Nearly 30 years ago, theoretical physicists introduced the “holographic principle,” a mind-bending theory positing that our three-dimensional universe is actually a hologram. Now physicists are applying that same principle to black holes, arguing in a new paper published in Physical Review X that a black hole’s information is contained within a two-dimensional surface, which is able to reproduce an image of the black hole in three dimensions—just like the holograms we see in everyday life.

Black holes as described by general relativity are simple objects. All you need to describe them mathematically is their mass and their spin, plus their electric charge. So there would be no noticeable change if you threw something into a black hole—nothing that would provide a clue as to what that object might have been. That information is lost.

But problems arise when quantum gravity enters the picture because the rules of quantum mechanics hold that information can never be destroyed. And in quantum mechanics, black holes are incredibly complex objects and thus should contain a great deal of information. As we reported previously, Jacob Bekenstein realized in 1974 that black holes also have a temperature. Stephen Hawking tried to prove him wrong but wound up proving him right instead, concluding that black holes therefore had to produce some kind of thermal radiation.

So black holes must also have entropy—technically, a means of determining how many different ways you can rearrange the atoms of an object and still have it look pretty much the same. Hawking was the first to calculate that entropy. He also introduced the notion of “Hawking radiation”: the black hole will emit a tiny bit of energy, decreasing its mass by a corresponding amount. Over time, the black hole will evaporate. The smaller the black hole, the more quickly it disappears. But what then happens to the information it contained? Is it truly destroyed, thereby violating quantum mechanics, or is it somehow preserved in the Hawking radiation?

The holographic principle emerged from string theory as a proposed solution to this information paradox in the 1990s. It holds that the information about a black hole’s interior could be encoded on its two-dimensional surface area (the “boundary”) rather than within its three-dimensional volume (the “bulk”). As Ars’ John Timmer wrote in 2011:

It’s possible… to figure out how much information has gotten drawn in to the black hole. Once you do that, you can see that the total amount can be related to the surface area of the event horizon, which suggested where the information could be stored. But since the event horizon is a two-dimensional surface, the information couldn’t be stored in regular matter; instead, the event horizon forms a hologram that holds the information as matter passes through it. When that matter passes back out as Hawking radiation, the information is restored. … The price was that the information is “hopelessly scrambled” when you do so.

Leonard Susskind and Gerard ‘t Hooft extended this notion to the entire universe, likening it to
a hologram: our three-dimensional universe in all its glory emerges from a two-dimensional “source code.” Juan Maldacena then discovered a crucial duality (technically known as the AdS/CFT correspondence)—what amounts to a mathematical dictionary that allows physicists to go back and forth between the languages of the two worlds. (Dualities in physics refer to theoretical models that appear to be different but can be shown to describe exactly the same thing. It’s a bit like how ice, water, and vapor are three different phases of the same chemical substance, except a duality looks at the same phenomenon in two different ways that are inversely related.)

“This revolutionary and somewhat counterintuitive principle proposes that the behavior of gravity in a given region of space can alternatively be described in terms of a different system, which lives only along the edge of that region and therefore in one less dimension,” Francesco Benini and Paolo Milan—both affiliated with SISSA in Trieste, Italy—wrote in their new paper. “And, more importantly, in this alternative description gravity does not appear explicitly. In other words, the holographic principle allows us to describe gravity using a language that does not contain gravity, thus avoiding friction with quantum mechanics.”

The debate over the black hole information paradox rages on, and in the meantime, Benini and Milan, among others, have turned their attention to producing a full, explicit explanation of a black hole’s thermodynamic properties. And the holographic principle proved to be a useful mathematical trick for making their calculations more tractable, at least in the case of certain theoretical types of black holes.

Entropy counts the number of ways you can rearrange things, but in a black hole, it’s unclear what is actually being rearranged. Bernini and Milan are suggesting that the answer comes from holography: we can calculate the entropy, not by looking inside the actual black hole but by looking at quantum fields in the dual theory that doesn’t have gravity at all. At least in a certain specific context; it will be interesting to see whether this approach can be extended to more general black holes.

“In this way, [black holes’] mysterious thermodynamic properties have become more understandable: focusing on predicting that these bodies have a great entropy and observing them in terms of quantum mechanics, you can describe them just like a hologram,” the authors wrote. “They have two dimensions, in which gravity disappears, but they reproduce an object in three dimensions.”

Why does it matter? “The result sets up these black holes as ideal toy models for running thought experiments that tackle subtle questions of quantum gravity,” Leopoldo Pando Zayas of the University of Michigan wrote in an accompanying commentary.

Observing quantum gravity?

Benini and Milan acknowledge that this is really just an initial step in the right direction toward a deeper understanding of black holes in hopes of resolving the conflict between general relativity and quantum mechanics with a viable theory of quantum gravity. The groundbreaking detection of gravitational waves by LIGO in 2016 and the extraordinary image of a black hole produced by the Event Horizon Telescope last year are additional hopeful developments.

“In the near future, we may be able to test our theoretical predictions regarding quantum gravity by observation,” they concluded. “And this, from a scientific point of view, would be something absolutely exceptional.”

As for what might come next, “A natural continuation of the work would be to move from mathematical aspects of state counting to deeper questions of black hole dynamics,” Pando Zayas wrote. “If the new microscopic approach can provide an explicit, nuts-and-bolts derivation of the rate of Hawking radiation, it will have answered one of the key questions of black hole dynamics and possibly provided the ultimate resolution of the information paradox.”

DOI: Physical Review X, 2020. 10.1103/PhysRevX.10.021037 (About DOIs).

https://arstechnica.com/?p=1681217