The Trouble With Physics: The Rise of String Theory, The Fall of a Science, and What Comes Next
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There are other cases in which string theory has led to discoveries in mathematics. In one very beautiful case, a certain toy model of string theory called topological string theory has led to striking new insights into the topology of higher-dimensional spaces. However, this is not by itself evidence that string theory is true about nature, for the topological string theories are simplified versions of string theory and do not unify the forces and particles observed in nature.
More generally, the fact that a physical theory inspires developments in mathematics cannot be used as an argument for the truth of the theory as a physical theory. Wrong theories have inspired many developments in mathematics. Ptolemy’s theory of the epicycles might well have inspired developments in trigonometry and number theory, but that does not make it right. Newtonian physics inspired the development of major parts of mathematics, and it continues to do so, but that did not save Newtonian physics when it disagreed with experiment. There are many examples of theories based on beautiful mathematics that never had any successes and were never believed, Kepler’s first theory of the planetary orbits being the signal example. So the fact that some beautiful mathematical conjectures are inspired by a research program cannot save a theory that has no clearly articulated core principles and makes no physical predictions.
The troubles that string theory faces go straight to the roots of the whole enterprise of unification. In the first part of the book, we identified huge obstacles plaguing earlier unified theories—obstacles that led to their failure. Some of these involved attempts to unify the world by introducing higher dimensions. The geometry of the higher dimensions turned out to be far from unique and wracked with instabilities. The basic reason, as we saw in the earlier chapters, is that unification always has consequences, which imply the existence of new phenomena. In the good cases—such as Maxwell’s theory of electromagnetism, the electroweak theory of Weinberg and Salam, special relativity, and general relativity—these new phenomena were quickly seen. These are the rare cases in which we can celebrate the unification. In other attempts at unification, the new phenomena are not quickly seen, or already disagree with observation. Rather than celebrating the consequences of unification, the theorist must cleverly try to hide the consequences. I know of no cases where this concealing of consequences led in the end to a good theory; sooner or later, the attempted unification was abandoned.
Both supersymmetry and higher dimensions have turned out to be cases in which enormous effort must be expended to hide the consequences of the proposed unifications. No two known particles turn out to be related by supersymmetry; instead, each known particle has an unknown partner, and you have to tune the many free parameters of such theories to keep the unknown particles from being seen. In the case of higher dimensions, almost all solutions of the theory disagree with observations. The rare solutions that do reveal something like our world are unstable islands in a vast sea of possibilities, nearly all of which look totally alien.5
Can string theory avoid the problems that befell the earlier higher-dimensional and supersymmetric theories? It’s unlikely, if only because there is much more to hide than there was in either Kaluza-Klein theory or supersymmetric theories. The mechanism proposed by the Stanford group to stabilize the higher dimensions might work. But the cost is high, as it leads to a vast expansion of the landscape of conjectured solutions. Hence, the price of avoiding the problems that doomed Kaluza-Klein theory is, at best, to adopt a point of view that string theorists initially rejected, which is that a vast number of possible string theories have to be taken equally seriously as potential descriptions of nature. This means that the original hope for a unique unification, and hence for falsifiable predictions about elementary-particle physics, has to be given up.
In chapter 11, we discussed the claims by Susskind, Weinberg, and others that the landscape of string theories may be the road ahead for physics and found these claims unconvincing. Where, then, does that leave us? In a recent interview, Susskind claims that the stakes are to accept the landscape and the dilution in the scientific method it implies or give up science altogether and accept intelligent design (ID) as the explanation for the choices of parameters of the standard model:
If, for some unforeseen reason, the landscape turns out to be inconsistent—maybe for mathematical reasons, or because it disagrees with observation—I am pretty sure that physicists will go on searching for natural explanations of the world. But I have to say that if that happens, as things stand now we will be in a very awkward position. Without any explanation of nature’s fine-tunings we will be hard pressed to answer the ID critics. One might argue that the hope that a mathematically unique solution will emerge is as faith-based as ID.6
But this is a false choice. As we will see shortly, there are other theories that offer genuine answers to the five great questions, and they are progressing quickly. To give up string theory does not mean to give up science; it just means giving up one direction that was once favored but failed to deliver what was hoped for it, in order to focus attention on other directions that now seem more likely to succeed.
String theory succeeds at enough things so that it is reasonable to hope that parts of it, or perhaps something like it, might comprise some future theory. But there is also compelling evidence that something has gone wrong. It has been clear since the 1930s that a quantum theory of gravity must be background-independent, but there is still little progress toward such a formulation of string theory that could describe nature. Meanwhile, the search for a single, unique, unified theory of nature has led to the conjecture of an infinite number of theories, none of which can be written down in any detail. And if consistent, they lead to an infinite number of possible universes. On top of this, all the versions we can study in any detail disagree with observation. Despite a number of tantalizing conjectures, there is no evidence that string theory can solve several of the big problems in theoretical physics. Those who believe the conjectures find themselves in a very different intellectual universe from those who insist on believing only what the actual evidence supports. The very fact that such a vast divergence of views persists in a legitimate field of science is in itself an indication that something is badly amiss.
So, is string theory still worth studying, or should it be declared a failure, as some suggest? The fact that many hopes have been disappointed and many key conjectures remain unproved may well be reason enough for some to give up working on string theory. But they are not reasons for research to stop altogether.
What if sometime in the future someone found a way to formulate a string theory that led uniquely to the standard model of particle physics, was background-independent, and lived only in the three-dimensional nonsupersymmetric world we observe. Even if the prospects for finding such a theory seem slim, it is a possibility—underscoring the general wisdom that a diversity of research programs is healthy for science, a point we’ll return to later.
So string theory is certainly among the directions that deserve more investigation. But should it continue to be regarded as the dominant paradigm of theoretical physics? Should most of the resources aimed at the solution of the key problems in theoretical physics continue to support research in string theory? Should other approaches continue to be starved in favor of string theory? Should only string theorists be eligible for the most prestigious jobs and research fellowships, as is now the case? I think the answer to all these questions must be no. String theory has not been successful enough on any level to justify putting nearly all our eggs in its basket.
What if there are no other approaches worth working on? Some string theorists have advocated supporting string theory because it is “the only game in town.” I would argue that even if this were the case, we should strongly encourage physicists and mathematicians to explore alternative approaches. If there are no other ideas, well, let’s invent some. Since there is no near-term hope that string theory will make falsifiable predictions, there is no particular hurry. Let’s encour
age people to look for a quicker path to answering the five key questions of theoretical physics.
In fact there are other approaches—other theories and research programs that aim to solve those five problems. And while most theorists have been focusing on string theory, a few people have been making a lot of progress on the development of these other areas. More important, there are hints of new experimental discoveries, not anticipated by string theory, that, if confirmed, will point physics in new directions. These new theoretical and experimental developments are the subject of the next part of the book.
III
BEYOND STRING THEORY
13
Surprises from the Real World
THE GREEK PHILOSOPHER HERACLITUS left us a lovely epigram: Nature loves to hide. It is so often true. There is no way Heraclitus could have seen an atom. No matter how much his fellow philosophers speculated about them, to see an atom was beyond any technology they might have imagined. These days, theorists make great use of nature’s tendency to inscrutability. If nature is indeed supersymmetric, or has more than three dimensions of space, she has hidden it well.
But sometimes the opposite is true. Sometimes the key things are right in front of us, there for the seeing. Hiding in plain sight from Heraclitus were easily perceivable facts we now take for granted, like the principle of inertia or the constant acceleration of falling objects. Galileo’s observations of motion on Earth did not use the telescope or the mechanical clock. As far as I know, they could have been made in Heraclitus’s time. He had only to ask the right questions.
So, while we bemoan how hard it is to test the ideas behind string theory, we ought to wonder what might be hiding in plain sight around us. In the history of science, there have been many instances of discoveries that surprised scientists because they were not anticipated by theory. Are there observations today that we theorists have not asked for, that no theory invites—observations that could move physics in an interesting direction? Is there a chance that such observations have already been made but ignored because, if confirmed, they would be inconvenient for our theorizing?
The answer to these questions is yes. There are several recent experimental results that point to new phenomena unsuspected by most string theorists and particle physicists. None is completely established. In a few cases, the results are reliable but the interpretations are disputed; in others, the results are too new and surprising to have been widely accepted.1 But they are worth describing here, because if any of these hints turns into a true discovery, then there are important features of fundamental physics that are not predicted by any version of string theory and will be hard to reconcile with it. Other approaches will then become essential, not optional.
Let us start with the cosmological constant, thought to represent the dark energy accelerating the universe’s expansion. As discussed in chapter 10, this energy was not anticipated by string theory, nor by most theories, and we have no idea what sets its value. Many people have thought hard about this for years, and we are more or less nowhere. I don’t have an answer either, but I have a proposal for how we might find one. Let’s stop trying to account for the cosmological constant’s value in terms of known physics. If there is no way to account for a phenomenon on the basis of what we know, then maybe this is a sign that we need to look for something new. Perhaps the cosmological constant is a symptom of something else, in which case it might have other manifestations. How are we to look for them, or recognize them?
The answer will be simple, because universal phenomena are ultimately simple. Forces in physics are characterized by just a few numbers—for example, the distance over which a force travels and a charge to tell us how strong it is. What characterizes the cosmological constant is a scale, which is the distance scale over which it curves the universe. We can call this scale R. It is about 10 billion light-years, or 1027 centimeters.2 What is weird about the cosmological constant is that its scale is huge compared with other scales in physics. Scale R is 1040 times the size of an atomic nucleus and 1060 times the Planck scale (which is about 10−20 times the size of a proton). So it’s logical to wonder whether scale R might reflect some totally new physics. A good approach would be to look for phenomena that happen on the same vast scale.
Does anything else happen on the scale of the cosmological constant? Let’s start with cosmology itself. The most precise cosmological observations we have are measurements of the cosmic microwave background. This is the radiation left over from the Big Bang, which comes to us from all directions of the sky. The radiation is purely thermal—that is, random. It has been cooling as the universe expands, and it is now at a temperature of 2.7 degrees Kelvin. The temperature is uniform across the sky to a high degree of precision, but at the level of a few parts in 100,000 there are fluctuations in it (see Fig. 13, top). The pattern of these fluctuations gives us important clues to the physics of the very early universe.
Over the last decades, the temperature fluctuations of the microwave background have been mapped by satellites, balloon-borne detectors, and ground-based detectors. One way to understand what these experiments measure is to think of the fluctuations as if they were sound waves in the early universe. It is, then, useful to ask how loud the fluctuations are at different wavelengths. The results give us a picture, such as that in Fig. 13, bottom, which tells us how much energy there is at the various wavelengths.
The picture is dominated by a large peak, followed by several smaller peaks. The discovery of these peaks is one of the triumphs of contemporary science. They are interpreted by cosmologists to indicate that the matter filling the early universe was resonant, much like the head of a drum or the body of a flute. The wavelength at which a musical instrument vibrates is proportional to its size, and the same is true in the universe. The wavelengths of the resonant modes tell us how big the universe was when it first became transparent: that is, when the initial hot plasma devolved, or “decoupled,” into separate realms of matter and energy some three hundred thousand years after the Big Bang, at which time the microwave background became visible. These observations are extremely helpful in tying down the parameters of our cosmological models.
Another feature we see in the data is that there is very little energy in the largest wavelength. This may be just a statistical fluctuation, because it involves a small number of pieces of data. But if it is not a statistical fluke, it can be interpreted as indicating a cut-off, above which the modes are much less excited. It is interesting that this cutoff is at the scale R, associated with the cosmological constant.
Fig. 13. Top: The sky as seen at microwave frequencies. Signals from within our galaxy have been removed, leaving an image of the universe as it was at the time when it cooled to the point that electrons and protons became bound into hydrogen. Bottom: The distribution of energy in the top image at different wavelengths. The dots represent data from WMAP and other observations, and the curve is a fit to predictions of the standard cosmological model.
The existence of such a cutoff would be puzzling from the point of view of the most widely accepted theory of the very early universe, which is inflation. According to the theory of inflation, the universe expanded exponentially fast during one extremely early period. Inflation accounts for the observation that the cosmic background radiation is so nearly uniform. It does this by ensuring that all the parts of the universe we see now could have been in causal contact when the universe was still a plasma.
The theory also predicts the fluctuations in the cosmic microwave background, which are hypothesized to be remnants of quantum effects during the period of inflation. The uncertainty principle implies that the fields dominating the energy of the universe during inflation fluctuate, and these fluctuations become imprinted on the geometry of space. As the universe expands exponentially, they persist, causing fluctuations in the temperature of the radiation produced when the universe becomes transparent.
Inflation is believed to have produced a huge region of the universe
with relatively uniform properties. This region is thought to be many orders of magnitude larger than the observable region, because of a simple argument about scales. If inflation had stopped just at the point where it created a region as large as we now observe, there must have been some parameter in the physics of inflation that selected a special time to stop, which just happens to be our era. But this seems improbable, because inflation took place when the universe had a temperature ten to twenty orders of magnitude greater than the center of the hottest star today; thus the laws governing it must have been different laws, which dominated physics only in those extreme conditions. There are many hypotheses about the laws that governed inflation, and none of them say anything about a time scale of 10 billion years. Another way to put this is that there seems no way for the present value of the cosmological constant to have anything to do with the physics that caused inflation.
Thus if inflation produced a uniform universe on the scale that we observe, it likely produced a universe that is uniform on much larger scales. This in turn implies that the pattern of fluctuations produced by inflation should go on and on, no matter how far you look. If you could see beyond the present size of the observable universe, you should continue to see small fluctuations in the cosmic microwave background. Instead, the data hint that the fluctuations may cease above the scale R.