Do theories of quantum gravity require that space-time is a lattice?

In summary, quantum gravity theories suggest that space-time is discrete rather than continuous, as evidenced by black hole thermodynamics, loop quantum gravity, and M-theory. This is supported by the equivalence of continuous and discrete information in information theory and various discussions in physics forums.
  • #1
james.goetz
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Do theories of quantum gravity require that space-time is a lattice instead of a continuum?

I guess this question has been addressed elsewhere, but I would appreciate hearing different points of view. Please dummy down the responses so a philosopher can understand it.
 
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  • #2
James, quantum gravity strongly implies a discrete spacetime. First, look at black hole thermodynamics. Specifically, a region has what is called a Bekenstein bound - a limit to the amount of information a region can contain, a maximum density. Trying to exceed this density will simply result in the growth of the event horizon around this region. Next, look at LQG, which is based purely around a dicrete spacetime, no question there. Finally, M-theroy also implies a discrete spacetime - without getting into detail, it breaks strings down into discrete 'string bits'. I see no possible way that spacetime couldn't be discrete on the Planck scale.
 
  • #3
See IS SPACETIME QUANTIZED here:
http://www.knowledgerush.com/kr/encyclopedia/Spacetime/

A different perspective:
http://arxiv.org/abs/1010.4354

“The equivalence of continuous and discrete information, which is of key importance in information theory, is established by Shannon sampling theory: of any bandlimited signal it suffices to record discrete samples to be able to perfectly reconstruct it everywhere, if the samples are taken at a rate of at least twice the bandlimit. It is known that physical fields on generic curved spaces obey a sampling theorem if they possesses an ultraviolet cutoff.”

Interesting discussions in these forums:

Good discussions here:
https://www.physicsforums.com/showthread.php?t=391989

https://www.physicsforums.com/showthread.php?p=3558771#post3558771
 

1. What is quantum gravity?

Quantum gravity is a field of theoretical physics that aims to reconcile the principles of quantum mechanics, which govern the behavior of subatomic particles, with the principles of general relativity, which describe the behavior of large-scale objects.

2. How does quantum gravity relate to space-time?

Quantum gravity theories attempt to describe the fundamental nature of space-time at the smallest scales. This is in contrast to general relativity, which treats space-time as a smooth, continuous fabric.

3. What is a lattice in the context of quantum gravity?

In quantum gravity, a lattice refers to a discrete, grid-like structure that is used to represent space-time at the smallest scales. This is in contrast to the continuous, smooth fabric of space-time in general relativity.

4. Do all theories of quantum gravity require a lattice structure for space-time?

No, not all theories of quantum gravity require a lattice structure for space-time. Some theories, such as string theory, do not rely on a lattice and instead propose an underlying structure of strings or membranes. Other theories, such as loop quantum gravity, do use a lattice structure.

5. What are the implications of a lattice structure for space-time in quantum gravity?

The use of a lattice structure in quantum gravity theories has implications for the behavior and properties of space-time at the smallest scales. It may also have implications for the quantization of space-time and the resolution of the problem of singularities in black holes.

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