Geometry as the Classical Limit: Examples and Analogies in Physics

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Discussion Overview

The discussion explores the concept of geometry as a classical limit of other theories in physics, examining examples and analogies across various fields such as thermodynamics, continuum mechanics, and general relativity. Participants consider the implications of these relationships and the underlying dynamics that may give rise to geometric descriptions.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant suggests that the geometry of the human body can be seen as a result of its internal structure, paralleling how geometry in general relativity might emerge from other dynamics.
  • Another participant proposes that equilibrium thermodynamics and continuum mechanics can be viewed as limiting cases of statistical mechanics and atomic theory, respectively.
  • A later reply affirms that the geometric aspects of general relativity may indeed arise from other dynamics, referencing string theory and loop quantum gravity as frameworks that explore this idea.
  • One participant reflects on past discussions regarding the nature of geometry in general relativity, questioning whether it is appropriate to seek underlying causes for geometric curvature, contrasting this with perspectives in quantum mechanics.

Areas of Agreement / Disagreement

Participants express varying views on whether geometry in physics should be interpreted as a result of underlying dynamics. While some agree that frameworks like string theory and loop quantum gravity explore these relationships, others question the appropriateness of seeking deeper explanations for geometric phenomena in general relativity.

Contextual Notes

The discussion includes assumptions about the nature of geometry and its relationship to underlying physical theories, which remain unresolved. There is also a tension between different philosophical perspectives on the role of physics in explaining nature.

ephen wilb
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Can anyone give other examples where the geometry is the classical limit of another theory? I can give one. For example. The body curves of a woman is geometric.. so the geometry is the result of the bones and internal structure of the physical body. Likewise, in General Relativity, could the geometric part also comes from some other dynamics? Can you give other systems where such occurs that geometry is just a large scale description of an underlying phenomenon?
 
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Equilibrium thermodynamics (and its geometrical structure) could be seen as a limiting case of statistical mechanics.

Continuum mechanics (and its geometrical structure) could be seen as a limiting case of a many-particle atomic theory
 
ephen wilb said:
Likewise, in General Relativity, could the geometric part also comes from some other dynamics?

Yes, this is the content of both string theory and loop quantum gravity.
 
Years ago I was asking in the google newsgroup why is the geometry curving in GR. The physicists mostly give me Bohr Line's about "It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature." Therefore it seems not a frame of mind to ask if the geometry is caused by other dynamics.. But yesterday I learned from the above previous message that String Theory and Loop QG content is precisely this exploration that the geometry may come from other dynamics. Is this not disobeying or violating Bohr statement? Can't we just say, the geometry curves and it is gravity. End of story? Remember in quantum mechanics.. physics don't ask why there is randomness... but in GR.. why is it right to ask what's or what it's curving?
 

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