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. 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: a 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 one out. Thus two of century’s greatest discoveries: the Standard Model of quantum mechanics and general relativity had little to do with each other. Efforts to add gravity to the Standard Model was like adding vinegar to milk.

Points to Strings

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 (Kaluza and Klein) 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? To them it was just an interesting thing to do. 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, backward 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. Maybe 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. 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 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 rope and tie one end to a railing or something else that does not move. Your rope will copy the behavior of real strings. Hold the rope and rotate your hand. 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. 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 22 parameters or constants that determined particle masses and force strengths. String theory supposedly 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.

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 personally 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. 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 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 a 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 life have so many rules that they always seem to get in the way? 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.

No one is confused about the three dimensions of space. 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 2 points, say two friends houses, Sally and Ben. You want to meet another friend 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 one Sally’s house. 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 your friend.

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.” 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 your friends 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 us 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? Discuss square well example.

Discuss square well example.

Lowest energy level without extra dimension

Additional energy level with extra dimension

R << a —> E11/Ek ~ 1019

So the first new level appears at an energy far above that of the low-lying original states. We therefore conclude that an extra dimension can remain hidden from experiments at a particular energy level as long as the dimension is small enough. Once the probing energies become sufficiently high, the effect of an extra dimension can be observed.

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 example actually does not have ten dimensions. It is four- dimensional. Once the distance from the point 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.

Knots in the Rope – Hidden Dimensions

Physicists were desperate to solve the problem of making strings move and have string theory work. They thought strings would answer many fundamental questions.

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. 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 - 2-dimensional views of a 7-dimensional space.

Assumption is that changes in the hidden dimensions can completely change the universe.

In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. It describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string.

Each quark is an individual string.

Heaviness, or more accurately, mass, is caused by the way the string is vibrating. The color of a quark in QCD is, in string theory, caused by the way the string is vibrating.

In spite of the fact that the universe is well described by four-dimensional spacetime, there are several reasons why physicists consider theories in other dimensions. In some cases, by modeling spacetime in a different number of dimensions, a theory becomes more mathematically tractable, and one can perform calculations and gain general insights more easily. There are also situations where theories in two or three spacetime dimensions are useful for describing phenomena in condensed matter physics. Finally, there exist scenarios in which there could actually be more than four dimensions of spacetime which have nonetheless managed to escape detection.

One notable feature of string theories is that these theories require extra dimensions of spacetime for their mathematical consistency.

Summarizing

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. 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. Some pictures:

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. 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 an imaginary 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 - not any longer!]. 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.

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 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?

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”.

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 1⁄2. 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?

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.

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?

You and your friend are doing two jigsaw puzzles of the universe. You both have an idea of how the universe looks. She watches Star Trek and you watch the Hubble telescope. The puzzle pieces are facts and ideas about the universe. Both begin, and soon she is ahead. You notice that she is using scissors to trim the pieces of the puzzle to make the pieces fit. You work the old-fashioned way.

You say, “You’re cheating” to your friend.

She says “I’m not cheating. These scissors were with my puzzle. There was a note telling me I wouldn’t get far without them” says your friend.

Her 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, your 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?

Quantum mechanics works much like your friend and her puzzle. It needs 22 tools to trim the theory into a good fit. These are the 22 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. Your friend’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 your puzzle, quantum mechanics and relativity wrap around each other and string theory wraps around both. String theory fills the hole in the center. You have fewer, smaller holes. Your friend agrees that your 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 possibly 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? 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.

The whole of relativity and 20th century physics follows naturally from string theory. Explaining the universe with only one constant is hard. 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. 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 mass they have, 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 raisin anti-raisin pair jumps out. Blop! Pea pairs fly up in a puff of steam. Then they fall back in. 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 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? 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. 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.

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(does not seem to be true).

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.

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? 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 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.

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.

Sabine Hossenfelder Why not string theory?

Because we might be wasting time and money and, ultimately, risk that progress stalls entirely.

In contrast to many of my colleagues I do not think that trying to find a quantum theory of gravity is an endeavor purely for the sake of knowledge. Instead, it seems likely to me that finding out what are the quantum properties of space and time will further our understanding of quantum theory in general. And since that theory underlies all modern technology, this is research which bears relevance for applications. Not in ten years and not in 50 years, but maybe in 100 or 500 years.

So far, string theory has scored in two areas. First, it has proved interesting for mathematicians. But I’m not one to easily get floored by pretty theorems – I care about math only to the extent that it’s useful to explain the world. Second, string theory has shown to be useful to push ahead with the lesser understood aspects of quantum field theories. This seems a fruitful avenue and is certainly something to continue. However, this has nothing to do with string theory as a theory of quantum gravity and a unification of the fundamental interactions.

For what quantum gravity is concerned, string theorist’s main argument seems to be “Well, can you come up with something better?” Then of course if someone answers this question with “Yes” they would never agree that something else might possibly be better. And why would they – there’s no evidence forcing them one way or the other.

I don’t see what one learns from discussing which theory is “better” based on philosophical or aesthetic criteria. That’s why I decided to stay out of this and instead work on quantum gravity phenomenology. For what testability is concerned all existing approaches to quantum gravity do equally badly, and so I’m equally unconvinced by all of them. It is somewhat of a mystery to me why string theory has become so dominant.

The reason is that academia is currently organized so that it invites communal reinforcement, prevents researchers from leaving fields whose promise is dwindling, and supports a rich-get- richer trend. That institutional assessments use the quantity of papers and citation counts as a proxy for quality creates a bonus for fields in which papers can be cranked out quickly. Hence it isn’t surprising that an area whose mathematics its own practitioners frequently describe as “rich” would flourish. What does mathematical “richness” tell us about the use of a theory in the description of nature? I am not aware of any known relation.

In his book Why String Theory?, Conlon tells the history of the discipline from a string theorist’s perspective. As a counterpoint, let me tell you how a cynical outsider might tell this story:

String theory was originally conceived as a theory of the strong nuclear force, but it was soon discovered that quantum chromodynamics was more up to the task. After noting that string theory contains a particle that could be identified as the graviton, it was reconsidered as a theory of quantum gravity.

It turned out however that string theory only makes sense in a 25-dimensional space. To make that compatible with observations, 22 of the dimensions were moved out of sight by rolling them up (compactifying) them to a radius so small they couldn’t be observationally probed.

String theorists are very proud of having a microcanonical explanation for the black hole entropy. But we don’t know whether that’s actually a correct description of nature, since nobody has ever seen a black hole evaporate. In fact one could read the firewall problem as a demonstration that indeed this cannot be a correct description of nature. Therefore, this calculation leaves me utterly unimpressed.

But let me be clear here. Nobody (at least nobody whose opinion matters) says that string theory is a research program that should just be discontinued. The question is instead one of balance – does the promise justify the amount of funding spend on it? And the answer to this question is almost certainly no.

Next it was noted that the theory also needs supersymmetry. This brings down the number of space dimensions to 9, but also brings a new problem: The world, unfortunately, doesn’t seem to be supersymmetric. Hence, it was postulated that supersymmetry is broken at an energy scale so high we wouldn’t see the symmetry. Even with that problem fixed, however, it was quickly noticed that moving the superpartners out of direct reach would still induce flavor changing neutral currents that, among other things, would lead to proton decay and so be in conflict with observation. Thus, theorists invented R-parity to fix that problem.

The next problem that appeared was that the cosmological constant turned out to be positive instead of zero or negative. While a negative cosmological constant would have been easy to accommodate, string theorists didn’t know what to do with a positive one. But it only took some years to come up with an idea to make that happen too.

String theory was hoped to be a unique completion of the standard model including general relativity. Instead it slowly became clear that there is a huge number of different ways to get rid of the additional dimensions, each of which leads to a different theory at low energies. String theorists are now trying to deal with that problem by inventing some probability measure according to which the standard model is at least a probable occurrence in string theory.

So, you asked, why not string theory? Because it’s an approach that has been fixed over and over again to make it compatible with conflicting observations. Every time that’s been done, string theorists became more convinced of their ideas. And every time they did this, I became more convinced they are merely building a mathematical toy universe.

String theorists of course deny that they are influenced by anything but objective assessment. One noteworthy exception is Joe Polchinski who has considered that social effects play a role, but just came to the conclusion that they aren’t relevant. I think it speaks for his intellectual sincerity that he at least considered it.

At the Munich workshop last December, David Gross (in an exchange with Carlo Rovelli) explained that funding decisions have no influence on whether theoretical physicists chose to work in one field or the other. Well, that’s easy to say if you’re a Nobel Prize winner.

Conlon in his book provides “evidence” that social bias plays no role by explaining that there was only one string theorist in a panel that (positively) evaluated one of his grants. To begin with anecdotes can’t replace data and there is ample evidence that social biases are common human traits, so by default scientists should be susceptible. But even considering his anecdote, I’m not sure why Conlon thinks leaving decisions to non-experts limits bias. My expectation would be that it amplifies bias because it requires drawing on simplified criteria, like the number of papers published and how often they’ve been cited. And what does that depend on? Depends on how many people there are in the field and how many peers favorably reviewed papers on the topic of your work.

I am listing these examples to demonstrate that it is quite common of theoretical physicists (not string theorists in particular) to dismiss the mere possibility that social dynamics influences research decisions.

How large a role play social dynamics and cognitive biases, and how much do they slow down progress on the foundations of physics? I can’t tell you. But even though I can’t tell you how much faster progress could be, I am sure it’s slowed down. I can tell that in the same way that I can tell you diesel in Germany is sold under market value even though I don’t know the market value. I know that because it’s subsidized. And in the same way I can tell that string theory is overpopulated and its promise is overestimated because it’s an idea that benefits from biases which humans demonstrably possess. But I can’t tell you what its real value would be.

The reproduction crisis in the life-sciences and psychology has spurred a debate for better measures of statistical significance. Experimentalists go to length to put into place all kinds of standardized procedures to not draw the wrong conclusions from what their apparatuses measures. In theory development, we have our own crisis, but nobody talks about it. The apparatuses that we use are our own brains and biases we should guard against are cognitive and social biases, communal reinforcement, sunk cost fallacy, wishful thinking and status-quo bias, for just to mention the most common ones. These however are presently entirely unaccounted for. Is this the reason why string theory has gathered so many followers?

Some days I side with Polchinski and Gross and don’t think it makes that much of a difference. It really is an interesting topic and it’s promising. On other days I think we’ve wasted 30 years studying bizarre aspects of a theory that doesn’t bring us any closer to understanding quantum gravity, and it’s nothing but an empty bubble of disappointed expectations. Most days I have to admit I just don’t know.

Why not string theory? Because enough is enough.

A Bit More on the Falsifiability Crisis

Supporters of string theory assert that the problem lies not with physicists but with a fact of nature — one that we have been approaching inevitably for four centuries. The dogged pursuit of a fundamental theory governing all forces of nature requires physicists to inspect the universe more and more closely — to examine, for instance, the atoms within matter, the protons and neutrons within those atoms, and the quarks within those protons and neutrons. But this zooming in demands evermore energy, and the difficulty and cost of building new machines increases exponentially relative to the energy requirement. It hasn’t been a problem so much for the last 400 years, where we’ve gone from centimeters to millionths of a millionth of a millionth of a centimeter — the current resolving power of the Large Hadron Collider (LHC) in Switzerland. We’ve gone very far, but this energy-squared is killing us. As we approach the practical limits of our ability to probe nature’s underlying principles, the minds of theorists have wandered far beyond the tiniest observable distances and highest possible energies. Strong clues indicate that the truly fundamental constituents of the universe lie at a distance scale 10 million billion times smaller than the resolving power of the LHC. This is the domain of nature that string theory, a candidate theory of everything, attempts to describe. But it’s a domain that no one has the faintest idea how to access. The problem also hampers physicists’ quest to understand the universe on a cosmic scale: No telescope will ever manage to peer past our universe’s cosmic horizon and glimpse the other universes posited by the multiverse hypothesis. Yet modern theories of cosmology lead logically to the possibility that our universe is just one of many.

Whether the fault lies with theorists for getting carried away, or with nature, for burying its best secrets, the conclusion is the same: Theory has detached itself from experiment. The objects of theoretical speculation are now too far away, too small, too energetic or too far in the past to reach or rule out with our earthly instruments. So, what is to be done? Physicists, philosophers and other scientists should hammer out a new narrative for the scientific method that can deal with the scope of modern physics.The issue in confronting the next step is not one of ideology but strategy: What is the most useful way of doing science?” Rules of the Game Throughout history, the rules of science have been written on the fly, only to be revised to fit evolving circumstances. The ancients believed they could reason their way toward scientific truth. Then, in the 17th century, Isaac Newton ignited modern science by breaking with this rationalist philosophy, adopting instead the empiricist view that scientific knowledge derives only from empirical observation. In other words, a theory must be proved experimentally to enter the book of knowledge.

But what requirements must an untested theory meet to be considered scientific? Theorists guide the scientific enterprise by dreaming up the ideas to be put to the test and then interpreting the experimental results; what keeps theorists within the bounds of science?

Today, most physicists judge the soundness of a theory by using the Austrian-British philosopher Karl Popper’s rule of thumb. In the 1930s, Popper drew a line between science and nonscience in comparing the work of Albert Einstein with that of Sigmund Freud. Einstein’s theory of general relativity, which cast the force of gravity as curves in space and time, made risky predictions — ones that, if they hadn’t succeeded so brilliantly, would have failed miserably, falsifying the theory. But Freudian psychoanalysis was slippery: Any fault of your mother’s could be worked into your diagnosis. The theory wasn’t falsifiable, and so, Popper decided, it wasn’t science.

Critics accuse string theory and the multiverse hypothesis, as well as cosmic inflation — the leading theory of how the universe began — of falling on the wrong side of Popper’s line of demarcation. To borrow the title of the Columbia University physicist Peter Woit’s 2006 book on string theory, these ideas are “not even wrong,”. I think, in the spirit of Popper: A theory must be falsifiable to be scientific.

Three non-empirical arguments that generate trust in string theory among its proponents.

First, there appears to be only one version of string theory capable of achieving unification in a consistent waySecond, string theory grew out of the Standard Model Third, string theory has unexpectedly delivered explanations for several other theoretical problems aside from the unification problem it was intended to address.

One concern with including non-empirical arguments is that it opens the floodgates to abandoning all scientific principles. One can come up with all kinds of non-empirical virtues when arguing in favor of a pet idea. Clearly the risk is there, and clearly one has to be careful about this kind of reasoning.

The trash heap of history is littered with beautiful theories, for example, 19th-century vortex theory of atoms. This Victorian theory of everything, Tait and Kelvin, postulated that atoms are microscopic vortexes in the ether, the fluid medium that was believed at the time to fill space. Hydrogen, oxygen and all other atoms were, deep down, just different types of vortical knots. At first, the theory seemed to be highly promising. People were fascinated by the richness of the mathematics, which could keep mathematicians busy for centuries, as was said at the time. Alas, atoms are not vortexes, the ether does not exist, and theoretical beauty is not always truth.

Except sometimes it is. Rationalism guided Einstein toward his theory of relativity, which he believed in wholeheartedly on rational grounds before it was ever tested. “I hold it true that pure thought can grasp reality, as the ancients dreamed,” Einstein said in 1933, years after his theory had been confirmed by observations of starlight bending around the sun.

The question for us is: Without experiments, is there any way to distinguish between the non-empirical virtues of vortex theory and those of Einstein’s theory? Can we ever really trust a theory on non-empirical grounds?

Even Popper saw value in the kind of thinking that motivates string theorists today. Popper called speculation that did not yield testable predictions metaphysics, but he considered such activity worthwhile, since it might become testable in the future. The question might be - how long should we wait for the future to come?

An important distinction exists in science between theories that scientists are certain about and those that are still being tested. The degree of confirmation of atomic theory shouldn’t even be measured in the same units as that of string theory. String theory is not, say, 10 percent as confirmed as atomic theory; the two have different statuses entirely. The problem with non-empirical confirmation is that it muddles the point. And of course some string theorists are happy of muddling it this way, because they can then say that string theory is confirmed, equivocating.

The idea of non-empirical confirmation forms an obstacle to the possibility of progress, because it bases our credence on our own previous credences. It takes away one of the tools — maybe the soul itself — of scientific thinking, which is do not trust your own thinking.

In considering how theorists should proceed, I think that work on string theory and other as-yet-untestable ideas should continue. Keep speculating, but give your motivation for speculating, give your explanations, but admit that they are only possible explanations. Maybe someday things will change and the speculations will become testable; and maybe not, maybe never. We may never know for sure the way the universe works at all distances and all times, but perhaps they can narrow the live possibilities to just a few. I think that would be some progress.

Do I think string theory is “not even wrong”?

Experimental results from the Large Hadron Collider show no evidence of the extra dimensions or supersymmetry that string theorists had argued for as "predictions" of string theory. The internal problems of the theory are even more serious after decades of research. These include the complexity, ugliness and lack of explanatory power of models designed to connect string theory with known phenomena, as well as the continuing failure to come up with a consistent formulation of the theory.

Are multiverse theories not even wrong? Yes, but that's not the main problem with them. Many ideas that are "not even wrong", in the sense of having no way to test them, can still be fruitful, for instance by opening up avenues of investigation that will lead to something conventionally testable. Most good ideas start off "not even wrong", with their implications too poorly understood to know where they will lead. The problem with such things as string-theory multiverse theories is that "the multiverse did it" is not just untestable, but an excuse for failure. Instead of opening up scientific progress in a new direction, such theories are designed to shut down scientific progress by justifying a failed research program.

My Thoughts

Sean Carroll has written that falsifiability is overrated as a criterion for distinguishing science from pseudo-science?

We must distinguish between being non-scientific and being unscientific. Philosophy is a subject which is almost certainly of its very nature non-scientific. We must not jump from this purely negative statement to the conclusion that it has the positive defect of being unscientific. The latter term can be properly used only when a subject, which is capable of scientific treatment, is treated in a way which ignores or conflicts with the principles of scientific method.

Some string theorists prefer to believe that string theory is too arcane to be understood by human beings.... One recent posting on a physics blog laid this out beautifully: 'We can't expect a dog to understand quantum mechanics, and it may be that we are reaching the limit of what humans can understand about string theory. Maybe there are advanced civilizations out there to whom we appear as dogs do to us, and maybe they have figured out string theory well enough to have moved to a better theory...

No one thinks that the subtle "demarcation problem" of deciding what is science and what isn't can simply be dealt with by invoking falsifiability. Carroll's critique of naive ideas about falsifiability should be seen in context: he's trying to justify multiverse research programs whose models fail naive criteria of direct testability (since you can't see other universes). This is however a straw man argument: the problem with such research programs isn't that of direct testability, but that there is no indirect evidence for them, nor any plausible way of getting any. Carroll and others with similar interests have a serious problem on their hands: they appear to be making empty claims and engaging in pseudo-science, with "the multiverse did it" no more of a testable explanation than "the Jolly Green Giant did it". To convince people this is science they need to start showing that such claims have non-empty testable consequences, and I don't see that happening.

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.

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.