We see the photon with less energy and if we could measure the deexcited atom we would see it balance the energy. The next line from the bottom is a nearby galaxy, this galaxy is moving, and so the rest system of the atom is moving with respect to us. We observe it as at the star level on the left of the image. In the center of mass system of the excited atom ("deexcited-atom and photon" )the spectral line is fixed if our rest frame coincides with the rest frame of the atom. This means we are dealing with special relativity equations. Let us take a simple redshift of a spectral line from a moving galaxy. But the Robertson-Walker metric doesn't admit such a vector field. Very often in the definition of energy you need a time-like Killing vector field to have a constant energy. You can find from the geodesic equation (using the Robertson-Walker metric) that the velocity is inverse proportional to the cosmic scale factor, so decrease with time.įrom another point of view, you can say that is the time dependence of the metric that breaks conservation of energy.Īt the end it really depends on the definition of energy you want to use. If the four velocity is time dependent, like in an expanding universe, the energy is not a conserved quantity. ![]() That is constant, and the energy is conserved. \mathcal =(1,0,0,0) $ in Minkowski space-time, we have: For a particle with four-momentum $ P^\mu $, measured by an observer with four velocity $ u^\mu $, is defined as: The energy of a particle is an observer-dependent quantity in General Relativity.
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