Quantum gravity and the geometry of space

Overall, the geometry of space plays a crucial role in the challenges faced by quantum gravity. In summary, the conversation discusses the relationship between abstract geometry, quantum gravity, and the behavior of space-time. It suggests that if space was more easily mappable as a 3D graph with unit interval spacing, many of the problems in quantum gravity would be simplified. However, the fact that this is not the case leads to the need to consider perturbation, renormalization, and degrees of freedom in understanding space-time behavior. The geometry of space is a key factor in the challenges faced by quantum gravity.
  • #1
Bach33
12
4

Homework Statement


This is more of a general question around quantum gravity and abstract geometry: It seems to me that if the geometry of space happened to be more conveniently mappable as a 3D graph, or network, with unit interval spacing between all adjacent points, then most of the problems that quantum gravity aims to solve would be very straightforward.


Homework Equations


I am wondering to what extent it is because a "quantum interval network" is not the geometry of space (the basic space-filling problem), that it is necessary in quantum gravity to consider e.g. perturbation, renormalization, and degrees of freedom etc?


The Attempt at a Solution

 
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  • #2
My initial thought is that because a quantum interval network is not the geometry of space, it is necessary to consider perturbation and renormalization in quantum gravity in order to understand the behavior of space-time. Additionally, in the case of a quantum interval network, there are degrees of freedom which need to be taken into account when considering the behavior of space-time.
 

FAQ: Quantum gravity and the geometry of space

What is quantum gravity?

Quantum gravity is a theory that aims to unify the principles of quantum mechanics and general relativity, which are currently our two best theories for understanding the behavior of matter and the structure of the universe at small and large scales, respectively.

How does quantum gravity relate to the geometry of space?

In quantum gravity, space is viewed as a dynamic and fluctuating entity, rather than a fixed and continuous background as in classical physics. The theory suggests that space and time are not fundamental, but rather emerge from more basic quantum building blocks.

What are the major challenges in developing a theory of quantum gravity?

One of the major challenges is the incompatibility between the principles of quantum mechanics and general relativity. Another challenge is the lack of experimental evidence and the difficulty of testing these theories at the scale where they would both be relevant.

What are some proposed solutions to the problem of quantum gravity?

Some proposed solutions include string theory, loop quantum gravity, and causal dynamical triangulation. These theories attempt to reconcile the principles of quantum mechanics and general relativity by proposing new fundamental structures and principles of the universe.

Why is understanding quantum gravity important?

Quantum gravity is important because it would provide a more complete and fundamental understanding of the universe, potentially allowing us to answer questions about the nature of time, space, and matter at the most fundamental level. It could also have practical applications in areas such as cosmology and the development of new technologies.

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