done. Special relativity uses Newton’s gravitation and it explained the Earth speed experiment. Special relativity says that nothing can move faster than the speed of light. Newton’s gravitational field, however, works instantly between two objects no matter how far apart. Even Newton noticed this and was uncomfortable. Einstein knew there was a mistake. Every mistake is an opportunity to learn. For special relativity, he thought about viewers moving past each other at constant speed. What would happen if their speed changed steadily? This is acceleration, and it leads to general relativity.
Gravity causes a constant acceleration. He considered gravity, the constant speed of light, and relativity, and he wondered what different observers see when accelerating. You wake up one day and found yourself in an elevator, and your weight is the same as before you went to bed. Are you still on Earth or are you in a rocket accelerating at one g, the acceleration of gravity? ξ Elevators have no windows so you couldn’t tell. Einstein concluded that an observer could not tell the difference between moving with a constant acceleration and being still in a gravitational field. Then he predicted that the light from a star, passing close to the sun, should bend toward the sun. How can that happen, since light has no mass? He discovered that anything with mass distorts spacetime. If the space around the sun is distorted, then paths that would be straight are bent, even the path of light that has no mass.
Fortunately, mathematicians, just fiddling around with an interesting problem, had discovered the math for curved space. It is hard to picture a three-dimensional curved space. The sun makes a big dent in spacetime, like a bowling ball on a soft bed. On Earth, we feel the sun’s dent weakly so far from the sun. It is still strong enough to keep the Earth in orbit.
During an eclipse of the sun, you can see stars that graze the surface. The eclipse blocks the sun’s glare and allows measurement of the position of those stars. [Figure space warp and sun blocked, illustrate] Their light bends exactly as predicted, making it appear that those stars have moved. This gives an alternative view of the gravitational force between masses. Mass distorts spacetime to make it look like there is a force.
Space and time, matter and energy are no longer the absolute unchangeable things they were in classical physics. In special relativity, space and time mix when speeds approach the speed of light. In general relativity, matter warps space. This is not just a local effect around stars like the sun. All of the matter in the universe shapes the universe itself. All of this started with a puzzling result in measuring the speed of the Earth.
Quantum Mechanics
Calculations of the color of hot objects kept making everything look much hotter—yellower and whiter than they were. This was frustrating. Everyone knows a heating element on a stove glows red. All efforts to calculate this color came out white-hot. After much study, the only way to get the right colors for hot objects was if hot atoms could not radiate any amount of light energy, but only amounts that were an integer times a certain small chunk of energy. That meant energy and light came in chunks. An atom could emit one chunk of energy or five, but it could not emit 4.7 units of energy.
Quantum means chunk. Quanta is plural, many chunks. Chunky bars come in quanta. The mechanics part in quantum mechanics means how quanta move and interact. Solving this physics problem changed our ideas about the very smallest objects and set limits on what we can know.
Quantum Land Playground
Imagine you and your strange alien friend, Qued, are in the quantum land playground. In quantum land, the chunkiness is exaggerated. You ask Qued for a push on the swing. He pushes hard but nothing happens. Qued gives a bigger push and you are swinging. At the high point, you are three feet off the ground.
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The strange creature Qued from the 26th dimension. |
“Push me higher.” With the next push, you are six feet off the ground. “That’s great.” You are amazed because even when you stop pumping and coast, you do not slow down a bit.
“Hey Qued.” You want to tell him about this but he thinks you want another push. Zap, instantly you are at nine feet. This is above the bars and you feel those bumps. You try dragging your feet to slow down but your feet slide over the ground without friction. [Figure Qued and kid – quantum swing, drawing]
“Qued, slow me down!”
He tries to grab the seat but that has no effect. “Hold on,” says Qued. “This is going to be rough.”
Qued stands right in front of the swing and it knocks him down. Your height drops to six feet. He does it twice more. You drop three feet each time so finally you stop.
Qued brushes himself off and says, “I’m glad the energy quanta aren’t any bigger.”
“What was happening, Qued?”
“The swing is quantized. You cannot just swing at any height you want. When I first pushed, I did not push hard enough, I did not give you a whole quantum of energy. The quantum is enough energy to get you swinging three feet high, or six feet if you have two, or nine feet when you absorb three energy quanta. The heights in feet are the energy levels of the swing system.”
You ask, “But why couldn’t I slow myself down?”
“Dragging your feet didn’t work because you can’t burn up a whole quantum of energy that way. Energy can only be absorbed or released as a full quantum. The only way to drop you down to a lower energy level was to absorb one quantum. To do that, I had to let the swing knock me down. Each time I went flying, I absorbed one quantum. It is just the same with atoms in your world. Electrons spin around the nucleus at various energy levels until they absorb a photon (light particle) with the right amount of energy to hop to a higher level. Now I’m going to go meet James to shoot some quantum pool.”
Atomic Physics
Quantum mechanics stimulated intensive research into atoms. After discovery of the electron, atoms became miniature solar systems with electrons orbiting the nucleus. The electrons gave problems. Physicists pictured the negative electrons circling around a heavy positively charged nucleus. Opposite charges attract. Why did the electrons not smash into the nucleus? ξ It gets worse. Maxwell’s equations imply that an orbiting charge makes electromagnetic waves. Making waves would make the electron lose energy and again spiral into the nucleus. Did the solution to these problems have anything to do with energy coming in well-defined chunks? ξ Of course, energy chunks solved the problem. Just the discovery that energy came in chunks was enough to change completely our view of the world.
Electrons circle the nucleus, but they cannot orbit just anywhere. Let us think about a city, Circleville, with circular streets, in rings around a central park. [Figure Circleville, illustration] Moscow and Paris are partly this way. When you park in Circleville, you can only park on a circular street. Parking on the grass is forbidden. Streets are at set distances from the central park. The closest you can get to the center of town is the street that circles the central park. The same is true of electrons around the nucleus. They can only be in particular orbits. Energy levels can be changed up or down only by an exact amount of energy. This explains why electron orbits are stable. When the electron is in its lowest energy level, there is nowhere lower to go. Thus, there is no way to crash into the nucleus. This would be like driving on the grass of the central park. That’s not allowed in Circleville. To make Circleville more like electrons around an atom, there are not any streets going between circles. Then the cars behave like electrons; they cannot drive to another circle. They have to circle around on the same street until they absorb or emit a lot of energy. Then pop! They appear on another street. Circleville is a far-fetched analogy. Cars could never disappear and reappear. Many physicists thought the same thing about electrons disappearing and reappearing at another level. It is pretty strange. ξ
We Are Certainly Uncertain
The uncertainty principle of quantum mechanics says that things on the atomic scale are not only chunky. They are fuzzy. A fundamental fact of quantum mechanics is that we can never know exactly the position and velocity of a particle. Quantum mechanics’ equations for the motion of elementary particles are equations for a wave. The wave only predicts the chance (probability) of finding a particle here or there. It is most likely located where the wave is the highest.
An oval balloon represents features of a wave function. The mid-section of the balloon represents the position wave function and the ends the velocity wave function. If you squeeze it in the middle, it pops out at the ends. If you accurately locate an electron, its velocity becomes more uncertain. The mechanical universe cannot happen because nature prevents us from accurately knowing both the position and velocity of an elementary particle. Chance did not feel right to many scientists, including Einstein. Some thought there must be a better theory that would remove the uncertainty.
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“I am convinced that God does not play dice with the universe.” A. Einstein |
No one has come up with such a theory. Chunks and fuzz are how things are on the atomic scale. [Figure chunky fuzzy particles, drawing] The nice universe ticking along like a clock does not apply. The universe limits our knowledge. We are not complex wind-up robots.
James thinks he understands uncertainty. “Qued, there are things in the ordinary world that are uncertain.”
“That’s true. We do not know what the weather will be a week from now or who will be elected president. These are two kinds of uncertainty. We could know who will be elected if we asked everyone, but the weather is chaotic. It depends on many more variables in such a way that a minor change in any variable can make a big change in the weather. A butterfly flapping it wings in Madagascar could be the cause of a hurricane in Florida. Really. Another unpredictable event is the decay of a radioactive atom. We know half of a batch of these atoms will decay in a period of time called the half-life, but we don’t know which atoms or exactly when they will decay.”
“When I flip this penny in the air, you don’t know if it will land heads or tails. That’s uncertainty, too.”
“James, I’ll bet a penny against yours that I do.”
“Okay you’re on.”
“Hold on while I set up my multi-laser ranging imager. It connects to this bio-implant computer.”
“That’s not a computer. It’s a freckle on your arm.”
“That spot is a data interface to my bio-computer, James. This other ‘freckle’ is my mainframe quantum computer. Besides, I do not have arms. I am ready.’
James starts flipping. He gets more and more excited and says, “You were able to predict ten for ten. How did you do that, Qued?”
“My equipment measured the spin, position, and velocity at the start of your coin toss. It is an easy calculation to determine its orientation as it falls. Therefore considering also roughness and elasticity of the floor, I can compute which side will be up.”
James asks, “If flipping a coin isn’t really random, why can’t we do the same thing with quantum processes get better equipment to measure what we need to predict radioactive decay of an atom?”
“The hidden variables I measured allowed prediction of the coin flip. Quantum processes have no hidden variables. That is why decay of an atom is unknown. In one half-life, an atom has a fifty percent chance of decaying. That is all we can know. There is no way around the uncertainty in quantum mechanics. In fact, there are at least three kinds of uncertainty. There is uncertainty due to chaos, the weather; uncertainty due to lack of enough information, coin flip; and quantum uncertainty built into the universe.”
Quantum Pool
James walks in and sees Qued setting up the pool table.
“Come James, and let’s shoot a little pool. This is quantum pool where the balls behave like sub-atomic particles do in the real world.”
“Where are the balls, Qued?”
“They are the different colored clouds on the table. The cue ball is the white cloud. The balls are a little fuzzy because on the quantum level, nothing ever stops, and our knowledge of things like position or energy is only approximate. If you shoot other balls at the balls on the table then you can tell from the collisions where the balls were. You still would not know where the balls are now because you would have knocked the ball out of position and given it some velocity. No matter what technique you use, knowledge is limited by the uncertainty.”
“Well I just tried a shot and missed the cue ball.” [Figure quantum pool, drawing]
“Yes, even the position and velocity of the cue ball are uncertain, but in quantum pool, you get to try until you connect. I usually shoot with the metal end of this.”
“Qued, I did it. I hit the cue ball with your garden hoe.”
“As the cue ball moves away, its cloud gets wider. Yes, it is spreading out, just as the wave equation says. Because it spreads out, we are less sure of the ball’s position. The brightness of the cloud shows where the ball is most likely located. That was a good shot. The cloud is brightest right in line with the number five ball.”
“Look at that. The white cloud passed right through the five-ball cloud. That’s not fair.”
“The cue ball as a particle can be anywhere in the cloud. Most likely it is at the center, but that time it was not.”
James gets some apple juice. “Now the cue ball cloud has spread out over most of the table.” Then he hears a ball fall off the table and asks, “What was that?”
“That was your cue ball. It tunneled through the pool table cushion. Remember, here we deal in probabilities. Even though it is a sturdy cushion, there is some probability that the ball can leak through the cushion. It did not make a hole through it. It did not jump over it. It just leaked through and suddenly it appeared on the other side. If this did not happen, most computers would stop working. Quantum effects are important in designing computers.”
“This quantum pool is sure hard.”
“That is true, James.”
“Look. Two new clouds are on the table. Are they balls? Where did they come from?”
“They are virtual balls. They pop up at random from the vacuum. The white cloud is a virtual cue ball. The black one is a virtual anti-cue ball. Watch, they will roll only a few inches and then annihilate each other. See; they are gone. Virtual elementary particles are continuously appearing and disappearing everywhere in the universe, even in outer space. They affect how particles interact with each other.”
| String Break! With your thumb and finger, hold both ends of a whole, raw piece of spaghetti. This is a stiff string like the ones in string theory. Holding the ends, slowly bend the spaghetti until it breaks. It almost always breaks into three pieces—not two. Try it again. Why does it do that? |
How Can We Understand Something We Cannot See?
At first physicists believed that three elementary particles: the proton, neutron, and electron were the only ingredients for making everything. How could they study the elementary particles that are smaller than atoms? The only way is to bounce the particles off each other.
Imagine it is your birthday. Your grandparents shipped a gift to you with strange directions for opening. Old people get a little strange. First, it is put in a pitch-black room. They included an air cannon that can fire different sized balls at the gift and they challenge you to shoot and then guess what it is. You decide to shoot the beach balls. You cannot see any balls hit, but you note where you aimed and at what angle the balls bounce back. If they do not return, they did not hit the present. From the hits, you can tell that it is roughly four feet wide and three feet high, but that is all. What is it? You switch to tennis balls. Now some of the balls go through in places that bounced back the beach balls. This means there are holes there smaller than beach balls. One is middle height in the center, and the gift is rounded on both ends. What is it? ξ Let us shoot marbles. When you do that, you find two-foot diameter rings at the front and back. The inside of the rings sometimes let a marble go through. Looking closely at the data, the rings seem to have wires, like spokes, going through them. What is it? ξ
Scientists have to shoot small particles to determine the structure of elementary particles. For a particle to be small, it has to have high energy. The smaller the features you want to see, the higher the energy needs to be. We could not detect the bicycle spokes until we used marbles. You can think of them as high-energy beach balls.
For all of the 20th century, physicists shot elementary particles at targets to understand the structure of matter. The first experiment was with radium that emits alpha particles. When aimed at a piece of aluminum foil, most went right through. One in 1000 bounced back toward the source as if they hit a brick wall. This showed that aluminum atoms were mostly empty space with a heavy center, the nucleus, which took up one thousandth of the area of the atom. The nucleus was heavy enough that an alpha particle hitting it was like bouncing a ball off a wall.
Some German scientists discovered that uranium released energy when hit with neutrons. Maybe you are wondering why someone would aim neutrons at uranium. A climber asked why he climbed Mt. Everest, said because it is there. That is a good answer for “Why shoot neutrons at uranium?” A scientist rarely knows the results of an experiment. Otherwise, why do it? World War II started and there was a lot of fear that the Germans could somehow turn uranium into a weapon, so we did. There was a huge concentration of physicists at Los Alamos. They made the atomic bomb. Along the way, they developed nuclear physics and quantum mechanics, and showed the way to nuclear power.
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| In the center is an eight story tall detector array and shielding at the Large Hadron Collider. |
We learned the most from small balls shot at the bicycle. Physicists have to use small particles. Particles behave like particles and like waves. Accelerating them to higher energy shortens their wavelength, making observation of more detail possible. At high energy, the collision can also cause a reaction producing new types of particles. When the particles are photons, their wavelength also decreases with energy. Thus, gamma rays show more details than red light.
Accelerators
Accelerators and colliders are the machines that produce high-energy particles. The first ones were metal donuts filled with vacuum. Magnets bent the path of the charged particles into a circle to stay in the donut. To get them to move faster, a microwave signal made a wave that the particles surf on to higher energy. Then the particles hit a target where nuclear reactions take place, sometimes making brand new particles. The first accelerators could fit on a desk. To get higher energy, accelerators had to be bigger. After World War II, building and using accelerators became a major effort in nuclear physics. This work is high-energy physics. An accelerator beam hits a stationary target. For even more energy, two high-energy beams accelerate and hit each other.
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| Aerial view of the countryside over the five-mile diameter LHC. At the top of the photo are the Swiss Alps. |
The biggest collider is the Large Hadron Collider, LHC, in Switzerland. The vacuum pipe that the beam follows is a circle five miles in diameter. The LHC gives protons a lot of speed or energy by creating strong electromagnetic waves that push them along. The protons divide into two groups that move in opposite directions through a ring shaped vacuum pipe. As they go faster, their mass increases. That is relativity. The particles then slam into each other. During the collision, the particle’s energy and mass can convert into new heavier particles. This process creates heavy unstable particles for study. Giant arrays of detectors six stories tall monitor the reactions. Many different detection techniques are available. Modern ones are ionization chambers and bubble chambers. The ionization chambers work very much like Geiger counters did, but at LHC, they are gigantic. The LHC energy may be high enough to make a black hole.
A problem with quantum mechanics was that it was not compatible with relativity. General relativity showed that gravity was due to a warping of space by anything that has mass. Quantum mechanics had discovered the constantly bubbling energy and virtual particles in the vacuum. The virtual particles shred up spacetime so badly that the equations of relativity give crazy results. They just do not apply.
In many other ways, quantum mechanics is impressive. Physicists can very accurately calculate the properties of atoms, molecules, and interactions of elementary particles. Particles had properties of both waves and particles. Virtual particles made their influence felt by how they changed reactions between particles. The properties of the elementary particles always were uncertain.
Accelerators produced two hundred different elementary particles. Having hundreds of elementary particles did not seem right. That many particles did not seem elementary any more. In addition, attempts to calculate the interactions between particles often gave infinite answers. Something big was wrong. The Standard Model solved both these problems. The excess particles were not elementary, but composed of other particles. A trick “solved” the infinity problem.
The Standard Model contains a method or recipe for calculating the interaction of particles with each other and with the forces of nature. The Standard Model rests upon special relativity, quantum mechanics, and the rule that particles are points, with radius of zero. Special relativity does not include gravity. The equations of the Standard Model do not work if any of these three things are wrong. Early accelerators showed that particles are not points. Ignore that. Still keep radius zero in the calculations.
Even though the calculations take the wrong radius, the calculations are very accurate, usually closer than one part per million. If you counted the number of grains of sand in a thimble, it would come out about a million. For your result to be as good as the Standard Model, your count could only be off by one grain of sand. To get that kind of accuracy the Standard Model needs to have nineteen physics constants inputted. These are things like the mass of the elementary particles, the strengths of the forces, and the magnitude of particle charges.
The Standard Model requires several tricks. One trick fixes the problem caused by requiring that the radius of the particles be zero. We saw with Newton’s Law of Gravitation that this results in infinity. The other trick comes from quantum mechanics itself. Particles are fuzzy and in turn, how they interact is fuzzy. Any interaction has a whole series of ways it might occur and a range of possible outcomes. Many of these variations are due to virtual particles popping up in the middle of the reaction. The Standard Model calculates the main possibilities and the probabilities that they will happen. The sum of the possibilities times their probability gives the Standard Model answer. Quantum pool showed some of the possibilities. Pool balls would end up in different pockets according to a probability curve, the wave function. Balls aimed at each other could hit or pass through each other without interacting. In addition, virtual particles can pop up. The virtual particles can appear in varying numbers, kinds, and places in an interaction. With balls shot at a bicycle, this would be as if a tennis ball changed into a virtual pair of beach balls, and back to a tennis ball while hitting the bike. In another possibility, the beach ball could become a virtual pair of marbles that annihilate and produce a tennis ball. There are dozens of other variations. This sounds crazy talking about balls and marbles, but in the quantum world, this behavior is normal. Therefore, there are many ways for a reaction to happen. Quantum mechanics has to calculate the likelihood of many possibilities and sum them up for the right answer.
To keep track, physicists use Feynman diagrams. Each diagram represents a possible interaction and defines the required calculation. Fortunately, the first few simplest possibilities contribute most of the answer. Physicists ignore the rest because they occur too rarely. The diagrams account for the quantum uncertainty in the wave function of the particle. There are always many possibilities. [Figure—bike Feynman diagram, drawing] This calculation is partly a trick because it does not give the right answer; it gives an approximate answer. The answer gets more accurate by considering more possibilities.
How can the Standard Model be accurate when many calculations give infinity? Along the way, infinities are removed by a clever math trick we will call the infinity stomper. This is like Infinity Wars. If one step of your calculation gives infinity, find a negative infinity to cancel it. When the infinities cancel each other, the leftovers are very accurate. Nobody likes this trick. It is as if we took infinity minus infinity equals almost zero. That is not valid math, but it works. Infinity stomping fails completely for anything involving gravity. For example, when the Standard Model calculates the mass of a particle, it could turn out to be heavier than a
Buick
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| Elementary particles create tiny bubbles as they move through ultra-cold liquid hydrogen. Magnets bend paths of the charged particles. |
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Elementary Particles
The Standard Model of quantum mechanics made sense of the many “elementary” particles. Most of them were not elementary. The result is only twelve truly elementary particles and five other particles that carry the four forces. The weak force, involved in radioactive decay, is unusual requiring both W and Z force particles. Half of the twelve particles are lightweight, for example the neutrino, electron, and muon. These lightweights are the leptons. Half the particles are quarks, -which provide most of the mass of the universe. All of matter is composed of these two groups. If you know a little about atoms, you may be wondering where the proton and neutron are. They are no longer elementary particles, because they contain three quarks. A neutron contains an up and two down quarks. The proton is two ups and a down. Gluons that carry the strong force hold the quarks together. Yes, the name gluons came from glue. The weak and strong forces are short range and act only between quarks in the nucleus. Passing gluons back and forth keeps the nucleus together. The electromagnetic and gravitational forces are long range.
There are three families of particles. They each have a particle similar to an electron, another particle similar to a neutrino and two quarks. Neutrinos have no charge and nearly zero mass. From family I to III, the mass of the particles increases. In everyday experience, we only observe the first family, and these four particles and the four forces make up our world. Quantum mechanics does not have a good explanation for the families. One family seems to be enough. The other two families only occur in high-energy collisions.
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photon |
electron |
mu |
tau |
Leptons |
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gluon |
neutrino |
mu neutrino |
tau neutrino |
Leptons |
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W, Z |
up |
charm |
top |
Quarks |
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graviton |
down |
strange |
bottom |
Quarks |
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I |
II |
III |
FAMILY |
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Each particle has an anti-particle. Anti-particles make up anti-matter. If a particle meets its anti- particle, they both annihilate with a burst of pure energy. All of their mass converts to energy. The equations in physics are the same for matter and antimatter. That makes most physicists believe there should be as much antimatter as matter in the universe. As astronomers look over the universe, they cannot find any antimatter. Anti-matter galaxies should be crashing into matter galaxies and be the brightest things in the sky. Why is this not happening if the laws of physics are the same for matter and antimatter? Neither quantum mechanics nor string theory has a widely accepted answer.
Forces exist only between particles with mass. Forces are due to the exchange of virtual force particles. This is hard to understand and harder to prove. There is no way to detect a virtual particle. This is another example where we have to believe the math. When calculating the effect of forces on elementary particles, the results are super accurate only if virtual force particles are included. Remember that a virtual particle is real for that short instant of time that it exists.
“Qued, I believe in force fields a little because I’ve played with magnets, but I don’t see how exchanging virtual particles can make a real force. Can you explain?” asked Goofer.
“Sure, Goofer, you get in between Courtney and James. They are going to experience the Goofer force. James, push Goofer at Courtney.” Goofer bounces into Courtney and pushes her backward.” Courtney, you just felt a force from the exchange of a Goofer particle.”
“Yes I did and it was repulsive.”
“Correct. Goofer brought some momentum to you and it pushed you away just like identically charged particles repel each other by exchange of a virtual photon.”
Goofer wants to know, “How can I become an attractive force?”
James mumbles, “I don’t think he can.”
“We have to remember that we are dealing with individual elementary particles and the uncertainty principle applies. That means that the position and velocity of all three of you are fuzzy. To be proper fuzzy particles you have to be vibrating like crazy.” The three kids become three blurry clouds, making shrieking sounds. “I’ll stop you two so you can see what Goofer does. Goofer’s position and velocity are fuzzy. In fact, even his existence is fuzzy.” Qued continues, “Watch what happens when I make Goofer into an attractive force.” Courtney and James were in a Goofer cloud. There were multiple images of Goofer going in all different directions.
James smiled and said, “The Goofer cloud is now big enough to surround Courtney and me. I’m feeling Goofer bumping me on all sides but mostly from behind.”
“I’m feeling the same thing. Those bumps are pushing us together,” said Courtney.
When Goofer solidified again he said, “I knew I was attractive to Courtney.”
“Applying the uncertainty principle to you, Goofer, shows how an exchange of force particles can create an attractive force but it’s even more complicated. An exchange sometimes uses two or more Goofers. Courtney and James also have uncertain position and momentum. They would start as separate blurs, and their probability waves would have different shapes since they are male and female. Physicists account for all this in the probability waves for the particles. When done correctly, the probability waves for the original particles are still a pair of bumps but they bend a little toward each other and the centers of the bumps get closer as time goes by. The result of such a calculation for real particles and forces is as accurate as we can measure.”
All this high-energy physics is so strange that maybe it is sounding to you like a sci-fi movie. Here is the opening scene. You are in a giant laboratory.
The mad scientist (Why are they always mad?) is explaining to his teen-age sidekick, “There are these virtual, not real particles, and they can never be detected, and they are used in a bookshelf full of difficult theory turned into terabytes of calculations by supercomputers to explain what happens when points of matter that can’t be seen, come together in a billion dollar accelerator, an international group of scientists buried in Switzerland, where thousands of supercomputers decide yes, that is the event we were looking for, and when the particular event appears we’ll know that the Klingons are preparing to invade or that string theory is correct.”
Even though it sounds like science fiction, it is all true, except for the Klingons.
Quantum mechanics does not have gravity. Strings naturally produce a force particle predicted for gravity, the graviton. No one has seen it. The exchange of virtual gravitons between particles causes gravity. Another possibility to give particles mass is the Higgs particle. Space would be full of Higgs particles. Other particles have to push through this Higgs sea and that makes mass. Discovery of the Higgs would complete the standard quantum mechanical model of elementary particles. There have been many efforts to detect the Higgs. They failed. Physicists hope the LHC will have enough energy to produce it. Strings naturally give mass to the elementary particles. The energy of the string vibration comes from and equals the mass, E = mc2. Longer strings and strings with more wiggles have greater vibration energy and greater mass.
Gravity does not fit in quantum mechanics. Physicists do not like this but can live with it. That is where things stood until black holes. The center of a black hole is extremely small, smaller than an elementary particle and therefore requires quantum mechanics but it contains the mass of many stars, requiring general relativity. They have a lot of gravity but it comes from a point. Quantum mechanics with gravity or string theory is required to understand black holes.
Entanglement
One of the stranger quantum phenomena is entanglement. Even physicists think this is spooky. Qued is going to demonstrate it to Goofer.
“Goofer, today we are going to learn about spin and entanglement. Elementary particles have a quantum property called spin. In some ways, it is like the spinning of a top but it has weird quantum properties and once spinning, the particle never runs down or stops. An electron’s spin is quantized and can have only one of two states, spin +½ (spin up) or spin – ½ (spin down). Like other properties of an electron, the spin is uncertain until we measure it. On average, half of a group of electrons will have spin +½, and the other half will have spin – ½.
“Okay, electrons spin only two ways, spin up, and spin down. I have a toy gyroscope that can spin on either end,” Says Goofer as he tiptoes around.
“You notice all the small boxes I have assembled?”
“Yeah, I’m falling all over them. What’s inside?” says Goofer.
“Each contains a penny. These pennies have the quantum property of entanglement. This is a property that real elementary particles have. You can shake up the boxes then look to make sure they are randomly heads or tails.”
Goofer shakes and opens one hundred boxes. “They look random, 52 heads and 48 tails. I got my hair tangled in box 34.”
“This entanglement happens when the pennies interact. We do that by touching two boxes together. When the pennies are entangled, they behave like electrons and must be in opposite states, one heads and one tails,” says Qued.
“How do we know which will be which?”
“That we can’t know,” says Qued. “The state of a penny is a quantum variable that is simply unknown until we make a measurement. We know that whenever we look at an individual penny, it has equal probability of being heads or tails. If an interaction entangles electrons, then we know that they will be in opposite states. Now touch together the sides of any two boxes. This entangles the pennies. Then open the boxes, and they will be opposite, one heads and one tails.”
Goofer gets busy. “You’re right. Every pair of boxes I have touched together and opened has one penny heads and one tails. No pairs are either both heads or both tails. How did you do that Qued? Do you have a hidden flipper in the second box so you can set the penny correctly? Maybe thin fiber optic cables connect them and allow each to sense the other. The pennies or boxes must be signaling each other.”
“No, Goofer, there is no communication between the pennies. By the standard interpretation of quantum mechanics each penny before or after entanglement is fifty percent heads and fifty percent tails. You ensured this by shaking up the boxes when we started.”
‘Does that mean they are on edge?”
‘They are not on edge. The penny’s heads state is like an electron with spin +½ or spin up. The tails state corresponds to an electron with spin down or spin –½. A penny on its edge would be like saying an electron is at spin zero. That’s forbidden for electrons and being on edge is forbidden for these pennies.”
Goofer, looking even more puzzled than usual, asks, “Then shouldn’t I see a blur of heads and tails when I open a box.”
“Not in a quantum universe. The act of observing forces the penny into one of the allowed states. Some physicists think it is meaningless even to ask what the penny is doing when we do not look at it. The penny exists in a well defined state when we do look at it.”
“What if we had a flash camera in the box and we trip it just before opening?”
“That would be equivalent to a measurement and would force the entangled particle into the opposite state. Quantum effects are normal for elementary particles. Everything is made of elementary particles and has quantum behavior. It is hard to see quantum effects for large objects.
“I don’t want to think about this. My brain is melting down like ice cream in frying pan, but I could work a good scam on Courtney. We entangle a pair of pennies. I give her one box and bet her I can guess if her penny is heads or tails. I look at mine and guess the opposite.”
Qued says, “That would work and you would guess it right every time, but I can tell you a more dramatic demonstration. She might wonder if the pennies or boxes could be communicating with each other. The fastest any signal can move is the speed of light. If the pennies are far apart before opening, then we can open them quickly before any information would have time to travel between the pennies. You and Courtney synchronize watches. After entangling a pair of boxes, you take one by rocket to Mars. You and Courtney open your boxes at the same time. The pennies will still be opposite. This is true even though it takes minutes for any signal to get from here to the Mars. In this example, there is no chance for one penny or box to signal the other. If one penny is heads, the other knows instantly to be tails.”
“I bet no one ever proves anything as crazy as entanglement.”
“Entanglement experiments usually use photons and measure the polarization of light. This experiment has been done and entanglement was confirmed, and the photons were in the correct states instantaneously.”
Goofer says, “That’s cool, Qued. Can you do anything with a pea under one of three shells? Meanwhile I’ll go get Courtney.”
Symmetry
Almost every paper in high-energy physics mentions symmetry. Something is symmetrical or has symmetry if it is similar to its original state after you apply a change. Daisies are symmetrical to a rotation. If you turn one the width of a petal, it looks the same. The human face is symmetrical to a reflection through a vertical plane at the middle of the face. An isosceles triangle (three equal sides) is symmetrical to a rotation of 120 degrees. Symmetry is not limited to physical things. We saw symmetry in Maxwell’s equations. There are symmetries in art and music.
There are many symmetries we take for granted. There is the linear symmetry of time. You are pretty much the same as you were a half hour ago. All the laws of physics are the same as they were a half-hour ago, and at any other time. Symmetry is very important to physics. A law of physics comes from every symmetry. The law connected to time symmetry is the conservation of energy. Energy cannot be created or destroyed. There is symmetry to spatial position. Moving an experiment twenty feet over does not change results. Symmetry to spatial position gives the law of conservation of momentum.
What’s Real?
There is the old brainteaser, “If a tree falls in an empty forest, does it make a sound?” Are things still there when we are not looking? We would say yes to both these questions but quantum mechanics leads in a different direction.
Quantum mechanics is weird in many ways but one of the weirdest things is how observation influences things on the quantum scale. We cannot see or touch an electron. When we look at TV, we are seeing light that happened when an electron hits the screen. At quantum pool, we learned that electrons are usually a wave. If they remained waves, the TV would be blurry. It is not, and if we used a microscope, we could look at individual light pulses from individual electrons hitting the screen. Why do we get “The Today Show” instead of a blur? That is the weird part. When we observe the electrons by tuning in, we collapse their wave functions or probability waves. What does that mean? Before we look, the electron is smeared out somewhere in the picture tube. It is most likely where its probability wave is highest. Once we look, it is 100% where we found it in “The Today Show” image on your TV. How did that happen? ξ I know fifty thousand physicists that would like someone to tell them how it happens. No one knows. It just happens.
The usual explanation is that the electron is everywhere until observed. Then pop. There it is somewhere at random inside the wave function. Another is that the electron is nowhere until we do a measurement. Another idea is that the electron follows all possible paths but in different universes. When we see it, we settle both of us into the universe where we see “The Today Show” with the electron lighting up a spot in the upper left corner.
This problem has led some physicists to consider if thoughts or consciousness has some connection to the quantum world. Physicists have wondered about this for nearly 100 years. What do you think changes the electrons from wave to particle? ξ
Summary of 20th Century Physics
Much more science happened in the twentieth century than in the rest of human history. The acceleration of research continues. The 20th century began with two minor problems. Their solution led to quantum mechanics and relativity. Relativity mostly changed our idea of space and gravity. Special relativity showed that time behaves similar to a space dimension. At speeds near the speed of light, objects shrink, clocks slow, and mass increases. Mass can convert to energy and vice versa.
Force is something we all know because we can feel gravity. Physics digs deeper and asks what produces the force. We looked at three versions of gravity. Newton believed it was a field. A mass just naturally makes the field. He gave an equation to calculate the field anywhere. Einstein described gravity as a warp of spacetime.
“Gravitation is not responsible for people falling in love.” A. Einstein
He gave equations to calculate the warp. These two theories almost agree. Einstein’s theory is better because it correctly predicted the bending of light by the sun. Quantum mechanics sees gravity as coming from exchange of gravitons but when applied it gives elementary particles heavier than a Buick. Gravity shapes the whole universe.
Quantum mechanics gives a series of results that are completely different from ordinary experience. Sub-atomic particles behave like both waves and particles. These particle-waves can tunnel through barriers. Our measurements on them always are uncertain. It is not a matter of buying new instruments or being more careful, the uncertainty is part of the universe. There is a good reason quantum mechanics seems so strange. It is concerned with objects far smaller than anything we can see or feel.
The number of elementary particles went from just the proton, neutron, and electron to about 200 more. High-energy accelerators discovered these. They get protons or electrons moving near the speed of light and slam them into a target. Putting that much energy into a tiny spot can create particles never before seen. In the last half of the 20th century, the Standard Model reduced the number of elementary particles to a dozen. Standard Model calculations often produced infinite results, but a trick called renormalization or infinity stomping can cancel the infinity and still leave very accurate results. It does not work for gravity.
Newton’s laws were wonderful. If you knew where everything is and the velocity of everything, then you could accurately calculate the past and the future. Quantum measurements, however, are fuzzy. It is impossible to measure anything without changing other things. Measurements come in pairs, like velocity and position. The more accurately you measure one, the less accurate the other becomes. This is the uncertainty principle. Therefore, the classical idea of finding the position and velocity of everything so you can predict the future cannot happen.
Quantum mechanics does not make sense to us. We operate in the normal sized world. Quantum effects also happen here but they are so small that we cannot detect them with the best instrumentation, and we certainly cannot see them. We touch one result of quantum mechanics when we use a computer. In fast computer chips, electrons often move by quantum tunneling. Nano-technology has to consider quantum effects. At the atomic scale and smaller, chunkiness and fuzziness rule.
Quantum mechanics and relativity deal with opposite ends of the universe, sub-atomic particles, and the whole universe. It is hard to imagine that a single theory could combine them. Worse than that, the equations of quantum mechanics do not know there is such a thing as spacetime or gravity. Quantum mechanics and relativity could not work together. Black holes require both and are a big problem to theoretical physics. Gravity was not the only problem. Eight of the elementary particles look like excess baggage. The universe might be fine without them. Physicists adjust nineteen physical constants to make the Standard Model work and fit the observed properties of the elementary particles. It would be nice if the theory predicted the values of the nineteen numbers. Even better would be to explain the origin of the elementary particles.
String theory is required to agree with both quantum mechanics and relativity results. Both are correct in their where they apply and they are very accurate.
String Theory
Quantum mechanics required accepting some bizarre new ideas: particle-waves, quanta, observers affecting reality, and uncertainty built into the world. String theory is going to make these seem ordinary. String theory, as the first scientific theory of everything, should explain all the forces and elementary particles. It should explain the origin and evolution of the universe. String theory should agree with the accurate results of quantum mechanics and relativity and become the foundation of the rest of science. Physicists came to string theory by observations of the biggest and smallest things in our universe. We do not have any experience of these realms. It is no wonder string theory is going to seem strange.
Our thoughts about the basic components of the universe have changed greatly since we first started thinking about it.
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Oh! Himmel! My mustache is slipping |
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“If at first an idea is not absurd, then there is no hope for it. Imagination is more important than knowledge.” A. Einstein |
In the last century, physicists discovered the twelve elementary particles. Surprisingly, eight of those twelve do not occur naturally and appear to be unnecessary. Coincidentally we are back to four modern “elements” or elementary particles that make up everything. String theory reduces that to one thing: string.
Many Beginnings of String Theory
Physicists realized that many of the problems in high-energy physics came from regarding particles as points. Many calculations of particle properties gave infinity. Within a few years of the first discoveries in quantum mechanics, some of its founders tried to replace the point with a more realistic small sphere. Even the best physicists could not make it work. Nevertheless, most physicists knew that particles were not points. Later there was only a small effort to replace points, because the Standard Model could give the right answers.
During the last century, physicists tried to unite the forces by making them different aspects of one force. This was successful for the strong, weak, and electromagnetic forces. Gravity was the odd man out. Thus the century’s two greatest discoveries: the Standard Model of quantum mechanics and relativity had little to do with each other. Efforts to add gravity to the Standard Model was like adding vinegar to milk. They led to lumps of infinities that made the calculations wrong. Adding the Standard Model to relativity made relativity go crazy because virtual particles rapidly pop up and disappear. This made spacetime twist, turn, and tear and that makes the equations of relativity break down. Nevertheless, it simply was not acceptable that the Standard Model and relativity did not fit together.
Many physicists would like to take credit for string theory. Like most things in science, string theory did not pop into existence from one person. It evolved from earlier work as many unrelated paths crossed. Soon after Einstein discovered relativity, two physicists tried to unite the only known forces, gravity and the electromagnetic force. They did it! This was astonishing since these two forces seem so different. The trick was adding another dimension to spacetime. In a universe with four space dimensions instead of our three, there was just one force. Let us call it electrogravity. When they calculated what electrogravity looked like in our familiar three space dimensions, this one force split and became two forces, gravity, and the electromagnetic force. This astonishing idea gave an amazing result. At the time, no one took it seriously. An extra dimension seemed too strange. The recently discovered nuclear forces did not fit the four-dimensional picture. For 50 years, the idea was lost.
Another push toward string theory came from the study of scattering of elementary particles. In these experiments, a beam of particles hits a target and the particles go flying in all directions. The equation that best described the results looked familiar. Scientists went back two hundred years to identify the equation as Euler’s equation describing the motion of a vibrating body like a guitar string.
Around the same time, some physicists started working out the behavior of quantized strings. Why? Because their TV was broken? Did they just think it was something interesting to do? Could they make it a homework problem for graduate students? ξ To them it was just an interesting thing to do like learning a new hip-hop dance move. They did not expect their work to be very significant. Some of the results were very strange.
They first worked out the behavior of real strings using classical physics. Then they turned on quantum mechanics by making the energy of the string come in quantum chunks. The results were interesting but they soon found that the strings could not move. That was not a good result if this were ever to become a theory of elementary particles, but it gets weirder.
The calculation also produced a tachyon particle. Tachyons move backwards, yes, sdrawkcab in time. Giving them energy slows them down. They have imaginary mass equal to a tenth of a Cheshire cat. They only exist in science fiction. This was a big hint that string theory would never apply to anything in the real world.
This was the situation at the start of string theory. Several things pointed vaguely to the idea of particles being like vibrating strings. Curiously, only one of these came from an experiment. The other ideas were theoretical. As a Moody Blues song puts it, “Thinking is the best way to travel.” Before this, experiments usually turned up something that theory could not explain. That would get the theorists going and experimenters would do more work in order to give theory people enough to build a new theory. After that, more experiments would confirm the theory. With string theory, theory took the lead and experiment has not been able to catch up.
String Theory with a Jump Rope
You can start to learn about string theory from life sized strings or rope. An interesting property of string is that it can only wiggle in particular ways. Grab your jump rope and tie one end to a railing or something else that does not move, like your Dad watching football. Your rope will copy the behavior of real strings. Hold the rope and rotate your hand the way you usually do when you play jump rope. A single bump goes round and round, and that pattern repeats as long as you keep your hand moving. Now try going slower and faster. The rope will not turn well at just any frequency but only turns well at the first speed you used.
You have just discovered the lowest energy level or lowest energy mode of vibration of your rope. If you start moving your hand much faster, you can get the rope moving nicely again but with two bumps. [Figure jump rope speeds patterns, illustrate] You have to look sharp but one bump is up, the other down, and then they switch. Notice it takes more energy to get your rope going with two bumps than one. The rope is also moving at a higher frequency of rotation. This is the second energy level. If you can get more speed, you can get three bumps. The energy of your jump rope is quantized. Only certain amounts of energy make it turn smoothly.
This is how the strings of string theory behave. Strings vibrate only in certain modes. The vibration modes have different amounts of energy. Using E = mc2, this gives a distinct mass for each mode. Elementary particles come only in certain masses. Maybe we are on to something. That is a smart jump rope. The different modes of vibration of strings correspond to the elementary particles in the universe. The first four modes of vibration of strings should correspond to neutrino, electron, up quark, and down quark.
Forces
There is only one kind of string. All the variety of things in the world is due to where and how strings vibrate. Each way a string vibrates is a different elementary particle. From quantum mechanics, we know elementary particles are complex and can be waves. That is their behavior at atomic size, but if you could look deep inside you would see a single tiny vibrating string. Instead of calling elementary particles elementary string vibrations, we will usually call them particles or elementary particles as most physicists do. Remember that from now on “elementary particles” means elementary strings.
One kind of string vibrating in different modes can generate the elementary particles. Other types of string vibration create the particles that carry force. Quantum mechanics took the forces and particles as the fixed properties of the world and built up the theory from there. The theory had nineteen parameters or constants that determined particle masses and force strengths. String theory explains all the forces and particles with one constant, the stiffness of the string.
In string theory, the four forces are united in a very profound way. The forces are the same thing, in a sense because they are just different vibrations of string. The personality of each force comes from the shape of spacetime and the mode of vibration of the string. Force particles and mass particles are fundamentally the same. Again they too are just string vibrating in different ways. You, bacteria, atoms, stars, everything is string vibrations. [Figure funny virtual particles with messages between strings, drawing]
The four forces differ in strength and the distance over which they act. They are so different that it is hard to imagine they could arise from different modes of vibration of string. The forces we know perssonally are electromagnetic and gravity. They both have a long range, which is why we know them; we can feel them. The electromagnetic force is fascinating because it accounts for things as different as lightning, magnets, light, radio, and x-rays. Strong and weak forces are nuclear forces that do not reach outside the nucleus. We do not feel them.
|
Comparison of the Four Forces |
|||
| FORCE | STRENGTH | RANGE | CARRIER |
| Strong force | Strong 10+3 | nucleus | gluon |
| Electromagnetic | Medium 10+1 | infinite | photon |
| Weak force | Weak 10-10 | nucleus | W+, W-, Z |
| Gravity | very weak 10-35 | infinite | graviton |
There is a huge difference in strength between gravity and electromagnetic force. The electromagnetic force is 10+36, a million quadrillion quadrillion, times stronger than gravity. However, that does not seem right – gravity holds us on the Earth. One followed by 36 zeros is a big multiplier. Gravity holds us down on Earth. Did you ever rub a balloon on someone’s hair? The static electricity makes their hair stands straight up. That’s the electromagnetic force generated by a little static electricity from hair beating the force of gravity produced by the
whole Earth, trying to pull it down. The electromagnetic force wins; your hair goes up, even though the Earth is huge and heavy.
String theory inherits the quantum mechanics view that forces are due to the exchange of virtual force particles. The four fundamental forces, electromagnetic, strong, gravity, and weak hold the world together by exchange of virtual force carrying strings. These are, respectively, the photon, gluon, graviton, and the W and Z bosons. These strings are vibrating at different notes or frequencies and can have different spin and mass.
| String Break! Silly String was discovered in 1972, the year that string theory began. That is suspicious. There is a tenth of a mile of string in a can. The army uses silly string. No, not to make the enemy laugh. In Afganistan, they spray it ahead before they enter buildings. Some buildings are booby-trapped. Silly string hangs on the trip wires, showing |  |
| where explosives are. Soldiers should be home where their kids can cover them in silly string. | |
String Surprises
String theory may be able do it all and explain everything, but it very quickly gets more complicated. The first complication is just the change from points in quantum mechanics to string. A point has no size. It has no direction. From all directions, it looks the same, completely spatially symmetric. Strings break that symmetry. A string has length. The length can point in a particular direction. The effect of a force still depends on the direction the force is pointing, but now may also depend on the direction the string is pointing.
When a point is still, it is still. Even if a string stops, it still vibrates near the speed of light. Therefore, strings must always obey the rules of relativity. Strings, like points, also have to obey all normal laws of physics, like conservation of energy, momentum, and angular momentum (spin). When a string moves in spacetime, its spin, mass, charges, and length stay the same. As a string moves, we cannot have one end show up in St. Louis and the other in New York.
A string can change shape. When bumping into other strings, strings can split or join the other strings. All this is much more complicated than what points can do. These complications result in many rules that strings must obey. Does your school have so many rules that no one ever gets a hall pass? String theory is just like that. There are so many rules that a string cannot move at all. This is not going to be a good theory of everything if nothing moves. You will never guess how physicists solved this problem. ξ
“We can’t solve problems by using the same kind of thinking we used when we created them.” A. Einstein
The Rope to School
No one is confused about the three dimensions of space. Thinking of your town, they are north south, east west, and height. Three numbers can locate anything in your room, on Earth, or out in space. The three dimensions are also the three different ways something can move. Hmmm, strings cannot move.
Imagine you tied a rope seven blocks long between your school and your house. Why? Well, tomorrow you are going to get drops in your eyes and you are sure you would get lost without the rope. You want to meet Courtney today at the rope. It is so long that you have to tell her more. You are very precise and tell her to meet you at 152 meters from the school end. At 152 meters is just one dimension. An ideal string (the abstract mathematical string in physics) has just one dimension. You go but she is not there. You call her back and find out that she was there ten minutes before you. You have to add the time. You agree to meet at the same point on the rope at 3:45 P.M. Time is one of the dimensions of spacetime. You need it to meet Courtney.
You meet and talk. Both of you decide to go back to your laptops and play with your computer controlled miniature mechanical bugs. “Let’s have the bugs meet at the same spot, 152 meters, at 5:10 PM Central time.” [James’ fig of rope, bugs, and neighborhood drawing] The bugs are one-tenth the size of a period but have excellent claws. They give good wireless video feedback to your computer allowing you to direct your bug to the right place and time but Courtney’s bug is not there. After a flurry of emails, you figure out that hers is on top of the rope and yours is on the bottom. You need another dimension to give the angle around the rope, and you decide to meet at 90 degrees.
For people meeting at the rope two dimensions were fine, time and the length along the rope. For the small bugs, we needed a third, the angle around the rope. The angle around the rope is an unnecessary small dimension to you. If you back up far enough from the rope, that dimension is invisible. We’re not done yet. The bugs are so small that they can push into the rope. We have to add how deep in the rope, giving four dimensions. Ropes are made of strings. If we had super-miniature bugs, we would need to say which string and add the angle and depth in the string giving seven dimensions. In addition, strings are made of threads – three more dimensions giving ten. Threads in turn are made of fibers so we could go on. We don’t have to because ultra-microbugs don’t come out until next year. The added dimensions in this example were small enough for kids to ignore. Only the miniature bugs could sense them. This example shows how some dimensions can be so small that they are invisible and ordinarily unnecessary to us. Is our rope really ten-dimensional? ξ
Knots in the Rope – Hidden Dimensions
Physicists were desperate to solve the problem of making strings move and have string theory work. They knew string could answer many fundamental questions. Therefore, no one fell off their chairs (well a few did) when the only way to make strings move was if space had ten dimensions. This is a very new thing. One way to look at it is to say this is crazy. Theorists gave it a positive spin, like politicians do, that no other theory ever determined the number of dimensions space should have. So now, we know we have been wrong all these years.
How can space have ten dimensions when all we experience are three? Only three of the dimensions are large. The other seven are tiny. The rope to school actually does not have ten dimensions. It is four-dimensional. Once the distance from the school is fixed, only the angle and distance into the rope and the time are required to locate a bug or any point in the rope. The coordinates just have to be very accurate to locate something as small as a particular fiber or bug.
String theory’s extra dimensions all curl up on each other into tiny, complicated, seven dimensional shapes that look like knots. The knots are about the size of a string. That is so small that no equipment will ever see them. A knot of curled up dimensions exists at every point in space. They might be like small chunks of Swiss cheese or more pretty like Play-Doh with twists and holes. The curled up dimensions exist at every point in space the way an angular dimension is at every point along the rope. Mathematicians have thought about spaces with many dimensions long ago and worked out the math to deal with objects having more than three dimensions. This made the work of physicist’s a little easier.
We do not notice the knots and bumpiness of space for the same reason we do not notice quantum effects. They are far too small. Take the period at the end of this sentence. The knots in space are much smaller than that. Put one hundred small dots across a period. Pick one of these dots and put a million dots across it. Pick one of those and put a million small dots across it. Better sharpen your pencils. You would have to do this division of a dot into a million dots five times to get as small as the curled up hidden dimensions of space.}
James finds himself and Qued looking at a large lumpy ball. Qued has a stringed instrument like a guitar-harp floating over his head.
Qued yells “James, come hear in this cave. I want to play you a song on my strinyar.”
“This isn’t a cave. We are at some kind of giant ball of cookie dough. Oh, here is a hole that is something like a cave. ” [Figure curled space and James & Qued on it, drawing]
“This is actually the curled up dimensions of your universe.”
“But Qued, that means either it’s expanded to a very large size or we are very, very small! ”
“Don’t worry. I will take care of that later. Now watch and listen as I play at the entrance to this hole. One song of your world, ‘Merry Had a Little Fuzzy White Quadruped’ is popular in my world.”
James smiles and says, “It’s not ‘Little Fuzzy White Quadruped.’ It’s ‘Mary Had a Little Lamb’.”
“Well that makes it simpler. I will play the start. Here goes. I hope I do not play wrong notes. No telling what would happen. Ma ♪ ry ♪ had ♪ a ♪ little ♫ lamb ♪ little ♫ lamb ♪ little ♫ lamb ♪”.
“Wow. With every note you played, I saw a vibrating string at the cave. They were different lengths, different colors, and had different numbers of waves. I think they went all the way through this cave to the other side. Some even wound around the lumpy ball.”
Qued replies, “Right. Thirteen notes produced thirteen strings. Only four notes were distinct therefore we saw only four different strings. The low notes were neutrino and electron, lightweight particles. The higher notes were the heavier up quark and down quark. These are the family of elementary particles occurring naturally. The notes I played caused the curled up dimensions to ring or resonate in a particular way. That ringing of the space created the particle. Let us move to another hole. I’ll play it again.”
James listens then says, “Okay, we got the same looking strings but the notes sounded like they were off key, at a higher pitch.”
“Look closely. I’ll play it again.”
“Now I see. These strings changed length and may have an extra wiggle.”
“Right again, more wiggles make them higher pitch. Being higher pitch means more energy and more mass. From this hole, we got the second family of strings, the mu strings: mu neutrino, mu, and the charm and strange quarks. In the third hole, we could make the tau family. High energy scattering experiments can produce the tau and mu families, but they quickly change into the first family particles. Three holes give three families of particles. Do you see that big bump to the right of you? Sit on it.”
James says, “There are all kinds of bumps here. You must mean this one. I must be gaining weight. It squashed right down under me.”
“Good, hold it down while I play the notes again. Eyes and ears at attention.”
“Now the song is different. The notes shifted both up and down compared to the first time. It is really a new melody. It is kind of like the Beatles’ “Maxwell’s Silver Hammer.” There are more distinct notes.”
“Excellent James. This shows how sensitive strings are to small details of the shape of the curled space. When you squashed that bump, you made the hidden curled dimensions for a different universe. The extra notes are elementary strings or particles that do not exist in your universe. It sings a different song than yours. The elementary particles and even the physics are different.”
“Wow, I did all that. Awesome.”
“Changes in the hidden dimensions can completely change the universe.”
James asks, “What makes strings have different charges and behave differently with the strong or weak force?”
“Good question. Explaining is hard to do without math, but the details of the vibrations and the curled space they are in or wind around determine all the properties of the strings. That determines all the elementary particles and their properties. They, in turn, determine all the properties of the universe.”
“Well, what about force strings?”
“This is one of the most amazing things about strings. String explains force and matter in the same way. Even though they seem very different to us, string theory explains everything as vibrations of string. The mode of vibration gives mass strings their charge, spin, and mass. Force strings are the same string but vibrating in a different way, in different dimensions. Climb down and I will try to make a force string. Here’s a good spot, I’ll try to make a graviton.” [Figure make graviton, drawing]
Qued produced four things that looked like glittery golden bowling pins. He started spinning, striking repeatedly at four places on the lumpy shape.
“Wow, you made a totally different thing, a vibrating loop like a hula-hoop. Waves are moving rapidly around the loop.”
“Yes, this is the graviton, a closed string.”
Lost in the Hidden Dimensions
Goofer greets Qued in his unique way, “Quedball, my alien bro.”
Qued replies, “May greetings fall over you, Goofer. ”
I want something from you. James told me there are ten dimensions. I want to know where they are. I’ll go see if the kids there are as cool as me.”
“The extra dimensions are everywhere, at every point in space. You will find, however, no kids. These dimensions are unimaginably small, and all wrapped up around each other.”
“So the extra dimensions are everywhere but they’re nowhere.”
“Exactly.”
“I need a little spaced time. If the extra dimensions are so small, then how do they affect us in our three dimensions?” says Goofer.
“They don’t and that’s the problem. They are small enough that there may never be any way to detect them. The extra dimensions give strings more ways to wiggle and that solves the problem that they could not move through the big dimensions of space. Wiggling in the hidden dimensions releases the strings from the requirements that kept strings from moving.”
“So the tiny dimensions don’t have any effect but they affect everything.”
“Goofer, you have the unique ability to cut right to the point in an obscure way. You may be a Zen master.”
“Zen I’ll see you later.”
Qued leaves Goofer to meet with James. Meet isn’t quite the word because {James finds himself and Qued looking at a large lumpy ball. Qued has a stringed instrument like a guitar-harp floating over his head.
Qued yells “James, come hear in this cave. I want to play you a song on my strinyar.”
“This isn’t a cave. We’re at some kind of giant ball of cookie dough. Oh, here is a hole that’s something like a cave. ” [Figure curled space and James & Qued on it, drawing]
“This is actually the curled up dimensions of your universe.”
“But Qued, that means either it’s expanded to a very large size or we are very, very small! ”
“Don’t worry. I’ll take care of that. Now watch and listen as I play at the entrance to this hole. One song of your world, ‘Merry had a Little Fuzzy White Quadruped’ is popular in my world.”
James smiles and says, “It’s not ‘Little Fuzzy White Quadruped.’ It’s ‘Mary Had a Little Lamb’.”
“Well that makes it simpler. I’ll play the start. Here goes. I hope I don’t play wrong notes. No telling what would happen. Ma ♪ ry ♪ had ♪ a ♪ little ♫ lamb ♪ little ♫ lamb ♪ little ♫ lamb ♪”
“Wow. With every note you played, I saw a vibrating string at the cave. They were different lengths, different colors, and had different numbers of waves. I think they went all the way through this cave to the other side. Some even wound around the lumpy ball.”
Qued replies, “Right. Thirteen notes produced thirteen strings. Only four notes were distinct therefore we saw only four different strings. The low notes were neutrino and electron, lightweight particles. The higher notes were the heavier up quark and down quark. These are the family of elementary particles occurring naturally. The notes I played caused the curled up dimensions to ring or resonate in a particular way. That ringing of the space created the particle. Let’s move to another hole. I’ll play it again.”
James listens then says, “Okay, we got the same looking strings but the notes sounded like they were off key, at a higher pitch.”
“Look closely. I’ll play it again.”
“Now I see. These strings changed length and may have an extra wiggle.”
“Right again, more wiggles make them higher pitch. Being higher pitch means more energy and more mass. From this hole, we got the second family of strings, the mu strings: mu neutrino, mu, and the charm and strange quarks. In the third hole, we could make the tau family. High energy scattering experiments can produce the tau and mu families, but they quickly change into the first family particles. Three holes give three families of particles. Do you see that big bump to the right of you? Sit on it.”
James says, “There are all kinds of bumps here. You must mean this one. I must be gaining weight. It squashed right down under me.”
“Good, hold it down while I play the notes again. Eyes and ears at attention.”
“Now the song is different. The notes shifted both up and down compared to the first time. It’s really a new melody. It is kind of like the Beatles’ “Hey Jude.” There are also more distinct notes.”
“Excellent James. This shows how sensitive strings are to small details of the shape of the curled space. We just made the hidden curled dimensions for a different universe. The extra notes are elementary strings or particles that don’t exist in our universe. It sings a different song than yours. The elementary particles and even the physics are different.”
“Wow, my butt did all that. Awesome.”
“Changes in the hidden dimensions can completely change the universe.”
James asks, “What makes strings have different charges and behave differently with the strong or weak force?”
“Good question. Explaining is hard to do without math, but the details of the vibrations and the curled space they are in or wind around determine all the properties of the strings. That determines all the elementary particles and their properties. They, in turn, determine all the properties of the universe.”
“Well, what about force strings?”
“This is one of the most amazing things about strings. String explains force and matter in the same way. Even though they seem very different to us, string theory explains everything as vibrations of string. Force strings are the same string but vibrating in a different way, in different dimensions. That in turn gives them their charge, spin, and mass. Climb down and I’ll try to make a force string. Here’s a good spot, I’ll try to make a graviton.” [Figure make graviton, drawing]
Qued produced four things that looked like glittery golden bowling pins. He started spinning, striking repeatedly at four places on the lumpy shape.
“Wow, you made a totally different thing, a vibrating loop like a hula-hoop. Waves are moving rapidly around the loop.”
“Yes, this is the graviton, a closed string.”}}
“Do closed strings move differently than open strings?”
“Yes, closed strings move easily and could even cross from our universe to another. Strings with mass have to stay in our universe.”
“So are there other universes?”
“Do you remember the Prime Directive from Star Trek? I must follow it. I am not to interfere with the natural development of intelligent life.”
“Well, that can’t apply to Goofer. I’ll ask him to ask you.”
How Is Space Shaping Up?
In order to allow strings to move, space has to have more dimensions. Now that strings can satisfy the restrictions on their motion, some truly amazing things happen. The strings can now vibrate in many new ways. Some of the vibration modes produce the elementary particles. Happily, other vibration modes correspond to the four forces of nature. Especially wonderful is that the gravitational force has a mode just as the other forces do. This means that gravity will no longer be the oddball force that cannot fit into quantum mechanics. The equations that predict the motion of strings under the four forces are just the same as the ones physicists used for the last century. Therefore, if a charged string interacts with an electromagnetic force string, the photon, Maxwell’s equations still give the correct results. Similarly, string theory reproduces the equations for the strong, weak, and gravitational forces. The forces were also united in a profound way since they were all due to vibrations of strings. All of this eluded physicists, even Einstein, for a century.
In string theory, the energy of the string and the details of the tiny curled space determine the elementary particles and forces and that determines everything about the universe. Just look out your window and think about that. ξ String theory derives all of physics for the last 100 years from the geometry of strings and spacetime. Everything depends on the geometry of our universe. It should not be surprising that for string theory to accomplish all this requires space to be more complex and have hidden dimensions.
Physicists, programmers, and mathematicians have constructed drawings that suggest the look of these spaces. No one knows which arrangement is correct. The curled space can have holes. Every hole produces a unique family of particles. The vibration of strings in the curled space defines the all of the properties of the particles.
| These are attempts to show what the curled up dimensions look like, |
however, these are 2-dimensional views of a 7-dimensional space.
This is a big problem in string theory. Like all theories, string theory has to prove itself by giving correct results for known data, the elementary particles, and by correctly predicting something new. Since the properties of the elementary particles depend on the shape of the space, you first have to know the geometry of the curled space. This is especially hard. You cannot sit outside a tiny knot and look it over like Qued and James did. Therefore, we have to look at the results, the elementary particles. To understand the space you must understand the elementary particles but to understand the elementary particles you have to understand the hidden curled space. This is where physicists have been stuck for thirty years.
Before strings, experimenters were the heroes in physics. Relativity and quantum mechanics both came from experiments that did not fit classical physics. String theory started with the thoughts of theorists. Experimenters had no evidence of extra dimensions or strings and still do not. Some physicists have been able to work backwards from the properties of the elementary particles to what types of curled shapes could produce them. They got fair agreement but this is not very satisfying because the big promise of string theory is to match nature without having to fit physical constants or hidden dimensions?
Use Your Brain’s Branes
While investigating the dimensions of spacetime in string theory, something unexpected popped up: branes. Branes, short for membranes, are lower-dimension spaces lying in a higher dimension space. We are familiar with some branes in our world. For example, a two brane is a surface, like a parking lot surface. You can call your homework a 2-brane. A zero-brane, a no-braner, is a point. A 1-brane is a string. A 3-brane is a volume. A 4-brane is a 4-brane. Well, it is a four-dimensional space that is hard to visualize or sense. Branes covers them all. Our universe could be inside a brane just as we have 1-, 2-, and 3-branes inside our space.
Imagine a soda straw with a fat orange bug inside. It does not have enough room to turn around. All it can do is go forwards and back. It lives in a one-dimensional world. The only dimension is how far it is in the straw. The bug’s universe is also finite; it has a measurable size. It also has ends. If he goes beyond an end, he falls out of his universe into one with more dimensions.
A soda straw is an example of one brane inside another. If we put the bug on the outside of the straw, do not worry. The bug has very sticky feet. We have moved it into a two dimensional world. It can go back and forth as before but now it can also go around. This bug universe is also finite. However, in the round direction, it has no ends, no boundary. If the bug goes far enough in the round dimension, it gets back to where it started. There is no boundary but that direction in space is not infinite. This is like our universe. It is finite but has no boundaries. A rocket launched in any direction would come back in about one hundred billion years from the opposite direction.
The bug’s universe illustrates again the idea of large dimensions and small curled dimensions. If our straw was miles long and we stood back from it, we would think the bug is in a world with one large dimension. We would not be able to see the tightly curled circular dimension around the straw. Note that at every point along the large dimension we have a curled dimension. This is similar to our space. We have four large dimensions of spacetime, and at every point, we also have seven curled dimensions.
We can make the long soda straw more like our universe by bending it so that the two ends come together. Then the ant would be in a universe that is finite but without ends in all directions, having one large and one small curled dimension. The bug’s large dimension curves so slightly that the bug never knows. Our four-dimensional spacetime is similar to the bug’s two-dimensional space. Gravity from all the mass in our universe warps our space into a curve. Our universe is finite and has no boundaries like the bug’s straw.
Other branes may share our space but not be detectable. The rule for strings in a brane is that open strings, strings with their ends free, cannot escape that brane. All strings with mass and all force strings, except the graviton, are open. They are stuck inside their brane. There could be another brane, another universe, just one mm from your nose and you would not know it. [Figure James and Qued, photos] How can that be true?
We see and feel by receiving photons. However, their photons stick to their brane and ours stick on ours. Weak and strong forces are stuck in the same way. Since all the strings with mass are also stuck, we cannot signal them by throwing a brick with a note tied on it. The only particle that crosses brane boundaries is the graviton. Therefore, a nearby brane is invisible, undetectable, and intangible. It may be as hard to prove there are other branes as it is to detect that angry duck on your head.
Gravitons, the closed gravitational force strings, are different. They can leak out of their brane. Some think this may be the reason that gravity is so much weaker than the other forces. Our graviton particles leak away. Gravity is not only weak. When masses are billions of light-years apart, gravity is even weaker than classical theory calculates. What could overcome the gravitational pull of our universe? If there were another universe (brane) next to ours, then the mass in the nearby brane would attract our galaxies. Their gravitons leak into our brane and pull on our galaxies. If gravitational waves exist and we knew how to make them, they could be a signal. They are so weak, however, that many experiments have failed to detect gravitational waves or gravitons from events as dramatic as supernovas and colliding galaxies. Another explanation would be a force working opposite to gravity. This is the favored explanation. This is dark energy.
One possible way to start the Big Bang, the start of the universe, is by branes colliding. String theorists struggle to understand branes because of these interesting possibilities.
| String Break! With your thumb and finger, hold both ends of a whole, raw piece of spaghetti. This is a stiff string like the ones in string theory. Holding the ends, slowly bend the spaghetti until it breaks. It almost always breaks into three pieces—not two. Try it again. Weird? |
Look Through Walls with Axions
Axions are predicted uncharged strings, many times heavier than a proton. Axions and photons of light convert into each other when they pass through a magnetic field. To see [Figure axions magnets wall, illustration] through a wall, you need a magnet on each side of the wall. Let light from an object shine through the first magnetic field. Some of the photons convert to axions. Axions pass easily through the wall in fact they can pass through miles of walls. As the axions go through the magnet on the other side, some become light again allowing you to see an object through the wall. Several experimenters have tried this, but results were not conclusive. Another experiment will use the Earth’s magnetic field to see if sunlight converts to axions that then pass through the Earth and convert to light again on the dark side. In other words, the experiment will try to see the sun through the Earth.
Supersymmetry
Many things have symmetry. Symmetry means you manipulate an object and what you get is an object very similar to what you started with. If you look at a right-handed glove in a mirror, you see a left-handed glove. If you look at that image in another mirror, it is back to looking right-handed. There is symmetry in nature, music, art, and mathematics. The universe is very symmetric. In fact, all physical symmetries that physicists can imagine do exist. In other words, the universe is as symmetrical as it can be. Each physical symmetry results in a corresponding law of physics. This feels right and appeals to our sense of beauty.
Mathematicians discovered a brand new type of physical symmetry involving spinning objects in a higher dimensional space. Physicists noticed that this symmetry did not have a law. What do you think physicists did? Ignored it since they already had more math than they could solve? Decided it just did not apply to our universe? Started looking for that symmetry in the world? Decided that the universe is still beautiful without that symmetry, so live with it? ξ To guess the right answer, you need to know about a strong belief many physicists have—if it is not forbidden, then it is allowed. If it could happen, then it does happen in nature. Physicists have found this to be true many times. One example was the prediction of anti-matter. Seventy years ago, some nuclear equations gave two answers, negative electrons and positive electrons. Five years later, positrons, positive electrons, appeared in tracks of cosmic rays. They were the first anti-matter discovered. For the new spin symmetry, the argument is even stronger. The math of spins allows this symmetry. To a physicist this symmetry must be real and exist in nature. This is supersymmetry. Strings are now often called superstrings.
You have to be very confident in your theories and the order in the universe to believe, that “If it is not forbidden, it’s allowed.” Do not try to apply this belief at home or school. It is a sure way to get into trouble.
“Mom, can I have a candy bar?
“No, dinner is in an hour.”
‘She didn’t say I couldn’t have a chocolate cake. Yummy.”
String theory first modeled strings that carry forces. To include strings with mass requires supersymmetry. This symmetry involves spin. Spin is a quantum property of elementary particles that resembles ordinary spin. Force strings have a whole number spin of 0, 1, or 2. Matter strings have spin ½. The halves are the jealous strings that will not allow another string of their kind in their energy level. Supersymmetry means that every whole spin string has a half spin partner with the same mass. If you do the supersymmetry spin transformation, you change the spin and a force string becomes a mass string or vice versa. The mass of the partners should be the same, but there are no elementary strings with the same mass. If we were discussing the mirror reversal symmetry, this is as if we used a mirror to change a left-handed glove to right handed, and instead it turned into a shoe.
This is the problem with supersymmetry. The spins of the partner particles will differ but their masses should be equal. However, no strings have the same mass. None of the twelve elementary strings has a partner. What do you think physicists did? Give up on the idea? Decide the supersymmetric strings exist but something made them turn out heavy? Start working on super-duper-symmetry? ξ You are getting used to these questions. Somehow, one partner has become heavy. They are so heavy that we have not seen them because we do not have accelerators with high enough energy to make them. Making heavy strings requires an accelerator with very high energy. A particle accelerator, the LHC, in Switzerland may produce them. Experimental evidence for supersymmetry at this high-energy accelerator would convince most physicists that string theory is the best model for nature.
| String Break! Did you ever try to walk through a wall? Atoms are mostly empty space. Why can you not go through all that mostly empty space with your mostly empty space? Electrons are jealous and do not allow another electron in their energy level. The wall electrons were there first and they have filled all available energy levels. When you push on a wall, the solidness is because your electrons cannot find an empty energy level. Your electrons are why you cannot get through a wall. Wolfgang Pauli explained this behavior. He also once told one of his students that his work was so bad that it’s “not even wrong.” – |
Duality
Duality is a very peculiar symmetry of string theory equations. You thought supersymmetry was strange enough. Here is a simple equation: R + B = C. Let us pretend C is some constant of the universe, like the speed of light. If R = 100 and B = 2 , then C = 102. Now comes the mysterious part. If this was one of the fundamental equations of string theory and R was a length (for example the size of the universe), then the string theory equation would still be true if we replace R with 1/R. R is huge so 1/R, the reciprocal, is very small but the equation is still correct.
Do not try this substitution in algebra class because you will be wrong. Using our original numerical values should convince you that our little equation does not have duality symmetry. To do this with the numerical values replace R = 100 with 1/R = 0.01, the equation is no longer true because C our constant of the universe changes from 102 and becomes 2.01.
Duality means there is a newly discovered connection between the universe as a whole and the size scale of strings. The same equations hold. The string theory equations show this same behavior with the force strength constant. Duality symmetry may lead us to deeper levels of understanding. The universe is trying to tell us something. Large is like small and weak is like strong. The universe begins small and strong, energy concentrated in a tiny point. Then comes the Big Bang and the universe moves toward large and energy becomes dilute. Strangely, understanding one extreme helps us understand the other.
All theories are a mix of facts that we use to make the theory fit reality, and facts we find by using the theory. Which way is more impressive, changing the theory to fit many facts, or finding many facts by applying the theory? ξ James and Courtney are doing two jigsaw puzzles of the universe. They both have an idea of how the universe looks. She watches Star Trek and James watches the Hubble telescope. The puzzle pieces are facts and ideas about the universe. Both begin, and soon Courtney is ahead. James notices that she is using scissors to trim the pieces of the puzzle to make the pieces fit. James works the old-fashioned way.
James says, “Courtney you’re cheating.”
“I’m not cheating. These scissors were with my puzzle. Qued left a note telling me I wouldn’t get far without them,” says Courtney.
Courtney’s puzzle looks messy with some big holes. The red pieces that represent relativity hardly ever touch the blue pieces of quantum mechanics. After a slow start, James’ puzzle goes together faster, getting complex, more beautiful, and bigger. There are only small holes. It roughly looks like a ying-yang symbol. Which puzzle would you like to work? ξ
Quantum mechanics works much like Courtney and her puzzle. It needs nineteen tools to trim the theory into a good fit. These are the nineteen constants needed to match mass, charge, force strengths and so on of the elementary particles. String theory needs only one constant, the stiffness of the string. Courtney’s puzzle gives a picture of the 20th century universe, and she has a big hole in the center. One side has something to do with relativity, the other quantum mechanics. There are other holes. In James’ puzzle, quantum mechanics and relativity wrap around each other and string theory wraps around both. String theory fills the hole in the center. James has fewer, smaller holes. Courtney agrees that James’ picture of the universe is more beautiful than hers is.
String theory can solve the puzzle of the universe. It has only one number to fit, yet relativity and quantum mechanics are part of it. That is amazing. It took 50 years to develop quantum mechanics and here string theory gives it free. That is one of string theory’s greatest accomplishments. A theory has to agree with all the old data of previous theories. Since relativity and quantum mechanics both follow from string theory, agreement is certain. If we lived in weightlessness, we would not know from experience that there was gravity, but using string theory we could conclude that there is a force of gravity and derive all of its properties. This is true of all the other forces. That is a big part of the evidence that string theory is a correct theory of everything.
String theory can do everything and explain everything that physicists have learned in the last hundred years. Should we burn all physics books and cancel our subscriptions to Scientific American? Do we stop putting billions of Euros into tunnels in Switzerland? Do we re-train physicists as school bus drivers? ξ Working out the details and applications of string theory could take hundreds of years. Maxwell’s equations are 150 years old, and they still provide many new practical applications. You are stuck with your school bus driver.
The whole of relativity and 20th century physics follows naturally from string theory. Do you remember Courtney and the missing paper? Explaining the universe with only one constant is harder than getting a one-sentence explanation from Courtney. The agreement of string theory with previous work is only a start. Physicists require a theory to predict new phenomena. Otherwise, it is only making explanations after the fact. Courtney was very good at that. String theory will sometimes be confusing, like quantum mechanics. It still has all the craziness of quantum mechanics – chunkiness, fuzziness, and the observer affecting reality. It is still controversial. It does a lot, but you have to accept a lot on faith. What you must accept does not make sense and has not been tested.
Problems with String Theory
Explaining gravity and the whole mess of elementary particles was great. Further progress for the last 20 years has been difficult. If you are beginning to understand science, you must be wondering where the predictions are. What experiments confirm string theory? For example, how closely can string theory calculate the mass of the electron from properties of the hidden spaces and the equations of string theory? That is the problem. String theory is the way to determine elementary particles properties, but there are several hard problems to solve. First, physicists do not even know the complete set of equations. Second, some of the equations have not been solved except approximately. Third, we do not know the exact shape of the hidden dimensions.
To calculate the properties of elementary particles, you need to know which of the possible curled hidden dimensional spaces our space is. If you know the correct space, you next have to find all the different ways that vibrating strings can wind around and through it. The curled space will have three holes, since we have three families of strings. Finally, you calculate all the different ways strings can vibrate. There are actually an infinite number of ways, but only the lowest energy modes will be stable and have low enough mass to exist in the world.
Some interpret the fact that we do not know the shape of the hidden dimensions to mean string theory is too generous. It can predict almost any kind of universe. If atoms were ten times as big as they are, you could make a few changes in the curled dimensions and string theory would agree. If you wanted the elementary particles to have only 1% of the weight they have, again a few changes in the hidden dimensions and string theory would agree. Physicists need something that can correct string theory’s ability to agree with crazy versions of the universe that do not exist. They want it to agree with our crazy universe.
It will take years to derive and solve the correct equations but then the crucial missing information is the size and shape of our curled dimensions. It is not clear how to solve that problem.
What’s In Your Vacuum?
Atoms, the solar system, the Milky Way, and even the universe are mostly empty space, vacuum. The vacuum is a problem for string theory. Quantum mechanics found that the vacuum is no longer a lot of nothing. It’s more like a mosh pit where kids throw each other up in the air. There is a better example. It is like a pot of oatmeal with raisins and split peas boiling on the stove. Splat! A raison anti-raison pair jumps out. Blop! Pea pairs fly up in a puff of steam. Then they fall back in. [Figure James’ vacuum oatmeal, drawing/illustration] This food flying out of the pot is like the virtual strings popping out of the vacuum. If you could see strings, you would see string anti-string pairs constantly appearing and disappearing back into the vacuum. The virtual strings popping out of the vacuum are real. They strongly affect particle behavior. Strings pop out of the vacuum because the vacuum contains energy. Quantum fluctuations of the energy in small regions of space produce virtual particles.
Quantum mechanics deals with probabilities. When strings interact, all sorts of variations are possible involving one or more virtual strings appearing during the interaction. To get the right answer you must consider all possible interactions and add them together. Those with many virtual strings are less likely than the simpler ones. The answer gets better as more complications are included. Virtual strings change the interactions between real strings. The real strings can pass them back and forth. A string might decay into other strings or produce several virtual strings. Considering more variations makes the quantum mechanics calculations more accurate.
A very simple experiment verified that the vacuum is gushing with particle anti-particle pairs. When two metal plates are moved close together, there is an unexplained force trying to move the plates even closer. The force happens because each plate’s inner surface is partially shielded from the virtual particles. The strength of the force by quantum mechanics is correct when including virtual particles.
String theory allows many different energies for the vacuum. A real fundamental theory of everything should predict the vacuum energy. Higher energy is like turning up the heat under our oatmeal. Depending on the setting, our kitchen and the universe can be very different. Vacuum energy and shape of the hidden dimensions are connected. You do not want to have to scrape oatmeal off the ceiling. String theory does not give a clue to what vacuum energy is correct. The result is that string theory can describe many very strange universes besides our own.
Physicists Disagree
Another problem is that no one can ever observe strings. An accelerator would have to be the size of the Milky Way to slam things together hard enough to make strings. The Klingons would never let it cross their territory.
It gets worse. So far, physicist cannot test any prediction of string theory. Thousands of physicists work hard on this problem. One important prediction is supersymmetry, which pairs up force and mass particles. New particles are required to do this, but none has been found.
Physicists often disagree. They check the assumptions, techniques, and conclusions of every new theory. They repeat experiments and math. String theory has not made a testable prediction. It requires belief in strange ideas: seven hidden dimensions, a doubling of the number of strings by supersymmetry, and almost an infinite number of bizarre universes. This is because there is no handle on the shape of our curly dimensions and the energy of the vacuum. There is a barrage of books, lectures, and blogs for and against string theory and string theorists. Some bloggers think string theory has religious significance. Compared to other physics controversies, this is like the War of the Worlds. Here are some excerpts from the Not Even Wrong blog of Peter Woit along with some [explanations in brackets].
From the Not Even Wrong Blog of Peter Woit
●”String theorists try to solve non-existent problems and propose absurd scenarios. They are wasting their time and ours by working on made up problems instead of the real ones.”
●”It’s difficult to figure out whether certain ideas in these papers were proposed seriously or as a satire [mean kind of humor]. The papers usually disagree with each other in details because they draw different boundaries between serious statements and jokes [Your papers are a joke and string theorists cannot even agree on what is funny].”
●”Most farmers, drivers, and supermodels realize that there is a difference between the future and the past. [Implying string theorists do not and that they are not as smart as supermodels].”
These comments are funny, but show there are loud opponents to string theory. There is more emotion around string theory than other theory. The arguments are louder. Because of the Internet, they are more public than before. At school, there are the cool kids and everyone else. In physics, it has been cool to be a string theorist.
Get Down Look Around String Theory
We have been looking at string theory the way someone in a skyscraper looks over a city. We’ve seen some of the big buildings and highways, but none of the details. You cannot know a city very well from 100 stories up. To know string theory really well takes six years of studying math after high school. Much of string theory is hard to explain in words but easy to explain in math, if you do not count the six years. We can look at a small piece of real, current string theory research. Below is an excerpt from a current research article. It gives an idea of how complicated string theory is. The article discusses long, heavy cosmic strings that may have formed during the Big Bang. Cosmic strings are the opposite of the tiny almost massless strings that replace elementary particles. They would be light-years long, and contain the mass of many stars. If cosmic strings interact, they emit radiation, other kinds of strings. The paper calculates what this radiation might be like.
We know many physicists disagree with string theory, and cosmic strings are only a possibility if string theory is correct. So why would these three Russian physicists figure out how these maybe strings interact and maybe make radiation? ξ This is an important part of science, filling in all the details. Physicists dig through all aspects of possible ideas to see if they can find something that definitely says strings exist and have these properties or they do not. The box below is a part of a paper published electronically at the end of 2006. Look it over and you will agree that string theory is complicated.
Even the title, “Dilaton and Axion Bremsstrahlung from Collisions of Cosmic (Super) Strings” needs some explanation. Axions and dilatons are unverified string vibrations. Both relate to gravity. Axions are heavy strings without charge that may be important in cosmology. Bremsstrahlung is German for braking radiation produced if cosmic strings collide. Your brakes get hot when you slow down. Therefore, bremsstrahlung for your bicycle or car is heat, infrared radiation. The article is typical, showing that mathematics and English are the universal languages of scientists. The last equation is the equation of motion for strings. In our human sized world, the equation of motion is just F = ma; force equals mass times acceleration.
Dilaton and Axion Bremsstrahlung from Collisions of Cosmic (Super) Strings
arXiv: hep-th (0612271v1 26 Dec 2006 E Yu Melkumova1, D V Gal’tsov2 and K Salehi3
Department of Physics, Moscow State University, Moscow, Russia. Full article at
arxiv.org/pdf/hep-th/0612271
String Theory Summary
In string theory, all elementary particles are tiny vibrating strings. They vibrate in ten spatial dimensions instead of the three we know. Each elementary particle including force particles are a particular mode of vibration of a string in this space. Consequently, string makes everything. Since strings are as small as anything can be, they cannot have any internal parts and we have found the most basic thing in the universe.
If you start with string theory, you can derive quantum mechanics and relativity. After 100 years, quantum mechanics and relativity are compatible. Strings are small but not zero sized so string theory does not give the infinite results found in quantum mechanics. Quantum mechanics calculations say the mass of a particle is as much as that of a Buick. String theory also solves the problem quantum mechanics has with gravity. It naturally has the graviton, force particle for gravity. Gravity becomes just another force and the forces are united (explained in one way) as vibrations of strings. Supersymmetry predicts that there are heavy partner strings to all the twelve strings we know. The Large Hadron Collider may have enough energy to make them.
String theorists are working to define the shape of the hidden dimensions, and determine the energy of the vacuum. Without this information, string theory can describes all kinds of crazy universes. Some have more forces; others turn quickly to black holes. Probing the hidden dimensions with elementary particles requires higher energies than we can imagine. Nothing yet points to one set of curly dimension or universe being ours. This makes some physicists speculate that there actually are many universes. Remember if it is not forbidden, it’s allowed.
Physicists and mathematicians are making progress in discovering and solving the string equations. A possible source of confirmation of string theory is the field of cosmology, study of the universe.
Cosmology – Mom, Where’d You Put My Universe
Cosmology is the study of the universe, not a small part like an atom, or a big piece like the Earth, but the whole thing. The most striking thing about the universe is that it is mostly empty space. There is a lot of space between the stars and even more between galaxies. Even on the atomic and sub-atomic scales, we found next to nothing and a whole lot of empty space. The only size scale where the universe looks full is our size scale. Our size scale is full of ants, rocks, trees, buildings, cars and so on. We are at the best size to enjoy a complex, interesting local environment. Being human sized does, however, make it hard to study the universe since it is 10+26 times bigger than we are. It also makes it hard to study strings, which are 10-35 times smaller than we are.
The most basic question about the universe is why there is anything. That answer is beyond our understanding and may always be. Cosmology does answer related questions. Does the universe change? If it does, is there a beginning and an end? Fifty years ago, many astronomers thought the universe was unchanging, always was, and always will be. Now we know that 13.7 billion years ago there was no universe, as we know it. Then tremendous energy and matter was concentrated in a point. We know there was a gigantic explosion called the Big Bang. It shot out all of the matter and energy at high speed. The universe is expanding still. Even though the Big Bang was a unique event at the far beginning of time, nuclear physics correctly calculates the mix of elements found in the early universe.
Cosmology has discovered two new puzzles, dark energy, and dark matter. String theory may solve these puzzles. It affects cosmology in other ways and cosmology may verify string theory.
Scientific Creation Story – The Big Bang
It began 13.7 billion years ago. That we know for sure. The usual assumption is that the universe was just vacuum. Maybe all that existed was a single point. All eleven dimensions were tightly curled up. All of space was the size of the tiny curled dimensions. Matter did not exist. Then this tiny region of vacuum filled with massive amounts of energy and about a bowling ball weight of matter. It exploded. This was the Big Bang.
There is no agreement on where the initial matter and energy came from. One idea is that we are experiencing part of an everlasting cycle in a universe that existed before the Big Bang. We do know that it starts at a super high temperature of 10+32 or one hundred quadrillion quadrillion degrees. The forces we know blended into one single force.
At 10-45 seconds, an almost unimaginably short time, the eleven dimensions split into two groups. A group of four expanded rapidly becoming spacetime. The other seven stayed curled up as the miniature extra dimensions of string theory. There were small density and temperature fluctuations caused by quantum uncertainty. These froze in place while the universe grew rapidly to the size of a ball. This was the big burp, called inflation. Space expanded so rapidly that the speed was greater than the speed of light. This is not a violation of relativity because relativity does not set limits on how fast space expands. It limits how fast matter can move.
The fireball cooled and expanded as energy converted to super heavy exotic strings, which we will never see on Earth. It then became a soup of gluons and quarks. It was not until 10-6 seconds, a millionth of a second, that protons and neutrons formed. By one second, neutrons and protons were able to start sticking together by nuclear fusion producing deuterium, helium, and lithium, the lightest elements. Even though the universe was hotter than the interior of a star, it was pitch black everywhere. Electrons changing orbit produce light, but it was still too hot for electrons to stay in orbit around atoms. Other particles would knock them free. Whew, that was a lot happening in one second.
At three minutes, the amounts of the lightest elements stopped increasing because the universe had cooled too much for fusion to continue. The calculated concentration of the lightweight elements matches that observed in the early universe. The universe kept cooling and expanding. The next big event was at 300,000 years. The temperature dropped below 3000 degrees K. This is cool enough for electrons to start circling atoms. When that happened, the universe was no longer dark. The electrons jumped into different orbits and emitted light.
Evolution of the Universe after the Big Bang
Event Description Time
Start A point containing matter and vast amounts of energy 0.0
Inflation Nearly instantaneous expansion to golf ball size 10-37 seconds
Gluons Gluon and quark soup forms < 10-6 seconds
Nucleons Cool enough for protons and neutrons to form 10-6 seconds
Fusion Nucleons stick together making heavier elements 1 second
Fusion ends The fireball temperature is less than the sun’s temperature 3 minutes
Light Electrons attach to nuclei and emit first light 300,000 years
Stars Gravity concentrates matter to form stars 10+8 years
Galaxies Stars attract each other into galaxies 10+9 years
Earth Dust and gases in the solar system form the Earth 4.5 billion years ago
Life on Earth Very primitive organisms form 3.5 billion years ago
Humans Our ancestors appear in Africa 100,000 years ago
The material from the Big Bang kept expanding. The combination of quantum fluctuation lumps and inflation work to give the distribution of matter that we observe in the universe. Gravity made the lumps get bigger, forming stars, galaxies, and superclusters of galaxies.
Fusion in stars produced the heavier elements like silicon, oxygen, nitrogen, and iron. These elements were then available to make rocky iron cored planets found around later generations of stars. Our sun is one of those stars. Earth formed 4.5 billion years ago. The first life developed after a billion years. Life continued to evolve. Now it is incredibly diverse and found almost everywhere. Humans have been around for only 100,000 years.
This is very different from the creation stories at the start of this book. It follows from observations. Thousands of scientists participated. Scientists checked and criticized results of other scientists. Who was taking data 13.7 billion years ago? We are. Can you guess how we are seeing the early universe? ξ The light we see from the most distant galaxies started on the way to us 13 billion years ago and shows us what things were like then. The cosmic microwave background tells us what the universe was like 300,000 years after the Big Bang when light first was able to escape from the fireball. The ancient creation stories filled our need for answers when no other answers were available.
Goofer says to Qued, “What up, Quedman? I’ve been wondering. Where did the Big Bang happen? I want to go there to see if there’s any rad stuff left hanging on the trees. You know, stuff I can sell to buy a motorcycle.”
“Goofer, the Big Bang happened everywhere. It even happened in your toilet.”
“That’s soooo far out. Who was sitting on it?”
Qued replied, “At the Big Bang all of space, the whole universe, was a tiny ball smaller than an electron. That space expanded explosively and is still expanding. Therefore, every bit of space, matter, and energy in your universe was in the Big Bang. Since everything was this point, the Big Bang happened everywhere. This is similar to why the universe seems to be expanding from every point in space. Space itself expands as the universe grows.”
“Whoa Quedball, too much info. You’re always good for a couple of Gigs more than my input buffer can hold. All I know is I’m going to sit on the pot very carefully.”
You can still listen to and even see the Big Bang on TV. The Big Bang filled the universe with bright light. Most of the light kept flying across space. Since then, the universe has expanded many, many times and that visible light stretched with the universe to longer wavelengths, becoming microwaves. TV’s detect microwaves. If you turn on your analog TV in between stations, you hear static. Some static is from our machines and electronics but most is from outer space from the Big Bang. If you do not have an analog TV, listen to the Big Bang on your AM radio. The static comes from all directions.
This is the cosmic microwave background. It is what is left of the flash from the Big Bang. Several satellites have accurately mapped the microwave background. At first, it looked uniform. With better detectors, the satellites found small changes in intensity corresponding to the quantum fluctuations.
Tools of Astronomy
How do we know there was a Big Bang? All astronomers have to work with is the feeble light from the stars. They have great tools to measure and analyze it. There are huge telescopes, including the orbiting Hubble telescope. They found that supernovas, stars blowing up, are all about the same brightness. Now if they find a distant supernova in another galaxy, from its brightness, they can tell how far away its galaxy is. You do the same thing when you guess how far away a firefly is by how bright it is. Dim ones are far away. Astronomers can map much of the universe because supernovas are bright and happen often. To go further, to the edge of the universe, they needed something brighter, quasars. Quasars are young galaxies wrapped around super-sized black holes. Would you like a super-sized black hole with that order of fries? Quasars also have nearly equal brightness. They are the brightest objects in the universe since the Big Bang. If a quasar were 30 light-years away from us, it would be brighter than the sun. The sun is light-minutes away. By comparison, Sirius, the brightest star is only nine light years away.
Supernovas and quasars are the astronomer’s fireflies. They carefully measure their brightness to find the distances to everything they see. Even though light travels very fast, the universe is so big that it takes nine years for light to reach us from Sirius. The distance light travels in a year is a light year. When we observe that star, we are looking nine years into the past. Some quasars are 13 billion light-years away. The light getting to us now, left soon after the Big Bang.
Besides brightness, it is easy to check the color of star light. Remember from relativity that if a star is moving toward you it looks bluer. If it is moving away, it is redder. Astronomers determine the color very accurately by spreading the light into all its colors, as a prism does. The amount of the color change gives the speed of the star. The result of looking at millions of galaxies is that all of the galaxies are red shifted. They are moving away from us. The further away they are, the faster they are moving away.
Oh no! Does this mean we are back at the center of the universe? No. If you blow up a spotted balloon, every spot moves away from every other. The distance a spot moves away is larger if it starts further away. If you do not have a balloon, you can put equal spaced spots on a rubber band. Take a piece of lined paper. Mark the locations of the spots onto the paper. Stretch the rubber band perpendicular to the lines so the lines can tell you how much a spot moved and its separation. You will find that the separation between spots has increased. Space, the rubber band, has expanded. The amount spots move away from one end of the rubber band is most for the spots furthest away from that end. If you cannot imagine this kind of expansion of a three-dimensional space, you are not alone. Space is expanding in three directions, like the rubber band expands in one direction. All parts of space are moving away from all other parts. There is no center of the expansion. The expansion of the universe is the best evidence for the Big Bang. Astronomers on another galaxy are also seeing red shifts. They find we are moving away from them at the same speed as they are moving away from us. Confused? ξ You may have to take a good look at your polka dot balloon or rubber band.
Another piece of evidence for the Big Bang is deuterium. The hydrogen atom is an electron circling around a proton. The strong force can bind a neutron to a proton by gluons – carrier of the strong force. With an electron orbiting the pair, we get a deuterium atom. Deuterium is all over the universe, but stars are not hot enough to make deuterium. Only the Big Bang can.
The Hubble telescope has produced enough scans to put together a picture of the whole universe. A good model of the universe is a pile of soap bubbles, all different sizes. The air in the bubbles represents empty space. The stars, galaxies, and galactic clusters are the soapy liquid. The soapy liquid wiggles through the empty space sometimes thick and sometimes thin. Some of the bubble walls are thick like the occasional walls of galaxies in the universe. The Milky Way is part of the Virgo cluster. The largest super cluster is the Great Wall, which reaches one-tenth the way across the universe. That is also the size of the largest hole, nearly empty region, of the universe.
Black Holes
Relativity predicted black holes. They happen whenever a heavy sun runs out of nuclear fuel. Then there is nothing to prevent gravity from squashing all of the sun into a small space, a black hole. They are black because gravity near the hole is so strong that nothing can escape, not even light. The escape velocity from a black hole is greater than the speed of light. Black holes are invisible. Astronomers detect black holes by the emissions of matter pulled into the hole. It is superheated and shines brightly.
At first, people thought this was a just a mathematical mistake. Now, we know that most galaxies have black holes. The center of the Milky Way has a very large black hole. Intense black hole gravity sucks in any nearby matter making the black hole larger and its gravity even stronger. In billions of years, most of the Milky Way will end up in the black hole. Growing larger is what black holes do best. Their gravity sucks nearby mass into the hole making its gravity and size increase.
Black holes can also be lightweight and very small, the size of an atom. Maybe the new LHC accelerator will have enough energy to make miniature black holes. Would the Earth end up sucked into the miniature black hole? Should we stop work on the large LHC accelerator? Stephen Hawking, a physicist paralyzed with ALS, works on black hole theory. He found that black holes are not totally black. Remember virtual strings? They form everywhere including at the edge of black holes. Sometimes only one string of the pair falls back into the hole and the other escapes. This makes black holes hairy. These escaping strings of weak radiation, the hair, make black holes directly visible. Large black holes radiate very weakly but subatomic black holes radiate intensely. This radiation energy has to come from the black hole by converting its mass into energy. Therefore, a subatomic black hole evaporates quickly. The LHC will not create a black hole that can gobble the Earth, if Hawking’s theory is correct.
If a black hole is rapidly spinning, then instead of a hole, it can form a black ring. This can only happen if there are hidden dimensions. Finding a black ring would confirm string theory. Astronomers have not found one.
Black holes challenge theory because mass in a black hole should compress into a point at their center. That point would have infinite density. Infinity means a big mistake. String theory to the rescue. Most physicists believe calculations that show a string is the smallest possible object in the universe. So one massive string could be at the center of every black hole. It would be very dense, but it not infinite.
In some ways, black holes behave like elementary particles. The characteristics of both are their mass, spin, and charge. There is a deeper connection through string theory. String theory can model certain kinds of black holes. String theory shows that combining branes in the right way creates a black hole. String theory implies that black hole centers do not get smaller than a string. The extreme conditions in the center of a black hole drastically affect the curled dimensions. In fact, some believe that if the curled up dimensions compressed to a point in a black hole, the universe would end. It was not hard to decide that string theory is correct that black holes do not collapse to a point. We are all still here and the universe has many black holes.
Ice, water, and steam are the three phases of water. Some theorists propose that black holes are related to elementary particles in the same way ice is related to water, a change of phase. Temperature determines the phase of water. The shape of the curled dimensions inside an object determines if it is a black hole or an elementary particle.
The biggest accomplishment of string theory of black holes is that it correctly gives their entropy and the change in entropy caused by matter falling into a black hole. Entropy is a mathematical way to measure randomness. Entropy always increases. This was puzzling applied to black holes because they seem very non-messy, non-random. Our mental picture of a black hole is a neat blacker than black sphere. If black holes were all that neat then a basic law of physics would be violated. The entropy of the universe would go down whenever anything fell into a black hole. All processes have to make the universe more random and messier. This makes the universe have higher entropy. An analysis of black holes using string theory gave the correct entropy and verified that the entropy of the whole universe always goes up.
Dark Matter
If the universe is heavy enough, gravity will eventually slow the galaxies, stop them, and pull them back together. This is just like throwing a ball straight up. Earth’s gravity pulls down any object moving up at less than the escape velocity, 25,000 mph. If we could throw that fast, the ball would continue rising and leave the Earth. If we were in space, standing on a small meteor, a boulder, we would not have to throw so hard. The boulder would not have enough mass to pull the ball back after we throw it. The escape velocity of a boulder is low.
The universe also has an escape velocity. The escape velocity for the universe depends on how heavy it is. If the universe is heavy enough, the galaxies will slow and reverse. The movement back together would continue until all matter is back again in a gigantic black hole. It is the big crunch. This made astronomers estimate the weight of all the matter in the universe to see if there was enough to turn around the galaxies. They calculated the weight using Newton’s equations. Thirty years ago, the calculated weight of the universe was not enough to pull the galaxies back in. The galaxies would continue moving away from each other forever. That result has changed.
Astronomers have known for thirty years that there was something wrong with our Milky Way galaxy. Big telescopes located the stars, dust clouds, and even the black hole at the center. They knew the stars far from the center would move much slower than the ones closer to the center. The planets move this same way. However, they found that the distant stars in the Milky Way are moving faster. This is a major embarrassment. From these results, galaxies could never form, and the Milky Way should fly apart. They then looked at the behavior of clusters of galaxies. Astronomers measured their motions and positions. They also were moving too fast. This was a calculation that even a freshman college student could make. The only explanation is that there is a lot more matter that we cannot see in the galaxies and clusters of galaxies. That matter does not emit light. To us it is invisible dark matter. Yes, this sounds silly, but remember, astronomers have been thinking about this for 30 years. Sometimes when the good explanations do not work, you have to get silly.
With this idea, astronomers analyzed how much dark matter would make the galaxies behave as they do. They conclude that there is five times as much dark matter as normal matter. It seems to collect in the outer edges of galaxies. Most is in the largest structures in the universe, the clusters of galaxies. Normal dark things like black holes, neutron stars, rocks, dust, burned out stars, and lost planets may account for a few percent of the dark matter. Astronomers started talking about WIMPS, Weakly Interacting Massive Particles that no one has seen. No joke, WIMPS. (You cannot make this stuff up.) Radioactive decay produces neutrinos. They appear to have no mass. Maybe they have just a little and collect around the galaxies. Other possible sources of dark matter come from string theory. Supersymmetry predicts heavy versions of all the strings we already know. The heavy neutralinos, the supersymmetric partner of the neutrino, should behave like a heavy neutrino and could make up dark matter. Another particle from string theory, axions, might make up part of dark matter. The LHC accelerator may be able to produce both. Cosmic strings, heavy strings from the Big Bang, are also a possibility. We can only guess what dark matter is. What do you guess? ξ Maybe it is that stack of turtles.
Dark Energy
With dark matter, the universe has enough gravitational pull to slow and turn around the galaxies. Before you go outside to look for blue, falling galaxies, there is one more thing. A strange new thing, first suspected in the 1990s, is dark energy. After the Big Bang, matter exploded into the universe. Adding in the dark matter makes the universe heavy enough to turn around the galaxies. Therefore, distant galaxies, right now, should be slowing down. Surprise. Galaxies are speeding up. Physicists are guessing how this can happen. ξ Gravity could become repulsive at great distances. Maybe some other unknown repulsive force, like a pressure, pushes matter away, expanding the universe. Since the electromagnetic force is so much stronger than gravity, it would not take much charge to push the galaxies apart. The equations of physics are symmetrical to sign of charge. Therefore, the universe should be electrically neutral. Einstein had a constant in his equation for gravity that produces a repulsive force. He put it in because everyone at that time thought that the universe was eternal. He adjusted the constant so that the universe would continue expanding slowly forever.
This is dark energy. None of these explanations makes astronomers happy. They are embarrassed to realize that all these years they only were aware of 5% of the universe. If the dark energy were converted to matter using E = mc2, then there would be three times as much matter from dark energy than from normal matter. Dark energy connects with string theory. It comes from the energy of the vacuum. If string theory is to become the theory of everything, it should predict the amount of dark energy and dark matter, and explain why it is there. The dark energy appears to be very small and positive.
A nice property of supersymmetry is that it predicts near zero vacuum energy. That agrees with our universe. If string theory calculates the correct vacuum energy and supersymmetric strings appear, it would be a strong confirmation of string theory. This would explain dark energy and dark matter.
Speculations
While most high-energy physicists research and debate string theory, some have gone on to ideas that are more controversial. Some of these ideas are at the frontiers of scientific thought. They are partly philosophical and perhaps outside the realm of science. Because of that, many are difficult to understand. These ideas may or may not end up being accepted.
Cosmic Strings
Besides possibly explaining dark energy and dark matter, string theory can affect cosmology in other ways. A cosmic string would be a gigantic, super heavy string that may be light-years long but only the width of a proton. They may have formed at the beginning of the Big Bang, when the state of the fireball was rapidly changing. They arise from a kind of phase change similar to the cracks made when water freezes. Cosmic strings would form when the Big Bang cools.
The sun’s gravity bends light rays if their path lies close to the sun. This was the discovery that confirmed relativity. The same bending happens in deep space if a light ray from a distant star passes near a heavy galaxy. The star light bends slightly blurring or even doubling the image of the star. A cosmic string would be heavy enough to bend the light of distant stars if the light passes near the cosmic string. This is a gravitational lens. Astronomers know many. If a distant galaxy, a cosmic string, and Earth were exactly in a line, the cosmic string’s gravity would also split the image of the distant galaxy into what would look like two blurry galaxies. [Figure cosmic line up, illustration] These distorted images do not last forever because the stars, galaxies, and cosmic strings are moving relative to each other and get out of alignment. Since cosmic strings would be so thin, the distorted images they would produce will last for a very short time. If a double image quickly disappears, that would be proof that a thin cosmic string passed between Earth and the distant galaxy. When galaxies cause lensing, the lens is long lasting since galaxies are much wider. Several astronomers report examples of this kind of cosmic string lensing. They have to be confirmed by other observers.
Cosmic strings would look like irregular lace covering the fireball just after the Big Bang. Super clusters of galaxies also look a lot like lace. The lace of cosmic strings, soon after the Big Bang, may have provided the starting point for today’s super clusters.
What Is Space?
This is the first time in history that we can ask such a fundamental question. We tend to believe space is constant. In classical physics, space and time never changed. They were the frame in which we hung our picture of reality. When a picture is interesting, no one notices the frame. Scientists did not notice space and time. We cannot ignore space and time anymore. Spacetime now is complicated. Einstein joined space and time together by special relativity. General relativity showed that mass warps spacetime. Quantum mechanics showed that empty space is not empty; virtual strings continuously pop into and out of existence. Empty space is full of energy.
In addition, string theory says space has seven tightly curled hidden dimensions. Having more dimensions makes for more questions. Why did only three space dimensions and time become large? What would the world be like with more large dimensions?
Some physicists speculate that empty space may be full of strings. In quantum mechanics, the theoretical Higgs particle gives elementary particles their mass. Pushing through strings could be the reason elementary strings have mass. It takes some force to push the space strings out of the way just as it also takes some force to move through a crowd.
Our ideas about space could also be out of date because of quantum entanglement. Entangled particles respond to each other as if there were no space in between. We now know that matter bends space. Can space distort in ways that are more dramatic? Can it tear, form holes and reattach?
Theoretical physicists are studying all of these ideas. There is no agreement on answers to these questions about space. This work is very important and there is an expectation that explanations would help the development of string theory. String theory claims that all the properties of the forces and elementary particles are the result of one kind of string vibrating different ways in a ten-dimensional space.
Wormholes
Wormholes have moved out of science fiction and into physics. These are distortions and tears of spacetime that could allow for travel faster than light, or even travel through time. Astronomers believe there is intelligent life on thousands of stars of the Milky Way. They are likely to be so far away that it would take many lifetimes to travel to their star. The speed of light is the absolute speed limit for anything moving in the universe. Therefore, without wormholes, we probably never will meet an alien. Wormholes have been in science fiction for 50 years and now one or two serious physics papers appear every month discussing wormholes.
You can make a model of a wormhole from a large piece of balloon. Fix the corners of the balloon then push up from the underside, bend your finger, and touch the balloon surface with the tip of your finger. That loop is almost a wormhole. The last step, which is nearly impossible, is to cut a hole at your fingertip and a similar hole in the balloon. Join the edges together and you have a wormhole. This is similar to a hollow handle of a pitcher. [Figure wormhole, illustration] To make a real wormhole, the same stretch, distortion, tear, and reconnection would happen to spacetime itself. No one has shown that this is possible. When you move through a wormhole, you end up suddenly in another part of spacetime. If wormholes exist, they could be pathways through time as well as space. A black hole distorts space most powerfully.
Time travel generates possible paradoxes. For example, you could go back in time and do something that would prevent your using a time machine. Even more dramatic you could do something that prevents your ever being born. What would happen then? ξ
Loop Quantum Gravity
Loop quantum gravity is a new theory in competition with string theory. It is nowhere near being a theory of everything as is string theory, but it does have some interesting features. In the sub-atomic world, everything is chunky and quantized. Why not space and time? ξ We think both are smooth. However, at a very small scale, could they be chunky without our knowing it? Physicists have a guess of the size of these quanta. To match well to quantum mechanics, space would have a length quantum of 10-35 meters. You might remember that this is the length of a string. Time quanta would be 10-47 seconds. One followed by 47 zeros, or put another way, it would take one hundred quadrillion quadrillion quadrillion time quanta to make just one second. At the speed of light, it takes a quantum of time to travel a quantum of length.
Like string theory, loop quantum gravity makes quantum mechanics compatible with gravity. It also solves the black hole shrinking to a point. The conditions in a black hole are extreme. However, if the radius goes to zero; the gravitational force and density become infinite. Does that sound familiar? String theory solved problems of zero radius and infinity for quantum mechanics. The solution was to replace zero radius particles with something incredibly small but not zero, a string. Loop quantum does a similar thing by replacing continuous space with space quanta. It also limits the amount of energy and mass that a space quantum can contain. Therefore, chunks of space in a black hole would fill until stuffed and then other space quanta would fill. These space quanta would also generate a strong repulsive force. This would prevent formation of a point with all the matter of the black hole. It is possible this would result in the big bounce.
What Is Time?
Time may be the biggest mystery. What is time? Why is there time? How can time be so different from space dimensions and still be tangled up with them by relativity? Why do we know the past but not the future? Did time have a beginning? Will it end? Does time change smoothly or is there a smallest unit of time like the tick of a clock? Can there be a universe without time? If you have ideas about these questions, then you are doing better than most physicists are. Physicists use time in all their work, but infrequently think about these basic questions. Physics equations are all valid with time running backwards.
String theory gives new ideas about time. String theory and loop quantum gravity imply there is a smallest unit of time 10-47 seconds, the time it takes light to travel the length of a string. Perhaps space and time start with the Big Bang. Perhaps they did not. If something caused the Big Bang, then there had to be time before the Big Bang. A collision of branes can start the Big Bang.
Maybe the universe endlessly repeats a cycle of Big Bang, and then expansion followed by contraction resulting in all the galaxies falling inward. They soon would form a giant black hole. That is the big crunch. This is where we have to speculate. What if something reverses the big crunch like gravity reversed the expansion? We then get the big bounce, which could look like another Big Bang, and this cycle could repeat forever. String theory can cause the big bounce by limiting the black hole to the size of a string. Calculations then show that a bounce would happen. Another way to reverse the big crunch is loop quantum gravity. Loop quantum gravity claims a volume of space can only hold so much energy. When the volume containing the black hole gets full enough, the next Big Bang could happen.
The energy of the Big Bang is so high that no theory knows how to handle it. Big advances in string theory will likely come from the study of black holes. If the Large Hadron Collider has enough energy to make a microscopic black hole, studying it would be a good test of modern theories.
Some versions of string theory predict tachyons. These strings travel faster than the speed of light but backward in time. They have other strange properties. If you give them energy, they slow down. They have imaginary mass. Most physicists change a theory when it makes tachyons. Some physicists still work with these theories to investigate tachyon behavior in more detail. Tachyons are a favorite of science fiction writers.
Many Universes
Imagine James is in a park and Qued comes by. Qued says, “Let’s go down to the lake. I have something amazing to show you.” A breeze has covered the lake in sparking wind ripples. “This is a nice set of ripples; I’ll freeze them. Now help me toss out the ping-pong balls in this bag.” The label on the bag says Universal Balls. No matter how many balls Qued throws out, the bag never gets empty. Qued points to the lake and says, “See how they end up mostly in the low spots of the ripples? Notice that not all low spots are the same depth. Some of the ripples have little ripples on the side and sometimes a ping-pong ball rests there. A few balls are near the top of a ripple in a little dip. I’m tired of tossing ping-pong balls.” He shakes the sack and a flood of balls comes out. At the same time, the shore disappears and it is lake, ripples, and balls in all directions as far as one can see. [Figure—ping pong universe and lake, drawing].
James, “Don’t touch any of the balls because now they are universes. All together, this is the multiverse. The lake surface is the energy level of the vacuum. It is not a constant. A universe can have a range of vacuum energies. String theory allows an enormous number of vacuums. Each state of the vacuum makes a different kind of universe with different forces, strings, and physical constants. Each universe has a different configuration of the curly dimensions.
The G in Newton’s equation for gravity sets the strength of the gravitational field. In some of these universes, G is 10,000 times bigger. With gravity so strong, all matter would collapse into a huge black hole. In another universe, the speed of light is only 10 mph. Another universe might be a single giant star. Some are cold and dark with matter smeared out evenly over the universe. Nearly all universes are too strange for life to evolve. Some may have only two elementary particles, only three forces, or even six forces. A few may support life weirder than we are. One is your universe.”
James asks,” Why can’t we see these other universes?”
“They may be like a marshmallow in rocky road ice cream. The marshmallow is our eleven-dimensional spacetime, a brane. The ice cream is also a brane, larger and having more dimensions. Other universes would be other marshmallows, nuts, or chocolate. We see when photons come from an object and enter our eye. Particles from one brane cannot reach or interact in any way with another brane. They cannot cross the brane gap.
Another variation of the multiverse proposes that, new universes can pop up inside other universes. [Figure—soap bubble universes, photo] This is similar to elementary particles leaking through walls. A part of a universe would slip into a different position, a different vacuum energy with different laws. With this model, the multiverse would look like a foam of soap bubbles with soap bubbles inside the bubbles inside of bubbles—universes within universes.
Other physicists say this is too much like claiming that an invisible duck is stomping on your head. The duck is angry, undetectable, weightless, invisible, not affected by any force, and silent and it is on your head in a different brane. The duck idea is designed to prevent arguments. There is no way to prove the duck is not there. There is no way to prove it is there. Scientists say the duck is not science but nonsense. The multiverse idea does not have a way to prove it true or false, similar to the invisible duck. However, the idea does come from a theory that may be the theory of everything. What do you think? Would you care if there were other universes? ξ Would you care if there were an invisible duck on your head? ξ
There is much debate about the multiverse. Some physicists claim, that if the equations describe other universes, then they must exist. There is that long history in physics that if something is not forbidden, then it is allowed or even required. These universes would be separate from us by so much space and time, or by some other impenetrable barrier, so that they are impossible to detect.
Does Thinking Affect Reality?
When we see something, there is an interaction between our body and the world. Our senses receive energy from the world. We process the data from our senses, analyze, and identify what we see, hear, or feel. While our mind does all this, reality does not change. In quantum mechanics, the act of observing subatomic particles does change reality. All quantum properties are fuzzy. Before a measurement, a property has a range of possible values. For example, electron spin is either spin up, +1/2, or spin down, -1/2. The wave equation gives these two possibilities equal probability, fifty-fifty. There are still different opinions about what this means. It does not mean the spin is the average, spin zero. Electrons cannot have spin zero. It could mean the spin is not valid; the spin does not exist; the particle or spin does not exist until we do a measurement; the spin is half up and half down; the spin in one universe is up and in another it is down. With a measurement, the electron suddenly is either spin up or down 100%. Before the measurement, the electron spin was vague. What happened? What caused the change? From the wide range of possible explanations, you can conclude that physicists are still debating this question from ninety years ago. Many suspect we are more than just a passive observer of reality. What do you think? ξ
One idea is that the electron follows all possibilities but in parallel universes. If a particle takes all possibilities then every spin measurement generates a parallel universe. These universes are different from the multiverse of string theory. They have the same hidden dimensions. Each of the universes has the same laws of physics. With a spin measurement, we make two universes out of one. One has our electron with spin up and one with spin down. Of course, that means we become two observers, one who just measured a spin up and the other measured spin down. Because of all the observations made in everyday life, copies of us would exist in practically an infinite number of universes.
Other physicists believe a particle does not have a location, spin, or velocity until we go to measure it. Our measurement creates the reality of the electron and its spin. Some would say the particle does not even exist until measured. All explanations of measurement of quantum properties and the collapse of the wave function mix together mind and reality. Though most physicists try to side step the issue, there is a link between the conscious choice to do a measurement, the equipment used, and the collapse of the wave function to the result of the measurement. We do a measurement and suddenly the ill-defined position of an electron becomes right there. In quantum pool, we could detect the pool balls as waves or as particles. They were waves until we did a measurement of position by having the ball drop into a pocket. Some physicists believe that consciousness itself has a link to a deeper reality that will help us make more sense of quantum mechanics. It appears that our conscious will to measure a particle’s properties forces it in some unknown way into a well-defined state. We and the universe are collections of elementary particles. If the universe has these properties, then so do we.
Entanglement is another situation where measurement changes reality. If two electrons entangle by a simple interaction and then separate, when we observe the state of one, then we also know the state of the other. It is as if each seems instantly to know the state of the other. How? ξ Physicists do not know. Entanglement occurs between any two interacting objects. For example, we would entangle with any electron we measure. We do not have a spin to flip, but our wave function, quantum description of what is knowable about us, is affected in the future by that electron and we affect it. We entangle with not only with the electron but also with everything else in the universe. Our entanglements are very weak, but not zero. As far as we know, these entanglements have no measureable effect.
Those most attached to a link between physics and consciousness believe we are the eyes, ears, and brains of the universe trying to understand itself. Through us, the universe examines, understands, evolves, and creates a bigger self. We are one with the universe. Mystics feel and believe this and so do some physicists. For the physicist, entanglement connects us to the universe and to each other. Science cannot prove mysticism. You either see it or you do not.
There is a recent art movement, post-modernism, which stresses how much our point of view affects our reality. Roughly, it is the idea that we create our own reality. Physics is saying a similar thing but in a limited way. This is almost Buddhism. Buddhists emphasize the importance of thought. Some believe all is mind that we exist as thoughts in a divine mind. Perhaps reality changes us. The reality change we see in quantum mechanics is really just a change in our consciousness. Observations leave reality unchanged but change us.
The unanswered questions about quantum mechanics leave the door open to speculation, some of it by esteemed physicists. Science narrows its point of view to what it can verify. Theories show how to calculate the results of measurements. Measurements can be repeated and results are very accurate. It appears that the universe is an interconnected whole and that changes are caused by us. Quantum effects are strong for sub-atomic particles, but they exist for even large particles like us. What do you think? Does an electron somehow know we are measuring so it shapes up as either spin up or spin down? Why? ξ Are we connected in a meaningful way to the entire universe and do we cause different realities to happen? ξ
Another explanation of quantum mechanics is that it is only an approximation to a better theory. This better theory would use hidden variables that are guiding quantum events. We just are not skillful enough now to detect these hidden variables. Carefully repeated physics experiments with polarized light prove that either everything is interconnected or that observation creates reality. It is amazing that work in a physics lab can say precise things about mysticism and philosophy. ξ
Intelligent Design
String theory has stirred up the debate about intelligent design. String theory allows many different universes. These universes can be very different from ours. Evolution of life requires a very small range of values for some of the physical universe’s physics constants, the nineteen numbers of quantum mechanics. In string theory, the shape of the curly hidden dimensions sets the values of the constants. Very few universes can support life. Conditions are too hard for life to evolve there. Some think this means our universe was specially designed for life, for us. Most scientists change it around. This universe works for us because if it did not, we would not be here. Since we are here, the universe has to be one that supports life no matter how rare such universes are. This is confusing, but they are two distinct points of view. Either we are here because the universe is designed for life, or the universe can support life, therefore we are here.
Most scientists would not use intelligent design as an explanation. It is like the invisible duck. You cannot prove intelligent design is true, and you cannot prove it is false. If you accept intelligent design, it could mean you stop looking for a scientific explanation. Therefore, you will not find a scientific explanation. A century ago, no one had a good explanation of why electrons did not fall into a nucleus. One possibility is that the atom was intelligently designed that way. If that was a satisfactory explanation, then we may not have discovered quantum mechanics and all the marvelous advances it brought to the 20th century. Other examples are the biological sciences, DNA, evolution, and gene therapy. Some believers in intelligent design think it is wrong to mess with what has been divinely designed. They will not discover the beautiful complexity of life or understand how life evolved into the wonderful diversity around us. They will not discover the causes and cures of genetic diseases.
One side says that since the world is complicated, and yet fits together so well, someone had to design it that way. The other side says yes, the world is complicated. That is how the world is, and yet, this complicated world follows from a few simple rules. Great complexity can come from simple rules. Intelligent design would replace large blocks of research, theory, and experiment. Intelligent design makes no predictions and there is no way to prove it false. What do you think? ξ
In debates between fundamentalists and scientist, you often hear the remark that “we don’t have to believe that, it’s only a theory.” Scientists are guilty of using the word theory in a number of ways, covering many levels of uncertainty. Scientists do not use a special word for theories like evolution that they have verified millions of times. These theories are true and only likely to change by expanding over more data and in adjusting small details. Scientists need a word for these well-proven theories.
Scientists, however, always keep an open mind, at least open a crack. For example, we might discover crews from flying saucers digging holes and burying bones from their planet, creating our fossils. Either look out for saucers or accept that evolution is a fact. Other true theories are mechanics, nuclear explosives, hydrodynamics, and electromagnetism. [Figure—Aliens burying bones, drawing] For these areas, theory means the highest level of scientific confidence. It means a group of related ideas explaining something in nature supported by lots of observations, data, verified predictions, and connections to other verified theories. What would you do if a well-verified theory of science contradicted one of your beliefs? ξ
Goofer says, “Qued, when scientists speculate they get really wild and hard to understand.”
“You are certainly correct. It is not important to remember the various arguments but just to know that physicists do more than experiments, solving equations, or building machines,” says Qued. “They are trying to understand the most basic things about the world. There are many exciting problems that the next generation of scientists will pursue.”
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“The most beautiful thing we can experience is the mysterious.” |
A. Einstein
Tying Up Loose Strings
The accomplishments of physics and the other sciences are very impressive. Science is involved in every manufactured item and affects everything in our lives. In the future, it will affect even more. Can science or the scientific method apply to everything? ξ No, there are large parts of experience like emotions, art, music, and faith that do not fit the scientific model. There are many other areas where the scientific method could apply such as politics, advertising, psychology, and education.
The greatest accomplishment of science will be the theory of everything. String theory is not yet there. String theory succeeds in ending the 100-year physics problem, the separation of relativity and quantum mechanics. It does this very elegantly. Right now string theory provides a framework that could become the theory of everything. It can explain the elementary particles and forces, the three families of strings, the strengths of the forces. It has not done most of this because the shape of the hidden dimensions is unknown. It is most amazing, that string theory with mathematics, a few laws, and a small bunch of equations, may explain everything. A great deal of theory and experiment is necessary to establish if string theory can do it. This is an exciting time to consider a career in science. You could become a part of the oldest and most successful effort to understand our world.
Everything and every force is the result of vibrations of strings. Strings vibrate in more than the four dimensions of spacetime. There are also seven tightly curled up dimensions. We may never be able to see these dimensions, unlike the four dimensions of spacetime. The shape of these dimensions sets the properties of the forces and particles. It also determines the laws of physics of the universe. String theory allows multiple universes.
Particles and forces are bound to branes, higher dimensional objects. The only exception is gravity’s graviton that moves between branes. Multiple universes can be very close but in different branes and not be detectable except by extremely weak gravitational effects.
Back to our very first question, do strings hold the world together? Most physicists would say yes. String theory does have problems, but it is still under construction. A theory of everything is a gigantic challenge. String theory makes many predictions. We just cannot accelerate particles to high enough energy to check them. Most important is that string theory pulls together all of physics into a beautiful consistent whole. String explains many things we know, like black holes, quantum gravity, elementary particles, quantum mechanics, relativity, the unification of forces, and the structure of the universe. It also requires things we may never be able to prove, like the seven extra dimensions and unlimited choices of universes. It is a theory of everything but it is just being discovered. That leaves lots of room for heated debate.
Is there a multiverse? Most physicists would say probably not. The big hope is that we will find an arrow saying this is our universe and the shape of our curly dimensions.
If string holds the universe together, then everything, energy, forces, and matter, is made from string. Strings vibrating in different spaces, at different frequencies, and interacting cause all the amazing things in our universe. Strings are always vibrating. The whole universe is always singing. You are part of the universe. You also are singing, in every little bit of you. Take time to listen to the music, the music of the spheres. It is the music between your ears.
This is the Sri Yantra.
It is optical art made in India thousands of years ago.
If you stare steadily at the center for five minutes,
You will have an interesting experience.
The lines may change into strings whose dancing makes music.
The music of the spheres.
String Theory for Kids (and Clever Adults) 