## The Trouble With String Theory

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- Published on Wednesday, 17 January 2018 21:54
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Particle physics is to physics what big game hunting is to field biology. While theoretical physicists pore over their mathematical models, particle physicists are out in the brush with their pith helmets and shotguns, speaking softly, carrying big accelerators and blowing stuff up real good.

In The Trouble With Physics, Lee Smolin takes us on a journey through the history and science of physics and identifies this sociological division as the heart of the eponymous trouble: string theory is a theoretical field being explored by scientists with a particle mindset.

Before I explain the significance of Smolin's conclusion, it is important to understand what string theory is, what problems it is attempting to solve and why, in Smolin's view, it has failed.

Problem Children

Smolin identifies five challenges facing physics:

1) Combine general relativity and quantum theory into a single complete theory

2) Resolve the problem of observer-dependence in quantum theory

3) Determine whether the particles and forces in quantum theory can be unified

4) Explain how the constants in the standard model of particle physics are chosen by nature

5) Explain dark matter and dark energy

Over the past few decades, string theory has emerged as the great hope for facing these five challenges. For those unfamiliar, string theory is a mathematical theory of particle physics which models all the subatomic particles in the universe (protons, neutrons, electrons, quarks, photons, etc) as bits of vibrating string. Like the notes played on a violin, the particles produced by a string depend on how the string vibrates. Once string theorists had this essential insight, the rest was just a small matter of deriving the vibration dynamics that produce the particles we've observed in nature. No worries. Should have that ready by this after-lunch.

25 years and 11 dimensions later, no such luck. Smolin gives string theory full marks for addressing problem three, an incomplete on problem one and a failing grade on the other three.

But how can this be? The answer, dear multi-dimensional bundles of vibrating string, lie as much in ourselves as in our stars. It's not just that the math of string theory is complex, though it certainly is. It's not just that the regions of the universe string theory explains lie far beyond the reach of experiment, though they do. In addition to these factors, Smolin tells us, it is that the very sociology of the physical sciences has lured physicists, like moths to a flame, into a trap of their own making.

The Unification Lure

The pursuit of physics is fundamentally a quest for unification. In the chest of every physicist beats a heart that wants nothing more than to discover that two complicated things are in fact one simple thing. In the previous century, the unifications of electricity and magnetism into electromagnetism, electricity and the weak nuclear force into the electroweak force and space and time into spacetime meant bold new theories of science and Nobel prizes all around. But even better than that, these unifications gave us a view of the universe that is simpler and more elegant than it was before.

Consider Einstein's famous equation E=MC^2. The math behind this equation is simple enough that any high school student should be able to understand it. Yet it unifies two concepts which had previously seemed completely unrelated: matter is energy. This is elegance. A century before Einstein, not only did we think matter and energy were unrelated, but we actually thought heat was a physical substance. This clumsy, awkward view of the universe was replaced with a unification so elegant, we expect people to be able to understand it before they are old enough to drive. This is the Holy Grail of physics. And as we all know, when it comes to Grails, it is important to choose...wisely.

Smolin's take is that string theorists have fallen into an elegance trap and that trap is a product of theorists attacking mathematics the way experimentalists attack data. The problem with that is math is not data. The aggressive take-no-prisoners sociology of experimental physics has a natural constraint: results. Hypotheses may be as bold and counter-intuitive as you like because at the end of the week, we'll see what comes out of the accelerator. But when your research is pure math, you have to be more conservative, staying within the bounds of established observation and suggesting experiments to be done before you proceed further.

In their quest for the elegant theory of everything, string theorists have broken free of these constraints and in doing so, of science itself. So complete is this break with science, in fact, that Smolin quotes prominent string theorists opining that perhaps it is science itself which needs to change to accommodate string theory and that quaint traditions like experiment and result should make room for the notion that every self-consistent mathematical model is in fact a physically real universe and for the anthropic principle, which is a polite term for intelligent design. So much for "elegance."

While we're speaking of unified elegance, every chapter in Smolin's book dissects one aspect of this failure using a combination of historical perspective, personal anecdote and popularized science. His prose moves so easily between stories about the early history of quantum physics, young physicists' encounters with the elder Einstein and easily digestible descriptions of complex theories that you barely notice when he shifts context. Smolin's text isn't about physics. It is physics. And not just the science of physics, but the history and the culture as well. If quantum physics has taught us nothing else, it has taught us that the observer affects the observed and Smolin has observed the world of physics like no other writer of popular science.

The Tangled String

Okay, so what went wrong with string theory, specifically? Smolin's analysis is far too multifaceted to do justice to here, but a good first order approximation goes something like this:

First and foremost, string theory is not background independent. As a theory of everything, according to Smolin, that right there should have disqualified string theory. Background independence means that a theory does not rely on any physical circumstances that do not originate from constructs within the theory itself. String theory, like quantum theory, is background dependent in that it relies on the existence of time and space. Strings vibrate in space over time and string theory does not describe what time and space are or how they come to be.

There are several problems with this. Problems so obvious that even Einstein could understand them. Even with the limited understanding of quantum gravity available in his day, Einstein could see that any theory of quantum gravity had to be background independent. Because gravity is about time and space. So time and space must vary with the very quantum field that quantum gravity describes. So that field can't be said to exist in time in space because it constitutes time and space.

Quantum theory does not have to be background independent because it's describing the behavior of matter and energy in time and space. Time and space are assumed. Relativity is a background independent theory. It does not depend on the existence of time and space. Time and space emerge from relativity. But relativity is not a quantum theory. This is the underlying problem with reconciling quantum theory to relativity: one is quantum and background dependent, the other is background independent but not quantum.

String theory ducks this problem by attempting to describe the quantum nature of gravity in a background dependent fashion. That a theory of a thing should not depend on the existence of that thing seems obvious in retrospect.

Background dependence, as it turns out, is the millstone around string theory's neck. And the reason is all those famous extra dimensions everyone is so excited about. Those familiar with string theory will recall that it posits that our universe consists of not four but eleven dimensions. The reason we can't see these extra dimensions is because they are wrapped up so tightly that they are invisible to us up here in the unfurled dimensions, just as a wire appears to be one dimensional from a distance but three dimensional close up. String theory models each point in spacetime as being wrapped by an eleven dimensional hypersphere and these spheres are arrayed in the three dimensions of spacetime we are familiar with.

The first problem with this is of course that no one has seen any of these dimensions. They are merely predicted by the math. And by "predicted by the math" we mean "the equations of string theory didn't balance out so we added extra degrees of freedom until they did." More on that later.

The second problem is that these dimensions don't act like relativity says dimensions should act. The fundamental principle of general relativity is that spacetime is flexible. It bends and warps. But none of the extra bound up dimensions are allowed to vary in the presence of gravitational fields. Because they would destabilize. And the universe would implode. Boom.

This leads to the third problem which is actually the zeroth problem which, stringlike, loops back to the first problem: the bogus nature of these dimensions is a product of the very psychosocial problem that plagues the development of the entire theory. It's a fractal fallacy with small images of itself embedded within itself. And the fallacy is this: the extra dimensions were not added because they were observed, they were added because they were needed mathematically to shoehorn string theory into the observable data. Doing that is a cardinal sin. It changes string theory from a theory of everything to a theory of anything and a theory of anything is a theory of nothing.

Scientific theories are supposed to set boundaries. They are supposed to say what is and what is not a part of the theory. This is how predictions are made and experiments conducted: on the edge of the known and the unknown. And you can only know what you don't know if your theory takes a stand on what is real and what is not. Scientists call theories that fail to clear this bar "not even wrong."

Time and again in the book we see string theory miss the boat and then get "rescued" by a new formulation, a new set of constraints and, what the heck, an extra dimension or two in order to explain a new observation or to wish a couple of hundred trillion solutions into the cornfield. That is exactly the opposite of how science is supposed to work. If string theory is so flexible that it can be bent to accommodate any possible observation, then it's no theory at all because it's fundamentally unfalsifiable.

This is where we start, sadly, getting into respected scientists saying that science itself is the problem with string theory. I can think of another so-called "theory" that's making the same claim and the company, frankly, is not very welcome.

The Dark Passenger

There are many other nails in string theory's coffin described in the book, from the historical blind alleys of just adding dimensions to unworkable theories to the ever-expanding catalog of viable solutions, but the one that is worth mentioning here is the problem of dark energy.

Dark energy is the name we've given to the unexplained phenomenon that appears to be accelerating the expansion of the universe. It is often related to Einstein's cosmological constant because it is mathematically and conceptually similar, though Einstein introduced it for erroneous reasons. For Einstein, the CC was needed to explain what he believed was a steady-state universe, neither expanding nor contracting. Once he was persuaded of the reality of the Big Bang, he called the CC his "greatest blunder." But just as you need the CC to stabilize a universe that theory says should be collapsing or expanding, you also need a CC to accelerate the expansion of a universe. And unlike Einstein, our new CC, dark energy, is used to describe a phenomenon we observed but didn't expect, not one we expected but didn't observe, so we have more reason to suspect it's valid.

For reasons understood by people above my pay grade, string theory as formulated before the discovery of dark energy absolutely precluded the existence of dark energy. In other words, the one, solid, testable prediction made by string theory...a prediction considered at the time to be a pretty safe bet...turned out to be dead, flat wrong.

So naturally string theory was reformulated, with a new set of constraints on the extra seven dimensions that describe a universe about as stable as peanut brittle. Even if string theory turns out to be true, at this point elegance is far, far in the rearview mirror.

A New Hope

But all is not lost. Smolin makes it clear that string theory is not a total wash. It has contributed some results to the big five questions and even though it may not be a theory of everything, when properly restrained it does appear to be a theory of something. And string theory's greatest weakness is also its chief virtue. Being almost pure math, even if it doesn't turn out to be physical, the work on string theory has contributed immensely to the mathematics of multiple dimensions and even to other quantum gravity theories like loop quantum gravity.

Smolin also points out that there are a good many other theorists out there, struggling behind the scenes, foregoing tenure, nursing their undernourished theories. And some of them are producing results. The most interesting such theories don't start like string theory, with a single unifying conjecture into which everything from the cosmic background radiation to the kitchen sink must be shoehorned no matter how many dimensions you have to add, but rather start with one or more of the big five questions and work backwards from what a meaningful solution...one that would admit to no (or very little) magical shoehorning...would look like.

Ultimately, what Smolin is arguing for is not the abrogation of string theory, but the breaking of the string theory orthodoxy. One of the characteristics of particle physicists is that they do not work and play well with others. They don't have to, because the aforementioned accelerator is their only master. But the culture of theory should be different, says Smolin. Theory should be collaborative, not competitive. Solutions should be simple, not complex. Problems should be considered from every angle. Theorists should be open to every idea that can move the ball down the field, not ideologically committed to revealed truth. And until you show us these extra dimensions, that's exactly what they are: a holy vision, not an emperical observation.

In the few short years since the publication of his book, an increasing chorus of skepticism has arisen. It is very possible at this point that string theory will face a serious backlash and be relegated to the supply closet of history, only to be taken out in a few decades when a new generation of rebels breaks with whatever the orthodoxy is at that time. That will be a shame, because for all its faults string theory has brought much to the table and should not be discarded thoughtlessly. To do so would be foolish. It would be tragic. It would be...human.