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The Principle of Relativity, (PR) may be summarised as the doctrine of no preferred frames of reference. It not only underlies SR in the absence of gravitational fields but GR with its gravitational fields as well.
It leads to the conservation of four-momentum and the concept of coordinate independent geometrodynamic objects.
As four-momentum, or energy-momentum, is conserved one frame dependent component of it, energy, is not in general conserved.
However it might be argued that once matter and its associated gravitational fields are introduced in GR, then a preferred frame of reference might be discerned. It is that co-moving with the Centre of Mass or centroid of that matter. Cosmologically it might be identified with that frame in which the CMB is globally isotropic co-moving with the surface of last emission.
But should such a frame of reference be preferred, except as a convenient frame in which to establish a coordinate system when solving the field equation?
I would humbly suggest that in the inertial Centre of Mass frame as energy is conserved, at least for a static system, then that frame should be preferred .
In other words whether the Centroid frame is considered preferred or not depends on whether the conservation of energy is considered important or not.
Just food for thought (and debate!)
Garth
It leads to the conservation of four-momentum and the concept of coordinate independent geometrodynamic objects.
As four-momentum, or energy-momentum, is conserved one frame dependent component of it, energy, is not in general conserved.
However it might be argued that once matter and its associated gravitational fields are introduced in GR, then a preferred frame of reference might be discerned. It is that co-moving with the Centre of Mass or centroid of that matter. Cosmologically it might be identified with that frame in which the CMB is globally isotropic co-moving with the surface of last emission.
But should such a frame of reference be preferred, except as a convenient frame in which to establish a coordinate system when solving the field equation?
I would humbly suggest that in the inertial Centre of Mass frame as energy is conserved, at least for a static system, then that frame should be preferred .
In other words whether the Centroid frame is considered preferred or not depends on whether the conservation of energy is considered important or not.
Just food for thought (and debate!)
Garth
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