Mon. Sep 26th, 2022
New research suggests that we can really describe black holes as holograms: they have two dimensions, in which gravity disappears, but they reproduce an object in three dimensions.
enlarge New research suggests that we can really describe black holes as holograms: they have two dimensions, in which gravity disappears, but they reproduce an object in three dimensions.

Gerd Altmann for Pixabay

Nearly 30 years ago, theoretical physicists introduced the “holographic principle,” a mind-boggling theory that holds that our three-dimensional universe is actually a hologram. Now physicists are applying the same principle to black holes, arguing in a new paper published in Physical Review X that a black hole’s information resides in a two-dimensional surface, which is able to create an image of the black hole. reproduce 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 electrical charge. So there wouldn’t be a noticeable change if you threw something into a black hole – nothing that would give a clue as to what that object might be. That information is lost.

But problems arise when quantum gravity comes into the picture, because according to the rules of quantum mechanics, information can never be destroyed. And in quantum mechanics, black holes are incredibly complex objects and so should contain a lot of information. As we reported earlier, Jacob Bekenstein realized in 1974 that black holes also have a temperature. Stephen Hawking tried to prove him wrong, but instead proved him right, concluding that black holes must therefore produce some type of thermal radiation.

So black holes must also have entropy — technically a way of determining how many different ways you can rearrange an object’s atoms and still make it look about the same. Hawking was the first to calculate that entropy. He also introduced the concept of “Hawking radiation”: the black hole emits a small amount of energy, decreasing its mass by a corresponding amount. Over time, the black hole will evaporate. The smaller the black hole, the faster it disappears. But what happens to the information it contains? Was it really destroyed, violating quantum mechanics, or was it somehow preserved in the Hawking radiation?

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

It is possible… to find out how much information has entered the black hole. Once you’ve done that, you can see that the total amount can be related to the area of ​​the event horizon, suggesting where the information might be stored. But since the event horizon is a two-dimensional surface, the information could not be stored in ordinary matter; instead, the event horizon forms a hologram that holds the information as matter passes through it. When that matter goes back out as Hawking radiation, the information is restored. … The price was that the information gets “hopelessly jumbled” if you do that.

Leonard Susskind and Gerard ‘t Hooft extended this concept to the entire universe and compared it to…
a hologram: our three-dimensional universe in all its glory comes from a two-dimensional ‘source code’. Juan Maldacena then discovered a crucial duality (technically known as the AdS/CFT correspondence) – which 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 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, except a duality looks at same phenomenon in two different ways that are inversely related.)

This revolutionary and somewhat counterintuitive principle proposes that the behavior of gravity in one region of space can alternatively be described in terms of another system, living only along the edge of that region and therefore in one dimension less,” Francesco Benini and Paolo Milan – both affiliated with SISSA in Trieste, Italy – wrote in their new paper. “And, more importantly, in this alternate 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, avoiding friction with quantum mechanics.”

Schematic of the so-called AdS/CFT correspondence (the holographic principle) in theoretical physics.
enlarge Schematic of the so-called AdS/CFT correspondence (the holographic principle) in theoretical physics.

APS/Alan Stonebraker

The debate over the black hole’s 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 turned out to be a useful mathematical trick to make their calculations more manageable, 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 suggest the answer comes from holography: we can calculate entropy not by looking into the actual black hole, but by looking at quantum fields in the dual theory that has no gravity at all. At least in some specific context; it will be interesting to see if this approach can be extended to more generalized black holes.

“In this way, [black holes’] mysterious thermodynamic properties have become more comprehensible: by predicting that these bodies have large 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 makes these black holes ideal toy models for conducting thought experiments that address subtle questions of quantum gravity,” wrote Leopoldo Pando Zayas of the University of Michigan in an accompanying commentary.

Observing quantum gravity?

Benini and Milan recognize that this is only a first step towards a deeper understanding of black holes in the hope of resolving the conflict between general relativity and quantum mechanics with a viable theory of quantum gravity. LIGO’s groundbreaking detection of gravitational waves 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 through 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 about black hole dynamics,” Pando Zayas wrote. “If the new microscopic approach can provide an explicit, accurate deduction of the velocity of Hawking radiation, it will have answered one of the most important questions about black hole dynamics and may provide the ultimate solution to the information paradox.”

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

By akfire1

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