What are the incompatibilities between GR and QM?

[Karlisbad]

What are the incompatibilities between GR and QM??

appart from the fact that GR is NOn-renormalizable (perturbatively ) since there are almos infinite types of UV divergences $$\int_{0}^{\infty}dxx^{n}$$ n=-1,0,1,2,3,4,...

What other incompatibilities are there?..if space weren't continuous but you could "triangularize" it somehow would these inconsistence disappear?? :shy:

 

[lightarrow]

There has recently been another thread on this subject:
How exactly are QM & GR incompatible?
https://www.physicsforums.com/showthread.php?t=138373

 

[denian]

I cannot provide a definitive answer to this question as it is still an area of active research and debate in the scientific community. However, I can provide some insights into the main incompatibilities between General Relativity (GR) and Quantum Mechanics (QM).

1. Different theories of spacetime: GR describes the behavior of gravity as a curvature of spacetime, while QM describes the behavior of particles and their interactions. These two theories have fundamentally different interpretations of how space and time behave, making it difficult to reconcile them in a single framework.

2. Different scales: GR is a classical theory that applies to macroscopic objects, while QM is a quantum theory that applies to microscopic particles. When trying to apply both theories to the same system, there are inconsistencies due to the different scales at which they operate.

3. Uncertainty principle: In QM, the uncertainty principle states that the position and momentum of a particle cannot be known simultaneously with 100% accuracy. However, in GR, the concept of a definite position and momentum of a particle is necessary to calculate its trajectory within the curved spacetime.

4. Non-renormalizability: As mentioned in the content, GR is non-renormalizable, which means that when trying to calculate certain quantities, the theory produces infinite values. This is not the case in QM, which is a renormalizable theory.

There are ongoing efforts to reconcile these incompatibilities through various approaches such as string theory, loop quantum gravity, and others. However, these attempts are still in their early stages and have not yet produced a definitive solution. As for the idea of "triangularizing" space, it is not a widely accepted concept in mainstream physics and does not address the fundamental differences between GR and QM.