This is a pretty fascinating claim, because I see the evidence for the big bang as having many effects on other theories. For example, what about redshifts? If redshifts are in fact a measure of recession, then we have solid evidence that galaxies are getting further apart, i.e., the universe is expanding. But if the redshifts we observe have some other source, that means that all our measurements of velocity in the universe are suspect, which has a pretty dramatic effect on all kinds of astrophysical theories. Which is it?

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Conserve energy. Commute with the Hamiltonian.