Geometry as the Classical Limit: Examples and Analogies in Physics

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In summary, the conversation discusses examples where geometry is the classical limit of another theory. Examples include the body curves of a woman being geometric, equilibrium thermodynamics and continuum mechanics being seen as limiting cases of statistical mechanics and many-particle atomic theory, and the possibility of the geometric part in General Relativity coming from other dynamics such as string theory and loop quantum gravity. The conversation also touches on the question of whether it is appropriate to ask about the cause of geometry in GR, given Niels Bohr's statement about physics concerning what we can say about nature rather than how it is.
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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
 
  • #3
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.
 
  • #4
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?
 

1. What is the concept of "Geometry as the Classical Limit" in physics?

The concept of "Geometry as the Classical Limit" refers to the idea that in certain physical systems, the classical laws of geometry can be used to approximate and describe the behavior of particles or objects. This is particularly useful in cases where quantum effects are negligible or can be ignored.

2. Can you give an example of "Geometry as the Classical Limit" in physics?

One example is the motion of planets in our solar system. While the laws of quantum mechanics apply to the individual particles that make up the planets, the overall motion and behavior of the planets can be described using classical laws of geometry such as Newton's laws of motion and Kepler's laws of planetary motion.

3. How does the concept of "Geometry as the Classical Limit" relate to Einstein's theory of relativity?

Einstein's theory of relativity is based on the idea that space and time are intertwined, and the geometry of space-time is affected by the presence of massive objects. This theory is an extension of classical geometry and explains how gravity works on a large scale, further supporting the concept of "Geometry as the Classical Limit" in physics.

4. Are there any limitations to using "Geometry as the Classical Limit" in physics?

Yes, there are limitations to using "Geometry as the Classical Limit" in physics. This concept is only applicable in certain physical systems where quantum effects are not significant. In cases where quantum mechanics is necessary for accurate predictions, the classical laws of geometry may not be sufficient.

5. How does understanding "Geometry as the Classical Limit" help in understanding the behavior of particles and objects?

Understanding "Geometry as the Classical Limit" allows for a simplified and more intuitive way of describing the behavior of particles and objects in certain physical systems. It also helps in bridging the gap between classical and quantum mechanics, providing a better understanding of how these theories relate to each other and how they can be used together to explain the behavior of particles and objects.

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