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Physics Bleg on the Holographic Principle

John on May 30, 2010 at 12:28 pm

Okay, I don’t do this too often, but sometimes there’s just no substitute for crowd-sourcing, especially for something this arcane.

I’m working on a paper about the realist/anti-realist debate in philosophy and how 20th century developments in physics have impacted the discussion. As often happens when I’m supposed to be working, I began daydreaming and was wondering why, in a 3-dimensional universe, the superscript to Einstein’s famous equation is a 2 instead of a 3. Shouldn’t the relationship have something to do with degrees of freedom? Anyway, a bird chirped and I forgot about it… That was sometime last week.

So today, I’m doing more work on the paper and I come across the holographic principle, which I’d not encountered before in my reading. This is really fascinating to me as it is a unique solution to the inclusion of information in physics, something which Christian physicist John Polkinghorne has discussed in his books. Here’s the gist:

The holographic principle is a property of quantum gravity and string theories which states that the description of a volume of space can be thought of as encoded on a boundary to the region—preferably a light-like boundary like a gravitational horizon. First proposed by Gerard ‘t Hooft, it was given a precise string-theory interpretation by Leonard Susskind.

In a larger and more speculative sense, the theory suggests that the entire universe can be seen as a two-dimensional information structure “painted” on the cosmological horizon, such that the three dimensions we observe are only an effective description at macroscopic scales and at low energies.

[...]

The holographic principle states that the entropy of ordinary mass (not just black holes) is also proportional to surface area and not volume; that volume itself is illusory and the universe is really a hologram which is isomorphic to the information “inscribed” on the surface of its boundary.

So this is my question for any physicists out there who may come across this: Does the superscript in Einstein’s equation lend credence to the holographic principle? Is the “two-dimensional information structure” the reason for this squared relationship between mass and energy? Is there at least speculation in this direction?

Please feel free to talk down to me and thanks in advance for your help.

Update 11/1: The search for the holographic universe continues.

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