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Does anyone have a simple explanation for this?
The way that it's been explained to me is a matching of degrees of freedom, which came from looking at black holes.
I run the danger of making an ass out of myself in front of experts, but that's never stopped me before. Plus, if they see my mangled description, it may encourage them to step in and correct me, thereby teaching me something :)
You can think of ``entropy'' as ``information'' in some sense---this was pioneering work done by Shannon long ago. Either way, black holes tell you that ``information'' scales as the surface area of some volume, not as the actual volume itself. This is because the entropy of a black hole is proportional to its surface area. Anyway, this gives you some motivation to think about why all of the information about what's inside the black hole should be stored at it's surface, as opposed to the singularity in the middle where (naively) it SHOULD be.
AdS space has a boundary, so you might think you should be looking on that boundary for some information about what's going on inside the AdS space. If you would have had this idea in 1997 you could have a pemanent position at IAS right now. It turns out that if you do some gravity calculations inside the AdS space, you get the exact same result as if you had done the calculations using a very special field theory living on the boundary of that space. In some cases, the gravity calculation is much easier than the field theory calculation, and in some cases it's the other way around.
Either way, this should be very exciting to you, because you have now a tool that actually LINKS gravity (which is a non-renormalizable field theory) with Super(symmetric) Yang Mills theory, which you can treat perturbatively in some cases. (Sometimes you can't treat it perturbatively, too.)
(Patiently awaiting criticism!)
The crucial expression is "It turns out". I think that nobody has been able to provide a SIMPLE explanation of WHY it turns out? And I think THIS is the thing that kurt.physics is looking for.It turns out that if you do some gravity calculations inside the AdS space, you get the exact same result as if you had done the calculations using a very special field theory living on the boundary of that space.
The crucial expression is "It turns out". I think that nobody has been able to provide a SIMPLE explanation of WHY it turns out? And I think THIS is the thing that kurt.physics is looking for.
Every?!?... every quantum gravity theory that I have seen (by accident or by design) reproduces this behavior.
Every?!?
Are you sure about that?
How about quantum gravity without supersymmetry?
More specifically, how about canonical quantum gravity based on the Wheeler-DeWitt equation, or on the loop representation? How about perturbative quantum gravity based on quantization of the Einstein-Hilbert action?
More precisely, they get a relationship between entropy OF THE AREA and surface area, which is a hardly surprising result. The nontrivial achievement of loop quantum gravity is that this entropy is finite (UV divergences are automatically removed without an ad hoc UV cutoff) and that the constant of proportionality is universal (if it is 1/4 for one kind of black hole, then it is also so for any kind of black hole). But it cannot explain why the entropy of the bulk is equal to the entropy of the surface. Instead, it merely uses a classical (not quantum) argument that simply states that the degrees of freedom inside the black hole are not visible to an outside observer.Like Loop Quantum Gravity? :) They DO seem to engineer the constant 1/4, but at least they get a reltionship between entropy and surface area.
Instead, it merely uses a classical (not quantum) argument that simply states that the degrees of freedom inside the black hole are not visible to an outside observer.
Essentially, yes.So then it's exactly Hawking's argument?
Does anyone have a simple explanation for this?
Ah but you are missing half of the point : as Ben mentionned in #3 already, calculations are sometimes simpler in the bulk/gravity and sometimes simpler on the boundary/CFT.AdS/CFT explains gravity as an effect produced by projecting particles and fields from a lower dimensional reality to a higher dimensional one.
Ah but you are missing half of the point : as Ben mentionned in #3 already, calculations are sometimes simpler in the bulk/gravity and sometimes simpler on the boundary/CFT.
So is the symmetry there or is something broken?
Can you clarify this?