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PF Gold
P: 3,274
 Quote by Nereid Slower with respect to what?
That is the question! As an answer I suggest, “With respect to a clock in the present epoch, compared by the transmission via electromagnetic radiation - light - of a time signal or the frequency of an atomic transition (i.e. red shift)”.

The overall gravitational field in the early universe was stronger than at present, therefore we might worry about having to include a cosmological gravitational red shift on top of the cosmological recession red shift.

However in fact these two red shifts are the same phenomenon, the null-geodesics diverge over curved space-time, but interpreted in two different ways.

As you cannot generally parallel transport a vector, the energy-momentum vector, across space-time curvature you cannot prove that masses remain constant; they have to be defined to be so by a measurement convention.

If atomic masses are assumed constant then the red shift is recessional, but if the measurement convention is that energy is conserved then the energy, i.e. frequency, of the photon conveying the information from the distant object is assumed constant and the red shift is interpreted as gravitational in origin.

These two interpretations are related by a conformal transformation. It depends on how you choose to define the standard by which ancient observations are compared with those of the present epoch.

Garth