Undergrad Holographic principle in continuous spacetime?

[Suekdccia]

TL;DR

Holographic principle in continuous spacetime?

Can the holographic principle be applied to spacetimes and metrics that are (fundamentally) continuous/smooth? Or only to discrete ones?

 

[OlderWannabeNewton]

The holographic principle applies to smooth spacetimes. It's a conjectured duality between quantum gravity and quantum field theory. You can expand both sides of the duality in G_N and to leading order you have a correspondence between low-energy semi-classical gravity (with smooth spacetimes) and UV complete quantum field theories. This UV/IR correspondence is very explicit in AdS/CFT.

 

[PeterDonis]

Or only to discrete ones?

What do you mean by a "discrete" spacetime? Is that even a coherent concept?

 

[Suekdccia]

What do you mean by a "discrete" spacetime? Is that even a coherent concept?

I was referring to quantized spacetime (where it would not be a continuum)

 

[PeterDonis]

I was referring to quantized spacetime (where it would not be a continuum)

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?

 

[OlderWannabeNewton]

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.

 

[PeterDonis]

canonically quantized quantum gravity, which is the closest thing to a discrete spacetime

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.

 

[Suekdccia]

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?

https://arxiv.org/abs/2209.14282 see section 2.3 in simplicial manifolds


Here https://physics.stackexchange.com/questions/133242/quantum-scales-and-the-flatness-of-space-time theories about quantized space time are also mentioned

 

[Demystifier]

The holographic principle is best understood in AdS/CFT form, and AdS is continuous, ergo ...