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Energy loss of a photon moving against gravity 
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#55
Sep810, 01:28 AM

P: 1,162

Intuitively I can picture what this would mean ;essentially a Cartesian system but am not sure if thats what your talking about in this context. 2) In this circumstance how do you differentiate between momentum and energy wrt a photon??? I can see why the energy would apparently increase (blueshift) relative to local electron frequencies but wouldn't this also be equivalent to an increase in momentum?? Also; viewed from a locale of higher potential wouldn't the speed of light decrease at lower levels? If this is the case, then how would this be related to an increase in momentum? Thanks 


#56
Sep810, 02:27 PM

PF Gold
P: 1,164

It does not necessarily mean flat (Minkowski) space. "Isotropic" means for example that if you observe a light speed signal expanding from a point (creating a sphere expanding at c according to a local observer) then in the coordinate system the light also expands at the same rate in all directions, still creating a sphere, but at a coordinate speed which is not necessarily exactly equal to c. In more general coordinate systems, the speed of light is not necessarily the same in different directions, so you can't even talk about the coordinate speed of light unless you also specify a direction. The interesting thing is that regardless of the direction in which the photon is travelling, the coordinate rate of change of momentum with time at a given point is always the same downwards pointing vector, equal to exactly twice the Newtonian force that would be experienced on an object of the same total energy at that point in the field. In general, for an object travelling at speed v, it is simply (1+v^{2}/c^{2}) times the Newtonian force, at least in fields where the weak approximation holds (that is, nowhere near a neutron star or worse). 


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