The Hidden Reality_ Parallel Universes and the Deep Laws of the Cosmos - Brian Greene [145]
Which perspective is right? The claim advanced by Susskind and others is that both are. Granted, this is hard to square with ordinary logic—the logic by which you are either alive or not alive. But this is no ordinary situation. Most saliently, the wildly different perspectives can never confront each other. You can’t climb out of the black hole and prove to the distant observer that you are alive. And, as it turns out, the distant observer can’t jump into the black hole and confront you with evidence that you’re not. When I said that the distant observer “sees” you immolated by the black hole’s Hawking radiation, that was a simplification. The distant observer, by closely examining the tired radiation that reaches her, can piece together the story of your fiery demise. But for the information to reach her takes time. And the math shows that by the time she can conclude you’ve burned, she won’t have enough time left to then hop into the black hole and catch up with you before you’re destroyed by the singularity. Perspectives can differ, but physics has a built-in fail-safe against paradoxes.
What about information? From your perspective, all your information, stored in your body and brain and in the laptop you’re holding, passes with you through the black hole’s horizon. From the perspective of the distant observer, all the information you carry is absorbed by the layer of radiation incessantly bubbling just above the horizon. The bits contained in your body, brain, and laptop would be preserved, but would become thoroughly scrambled as they joined, jostled, and intermingled with the sizzling hot horizon. Which means that to the distant observer, the event horizon is a real place, populated by real things that give physical expression to the information symbolically depicted in the chessboard, Figure 9.2.
The conclusion is that the distant observer—us—infers that a black hole’s entropy is determined by the area of its horizon because the horizon is where the entropy is stored. Said that way, it seems utterly sensible. But don’t lose sight of how unexpected it is that the storage capacity isn’t set by the black hole’s volume. And, as we will now see, this result doesn’t merely highlight a peculiar feature of black holes. Black holes don’t just tell us about how black holes store information. Black holes inform us about information storage in any context. This paves a direct path to the holographic perspective.
Beyond Black Holes
Consider any object or collection of objects—the collections of the Library of Congress, all of Google’s computers, the CIA’s archives—situated in some region of space. For ease, imagine that we highlight the region by surrounding it with an imaginary sphere, as in Figure 9.3a. Assume further that the total mass of the objects, compared with the volume they fill, is of such an ordinary run-of-the-mill magnitude that it’s nowhere near what it takes to create a black hole. That’s the setup. Now for the pivotal question: What is the maximum amount of information that can be stored within the region of space?
Figure 9.3 (a) A variety of objects that store information, situated within a well-marked region of space. (b) We augment the region’s capacity for storing information. (c) When the amount of matter crosses a threshold (whose value can be calculated from general relativity),11 the region becomes a black hole.
Those unlikely bedfellows, the Second Law and black holes, provide the answer. Imagine adding matter to the region, with the aim of augmenting its information storage capacity. You might insert high-capacity memory chips or voluminous hard drives into the bank of Google’s computers; you might provide books or jam-packed Kindles to augment the Library of Congress collection. Since even raw matter carries information—Are the steam’s molecules here or there? Are they moving at this speed or that?—you also cram every nook and cranny of the region with as much matter as you can get your hands on. Until you reach a critical juncture. At some point, the