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THE FABRIC of the COSMOS, Brian Greene, 2004
```(annotated and with added bold highlights by Epsilon=One)
```(annotated and with added bold highlights by Epsilon=One)
Chapter 16 - The Future of an Allusion
Is the Universe a Hologram?
A hologram is a two-dimensional piece of etched plastic, which, when illuminated with appropriate laser light, projects a three-dimensional image. (6) In the early 1990s, the Dutch Nobel laureate Gerard 't Hooft and Leonard Susskind, the same physicist who coinvented string theory, suggested that the universe itself might operate in a manner analogous to a hologram. They put forward the startling idea that the comings and goings we observe in the three dimensions of day-to-day life might them-selves be holographic projections of physical processes taking place on a distant, two-dimensional surface. In their new and peculiar-sounding vision, we and everything we do or see would be akin to holographic images. Whereas Plato envisioned common perceptions as revealing a mere shadow of reality, the holographic principle concurs, but turns the metaphor on its head. The shadows—the things that are flattened out and hence live on a lower-dimensional surface—are real, while what seem to be the more richly structured, higher-dimensional entities (us; the world around us) are evanescent projections of the shadows.*
Again, while it is a fantastically strange idea, and one whose role in the final understanding of spacetime is far from clear, 't Hooft and Susskind's so-called holographic principle is well motivated. For, as we discussed in the last section, the maximum entropy that a region of space can contain scales with the area of its surface, not with the volume of its interior. It's natural to guess, then, that the universe's most fundamental ingredients, its most basic degrees of freedom—the entities that can carry the universe's entropy much as the pages of War and Peace carry its entropy—would reside on a bounding surface and not in the universe's interior. What we experience in the "volume" of the universe—in the bulk, as physicists often call it—would be determined by what takes place on the bounding surface, much as what we see in a holographic projection is determined by information encoded on a bounding piece of plastic. The laws of physics would act as the universe's laser, illuminating the real processes of the cosmos—processes taking place on a thin, distant surface—and generating the holographic illusions of daily life.
We have not yet figured out how this holographic principle might be realized in the real world. One challenge is that in conventional descriptions the universe is imagined either to go on forever, or if not, to wrap back on itself like a sphere or a video game screen (as in Chapter 8), and hence it wouldn't have any edges or boundaries. So, where would the supposed "bounding holographic surface" be located? Moreover, physical processes certainly seem to be under our control, right here, deep in the universe's interior. It doesn't seem that something on a hard-to-locate boundary is somehow calling the shots regarding what happens here in the bulk. Does the holographic principle imply that that sense of control and autonomy is illusory? Or is it better to think of holography as articulating a kind of duality in which, on the basis of taste—not of physics—one can choose a familiar description in which the fundamental laws operate here in the bulk (which aligns with intuition and perception) or an unfamiliar description in which fundamental physics takes place on some kind of boundary of the universe, with each viewpoint being equally valid? These are essential questions that remain controversial.
But in 1997, building on earlier insights of a number of string theorists, the Argentinian physicist Juan Maldacena had a breakthrough that dramatically advanced thinking on these matters. His discovery is not directly relevant to the question of holography's role in our real universe, but in the time-honored fashion of physics, he found a hypothetical context—a hypothetical universe—in which abstract musings on holography could be made both concrete and precise using mathematics. For technical reasons, Maldacena studied a hypothetical universe with four large space dimensions and one time dimension that have uniform negative curvature—a higher dimensional version of the Pringle's potato chip, Figure 8.6c. Standard mathematical analysis reveals that this five-dimensional spacetime has a boundary (7) that, like all boundaries, has one dimension less than the shape it bounds: three space dimensions and one time dimension. (As always, higher-dimensional spaces are hard to envision, so if you want a mental picture, think of a can of tomato soup—the three-dimensional liquid soup is analogous to the five-dimensional space-time, while the two-dimensional surface of the can is analogous to the four-dimensional spacetime boundary.) After including additional curled-up dimensions as required by string theory, Maldacena convincingly argued that the physics witnessed by an observer living within this universe (an observer in the "soup") could be completely described in terms of physics taking place on the universe's boundary (physics on the surface of the can).
Although it is not realistic, this work provided the first concrete and mathematically tractable example in which the holographic principle was explicitly realized. (8) In doing so, it shed much light on the notion of holography as applied to an entire universe. For instance, in Maldacena's work, the bulk description and the boundary description are on an
absolutely equal footing. One is not primary and the other secondary. In much the same spirit as the relation between the five string theories, the bulk and boundary theories are translations of each other. The unusual feature of this particular translation, though, is that the bulk theory has more dimensions than the equivalent theory formulated on the boundary. Moreover, whereas the bulk theory includei gravity (since Maldacena formulated it using string theory), calculations show that the boundary theory doesn't. Nevertheless, any question asked or calculation done in one of the theories can be translated into an equivalent question or calculation in the other. While someone unfamiliar with the dictionary would think that the corresponding questions and calculations have absolutely nothing to do with each other (for example, since the boundary theory does not include gravity, questions involving gravity in the bulk theory are translated into very-different-sounding, gravity-less questions in the boundary theory), someone well versed in both languages—an expert on both theories—would recognize their relationship and realize that the answers to corresponding questions and the results of corresponding calculations must agree. Indeed, every calculation done to date, and there have been many, supports this assertion.
The details of all this are challenging to grasp fully, but don't let that obscure the main point. Maldacena's result is amazing. He found a con-crete, albeit hypothetical, realization of holography within string theory. He showed that a particular quantum theory without gravity is a translation of—is indistinguishable from—another quantum theory that includes gravity but is formulated with one more space dimension. Vigorous research programs are under way to determine how these insights might apply to a more realistic universe, our universe, but progress is slow as the analysis is fraught with technical hurdles. (Maldacena chose the particular hypothetical example he did because it proved relatively easy to analyze mathematically; more realistic examples are much harder to deal with.) Nevertheless, we now know that string theory, at least in certain contexts, has the capacity to support the concept of holography. And, as with the case of geometric translations described earlier, this provides yet another hint that spacetime is not fundamental. Not only can the size and shape of spacetime change in translation from one formulation of a theory to another, equivalent form, but the number of space dimensions can change, too.
More and more, these clues point toward the conclusion that the form of spacetime is an adorning detail that varies from one formulation of a physical theory to the next, rather than being a fundamental element of reality. Much as the number of letters, syllables, and vowels in the word cat differ from those in [/I]gato, its Spanish translation, the form of space-time—its shape, its size, and even the number of its dimensions—also changes in translation. To any given observer who is using one theory to think about the universe, spacetime may seem real and indispensable. But should that observer change the formulation of the theory he or she uses to an equivalent, translated version, what once seemed real and indispensable necessarily changes, too. Thus, if these ideas are right—and I should emphasize that they have yet to be rigorously proven even though theorists have amassed a great deal of supporting evidence—they strongly challenge the primacy of space and time.
Of all the clues discussed here, I'd pick the holographic principle as the one most likely to play a dominant role in future research. It emerges from a basic feature of black holes—their entropy—the understanding of which, many physicists agree, rests on firm theoretical foundations. Even if the details of our theories should change, we expect that any sensible description of gravity will allow for black holes, and hence the entropy bounds driving this discussion will persist and holography will apply. That string theory naturally incorporates the holographic principle—at least in examples amenable to mathematical analysis—is another strong piece of evidence suggesting the principle's validity. I expect that regardless of where the search for the foundations of space and time may take us, regardless of modifications to string/M-theory that may be waiting for us around the bend, holography will continue to be a guiding concept.
Again, while it is a fantastically strange idea, and one whose role in the final understanding of spacetime is far from clear, 't Hooft and Susskind's so-called holographic principle is well motivated. For, as we discussed in the last section, the maximum entropy that a region of space can contain scales with the area of its surface, not with the volume of its interior. It's natural to guess, then, that the universe's most fundamental ingredients, its most basic degrees of freedom—the entities that can carry the universe's entropy much as the pages of War and Peace carry its entropy—would reside on a bounding surface and not in the universe's interior. What we experience in the "volume" of the universe—in the bulk, as physicists often call it—would be determined by what takes place on the bounding surface, much as what we see in a holographic projection is determined by information encoded on a bounding piece of plastic. The laws of physics would act as the universe's laser, illuminating the real processes of the cosmos—processes taking place on a thin, distant surface—and generating the holographic illusions of daily life.
We have not yet figured out how this holographic principle might be realized in the real world. One challenge is that in conventional descriptions the universe is imagined either to go on forever, or if not, to wrap back on itself like a sphere or a video game screen (as in Chapter 8), and hence it wouldn't have any edges or boundaries. So, where would the supposed "bounding holographic surface" be located? Moreover, physical processes certainly seem to be under our control, right here, deep in the universe's interior. It doesn't seem that something on a hard-to-locate boundary is somehow calling the shots regarding what happens here in the bulk. Does the holographic principle imply that that sense of control and autonomy is illusory? Or is it better to think of holography as articulating a kind of duality in which, on the basis of taste—not of physics—one can choose a familiar description in which the fundamental laws operate here in the bulk (which aligns with intuition and perception) or an unfamiliar description in which fundamental physics takes place on some kind of boundary of the universe, with each viewpoint being equally valid? These are essential questions that remain controversial.
But in 1997, building on earlier insights of a number of string theorists, the Argentinian physicist Juan Maldacena had a breakthrough that dramatically advanced thinking on these matters. His discovery is not directly relevant to the question of holography's role in our real universe, but in the time-honored fashion of physics, he found a hypothetical context—a hypothetical universe—in which abstract musings on holography could be made both concrete and precise using mathematics. For technical reasons, Maldacena studied a hypothetical universe with four large space dimensions and one time dimension that have uniform negative curvature—a higher dimensional version of the Pringle's potato chip, Figure 8.6c. Standard mathematical analysis reveals that this five-dimensional spacetime has a boundary (7) that, like all boundaries, has one dimension less than the shape it bounds: three space dimensions and one time dimension. (As always, higher-dimensional spaces are hard to envision, so if you want a mental picture, think of a can of tomato soup—the three-dimensional liquid soup is analogous to the five-dimensional space-time, while the two-dimensional surface of the can is analogous to the four-dimensional spacetime boundary.) After including additional curled-up dimensions as required by string theory, Maldacena convincingly argued that the physics witnessed by an observer living within this universe (an observer in the "soup") could be completely described in terms of physics taking place on the universe's boundary (physics on the surface of the can).
Although it is not realistic, this work provided the first concrete and mathematically tractable example in which the holographic principle was explicitly realized. (8) In doing so, it shed much light on the notion of holography as applied to an entire universe. For instance, in Maldacena's work, the bulk description and the boundary description are on an
absolutely equal footing. One is not primary and the other secondary. In much the same spirit as the relation between the five string theories, the bulk and boundary theories are translations of each other. The unusual feature of this particular translation, though, is that the bulk theory has more dimensions than the equivalent theory formulated on the boundary. Moreover, whereas the bulk theory includei gravity (since Maldacena formulated it using string theory), calculations show that the boundary theory doesn't. Nevertheless, any question asked or calculation done in one of the theories can be translated into an equivalent question or calculation in the other. While someone unfamiliar with the dictionary would think that the corresponding questions and calculations have absolutely nothing to do with each other (for example, since the boundary theory does not include gravity, questions involving gravity in the bulk theory are translated into very-different-sounding, gravity-less questions in the boundary theory), someone well versed in both languages—an expert on both theories—would recognize their relationship and realize that the answers to corresponding questions and the results of corresponding calculations must agree. Indeed, every calculation done to date, and there have been many, supports this assertion.
The details of all this are challenging to grasp fully, but don't let that obscure the main point. Maldacena's result is amazing. He found a con-crete, albeit hypothetical, realization of holography within string theory. He showed that a particular quantum theory without gravity is a translation of—is indistinguishable from—another quantum theory that includes gravity but is formulated with one more space dimension. Vigorous research programs are under way to determine how these insights might apply to a more realistic universe, our universe, but progress is slow as the analysis is fraught with technical hurdles. (Maldacena chose the particular hypothetical example he did because it proved relatively easy to analyze mathematically; more realistic examples are much harder to deal with.) Nevertheless, we now know that string theory, at least in certain contexts, has the capacity to support the concept of holography. And, as with the case of geometric translations described earlier, this provides yet another hint that spacetime is not fundamental. Not only can the size and shape of spacetime change in translation from one formulation of a theory to another, equivalent form, but the number of space dimensions can change, too.
More and more, these clues point toward the conclusion that the form of spacetime is an adorning detail that varies from one formulation of a physical theory to the next, rather than being a fundamental element of reality. Much as the number of letters, syllables, and vowels in the word cat differ from those in [/I]gato, its Spanish translation, the form of space-time—its shape, its size, and even the number of its dimensions—also changes in translation. To any given observer who is using one theory to think about the universe, spacetime may seem real and indispensable. But should that observer change the formulation of the theory he or she uses to an equivalent, translated version, what once seemed real and indispensable necessarily changes, too. Thus, if these ideas are right—and I should emphasize that they have yet to be rigorously proven even though theorists have amassed a great deal of supporting evidence—they strongly challenge the primacy of space and time.
Of all the clues discussed here, I'd pick the holographic principle as the one most likely to play a dominant role in future research. It emerges from a basic feature of black holes—their entropy—the understanding of which, many physicists agree, rests on firm theoretical foundations. Even if the details of our theories should change, we expect that any sensible description of gravity will allow for black holes, and hence the entropy bounds driving this discussion will persist and holography will apply. That string theory naturally incorporates the holographic principle—at least in examples amenable to mathematical analysis—is another strong piece of evidence suggesting the principle's validity. I expect that regardless of where the search for the foundations of space and time may take us, regardless of modifications to string/M-theory that may be waiting for us around the bend, holography will continue to be a guiding concept.
*If you're reluctant to rewrite Plato, the braneworld scenario gives a version of holography in which shadows are put back in their proper place. Imagine that we live on a threebrane that surrounds a region with four space dimensions (much as the two-dimensional skin of an apple surrounds the apple's three-dimensional interior). The holographic principle in this setting would say that our three-dimensional perceptions would be the shadows of four-dimensional physics taking place in the region surrounded by our brane.