What is the physics behind GR's diffeomorphism invariance?

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SUMMARY

The discussion centers on the physical motivation behind the diffeomorphism invariance in General Relativity (GR). It establishes that while relativistic equations are invariant under the Poincaré group in flat spacetime, GR requires invariance under general diffeomorphisms due to the curvature of spacetime. This principle ensures that the laws of physics remain consistent across different observers and coordinate systems. The conversation also highlights the significance of the equivalence principle and the dynamical nature of the metric tensor in linking gravity to diffeomorphism invariance.

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  • Understanding of General Relativity (GR) principles
  • Familiarity with tensor calculus and differential geometry
  • Knowledge of the equivalence principle in physics
  • Basic concepts of the Poincaré group and its role in spacetime
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  • Study the implications of the equivalence principle in General Relativity
  • Explore the role of the metric tensor in dynamical systems
  • Research the concept of gauge theory gravity and its relation to diffeomorphism invariance
  • Examine the "hole argument" and its significance in the context of GR
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Physicists, mathematicians, and students interested in advanced topics in General Relativity, particularly those exploring the foundational principles of diffeomorphism invariance and its implications for the laws of physics.

  • #31
stevendaryl said:
The third is subtler, and I don't know whether it is equivalent to the second, or not. It's something like "the indistinguishabilty of points".

I don't understand this well either, but here are some thoughts. It's usually said here that the hole argument says that observables must be relational in gravity. I don't understand this because I think observables must also be relational in special relativity, ie. relative to an inertial frame.

However, what is known is that in pure gravity, there are no gauge invariant local observables. Classically, this problem can be solved if matter is introduced, so that relational aspects of the matter distribution create local observables. There's a discussion of this around Eq 1.1 of http://arxiv.org/abs/gr-qc/9404053.

The quantum situation seems trickier, eg. http://arxiv.org/abs/hep-th/0106109, http://arxiv.org/abs/hep-th/0512200.
 

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