If our universe is a 4-manifold (i.e. with every point in space-time already existing) does this imply that there is zero net energy (as net energy would do work and so change the universe)?

If so, how do we account for the fact that our current experience of the universe is very far from net zero energy? Are there stores of negative energy out there? (Or, more likely, have I misunderstood this question?!)

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    $\begingroup$ The universe as modeled as 4-manifold by GR doesn't conserve energy globally, because it violates the Noether theorem for time translation invariance. Thus I wouldn't expect we have zero net energy except at some moment in the universes history. $\endgroup$ Jun 13 '17 at 14:53
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    $\begingroup$ I don't see that our universe being a 4-manifold is relevant to your question. Despite that, it is thought by some (many?) that our universe has a net zero energy simply because any energy input via expansion is cancelled out by negative gravitational potential energy. This may be useful reading. $\endgroup$
    – zephyr
    Jun 13 '17 at 17:48
  • $\begingroup$ 4-manifold because it implies there is nothing "special", or "real" if you prefer, about time. $\endgroup$ Jun 20 '17 at 12:20
  • $\begingroup$ If somebody would like to write up the GR point as an answer I'd be happy to accept it $\endgroup$ Aug 17 '17 at 18:25

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