Does String theory make any sense?

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. Some scientists 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.

Eventually I would like the answer the questions:

What Is String Theory? (First “simple” pass)

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. Discussion of these theories will be the major task of this class.

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 exponent. For example, in this notation, 822 to the nearest power of ten is 1000 or 10+3 in shorthand. 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. If you wrote it as a fraction, it would be 1/1,000,000,000,000,000. That is small. It is one quadrillionth. In shorthand, it is 10-15 meters. Big things can be very big and small things can be 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. 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

StringProtonAtomBacteriaKidEarthSolar SystemMilky Way Universe

10-35 meters10-15 meters10-11 meters10-5 meters1 meter10+8 meters10+13 meters10+21 meters10+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? There sure is. Atoms are made of elementary particles. To see that small we need a different tool, particle accelerators. 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 now look next at some of the oldest theories of everything.

Myths and Creation Stories

Humans 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? 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. Let us 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? Where did those ancestors in the ground come from? Can things pop into existence out of nothing? 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? 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? 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. The story of string theory is going to seem even stranger to you. That was like Pandora’s Boxand 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? 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. 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? Which is the better theory Ptolemy, or Copernicus?

If they both accurately fit observations, which is the better theory? Good, 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.

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.

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.

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.

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.

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 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? In the real world, values of measurements can equal zero but they cannot be infinite. Only string theory says that it 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? 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. 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.

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. Physicists 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 does physics and other sciences work? Is it different from myth? 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. In science, there are often several theories. A theory must match current data. It should make good predictions and there should be a way to show it is wrong. What if two theories make good predictions and fit the current information? What should you do then? Pick the simple one. The simplest theory is the one that has the fewest assumptions, and depends on the least number of unproven facts.

Everything should be made as simple as possible, but not simpler! — Einstein

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? Our world is very orderly. 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. 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 times even though mathematicians not heading in that direction. Einstein could not figure it out. What do you think? How can ideas that start in mathematician’s imagination lead to detailed explanations of the world?

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? — 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 1000s of checkers. Predictions are very important because a clever scientist 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. Philosophers and scientists 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? 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 and some want to deny that falsifiability is necessary!

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? Should we apply to these sources of information some of the rules of science? 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. People 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. Physicists would need new jobs. 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. 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? 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? Do you feel like a robot with your life determined by physics? 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.

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.

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. Coach says, “There’s nothing in the rules against pitching from a four-wheeler. If it’s not forbidden, it’s allowed.”

Your coach 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 is wicked fast. He then puts the four-wheeler in reverse and drives backward back to second base.

Between innings, you hear their pitcher telling their coach, “My pitch is still slow coach. It doesn’t look any faster to me.”

Their coach 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? 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 this. 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.

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?

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? 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. 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. Their coach 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.

His coach 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.”

His coach 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? 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? Would the shape of Florida have changed? If you walked up a creek to get to your friend’s house, would that change? 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 high-flying clocks, there are two relativistic effects a slow down from their speed, and a quickening from being in orbit since gravity is weaker up there. The latter comes from general relativity. Global positioning satellite systems need corrections for relativity.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. 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 house. You list what it is and where it is. It is a shorter list if your house is neat. It takes more words to describe a mess.

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, B, and electric field, E, in free space are:

Maxwell’s equations for Electric and magnetic Fields

r ·E = 0 r ·B = 0

r⇥E =@B

@tr⇥B =

@E

@t

The equations are just for looking at. They are a powerful set of equations and not bad looking as equations go. Physicists call them elegant, even beautiful. The E and B, electric and magnetic fields, behave in the same way. Put more elegantly, the equations are symmetric in E and B. If you switch B and E, you get back the same equations.

The triangle symbol (gradient) 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 are so 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

" · 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’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?

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.

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. Their light bends exactly as predicted, making it appear that

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.

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. 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? 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? 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. 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. Electrons seemed to be disappearing and reappearing at another level. It is pretty strange. 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.

No one has come up with such a theory. Chunks and fuzz are how things are on the atomic scale. The nice universe ticking along like a clock does not apply. The universe limits our knowledge. We are not complex wind-up robots. 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. 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? 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?

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.

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. 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.

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. 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. 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 car.

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. 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.

Elementary Particles

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.

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 an assistant, “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. The story of string theory is going to seem even stranger to you. 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. Higgs discovery completed

the standard quantum mechanical model of elementary particles.

One of the stranger quantum phenomena is entanglement. Even physicists think this is spooky.

Let us talk 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 +1⁄2 (spin up) or spin – 1⁄2 (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 +1⁄2, and the other half will have spin – 1⁄2.

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

Electrons spin only two ways, spin up, and spin down. I have a toy gyroscope that can spin on either end,” Consider some small boxes each containing 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.” Shake and open one hundred boxes. They look random, 52 heads and 48 tails.

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.

How do we know which will be which? That we can’t know. 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.” Every pair of boxes touched together and opened has one penny heads and one tails. No pairs are either both heads or both tails. How did that happen? Is there 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.

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. 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 +1⁄2 or spin up. The tails state corresponds to an electron with spin down or spin –1⁄2. 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.

Then shouldn’t we see a blur of heads and tails when we 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 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.

Suppose entangle a pair of pennies. and give you one box and bet I can guess if penny is heads or tails. Look at mine and guess the opposite.”

That would work and you would guess it right every time, but I can tell you a more dramatic demonstration. 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. Synchronize watches. After entangling a pair of boxes, you take one by rocket to Mars. Both open 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.” SymmetryAlmost 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.

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.

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.

Quantum mechanics is weird in many ways but one of the weirdest things is how observation influences things on the quantum scale. 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.

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? 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.

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. Supposedly, 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.

We shall now see!We now delve deeper into the physics of Elementary Particles and

then come back to String Theory.