The discussion centers on the applicability of the holographic principle to continuous versus discrete spacetimes. Participants explore whether the principle is limited to discrete models or if it can also be applied to smooth, continuous spacetimes, particularly in the context of quantum gravity and quantum field theory.
Participants express differing views on whether the holographic principle is applicable to discrete spacetimes, with no consensus reached on the validity of the concept of discrete spacetime or its implications for the holographic principle.
There are limitations in the discussion regarding the definitions of "discrete" and "quantized" spacetimes, as well as the lack of established models for quantized spacetime. The discussion reflects ongoing uncertainty and exploration of these concepts.
What do you mean by a "discrete" spacetime? Is that even a coherent concept?Suekdccia said:Or only to discrete ones?
I was referring to quantized spacetime (where it would not be a continuum)PeterDonis said:What do you mean by a "discrete" spacetime? Is that even a coherent concept?
Nobody has a working model of "quantized spacetime" so I have no idea what your implied claim in the OP that the holographic principle "works" for "discrete spacetime" is based on. Do you have any references?Suekdccia said:I was referring to quantized spacetime (where it would not be a continuum)
As mentioned, the holographic principle is a conjectured duality between QG and QFT. So it applies to canonically quantized quantum gravity, which is the closest thing to a discrete spacetime. But it's just a conjecture, so it doesn't mean much. The most explicit version of the duality applies to low energy limits of string theory, for which spacetime is continuous.Suekdccia said:I was referring to quantized spacetime (where it would not be a continuum)
Not really. It includes superpositions of different spacetime geometries, and I suppose the spectrum of such geometries could be discrete under certain conditions, but each individual geometry is still a continuous spacetime geometry.OlderWannabeNewton said:canonically quantized quantum gravity, which is the closest thing to a discrete spacetime
https://arxiv.org/abs/2209.14282 see section 2.3 in simplicial manifoldsPeterDonis said:Nobody has a working model of "quantized spacetime" so I have no idea what your implied claim in the OP that the holographic principle "works" for "discrete spacetime" is based on. Do you have any references?