At first glance, there is not the slightest doubt: to us, the universe looks three dimensional; however, the “holographic principle” asserts that a mathematical description of the universe actually requires one fewer dimension than it seems. In short, what we perceive as three dimensional may just be the image of two dimensional processes on a huge cosmic horizon.
As astrophysics Brian Koberlein notes, “Tis the season for claims that the universe is a hologram again. Just to be clear, there’s no observational evidence that the universe is a hologram…but there is some interesting theoretical work regarding the holographic principle that is worth discussing.”
He continues by summarizing the research, “This is not a general proof, and it doesn’t show that the holographic principle does work for a flat universe like ours, only that it might when it comes to quantum systems. There’s a lot more work to do before anyone can say with certainty that there is a flat space version of AdS/CFT correspondence. And even then it won’t mean the universe is a hologram.”
Everybody knows holograms from credit cards or banknotes. They are two dimensional, but to us they appear three dimensional. “In 1997, the physicist Juan Maldacena proposed the idea that there is a correspondence between gravitational theories in curved anti-de-sitter spaces on the one hand and quantum field theories in spaces with one fewer dimension on the other”, says Daniel Grumiller (TU Wien). In short, this is about surfaces, not imaginary holograms.
Gravitational phenomena are described in a theory with three spatial dimensions, the behaviour of quantum particles is calculated in a theory with just two spatial dimensions—and the results of both calculations can be mapped onto each other. Such a correspondence is quite surprising. It is like finding out that equations from an astronomy textbook can also be used to repair a CD-player. But this method has proven to be very successful. More than ten thousand scientific papers about Maldacena’s “AdS-CFT-correspondence” have been published to date.
For theoretical physics, this is extremely important, but it does not seem to have much to do with our own universe. Apparently, we do not live in such an anti-de-sitter-space. These spaces have quite peculiar properties. They are negatively curved, any object thrown away on a straight line will eventually return. “Our universe, in contrast, is quite flat—and on astronomical distances, it has positive curvature”, says Daniel Grumiller.
However, Grumiller has suspected for quite some time that a correspondence principle could also hold true for our real universe. To test this hypothesis, gravitational theories have to be constructed, which do not require exotic anti-de-sitter spaces, but live in a flat space. For three years, he and his team at TU Wien (Vienna) have been working on that, in cooperation with the University of Edinburgh, Harvard, IISER Pune, the MIT and the University of Kyoto. Now Grumiller and colleagues from India and Japan have published an article in the journal “Physical Review Letters.”
Koberlein asserts that the paper has shown “that the holographic principle can apply to flat space models, at least in some cases.”
“If quantum gravity in a flat space allows for a holographic description by a standard quantum theory, then there must by physical quantities, which can be calculated in both theories—and the results must agree”, says Grumiller. Especially one key feature of quantum mechanics—quantum entanglement—has to appear in the gravitational theory.
When quantum particles are entangled, they cannot be described individually. They form a single quantum object, even if they are located far apart. There is a measure for the amount of entanglement in a quantum system, called “entropy of entanglement”. Together with Arjun Bagchi, Rudranil Basu and Max Riegler, Daniel Grumiller managed to show that this entropy of entanglement takes the same value in flat quantum gravity and in a low dimension quantum field theory.
“This calculation affirms our assumption that the holographic principle can also be realized in flat spaces. It is evidence for the validity of this correspondence in our universe”, says Max Riegler (TU Wien).
Koberlein clarifies the significance of this find: “What the team found was that a calculation in standard quantum theory of a particular entanglement property dealing with entropy gave the same result when done using a holographic version. In other words, the standard and holographic versions are mathematically equivalent.”
(Source: Techniscience Universitat Wien)