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Consider the following thought experiment. Suppose we initialize a parallel plate capacitor with the plates of area $A$ separated by a distance $d$ in empty space. The energy in the capacitor is approximated as $E\approx\epsilon_0 Ad$. Let a large amount of time pass by. Assume that the distance between the plates increases due to the expansion of the universe (and in that case $A$ increases as well.) Then it seems our capacitor has now gained some potential energy "from nowhere".

Now I have read that, though the spacetime metric is observed to be expanding on large scales, it does not follow that spacetime is expanding on small scales. But it might be.

Also, I know this is a silly example, as we should not expect laws of household capacitors to hold on cosmological scales. Perhaps someone could come up with a more sophisticated example. What I am getting at, is that in many physical systems, the potential energy of that system is related to the distance between the components of that system. If the distance between the components changed due to the expansion of the universe, it would seem the potential energy of the system also changed. Yet, no work was performed upon the system. What is the discrepancy here? Where did the difference in energy go? (I think this general way of looking of the problem should overcome the objection that spacetime might not be expanding on small scale. Just define our system to occur on some scale where expansion is observed.)

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    $\begingroup$ Energy is not conserved in an expanding universe because it doesn't have time translation symmetry - the universe evolves in a preferred time direction. $\endgroup$
    – Avantgarde
    Feb 28 at 3:38
  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/35431/2451 and links therein. $\endgroup$
    – Qmechanic
    Feb 28 at 4:31