I Invariant definition of acceleration in Newtonian physics vs proper acceleration in GR

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The discussion centers on the existence of an invariant definition of acceleration in Newtonian physics, akin to proper acceleration in General Relativity (GR). It highlights that in Newtonian physics, an accelerometer reading of zero does not necessarily indicate no acceleration due to gravitational forces. The concept of inertial frames is crucial for defining inertial motion, leading to some circular reasoning in traditional Newtonian formulations. Newton-Cartan gravity is presented as a framework that incorporates features of GR, such as curved spacetime and the equivalence principle, allowing for a more nuanced understanding of acceleration. Ultimately, the conversation emphasizes the complexity of defining acceleration across different gravitational contexts and formulations.
  • #31
cianfa72 said:
So, as you pointed out in post #24, in section 2 in that paper (in particular in 2.1) a global condition on ##\tau## is actually implicitly assumed.
I don't know if it is, because I don't know if that entire section was intended to just cover standard Newtonian gravity, or whether it was intended to cover a more general category of models that all use the same general formalism.
 

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