Thoughts, Ideas, Observations

Physics Hanging by a Thread

Brian Greene, The Elegant Universe:  Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory.  New York:  Vintage Books, 2003.  (First edition 1999)

Peter Woit:  Not Even Wrong:  The Failure of String Theory and the Continuing Challenge to Unify the Laws of Physics.  London:  Jonathan Cape, 2006.

Reviewed by John Bedell

In 1919 a German mathematician named Theodor Kaluza was playing around with Einstein's new theory of gravity, now known as general relativity, when he made a remarkable discovery: formulated in five dimensions, relativity produces the standard equations that describe electricity and magnetism. Nobody knows what to make of this odd fact. Einstein himself showed that Kaluza's work contains certain technical problems that prevent its being useful physics, but this discovery hints that our physical laws are expressions of some deeper law that would tie all of our theories together.  Ever since then, physicists have been searching for that underlying unity, for a "grand unified theory" or a "theory of everything."  The latest expression of this unifying dream is something called string theory.  What is it, and why has it become so controversial?

From the eighteenth century until the 1970s, scientists made continual progress in understanding matter at its smallest scales. First through chemistry and the atomic theory, then through the study of electricity, and finally through sub-atomic physics, they gradually expanded our knowledge of the most fundamental physical things. In the twentieth century physicists brought forth one of humanity's strangest and most marvelous creations, the quantum theory. Through arcane mathematics and ingenious experiments they learned to understand things that seem at first completely beyond comprehension. Protons and electrons do not follow the rules of the familiar, macroscopic world, yet we have somehow stretched the human brain to encompass the incredible strangeness of the quantum realm.  Using our own logic, we have come to comprehend a logic that turns everything we thought we knew on its head. In the 1960s physicists refined quantum theory into a set of "gauge theories" that describe three of the four basic forces of the universe as mathematical fields. This "standard model" is astonishingly precise and tells us almost everything we want to know about electrons and quarks, the basic building blocks of the universe.

Then, some time in the 1970s-- Peter Woit gives the exact date of 1973-- progress in particle physics slowed to a crawl. At that point the standard model was completed, and since then nothing solid has been added to our understanding of the sub-atomic world. The standard model is incredibly impressive, but nobody thinks it is complete or finished. First, it ignores gravity, the most familiar of the four basic forces; when you try to combine quantum mechanics with general relativity you get mathematical nonsense. Second, it is in many ways arbitrary. Some of the equations have many possible solutions, and the only way we know which one is correct is through experiment; physicists would much prefer laws that have only one possible solution and that therefore make predictions about the world that we can verify experimentally. Third, in its simplest and most elegant form it gives all particles a mass of 0. To give things mass it requires the postulation of an entity called the "Higgs field", with an as-yet unobserved particle called the Higgs boson (the only particle in the standard model that has not yet been observed), and many physicists find this construction dubious.

Why did progress in particle physics stop in the 1970s? Most people would agree that the root of the problem is on the experimental side. From Galileo to the 1970s, theoretical physics was closely tied to experiment: experimenters discovered things, which theoreticians explained; theoreticians made predictions, which experimenters tested. Sub-atomic physics was driven throughout the post World War II period by increasingly powerful atom smashers. However, since 1970 the accelerator labs have produced few new discoveries, and these have confirmed the standard model rather than challenging it or helping us to get beyond it.  The resolving power of these quantum microscopes increases only with the square root of the instrument's power, and we have reached the point at which real progress seems to require an enormous leap in resolution. With the Cold War behind us, nobody is interested in paying the cost for such an instrument, which would run into the tens of billions of dollars. Why should governments or taxpayers care, since, as we said, the standard model already answers almost every practical question about the sub-atomic world?

The situation in theoretical physics is essentially this:  we have an incomplete, unsatisfying (although supremely useful) fundamental theory, but no new data that would help us to go beyond what has already been done. In earlier centuries, work on these questions might simply have stopped, but we now have numerous research institutes and graduate physics departments where work in theoretical physics is supposed to go on, and the people who work in them have to do something.  Besides, the curiosity of physicists has been aroused by the power of the standard model, and many of them feel in their hearts that a complete "theory of everything" is only a few steps away. So work in theoretical physics goes on.

And what is it that theoretical physicists do? They study string theory. String theory in its various permutations is the only candidate for a final theory of the physical nature of the universe that anyone takes seriously.  However, a lot of people don't take it seriously.  String theory tantalizes physicists and mathematicians with glimpses of a perfect theory that explains everything about the universe in terms of its basic geometry.  Yet, despite an enormous amount of mental effort expended by hundreds of the world's smartest people, string theory remains little more than a set of calculation techniques.  Its equations have never been worked out, and it exists in several different forms that may be different ways of expressing the same deep mathematical truth, but then again may not be reconcilable with each other.  It has yet to make any predictions that can be tested with any conceivable experiment.  It is so arcane and difficult to understand that only people who devote their careers to it have any chance of following the discussion, which means that only people with a deep commitment to its success are qualified to speak about whether it is really making progress.  Some outsiders have always viewed the whole edifice with alarm and disdain, and the debate has at times grown very ugly.

Thanks to the two books under review here, non-physicists can now get some understanding of what string theory is and what is at stake in the controversy.  Brian Greene is a string theorist who has recently embarked on a second career expounding his vision of the universe to a broad public, writing The Elegant Universe and another book and starring in a NOVA episode.  Peter Woit is a casualty of the string theory revolution; he trained in theoretical physics but had no interest in strings, with the result that he couldn't get a job and wound up as a lecturer in mathematics.  Let's take their two books together, and see what we come up with.

The Elegant Universe is a marvelous book, and if you really want to know something about string theory I recommend it highly.  Brian Greene has a knack for explaining mathematical arcana in ordinary language, and I found his presentation enjoyable.  He is likable and his enthusiasm for physics is infectious.  Yet Greene regularly says things that make me uneasy.  Greene several times says that string theorists have "discovered" things, when he means that they have been produced mathematically. True, mathematicians use the same language, but for physicists "discovered" usually implies something more concrete.  Greene is fascinated with mathematical order and in particular with the property known as "symmetry." Symmetry simply means that when you perform some operation on an object, it ends up the same as when you started.  Thus the facade of a classical building has "mirror symmetry", because if you reflect it in a mirror it doesn't change.  Some of the basic symmetries we observe in nature are that the laws of physics do not change over time, and they are the same in every place.  Trying to make the sub-atomic world as symmetrical as possible, physicists in the 1970s created "supersymmetry," which requires that each particle we know have a supersymmetric particle of a much higher mass. (Thus the "super" in "superstrings," since string theory is supersymmetric.)  None of these particles has ever been observed, so supersymmetry remains a speculation, but Greene seems to regard it as already established because of its pleasing completeness:

. . . from an aesthetic standpoint, physicists find it hard to believe that nature would respect almost, but not quite all of the symmetries that are mathematically possible.  Of course, it is possible that an incomplete utilization of symmetry is what actually occurs, but it would be such a shame.  It would be as if Bach, after developing numerous intertwining voices to fill our an ingenious pattern of musical symmetry, left out the final, resolving measure. (p. 174)

calabi-yau shapeWhat is string theory?  String theory assumes that sub-atomic particles are not dimensionless points, as posited in the standard model, but one-dimensional strings with a length of about 10-33 meters.  Most versions of the theory suppose that these strings are actually loops.  The strings can vibrate in different ways, and these vibratory modes create all of the various sub-atomic particles.  That is, an electron is a string vibrating in one way, while a photon is a string vibrating in some other way.  In order to make the math work out, physicists have had to assume that the universe has many more spatial dimensions than the three we can sense; 10 is the current favorite number.  According to the theory, we can't sense the seven extra extra dimensions because they are curled up into very tiny spaces.  Imagine life on the surface of a garden hose: this universe would have one extended dimension, the length of the hose, and one dimension that is curled up, since if you walk around the hose you very quickly end up where you started.  The extra dimensions of string theory are not curled into circles, but into intricate structures called Calabi-Yau manifolds.  (A 2-dimensional rendering of one of these 6-dimensional forms is shown below.)  Because the properties of the strings depend very sensitively on the geometry of the particular Calabi-Yau shape into which you fold the dimensions, string theorists spend a great deal of time working on the geometry of Calabi-Yau manifolds.

String theory has certain appealing characteristics that keep people working at it, even though the math is incredibly difficult and the results meager.  Analyzing the paths of tiny, vibrating loops through space turns out to produce many of the key equations of modern physics.  As Greene writes, "numerous features of the standard model -- features that had been painstakingly discovered over the course of decades of research -- emerged naturally and simply from the grand structure of string theory."   Physicist Michael Green went further, saying that "the moment you realize that almost all of the major developments of physics over the last hundred years emerge -- and emerge with such elegance -- from such a simple starting point, you realize that this incredibly compelling theory is in a class of its own."  String theory predicts the existence of gravity, so it seems in principle able to reconcile relativity with quantum mechanics.  Using its tools one can make calculations about situations where the standard model breaks down completely, such as the inside of a black hole.  (There's no way of knowing if the calculations are correct, but at least string theory is in principle (again) able to make them.)  While most string theorists admit that their field has as yet made little contact with experimental data, most say that they just need more time.  The mathematics is so difficult, they say, and the concepts so new, that it is unfair to judge what the theory may become on the basis of what it is capable of doing now.

Peter Woit is unimpressed.  Woit is one of those characters who have hung around the edges of the academic world, never quite making it in.  From his position as a lecturer in mathematics he has watched the progress of string theory, and his disgust seems to have grown with each passing year. He includes in this book some numbers showing how grim the academic job market is for theoretical physicists, and how tightly string theorists have locked up the best jobs.  Some of these passages reek of bitterness, and I am sure that many people who make it that far in the book will conclude from them that Woit is just a disgruntled loser.  I have a feeling, though, that Woit's reputation is in little danger on this score, because I doubt many people will make it that far.  The book is written without equations, but it is full of math, so much so that I think I understood about half of it.  It seems to me that the book is too technical for anyone other than mathematicians and physicists, but not technical enough to satisfy them, leaving it in a very odd position.

And yet, despite the contrast between Woit's bitterness and Greene's infectious enthusiasm, I think Woit has by far the better argument.  Woit explains quantum field theory and the math on which it is based in some detail (most of the book consists of this exposition), and using this base he is able to show how limited and unimpressive string theory actually is.  As Woit would have it, string theory isn't even a theory, just a way of making calculations based on the assumption that there is an underlying theory that has certain characteristics.  The way that theory is imagined has evolved over time (the current version is called "M theory"), but no one has been able to write down any of its equations.  If Woit is right that string theory is only a tantalizing dead end, then his picture of the physics community is disturbing.  According to Woit, the only way for a theoretical physicist to get a job is to throw himself into string theory and produce articles on 10-dimensional geometry, and by the time he has written enough to get tenure he has committed too much of his life to string theory to ever get out and work on something else.  Thus all the best theoretical physicists are working on strings, and nobody is looking for an alternative theory.  Attacks from outsiders have turned the string community into a sort of cult, intolerant of criticism and ready to make personal and institutional attacks on anyone who publicly expressed doubts about what they are doing.

I find this troubling. I am extremely skeptical of string theory because I don't think we are smart enough to figure out the laws of the universe without experimental data.  Modern science leapt far beyond anything humanity knew before because scientists began to insist that theories be based on carefully executed experiments or other precise observations.  Medieval and ancient science did not have this experimental basis, which is why scientists before Galileo were wrong about almost everything. Newton was not smarter than Aristotle, but he approached science in a different way, with an insistence on agreement between theory and data.  String theory in this sense takes us back to the kind of airy speculation that characterized "natural philosophy" before Galileo, and I can't see how this is a good thing.  Of course, we know much more physics than the ancient Greeks, and we understand much better what mathematical form a fundamental theory should take, but that doesn't mean we can dream up such a theory in our heads. It may be true that much of modern physics "emerges naturally" from the structure of string theory, but it is also possible that string theorists have found those things because they already knew to look for them, like psychics announcing their predictions at the end of the year.  As in the strange case of electromagnetism sprouting from the 5-dimensional form of general relativity, the remarkable results produced by string theorists hint at some deeper truth, but what that truth is remains elusive.

I have a feeling that the whole edifice of contemporary physics is in for some serious shocks.  In particle physics we have no new data and attempts to expand our current, incomplete theories seem to be going nowhere.  Meanwhile, in cosmology there is an embarrassment of new data, but it is not of a very comforting kind: unexplained entities (inflation, dark matter, dark energy) are proliferating in the models like the epicycles that medieval astronomers used to make their observations fit with an earth-centered universe.  I found it very interesting that some of our leading physicists seem to share my bewilderment; both Edward Witten and Steven Weinberg told Nova that we just may not be smart enough to understand the fundamental laws of the universe. I rather suspect that we are, provided we have the necessary data  I think were are due for a new revolution in physics, perhaps as profound as the quantum revolution of the twentieth century, and that the frustrations of current physicists are only the prelude to that new leap. Some form of string theory may well be part of that revolution, but I doubt it.

July 14, 2006

Further reading:

Good article on strings at wikipedia.

Nova page accompanying The Elegant Universe.

Peter Woit's Blog

From the 
Commonplace Book

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Commonplace Book
On the Dead
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Raymond Aron, Jean-Paul Sartre, and the Limits of Being Right

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How the Mind Works

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Clearer proofs, in the discovery of secrets, and in the investigation of the hidden causes of things, are afforded by trustworthy experiments and by demonstrated arguments, than by the probably guesses and opinions of the ordinary professors of philosophy.

--William Gilbert

I guess it's possible that string theory could be wrong. But if it is in fact wrong, it's amazing that it's been so rich and has survived so many brushes with catastrophe and has linked up with the established physical theories in so many ways, providing so many new insights about them. I wouldn't have thought that a wrong theory should lead us to understand better the ordinary quantum field theories or to have new insights about the quantum states of black holes.

--Edward Witten

String theorists make excuses, not predictions. 

--Richard Feynman