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We only can speak about the energy density in a container if its energy content is independent from its dimension -so could, in principle, have any value at all. If in Einstein’s statement “People before me believed that if all the matter in the universe were removed, only space and time would exist. My theory proves that space and time would disappear along with matter” we may replace ‘matter’ with ‘energy,’ then the energy content of the universe is not independent from its volume. Doesn’t this mean that we cannot then speak about the energy density of the universe as a whole?

Qmechanic
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Anton
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    Didn't you already ask this? The question is basically meaningless. For a start space and time wouldn't disappear along with matter. The solution to Einstein's equations with a zero ASDM mass is simply flat spacetime i.e. the Minkowski metric. – John Rennie Apr 30 '18 at 07:51
  • @John. What is ASDM mass? Do you mean that in a universe devoid of any energy still is a real, physical universe and that in such universe space and time exist? Though such abstract, empty, mathematical space and time may be interesting; if it only makes sense to speak about the distance and motion of real objects (i.e., which have energy) if it matters, energetically how large their distance and relative velocity exactly is, if there is energy involved in a change of their distance or velocity, then space and time don’t exist in a physical sense in the absence of energy. – Anton Apr 30 '18 at 08:50
  • @John. Only if we were to conceive of spacetime as something which exists even in the absence of energy, something the properties of which don’t depend on, aren’t affected by the presence of energy -if the meter and second would be defined even in a completely empty universe- might it make sense to speak about the energy density of the universe. – Anton Apr 30 '18 at 08:50
  • @John, Qmechanic.

    No, this exact question hasn’t yet been asked and answered. As according to big bang cosmology the expansion rate of the universe (also) depends on the density of the vacuum- / zero-point / dark energy / cosmological constant (of which nobody knows why it is so much smaller than calculated), mine is a legitimate question.

     – Anton Apr 30 '18 at 09:04
  • This is much less mysterious than you seem to think. You can take Einstein's equations for GR, set the matter and energy to zero and you still find solutions. These are called vacuum solutions and they are perfectly good spacetimes. – John Rennie Apr 30 '18 at 09:09
  • Minkowski space is a perfectly good abstract, imaginary spacetime, not something you can actually visit and inspect. In a universe devoid of any energy the meter and second aren’t defined, there is nothing to compare their length and duration with, nothing to use your yardstick and clock to measure distance and duration of. – Anton Apr 30 '18 at 09:33
  • If I have understood general relativity (correct me if I’m wrong), then it is the presence of energy which turns an abstract, mathematic space where all points are identical except for their arbitrarily assigned coordinate numbers into a real, physical spacetime -where the observed pace of clocks and length of rods varies from one point, one distance to the next, however slightly. – Anton Apr 30 '18 at 09:33
  • Possible duplicates: https://physics.stackexchange.com/q/2838/2451 , https://physics.stackexchange.com/q/349768/2451 and links therein. – Qmechanic Apr 30 '18 at 09:40
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    Consider yourself corrected. – John Rennie Apr 30 '18 at 09:41
  • What type of energy? Energy of matter? Gravitational energy? – Qmechanic Apr 30 '18 at 09:45
  • @Qmechanics. No, this exact question hasn’t yet been asked. If the expansion rate of the universe depends on the cosmological constant -the density of which could have any value (resulting in universes with different expansion rates), then the total energy content of the universe is independent of its volume and hence its energy density. – Anton Apr 30 '18 at 23:51
  • @Qmechanic. While it would be neat if the total energy of the universe would be zero, this is not the case if the expansion rate -the energy content- of the universe could have been different. This raises another interesting question: https://physics.stackexchange.com/q/403014/ – Anton Apr 30 '18 at 23:51

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