Current status of Tom Banks' Holographic space time?

[AAAdrian]

Interested in Banks' HST these days,
for discussion,here are some abstract and an email from L.Smolin.

Many thanks for writing. FIrst, let me say that I am a huge fan of Tom B, and read and think about many of his papers. My own impression is that he greatly weakens the power and influence of his thought by hiding his pretty radical ideas in the
language of adS/CFT tc, which is incapable of fully expressing them. Same thing for Willy F. At least the importance of Ted Jacobson's work has gotten through to them.
As for their Holographic Spacetime, I like the idea, but my understanding is it is essentialy the model of quantum spacetime that Fotini Mrkopoulou proposed some years earlier under the name of quantum causal histories. In my opinion that was too bad because thy could make good use of the further work by her on coarse graining and RG based on Cremmer-Cohen's ideas and Heyting algebras.

A recent conclusive paper as well https://arxiv.org/abs/2201.06988

The formalism of Holographic Space-time (HST) is a translation of the principles of Lorentzian geometry into the language of quantum information. Intervals along time-like trajectories, and their associated causal diamonds, completely characterize a Lorentzian geometry. The Bekenstein-Hawking-Gibbons-'t Hooft-Jacobson-Fischler-Susskind-Bousso Covariant Entropy Principle, equates the logarithm of the dimension of the Hilbert space associated with a diamond to one quarter of the area of the diamond's holographic screen, measured in Planck units. The most convincing argument for this principle is Jacobson's derivation of Einstein's equations as the hydrodynamic expression of this entropy law. In that context, the null energy condition (NEC) is seen to be the analog of the local law of entropy increase.
I'd like to know what the community's ideas are on the basic principles and viability of HST,and also as Smolin has pointed out,the implications of Jacobson's work and the correlations with HST.

 

[AAAdrian]

implications of Jacobson's work and the correlations

For this you might want to see this thread ,and its mentioned paper.

 

[mitchell porter]

HST is an isolated research program. The only people working on it are Banks and Fischler and a few recent collaborators. This is not that unusual for theoretical physics - there are plenty of people, including even Nobel Prize winners, who become a one-person school of thought, publishing a series of papers exploring some hypothesis that others just do not take up.

Perhaps I should emphasize that HST is not the only theory with a holographic approach to space-time! "AdS/CFT" and "celestial holography" have probably the best foundations. Then there are also results like the Bekenstein bound and the Bousso bound which are supposed to apply in regions of space-time. The search for a holographic theory of quantum gravity is in part, an attempt to identify a theory in which these bounds are somehow ubiquitously built into its foundations. The main stumbling block has been de Sitter space (although spatially closed universes in general, are also a challenge). There is no real consensus on how holography in de Sitter space works.

HST is characterized by a specific set of technical hypotheses about quantum gravity. For example, you will here Banks talking a lot about causal diamonds.

A causal diamond consists of an expanding light cone, and then a contracting light cone. The point is that any local causal connection between the bottom point and the top point, must be mediated by events within the causal diamond. That much is just basic relativity. In quantum field theory, it can be expressed as a statement about commutation relations among observables, inside and outside the light cone.

HST wants to go further and build a holographic theory in terms of causal diamonds. This is where the technical hypotheses enter. There are hypotheses for how the quantum theory works inside an individual causal diamond - for example, the Bousso bound on the entropy within the diamond, in HST corresponds to a bound on the dimension of the Hilbert space required to describe events in the diamond's interior - and there are also hypotheses for how the Hilbert spaces of nested or overlapping causal diamonds should be related.

You could say that the reason for the limited interest in HST is a mix of (1) the specific axiomatic hypotheses that are supposed to define HST (2) the lack of concrete mathematical examples satisfying these hypotheses (3) the extent to which Banks in particular says that HST implies various things, apparently on the basis of obscure personal intuitions about what the theory should say.

If you could ask people like Strominger or Vafa or Susskind for their opinions of HST, presumably you would get a more technical assessment. They might say something like, I just don't agree with this particular postulate of HST, that's not how the operator algebras in quantum gravity should work, and then they could tell you how *they* think it works. But the previous paragraph sums up my impression of the gap between HST and other schools of thought.

In his email to you, Lee Smolin mentions Fotini Markopoulou's formalism of causal quantum histories (CQH). From what I recall, that's basically a partially ordered set of Hilbert spaces, with the partial order meant to represent the causal order in a Lorentzian space. It may actually be true that HST formalism is a CQH formalism with a lot of extra structure.

Also, you ask about the relation to Ted Jacobson's thermodynamic approach to gravity. That's a good question, and in fact I think the attitude to Jacobson's result is a good test of a quantum-gravity school of thought, because (unlike HST, which I suspect is too specific of a hypothesis), I think Jacobson's result probably *is* necessarily part of any theory of gravity that has a chance of being correct. I may get back you on this topic, when I have something to say about it. :-)