Where is the Physical Singularity under the Holographic Principle?

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, using the holographic principle, the observable universe has a 2-sphere boundary. This boundary acts like an event horizon of a Schw black hole.

The question: event horizons are coordinate singularities in GR that enshroud physical singularities. Since the edge of the observable universe is the event horizon, then where is the physical singularity "within" the holographic universe?

• "event horizons are coordinate singularities in GR that enshroud physical singularities." This is not always true. For a simple counterexample, see the event horizon that is approached in Rindler coordinates. Jan 22, 2019 at 14:04
• Perhaps I shouldn't have phrased it that way. The main point is that coordinate singularities come in hand with physical singularities in GR. Of course, just find the right coordinate system to remove the coordinate singularity, but that still leaves the physical singularity. It seems to be that if I calculate the Kretschmann scalar for the metric of the holographic universe then it would not be divergent anywhere....? Also, why the down vote? Jan 22, 2019 at 14:51

One of the major advantages of a picture like that is that it eliminates the singularity, entirely -- all of the dynamics can be described as degrees of freedom on the boundary and you don't have to worry about having quantum mechanics having some sort of principle that saves you from physical singularities. You merely have to deal with smooth theories on smooth boundary manifolds.

This question is strange to me. It's asking "where is the place for the pathological thing in a picture without a clear pathology?"

• Your last sentence makes much sense to me now. I suppose I'm confronting something that's been hammered into me: the event horizon arises because there is a physical singularity in a GR metric. Having a coordinate singularity (event horizon at edge of universe) without a physical singularity seems pathological to me. Jan 22, 2019 at 15:20
• @N.Steinle : why? The rindler metric has a coordinate singularity (that even represents something physical), but is just a coordinate system on Minkowski space. Jan 22, 2019 at 15:27
• And, i would point out that on the boundary, there are no horizons, either. The spacetime is a dynamical theory ON the horizon. You make no reference to the bulk at all. Jan 22, 2019 at 15:28
• Thank you for entertaining my confusion, and for the counterexample. So then there's no big bang singularity, either, in the holographic universe? Jan 23, 2019 at 14:29
• @N.Steinle : I don't know how string theorists deal with the cosmological singularity, because it is not obscured by a horizon, and lives on the physical boundary of the spacetime Jan 23, 2019 at 16:49

It was t’Hooft that came up with the holographic principle well before Bekenstein claimed and Hawking proved that entropy was proportional to area. Quite what this principle was is difficult to determine from the literature since it seems to have gotten buried under many different claims and counter-claims. The main idea seems that certain properties which might seem to be determined by physical dimension, is in fact determined by a dimension lower.

It’s a rather large jump to go from a specific claim like the above to then suppose that volume is ontologically illusionary. It’s the kind of jump all too readily made when large claims about multiverse, landscapes and the like are made without much care for evidence and plausibility and when the main care is for marketing the hype.

It’s not a jump that is at all necessary. For example, results by Causal Dynamical Triangulations, a theory of QG show that at the planck scale dimension becomes 2d. This is in line, in some sense, with t’Hoofts Holographic principle. This does not mean, physically and philosophically speaking, that our 3d macroscopic world has suddenly become illusionary. In fact, far from it.

• This doesn't appear to answer the question, which was "where is the singularity?" Jan 22, 2019 at 14:40
• @probably_someone: If it isn’t clear, I’m saying that the question is ill-formed and I’ll-informed. There’s little point in answering such questions in the terms that they are given. Say for example somebody asked ‘where are the Ogres in the singularity’. What would you say my response should be? Jan 22, 2019 at 14:43
• Then I would recommend explicitly stating what you just said in your answer. Jan 22, 2019 at 14:45
• @probably_someone: I’d rather leave it as it stands. I don’t feel that one explicitly needs to say ‘No’ to see that what I’ve written implicitly says ‘No’. Jan 22, 2019 at 14:50
• To be honest, I'm trying to figure out how to make this question more well-defined. I'm clearly confused by the actual content and the "marketing" rhetoric of the holographic universe. If we're treating the entire universe as a coordinate singularity, then it seems reasonable to suspect there's a physical singularity about, otherwise how is holography more than just a coordinate trick? Jan 22, 2019 at 15:16