The holographic principle applies to smooth spacetimes, establishing a duality between quantum gravity (QG) and quantum field theory (QFT). This principle is particularly evident in the AdS/CFT correspondence, which relates low-energy semi-classical gravity to UV complete quantum field theories. While some discussions suggest the possibility of quantized spacetime, no working model currently exists, and the holographic principle is primarily relevant to continuous spacetimes, especially within the context of string theory.
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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?