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

  For the most part, except for a cadre of philosophically minded theorists, no one much worried about this issue for a long time. Physicists are trained to calculate things from first principles, and moreover the remarkable successes of particle physics in the 1970s had demonstrated that it should be possible to explain all of the observed phenomena at subatomic scales using three simple and elegant theories. It is true that in order for objects such as stars to operate and to be able to cook light elements such as hydrogen and helium into heavier elements such as carbon, oxygen, nitrogen, and all the other substances so vital to life on Earth, some remarkable coincidences seemed to be required at the level of nuclear physics. But, coincidences happen all the time, and indeed without knowing all of the spectra of possibilities, the fact that the observed route to stellar burning seemed to depend on some numerical fine-tuning was not particularly extraordinary, even if some intrepid speculators did write articles and books on the subject.

  Then along came dark energy. Suddenly there was a parameter in nature that was so strange that no sensible explanation of its existence seemed within sight. Physicists began to explore possibilities that had otherwise seemed perhaps too distasteful, and Weinberg and his collaborators asked themselves the question: If there are possibly an infinite number of different universes, and if each universe could have a different value of the energy of empty space, what value might we expect to measure in a universe full of stars and galaxies that is over ten billion years old?

  The somewhat surprising answer to this question is that one would expect, without knowing the details of what might be the a priori probability of having a universe with a given vacuum energy, that a universe in which galaxies could form after billions of years and astronomers could measure their properties would seem to require that this energy not be much larger than about five to ten times the vacuum energy we currently infer. Given that naive estimates based on quantum mechanics and relativity would suggest a value that is 10120 times larger, the anthropic argument provides an estimate that is far closer to the value we apparently live with in our universe.

  At present, it is fair to say that this anthropic “explanation” of a vacuum energy that is comparable to the value we actually measure is one of the few viable proposals on the table. Having said that, however, it is important to realize that at this stage it is virtually impossible to know if this explanation really is an explanation at all. For example, while Weinberg and company did a calculation to show that if the vacuum energy alone were freely varying among all possible universes, one might expect a value comparable to what we see in our universe. Without a fundamental theory that tells us which fundamental free parameters are variable, and which are fixed by fundamental laws, it is hard to know how seriously to take this simple first guess.

  This, ultimately, is the fundamental problem in my mind with anthropic arguments. They may seem suggestive, but without a fundamental theory they can never be more than this. Indeed, as I have said on at least one public occasion, the anthropic principle is something that physicists play around with when they don’t have any fundamental theory to work with, and they drop it like a hot potato if they find one. Nevertheless, while my own biases about this notion are clear, it is fair to say that the moment one recognizes the possibility that multiple separated universes might exist, due either to separate inflationary phases in an otherwise infinite volume, or to the existence of higher dimensions, an anthropic explanation of fundamental parameters in our universe becomes at least a reasonable logical possibility. It is for this reason that a variety of sensible and distinguished individuals had begun to advocate this idea, and why it is at least worth examining further, even before string theory adds its two cents.

  This finally brings us back to M-theory. Faced with the prospect that this theory may ultimately predict a virtually uncountable set of possible universes, some string theorists did a 180-degree about-face. Instead of heralding a unique Theory of Everything that could produce calculable predictions, they are now resorting to what even a decade ago they may have called the last refuge of scoundrels.

  But, when string theorists take a position, they do it with flair. In attempting to graphically explore the different ground states of a subset of the set of all string vacua, some theorists realized that the diagrams looked like complicated landscapes, with billions and billions of sharp mountains and deep valleys. Physicists Joe Polchinski, Raphael Bousso, and Leonard Susskind felt that the images were so striking that they capitalized on the description, and invented what they called “the landscape.”

  You can guess the argument by now. String theory/M-theory predicts more than 10100 possible configurations in which a three-dimensional universe might arise from a higher-dimensional framework (even though no one quite knows how many dimensions are truly fundamental). So, among all these vacua there are likely to be some with extremely small values for the vacuum energy, comparable in fact to what we measure today. These would be anything but generic universes, and would certainly not be what an otherwise unbiased observer would predict to find in a random universe. But, perhaps there are no unbiased observers! If observers like ourselves can exist only in universes that have at most an extremely small cosmological constant, then as long as the M-theory landscape provides that possibility somewhere, then that is where we will find ourselves. What is perhaps most amazing about this is the degree to which this new reliance on postdiction is being adopted in parts of the community. In the end, it may be correct. It may be that string theory cannot predict from first principles a parameter as fundamental as the ground state energy of our universe. It may merely be an environmental accident, after all. Still, this is a far cry from the excitement about a Theory of Everything raised twenty years ago during the first flush of enthusiasm associated with string theory, extra dimensions, and the new potential for unifying quantum mechanics and general relativity. Indeed, after the incredible journey of physics during the past century, after all the remarkable discoveries, theoretical and experimental, discussed in this book, this proposal seems rather like an anticlimax. As Edward Witten has commented, politely, about this approach: “I’d be happy if it is not right. I would be happy to have a more unique understanding of the universe.”

  His point is well taken. A cynical individual might suggest that some string theorists have embraced landscapes because since the theory cannot apparently predict anything anyway, it is gratifying to find a quantity that reinforces the notion that ultimately no fundamental constant in our universe is predictable. Nevertheless, as Witten’s remark underscores, if the landscape turns out to be the main physical implication of the grand edifice of string theory or M-theory, then instead of precise predictions about why the observable universe of three large and expanding spatial dimensions must be the way it is, we might be left with the mere suggestion that anything goes. What was touted twenty years ago as a Theory of Everything would then instead have turned quite literally into a Theory of Nothing. But the good news is that we don’t yet know. The more we explore the ideas of string theory, M-theory, and Braneworlds, the more it becomes clear that we understand far less than we thought about what might be possible in nature. Even the fundamental concepts of strings and dimensions—which lay at the heart of the original 1984 revolution—may now be beginning to melt away.

  Will whatever physical theory results in the aftermath of all this, following whatever discoveries are made by experimentalists in the coming decades and by theorists in the coming centuries, resemble any of the speculative, if beautiful, mathematical notions at the heart of the current focus of research? That, I believe, is anyone’s guess. I have recently discussed this question with two active string theorists, John Schwarz and Nati Seiberg, and perhaps not surprisingly both still feel that the mathematical insights already gleaned from string theory are so powerful that whatever ultimate theory we may derive for the workings of nature at fundamental scales, it will contain at least the germ of present string theory ideas. I admi
t that, during the course of thinking about these issues as I have written this book, I myself have run hot and cold. There have been moments when the remarkable depth of the mathematical insights being explored in the course of recent years has left me awed, and there have been times when the sheer hubris of the claims, and the lack of associated results has left me shaking my head in disbelief. But I want to make it clear that while I think it is certainly possible and, given historical perspective, perhaps even likely that all of the formalism currently being explored is a mere house of cards, and that it might tumble as soon as the force of some new experiment or observation overwhelms it, this does not mean the effort is not worthwhile. If the joy of the search exceeds the pleasure of the finding, then we continue to be joyfully engaged in an intellectual struggle that shows no signs of ending and in which hidden universes have always been a part. To make progress in our attempt to understand the universe at its most fundamental level, we need to fearlessly open up new paths into otherwise unexplored places, and we must not be afraid of wrong turns and dead ends, even if, like the ether squirts of the nineteenth century, that is what ideas such as grand unification or string theory ultimately turn out to be. No doubt we are hardwired to believe that the universe of our experience cannot be all that there is. This would certainly explain the persistence of religious faith in an apparently unfair world of toil and struggle without obvious purpose. Perhaps that, too, is why we keep returning to the notion that just beyond our reach, just behind the mirror, lies the key to knowledge.

  But even if in the end this longstanding pursuit of extra dimensions proves to have been a grand illusion, generations of dreamers have been inspired by it to keep on dreaming, and generations of seekers to keep on seeking. We have learned and will in the process continue to learn more about nature and our own place within the cosmos. And I believe one could make a good argument that such efforts make life worthwhile. For those who may be less romantic, there is another plus. In our continued and possibly flawed search for hidden universes and extra dimensions, we are certain to stumble upon unexpected and undoubtedly unrelated natural wonders that are currently beyond our wildest imagination, and that may have a direct impact upon our own future. If the past is any guide, one thing seems certain: The universe always seems to come up with new ways of surprising us.

  E P I L O G U E

  TRUTH AND BEAUTY

  In . . . Philosophical Theories as well as in persons, success discloses faults and infirmities which failure might have concealed from obser- vation.

  —John Stuart Mill, On Liberty

  On January 30, 1991, the physicist John Bardeen died. An obituary appeared in various major papers around the country, but most people then, like most people now, would hardly recognize the name—in spite of the fact that it is arguable that Bardeen changed the face of the twentieth century as much as any other scientist of his era. He was the only physicist ever to win two Nobel Prizes in physics. The first was for the invention of the transistor, which, as I have mentioned already, is at the very basis of almost all of modern technology. The second was for the explanation of superconductivity, the remarkable property of some materials to allow currents to flow without resistance of any kind below a certain temperature, a phenomenon whose technological impact will most surely grow in this century.

  Yet, even among lay people with an interest in science, I would venture to suggest that there is more interest in string theory than superconductivity, in spite of the fact that the former has yet to have any clear impact on our understanding of the physical universe, much less our daily lives. This is not meant to be judgmental. Rather, it simply reflects something that I think is deeply ingrained in the human psyche. “Space” and “time” are among the very first concepts that are framed as our own consciousness emerges shortly after the fog of birth. So it is not surprising that considerations of the ultimate nature of space and time may continue to appear more interesting than the things that merely happen within space and time.

  I began this book wondering about what drove an ancient ancestor to leave an imprint of his or her child’s hand on a cave wall. I suggested that it was to create a measure of permanence, something that might live on, as it in fact did, long after the participants in this artistic enterprise were gone. Time is our ultimate enemy, and to conquer time means first trying to understand it. Time is a subtler concept than one might imagine. Both future and past are not directly experienced, but must be intellectualized. Space, on the other hand, while immediate and visceral, nevertheless taunts us with its mysteries every time we do something as simple as gazing out at the horizon. Recall that for early European sailors the horizon represented the end of a world that we now know has no end. If we can be so easily fooled here on Earth, what do the more exotic mysteries that lie out in the darkness of the night sky hold for us?

  Yet recall that I also ended the first chapter of this book with a warning from the famous French chemist Antoine Lavoisier about guarding against flights of the imagination regarding things one can neither see nor feel. His warning, of course, continues to go unheeded. Indeed, this book pays homage to the history of the remarkably constant human impetus, both scientific and artistic, to first imagine and then explore the reality that exists beyond our direct sensory experience. Nevertheless, in spite of all the excitement regarding the possible existence of extra dimensions, I confess yet again to being an agnostic. Perhaps it is more appropriate to call myself a skeptic. This position sometimes gets me into trouble, especially in public debates, but I am nevertheless proud to be part of a noble tradition in science. I earlier referred to Richard Feynman’s statement that science is “imagination in a strait-jacket.” Most good ideas are wrong, in that nature does not choose to exploit them. If that were not the case, doing science would be far easier. I do remain fascinated with the myriad possibilities for new and hidden realities afforded by extra dimensions, but I try to temper my enthusiasm with the realization that, like Fox Mulder, I “want to believe.” Large, hidden extra dimensions are seductive, and I wish that they were true in the same sense that I wish I could use a warp drive to travel to distant stars, to go where no man or woman has gone before. We may indeed be on the threshold of discoveries that will truly change everything, that will further inspire a generation of artists and writers, and vindicate once again the wildest imaginings of science fiction writers. But there is no evidence at this time that any such imminent breakthrough is likely or inevitable. There are beautiful theoretical arguments that are strongly seductive, as I have tried to describe, but there were beautiful theoretical arguments in 1970 that were also strongly suggestive—but also wrong—that string theory might provide a fundamental theory of the strong interaction. Equally beautiful theoretical arguments prompted Kaluza and Klein to make their bold proposals, but we now understand those elegant concepts were introduced before their proper time. Kaluza and Klein could never have known that the theory they were exploring was missing key features of reality, including two of the strongest forces in nature. Perhaps we are in the same boat today.

  Today’s confused and tentative explorations of possibly infinite extra dimensions and infinite landscapes of extra-dimensional worlds must be seen as simply the most recent expression of a longstanding scientific and cultural tradition. One can marvel, for example, at the remarkable resemblance between the claim that elementary charges in our space are merely the ends of fundamental strings that may stretch out into higher dimensions, and the nineteenth-century claim that these charges were “ether squirts”—places where a four-dimensional ether flowed into our threedimensional world. Such eerie resemblances imply neither that current science is pure fiction, nor that the ill-founded speculations of the 1870s bore some hidden truth. To make such arguments would be just as misplaced a notion as subscribing to the claims that a resemblance between ancient Eastern mystical writings and some of the tenets of quantum mechanics implies the ancient writers had any idea of even what hydrogen was, much less
how to calculate the spectrum of light emitted by it. Similarly, it has been stated many times since 1984 that the remarkable discovery of string theory in the 1970s and its rediscovery in the 1980s was a unique situation in the history of physics: We were living in the twentieth century, having accidentally discovered the physics of the twenty-first or twenty-second century. That could, in fact, be true. But we have no proof that it is or was. It is just as likely to be true that we are instead reliving the delusional enthusiasm for the extra dimensions of the nineteenth century. That is also cause for neither despair nor hope, in my opinion. It is simply an inevitable product of living in confusing times. But being confused is cause for hope. Perhaps there is no state more desired by theoretical physicists than being confused, for it is confusion that compels us to seek out new knowledge and the opportunities for breakthroughs.

  As we thus celebrate the remarkable ideas that have emerged from the solid scientific progress of the past century, we must be careful to keep things in perspective. I can think of no better way to do this than to relate the intertwined discussions of three of the most accomplished theoretical physicists of my own generation: David Gross, Frank Wilczek, and Edward Witten. All three have played important roles in the stories related in the preceding pages.