Holographic principle in continuous spacetime?

In summary, the "Holographic principle in continuous spacetime" explores the idea that all the information contained within a volume of space can be represented as a theory on its boundary, suggesting a fundamental relationship between space, information, and gravity. This principle challenges traditional notions of spacetime by proposing that the physical reality we perceive may emerge from lower-dimensional data encoded on the boundaries of our universe. Researchers investigate implications for quantum gravity, black hole thermodynamics, and the nature of reality itself, aiming to unify general relativity with quantum mechanics.
  • #1
Suekdccia
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TL;DR Summary
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?
 
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  • #2
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.
 
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  • #3
Suekdccia said:
Or only to discrete ones?
What do you mean by a "discrete" spacetime? Is that even a coherent concept?
 
  • #4
PeterDonis said:
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)
 
  • #5
Suekdccia said:
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?
 
  • #6
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.
 
  • #7
OlderWannabeNewton said:
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.
 
  • #9
The holographic principle is best understood in AdS/CFT form, and AdS is continuous, ergo ...
 

FAQ: Holographic principle in continuous spacetime?

What is the holographic principle?

The holographic principle is a theoretical concept in physics that suggests that all the information contained within a volume of space can be represented as a theory on the boundary of that space. This idea implies that the three-dimensional world we perceive may be an effective description of a more fundamental two-dimensional reality. It emerged from considerations in black hole thermodynamics and string theory, indicating a deep connection between gravity and quantum mechanics.

How does the holographic principle relate to black holes?

The holographic principle originated from the study of black holes, particularly the observation that the entropy of a black hole, which is a measure of the information content, is proportional to the area of its event horizon rather than its volume. This suggests that the information about the matter that falls into a black hole is encoded on its surface, leading to the idea that our universe may also encode information on its boundaries, rather than within its volume.

What implications does the holographic principle have for spacetime?

The holographic principle challenges our traditional understanding of spacetime by proposing that our usual three-dimensional view may be an emergent property of a more fundamental two-dimensional structure. This has profound implications for theories of quantum gravity and suggests that spacetime itself may not be a fundamental entity but rather a derived concept that arises from more basic, non-spatial degrees of freedom.

Can the holographic principle be tested experimentally?

Testing the holographic principle directly poses significant challenges due to the high-energy scales and complex conditions required. However, researchers are exploring indirect methods, such as studying the behavior of black holes, analyzing cosmological phenomena, and examining quantum entanglement. Advances in experimental techniques and theoretical models may provide insights that could validate or refute aspects of the holographic principle in future studies.

What are the current challenges in understanding the holographic principle?

One of the main challenges in understanding the holographic principle is the lack of a complete and unified theory that incorporates both quantum mechanics and general relativity. Additionally, reconciling the holographic nature of spacetime with our observations of the universe, including the dynamics of gravity and quantum field theories, remains an open question. Researchers are also grappling with the implications of the principle for the nature of reality, information, and causality.

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