An expanding universe is a solution to Einstein's equations. So particles become farther apart with time. I wonder how the conservation of energy is accounted for in this expansion. Does the gravitational potential energy increase as the expansion of space creates greater distance between objects (galaxies)? Does the velocity created by increasing distance also contribute to the kenitic energy of galaxies? It seems that expanding space would contribute to both potential and kenitic energy when normally you'd expect a decrease of kenitic energy with an increase of potential energy. I doubt that the expansion of space contributes to the kenetic energy of receeding galaxies. For I am told that the expansion can be faster than light. And that would cause the relativistic mass to increase to infinity if the expansion contributed to the velocity of galaxies. So if the expansion of space does not contribute to the momentum or kenetic energy of galaxies, but it does contribute to the gravitational potential energy, then the conservation of energy is violated unless mass decreases with expansion. Right?
Relativistic mass is a missnomer. As we have been through this several times here now, mass as defined in modern relativity does not change with speed. Even if it did, you wouldn't be able to apply special relativistic dynamics to such a general relativistic scenario. In general relativity it is not energy and momentum(components of the momentum four vector) that are conserved, but is the energy parameter and momentum parameters that are conserved. Those conserved parameters of the motion are invariants found with the use of Killing vectors characteristic of the spacetime. http://www.geocities.com/zcphysicsms/chap5.htm#BM5_5 For a comoving frame galaxy in an expanding universe, its energy parameter is equal to its mass which does not vary with speed, nor with cosmological time as the universe expands. That energy parameter and its momentum parameters are what is conserved.
I'm not sure how this applies to my concerns. I'm left with the question of potential and kinetic energies. Are you saying, then that, yes, the classical ideas of potential and kinetic energies are not conserved and do indeed change with expansion? How would you define a "comoving frame" in a universe where space itself expands? My original concern was that if a photon is redshifted by leaving a gravitational potential well from a heavy object, then wouldn't the expansion of the universe also mean that this photon was becoming more distant from objects and gaining gravitational potential energy due to increased distance, so that it would have to be redshifted as well. I don't see the difference. The photon is becoming more distant from other galaxies, right? The potential energy is increasing due to that increase in distance, right? There would have to be a corresponding decrease in the photon's frequency-energy visible as a redshift, right? And then I remembered that photons can be converted into massive particles and back again. So if the photon decrease in energy, then so would any mass particle it could be converted to. A photon of sufficient energy could be converted to a massive particle with no velocity, then the universe could expand, and the massive particle could be converted bact to a photon. If the resulting photon in this scenario must have the same decreased energy as a photon that is not converted, then the rest mass just before the final conversion must have decrease by the same emount as the un-converted photon would be. What's wrong with this argument?
Mike 2 - It is more likely that the effective inertia of a given mass will increase with expansion - recall that a mass can be described in terms of the energy in its gravitational field - and for a small universe, the energy in the field is less than for a larger universe - the energy density is inversely proportional to the 4th power of the radial distance from the mass center at all distances beyond the radius of the mass surface ... integration over a distance equal to the Hubble sphere at the present epoch will yield less energy than integration over the expanded sphere in 10 billion years - as it turns out, the mass of an isolated object appears to increase linearly with expansion - an interesting consequence to this is that for an isolated mass M. the MG product can be constant during expansion, even though G diminishes as 1/R - but all tests to measure G always involve the MG product - as for example in the radar ranging experiments that are frequently cited in support of the constancy of G. As for as the totality of the cosmic energy, it is worth pondering why the total cosmic energy is approximately equal to the numerical value of the Hubble radius squared - and the density is approximately equal to 1/R.
I may be wrong, but it seems to me that GR does not determine what the mass of particles should be, it only determines the gravitational field once the mass of the particles are given. Is this correct? If so, then GR cannot answer my question.