The Holographic Universe: Black Holes, Information, and the Mathematics


The ‘holographic principle,’ the idea that a universe with gravity can be described by a quantum field theory in fewer dimensions, has been used for years as a mathematical tool in strange curved spaces. New results suggest that the holographic principle also holds in flat spaces. Our own universe could in fact be two dimensional and only appear three dimensional — just like a hologram.

I’ve read much of the work surrounding this for years, but in the past few years this notion of the universe as a hologram has become more and more valid with the math that supports it being testable and already offering proofs. The truth of it is yet to be tested empirically, but the mathematical proofs support the feasibility of the empirical testability at some point in the future.

As Science Daily recently reported up until now, this principle has only been studied in exotic spaces with negative curvature. This is interesting from a theoretical point of view, but such spaces are quite different from the space in our own universe. Results obtained by scientists at TU Wien (Vienna) now suggest that the holographic principle even holds in a flat spacetime.

The notion that our visible universe is a projection from a 2 dimensional surface or flat horizon of information seems wild, yet this is what the math is describing. “The fact that we can even talk about quantum information and entropy of entanglement in a theory of gravity is astounding in itself, and would hardly have been imaginable only a few years back. That we are now able to use this as a tool to test the validity of the holographic principle, and that this test works out, is quite remarkable,” says Daniel Grumiller.

Nature reports that in two papers posted on the arXiv repository, Yoshifumi Hyakutake of Ibaraki University in Japan and his colleagues now provide, if not an actual proof, at least compelling evidence that Maldacena’s conjecture is true.

In 1997, theoretical physicist Juan Maldacena proposed1 that an audacious model of the Universe in which gravity arises from infinitesimally thin, vibrating strings could be reinterpreted in terms of well-established physics. The mathematically intricate world of strings, which exist in nine dimensions of space plus one of time, would be merely a hologram: the real action would play out in a simpler, flatter cosmos where there is no gravity.

Maldacena’s idea thrilled physicists because it offered a way to put the popular but still unproven theory of strings on solid footing — and because it solved apparent inconsistencies between quantum physics and Einstein’s theory of gravity. It provided physicists with a mathematical Rosetta stone, a ‘duality’, that allowed them to translate back and forth between the two languages, and solve problems in one model that seemed intractable in the other and vice versa (see ‘Collaborative physics: String theory finds a bench mate’). But although the validity of Maldacena’s ideas has pretty much been taken for granted ever since, a rigorous proof has been elusive.

In one paper, Hyakutake computes the internal energy of a black hole, the position of its event horizon (the boundary between the black hole and the rest of the Universe), its entropy and other properties based on the predictions of string theory as well as the effects of so-called virtual particles that continuously pop into and out of existence (see ‘Astrophysics: Fire in the Hole!‘). In the other, he and his collaborators calculate the internal energy of the corresponding lower-dimensional cosmos with no gravity. The two computer calculations match.

What’s interesting is the notion that information never disappears only the projection that is being played out. The information of which we and the universe are made exists on the outer surface of the universe and remains. So what does this tell us? It can always be retrieved if one had the technology to do so. Leonard Susskind in a youtube film describes the details in a simplified form. We are a projection from the Outside in of an informational hologram being projected into the inner void of the universe – mere images from the stored information surrounding the universal sphere directed internally just like the objects that fall into a Black Hole. His main point is that information never disappears. What he means by that is that the Information is about distinctions, distinctions between things – a hydrogen atom is not an oxygen atom, an oxygen atom is not a hydrogen atom, there are distinctions between these that are fundamental to physics and the universe, and these distinctions never disappear.

This fundamental principle of physics would lead to a decades long battle between Hawking’s and Susskind over their respective principles. Hawking believed all information was lost the moment it entered a black hole, Susskind believed it was retained. So ultimately Susskind won out only as other physicists began to invest mathematics in solving this issue. Out of this the new paradigm of the holographic universe arose out of bringing quantum mechanics and string theory into solving this issue. The great thing that came out of this is that if we know the surface area of an object we can calculate or quantify the amount of information hidden in that object. So that the information contained in a black hole, or even the universe can be quantified. There is a relation between the surface and the information contained in the black hole or universe.

Yet, the big problem now is how to extract that information and reconstruct what is being held. To do that scientists are working on ‘gravity’, for it is gravity that holds the key to the extraction of the information contained. This is a whole new problem.

The Black Hole as this mathematical model details is itself covered by a flat surface of quantum information of all the objects that fall into it. Yet, as Susskind admits the notion of the holographic metaphor is only analogy of the math, and not to be mistaken for the mathematical theorems supporting it. It’s close but we as humans were not made to comprehend the advanced mathematical functions of modern physics of 10 dimensions, etc. So until some better visualization of the data comes along this is what we have:

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