Discussion Overview
The discussion revolves around the challenges and mathematical considerations involved in merging Einstein's Field Equations with Quantum Mechanics and Quantum Field Theory. Participants explore various theoretical frameworks, known problems, and the implications of non-renormalizability in this context.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
- Mathematical reasoning
Main Points Raised
- Some participants note that if a solution existed for merging GR and QM, a theory of quantum gravity would already be established.
- Linearized General Relativity (GR) can be quantized as an effective QFT, but it is considered non-renormalizable, introducing complications in the mathematical formulation.
- One participant suggests quantizing the gravitomagnetic field similarly to how the electromagnetic field is quantized.
- There is mention of Kaluza-Klein theory as a potential approach, although some participants clarify that this may not align with the original intent of the question.
- Concerns are raised about the mathematical difficulties in merging GR and QM, particularly regarding the Riemann curvature and the implications of non-renormalizability.
- Some participants express frustration over the lack of detailed mathematical explanations available in the forum, suggesting that textbooks may be necessary for deeper understanding.
- String theory and loop quantum gravity are mentioned as attempts to merge gravity with quantum mechanics, but participants highlight ongoing challenges and frustrations within these frameworks.
- Participants discuss the difficulties of applying QFT in curved spacetime and the absence of black hole treatment in standard QFT.
Areas of Agreement / Disagreement
There is no consensus on how to effectively merge GR with QM. Participants express differing views on the feasibility of various approaches, the significance of non-renormalizability, and the adequacy of existing theories like string theory and loop quantum gravity.
Contextual Notes
Participants note that the inability to merge GR and QM is a mainstream issue, yet the specific mathematical reasons for this remain unresolved in the discussion. The complexity of the topic and the need for a solid background in both quantum field theory and general relativity are emphasized.