The Hidden Reality_ Parallel Universes and the Deep Laws of the Cosmos - Brian Greene [147]
The Fine Print
That familiar reality may be mirrored, or perhaps even produced, by phenomena taking place on a faraway, lower-dimensional surface ranks among the most unexpected developments in all of theoretical physics. But how confident should we be that the holographic principle is right? We are navigating a realm deep in theoretical territory, and relying almost exclusively on developments that have not been experimentally tested, so there is surely grounds for skepticism. There are many places where the argument could be forced off course. Do black holes really have nonzero entropy and nonzero temperature, and, if so, do the values conform to theoretical predictions? Is the information capacity of a region of space really determined by the amount of information that can be stored on a surface that surrounds it? And on such a surface, is one bit per Planck area really the limit? We think the answer to each of these questions is yes because of the coherent, consistent, and carefully constructed theoretical edifice into which the conclusions perfectly fit. But since none of these ideas has been subject to the experimenter’s scalpel, it is certainly possible (though in my view highly unlikely) that future advances will convince us that one or more of these essential intermediate steps are wrong. That could lay to waste the holographic idea.
Another important point is that throughout the discussion, we’ve spoken of a region of space, of a surface that surrounds it, and of the information content of each. But since our focus has been on entropy and the Second Law—both of which concern themselves primarily with the quantity of information in a given context—we’ve not elaborated on the details of how that information is physically realized or stored. When we talk about information residing on a sphere surrounding a region of space, what does that really mean? How does the information manifest itself? What form does it take? To what extent can we develop an explicit dictionary that translates from phenomena taking place on the boundary to those taking place in the interior?
Physicists have yet to articulate a general framework for addressing these questions. Given that gravity and quantum mechanics are both central to the reasoning, you might expect that string theory would provide a potent context for theoretical explorations. But when ’t Hooft first formulated the holographic concept, he doubted that string theory would be able to advance the subject, noting, “Nature is much more crazy at the Planck scale than even string theorists could have imagined.”13 Less than a decade later, string theory proved ’t Hooft wrong by proving him right. In a landmark paper, a young theorist showed that string theory provides an explicit realization of the holographic principle.
String Theory and Holography
When I was called to the stage at the University of California, Santa Barbara, to give my talk at the annual international string theory conference in 1998, I did something I’d never done before and suspect will never do again. I faced the audience, threw my right hand to my left shoulder and my left to my right shoulder, and then with both hands in succession grabbed the seat of my pants, bunny-hopped, and made a quarter turn, followed, thankfully, by audience laughter, which covered the three remaining steps necessary to reach the podium, where I began my talk. The crowd got the joke. At the banquet the night before, the conference participants had performed a song-and-dance celebrating—as only physicists can—a spectacular result of the Argentinian string theorist Juan Maldacena. With lyrics like “Black holes used to be a great mystery; / Now we use