Hiding in the Mirror: The Quest for Alternate Realities, From Plato to String Theory (By Way of Alicein Wonderland, Einstein, and the Twilight Zone)

by Lawrence M. Krauss

  Another imaginative tack has been to use Braneworlds to almost completely avoid the outstanding issues associated with inflationary universe models. Paul Steinhardt at Princeton and Neil Turok at Cambridge have recently proposed using a Braneworld scenario to allow a return to the “cyclic universe” models that were in vogue before the success of the current big bang picture. They have proposed a model called the ekpyrotic universe. In the ekpyrotic universe the current period of accelerated expansion observed in our space is related to the separation of our brane and another one embedded in some higher dimensions. Ultimately, however, these two branes will stop moving apart and will begin to draw closer together. When this happens, our universe will undergo a collapse and reheat again in a reverse of the current big bang expansion. These two branes will eventually cross through each other, producing a burst of energy that will generate another big bang expansion that might proceed again for billions of years as the two branes once again separate. Ultimately, as the interaction energy between the branes begins to dominate, our brane will once again experience an exponential expansion just before the attraction between the branes once again causes them to stop separating and repeat the whole process. The interesting aspect of this model, and the part that has a certain science fiction charm, is the fact that the period of inflationary expansion that ultimately causes the universe to look flatter and smoother happens near the end of each big bang expansion phase instead of at the beginning. Thus, the reason our universe looks isotropic is that in the cycle that preceded ours, before all stars, galaxies, and civilizations in that expanding universe were subsequently destroyed in a big crunch preceding our own big bang, astronomers in that doomed universe would have measured their universe to be undergoing an accelerated expansion, just as we are measuring today.

  As aesthetically pleasing as such an oscillating universe with no beginning and no end might be, however, in order for it to be viable one must ensure that the isotropic, relatively uniform universe that supposedly results during the final accelerating expansion in one phase can survive the subsequent collapse and collision of the two branes to produce isotropic conditions for the next big bang. It is not at all clear that this is possible. In particular, one must make certain that the two colliding branes are precisely aligned as they collide in order for this picture to be viable. Of greater concern, perhaps, is that if one asks what the natural period is for this oscillating universe to go through each cycle, the timeframe is of the order of the Planck time, about 10–43 seconds! In order to produce universes that expand for at least ten billion years, the parameters of these models must therefore be very carefully fine-tuned.

  By now I hope you get the general flavor of the dilemma. Braneworlds provide lots of new possibilities for cosmology and the early universe, but nothing yet to write home about, or at least, it seems to me, nothing that yet seems much more attractive than the theories we already have. But there remains hope, in the form of the one inexplicable, crazy facet of modern cosmology that so far has resisted all efforts to even begin to understand it: dark energy. The fact that empty space appears to carry an energy that is large enough to dominate the expansion of the universe today, yet is 120 orders of magnitude smaller than what one would expect on the basis of conventional ideas associated with the quantum physics of four dimensions, literally begs for some out-of-this-world ideas to explain its existence.

  The key problem associated with trying to describe dark energy in terms of fundamental particle physics is that the effect of dark energy is primarily felt at large scales. On the scale of the solar system and smaller, for example, the gravitational forces associated with matter (i.e., the sun and planets) overwhelm the minuscule repulsive effect induced by a small cosmological constant. But on the scale of clusters of galaxies and larger, the repulsive force due to this energy of empty space dominates. The problem is actually even more serious than this. The focus of our efforts to understand the fundamental laws of nature has involved examining phenomena at ever-smaller scales. When we first began to explore the nature of atoms we discovered the laws of quantum mechanics. Similarly, as we explored the nature of the nucleus, we discovered the weak and strong forces. If all of these get unified in some grand unified model, we expect the new physics might appear on scales much smaller than this. Even those models that place a string theory scale near the electroweak scale predict that if new physics appears, it will be on scales smaller than those that we have currently been able to measure.

  Indeed, we now realize precisely how it is possible that new physics can emerge on ever-smaller scales without impacting upon the wellunderstood explanations of how the universe operates on larger scales. Quantum mechanics, for example, is largely irrelevant when considering the motion of baseballs or cannonballs, which is why Newton didn’t have to know about it when he developed his classical laws of motion. But the problem with trying to understand dark energy from a fundamental physics perspective is that it appears to be a large-scale phenomenon, relevant to the expansion of the entire universe. The actual amount of energy associated with empty space in the room in which you are reading this is incredibly small—so small, in fact, that it is hard to imagine how any revision of the laws of physics that might accommodate it would not also dramatically affect physics on all higher-energy scales. This, in a nutshell, is the fundamental problem that has bedeviled all attempts, including string theory attempts, to resolve the cosmological constant problem on fundamental grounds.

  In this regard, a particularly creative and novel use of the Braneworld idea was proposed by Gia Dvali—whose name has already come up several times as one of the most active and inventive young theorists in this area today. Dvali, with his NYU colleagues Gabadadze and Porrati, examined in a series of papers a possibility that was in some sense diametrically opposed to the extra-dimensional scenarios that had been considered previously.

  They imagined an infinite-volume extra-dimensional space in which gravity could propagate. They then argued that if one were confined—as we presumably are—to a four-dimensional brane, then under certain circumstances, for relatively short (on a cosmic scale) distances and times, one might actually measure the gravitational interaction between objects on our brane to be that calculated by Newton and Einstein. However, over long times and distances the gravitational fields could “leak” into the extra dimension. The net effect would be to change the nature of gravity at large distances and times, not small ones.

  Not being ones to hedge their bets, Dvali and colleagues pointed out that there were two different ways that this kind of mechanism might address both the nature of the dark energy that is apparently driving the observed accelerated expansion of the universe, and the broader and more fundamental cosmological constant problem. It would do this by getting rid of both of them.

  As far as the nature of dark energy is concerned, one of the interesting implications of modifying gravity at large scales is that one might modify Einstein’s equations in a way that would produce accelerated expansion on sufficiently large scales, even without any dark energy as a source. This is, of course, very attractive, because dark energy isn’t.

  Nevertheless, even if one were to get rid of the need for dark energy, one still has to explain why its value isn’t gigantic. Specifically, we would need to solve the cosmological constant problem by explaining why quantum mechanics doesn’t produce a vacuum energy that results in even greater acceleration than we would observe today from these additional new gravitational shenanigans at large distance. Here again, Dvali and colleagues provided at least the germ of an interesting idea. If, on the largest scales, gravity is really five-dimensional, and not fourdimensional, then the relevant vacuum energy to which gravity would be sensitive is the full vacuum energy in five dimensions. It just might be possible to imagine symmetries, like supersymmetry, that could be exact in five or higher dimensions, while broken in our four-dimensional world. Such symmetries might imply that the higher-dimensional vacuum energy was zero. Thu
s, even if there existed a nonzero cosmological constant on our brane, it could be that gravity on large scales would not “feel” this cosmological constant. These ideas are fascinating, in part because they are so heretical and counterintuitive. Unfortunately, however, they are also quite provisional. There are a lot of “mights” in the preceding paragraph, and no real model including all of these features has been developed and explored. What is worse is that this possibility may in fact have already been ruled out by observations.

  As Dvali and his colleagues have shown, the presence of such infinitevolume extra dimensions is not completely hidden. Because of the nature of general relativity, it turns out that, in their models, the effect of five dimensions changes gravity slightly on all scales, so there must be small corrections to the Newtonian gravitational attraction between all objects, no matter how small or close. However, very high-precision experiments that have been conducted on our solar system would strongly constrain the magnitude of any such possible corrections to the force between the sun and the inner planets, for example. If one is an optimist, one might hope that as these measurements improve, deviations will be seen that imply that perhaps gravity on large scales really is leaking away. In any case, for the moment the upper bounds on what is allowed come very close to the level one might expect from such extra-dimensional effects, but work remains to be done to verify this in detail. We are thus left at present with the somewhat uncomfortable situation that Braneworlds, for all of their hope and hype, haven’t yet demonstrated what it takes to be compelling. Their major virtue at this point in time is that some of their consequences are at least in principle testable, via either cosmological observations or the next generation of particle accelerators. Which brings us back at long last to string theory, M-theory, and the Theory of Everything. Ultimately we should recall that Braneworld ideas seem at best poor approximations to reality, if string theory is correct. What the notion of large or possibly infinite extra dimensions has done is borrow some of the facets of string theory while ignoring the bulk of the theory (forgive the pun), about which, as I have explained, we currently only have the vaguest notions. It seems to me to be a very big long shot that an apparently ad hoc choice of what to keep and what to ignore will capture the essential physics of our universe. To truly understand the origin and evolution of our universe from its earliest moments, if M-theory really corresponds to reality, we will almost certainly be required to understand that theory better than we currently do. And as I have now stressed several times, one of the most significant areas where string theory has had no success thus far (amidst a long list), and where it may ultimately rise or fall, is the attempt to understand the energy of empty space. String theory never explained why the vacuum energy should be precisely zero when we thought that was the case in the 1980s and 1990s, nor did it predict that it might be nonzero but unbelievably tiny, as it would seem to be in order to explain current cosmological observations. Braneworld proposals notwithstanding, it is most likely that to understand why empty space appears to gravitate the way it does will require a complete theory that merges quantum mechanics and gravity. At present M-theory/string theory is the only game in town, even if no one yet knows what the rules are.

  So, even as the nature of M-theory seems to be increasingly elusive and the likelihood that a higher-dimensional theory will clearly resolve other fundamental questions in particle physics is becoming murky, some string theorists have now turned their attention to this fundamental puzzle in the hopes that cosmology might provide a beacon that has otherwise been lacking that can illuminate these dark and hidden worlds. This has resulted in yet another fascinating sociological metamorphosis of the theory, with warts becoming beauty marks. The presence of dark energy may have completely changed the landscape of modern cosmology, but string theory was not to be outdone: It has produced its own landscape.

  Recall that one of the apparent vagaries of string/M-theory is the fact that even if the underlying symmetry structure and number of dimensions associated with the theory were to become explicitly known, the fundamental nature of physics in our three-dimensional space might nevertheless remain undetermined. This is because in order to reduce the theory from ten or eleven dimensions to four, one generally must compactify the extra dimensions, or at least explain how they might be otherwise unobservable in our space at the present time. For now, there is no guiding mathematical principle that tells us which compactifications are reasonable. The number of different corresponding possible ground states of our universe corresponds roughly to the number of inequivalent possible compactifications. With ten dimensions to start with, and a host of Calabi-Yau possible compactification manifolds, for example, it has been estimated that there may be more than 10100 different possible inequivalent ground state configurations that might describe viable four-dimensional universes, and that might result from a single underlying M-theory. When this was first realized, it looked like bad news for string theory, because it meant that any hope of predictability might go down the drain. Without any way to choose between different ground states, each of which would represent a four-dimensional universe that might have a different configuration of forces and underlying symmetries and a completely different spectrum of elementary particles, the long-sought uniqueness of string theory seemed ephemeral at best. For some time this final step, compactification, was frankly not emphasized in discussions heralding the beauty of string theory.

  But with an exceedingly small vacuum energy apparently present in our universe, suddenly the terms have changed. The plethora of possible ground states of the theory, and the nonuniqueness of string-theoretic predictions, have become a virtue, offering hope where none had appeared before. The source of this sudden optimism stems from a calculation first performed by physicist Steven Weinberg with collaborators Paul Shapiro and Hugo Martel at the University of Texas, which in turn has its basis in one of the most slippery ideas in twenty-first-century physics, which is somewhat pompously called the “anthropic principle.”

  The anthropic principle is deceivingly simple to state and equally difficult to fully come to terms with. It is based on the suggestion that some, or perhaps all, of the fundamental constants in nature describing elementary particle interactions are what they are because if they took on different values, we wouldn’t be here to measure them.

  When one first hears this, it sounds like either a truism or a religious claim. But it is far from either. It does not imply, as some fundamentalists have tried to argue, that physics is on the verge of proving that the universe was created specifically for humankind to live in. Rather, at its best, it suggests that it is at least possible that, if the underlying theory of the universe does not uniquely predict the nature of particles and fields that can exist, then there may be no fundamental dynamical reason why the universe we live in is the way it is.

  I should say at the outset that this idea goes completely against the grain of the entire history of physics over the past four hundred years. Generations of physicists have believed that their job was to explain why the universe has to behave the way it does, rather than why most possible universes would behave differently. Nevertheless, in the back of the minds of those physicists who have tried to derive new fundamental laws over the years, the nagging question asked in public by Einstein early in the past century has continued to burn a hole. As he put it, using a religious metaphor: “Did God have any choice in the creation of the Universe?” By posing this question, Einstein in effect wondered whether there might be only one consistent set of laws that could result in a workable universe. Could it be that, if the electron was not 1/2000 of the mass of the proton, or if the electromagnetic force was not forty orders of magnitude stronger than gravity, the logical consistency of whatever underlying theory governs the physical workings of the universe would fall to pieces? Or, could one imagine a plethora of possible universes, each of which had different values for these quantities, and each of which could still form a logical and consistent whole?
If the former is true, a Theory of Everything has teeth. If the latter is true, then physics is ultimately, as John Preskill at Caltech once put it to me, an “environmental science,” with even the fundamental laws of nature being determined by possible “environmental” accidents.

  All of this metaphysical speculation began to take on greater significance in the latter part of the twentieth century as new ideas in physics spawned new ideas in cosmology. For example, once inflationary theory became widely accepted as a wonderful candidate idea to resolve various puzzles in the nature of observational cosmology, it was quickly recognized and stressed by the physicist Andrei Linde—one of the most inventive of the inflationary pioneers—that its principles would in general imply that the entire visible universe is likely to be merely a part of an incredibly complicated “metaverse” of causally disconnected universes. Some of these may be collapsing, others expanding, some may only now be experiencing a big bang expansion, and others may have long ago ended inside of cosmic black holes. The possibility that many different universes might exist even in our mere three-dimensional space became compounded by the possibility that a higher ten-or eleven-dimensional space might settle into one of a virtually uncountable total number of possible ground states. The natural question then becomes: Did a single universe settle into a single ground state, or could it be that there are a host of different universes in a kind of “metaverse,” each of which could settle into a different possible ground-state configuration?