Quantum Mechanics and General Relativity: Understanding H Y = E Y and T Y = G Y

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Discussion Overview

The discussion revolves around the relationship between quantum mechanics and general relativity, specifically exploring the equation H Y = E Y from quantum mechanics and the proposed analogy T Y = G Y from general relativity. The scope includes theoretical implications and conceptual exploration of these equations.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants propose that T Y = G Y could be a meaningful analogy to H Y = E Y, questioning the validity of such a formulation.
  • One participant humorously responds to the proposal with a chuckle, suggesting skepticism or light-heartedness regarding the analogy.
  • A question is raised about the interpretation of Y in the context of T Y = G Y, indicating a need for clarification on the variables involved.
  • Another participant argues against the proposed analogy, stating that G already incorporates derivatives of the metric, making T=G a differential equation. They suggest that the metric should be treated as a quantum field, akin to the wave function in quantum mechanics, and maintain that the equation should remain as T=G.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the validity of the proposed analogy T Y = G Y, with some expressing skepticism and others providing counterarguments. The discussion remains unresolved regarding the implications of this analogy.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the variables and the definitions of T and G. The relationship between the equations is not fully explored, and the implications of treating the metric as a quantum field are not clearly defined.

Rothiemurchus
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Generally we write H Y = E Y in quantum mechanics.

Would it make any sense to use T ( stress-energy tensor) from general relativity and G (curvature) to write :

T Y = G Y
 
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T Y = G Y

chuckle
 
What would you call Y in that case ?
 
Rothiemurchus said:
Generally we write H Y = E Y in quantum mechanics.

Would it make any sense to use T ( stress-energy tensor) from general relativity and G (curvature) to write :

T Y = G Y


Well, this is not what people do, no. Because G already contains derivatives of the metric, so T=G is already a differential equation. So it's the metric itself which is treated as a quantum field (so roughly speaking, it is treated like the psi of qm) and the equation is kept as T=G.

Pat
 

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