Into the Unknown by Kelsey Johnson

Author:Kelsey Johnson [Johnson, Kelsey]
Language: eng
Format: epub
Publisher: Basic Books
Published: 2024-10-15T00:00:00+00:00

Information is lost in topologically nontrivial metrics, like the eternal black hole. On the other hand, information is preserved in topologically trivial metrics. The confusion and paradox arose because people thought classically, in terms of a single topology for spacetime. It was either R4, or a black hole. But the Feynman sum over histories allows it to be both at once. One cannot tell which topology contributed the observation, any more than one can tell which slit the electron went through, in the two slits experiment.20

If black holes both do and do not exist, then we have a loophole for information. I realize that because Hawking said this, many people will be inclined to take it as the gospel truth. To be sure, he was a brilliant human, but even he had to make approximations in these calculations that we need to keep our eyes on.

The next option is the holographic principle (aka anti–de Sitter/conformal field theory correspondence, aka AdS/CFT). Sorry about the jargon, but if you want to crash a physics party, mention “AdS/CFT” at the door, and the host will assume you are a card-carrying member. This principle relies on string theory, which itself can be a bit polarizing in the community (we will talk about string theory in more detail in the chapter on other dimensions). For the record, I am currently inclined toward string theory, but withholding a smidge of confidence if for no other reason than theorists unhindered by actual observations make me uneasy.

Even before the Hawking talk in 2004, AdS/CFT was becoming a crowd favorite for solving the information paradox. There is way too much to unpack here, so I’m going to leave most of it in a suitcase you can choose to open later with a wealth of material online. In brief, AdS/CFT is duality between quantum field theory and general relativity that emerges from string theory and results in a holographic principle—which can encode information on the surface of a black hole.

In brief, the idea is that the full 3D information of an object can be stored on a 2D surface (i.e., a hologram)—this may seem like it ought to be impossible, but you may well have proof of this concept in your pocket right now; many credit cards use holograms, or if you happen to have a $100 bill around, you can check that for holographic behavior, too.

One circumstantial bit of evidence that supports the holographic principle is that theory suggests the entropy of black holes increases as the radius squared. If that behavior doesn’t seem odd at first blush, think about it this way: one might expect the entropy of larger objects to be higher—in other words, one might expect entropy to increase with volume, and volume increases with radius cubed. However, the surface area of an object increases with radius squared—which is the same theoretical behavior of the entropy needed for black holes. This counterintuitive tidbit suggests that there is something special about the surface of the black hole that has to do with entropy.

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