Mass(-energy-momentum) curves space(-time).
However - what is space-time?
Is it (the background) necessarily flat(without something in it) ?
If there were an empty universe - is there still spacetime in it - or not?
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$\begingroup$ what is space-time? This site has an expectation that users asking questions have done at least a minimal amount of “due diligence”. Please read the Wikipedia article on spacetime and then ask questions about specific things that are still unclear. $\endgroup$– GhosterCommented Oct 7, 2023 at 5:09
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$\begingroup$ Is it necessarily flat? Your first statement was that energy and momentum curve spacetime, so how could it be “necessarily” flat? $\endgroup$– GhosterCommented Oct 7, 2023 at 5:15
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1$\begingroup$ If there were an empty universe - is there still spacetime in it - or not? What experiment is going to settle this? It might be a relevant question to a philosopher, but not to a physicist. Physicists can certainly imagine empty universes with “nothing but flat spacetime”, but we don’t live in one. $\endgroup$– GhosterCommented Oct 7, 2023 at 5:16
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What is spacetime ?
Spacetime is simply any framework of co-ordinates that locates each event in terms of its location in space, which is denoted by three spatial co-ordinates (conventionally called $x, y$ and $z$), and its location in time, denoted by a fourth co-ordinate (conventionally called $t$).
Spacetime is not specific to Einstein's theories of special and general relativity. It is, for example, possible to formulate Newtonian dynamics in terms of spacetime co-ordinates, although in Newtonian dynamics the time co-ordinate is the same for all observers. They key thing that changes in relativity is that the framework of spacetime co-ordinates at each specific point depends (in a very precise way) on the distribution of mass/energy in the universe.
Is it necessarily flat without something in it ?
According to Einstein's original theory of general relativity, yes, spacetime in an empty universe would be flat and unchanging (static). However, we now believe that a constant term, called the cosmological constant, must be added to Einstein's original equations. This constant term means that spacetime in an empty universe would not be static, but would be gradually expanding. This is sometimes referred to as the "energy density of empty space" or the "vacuum energy", and is associated with the hypothesised existence of dark energy.
If there were an empty universe is there still spacetime in it ?
We believe so. However, physics is an empirical science, so we cannot be certain of this until we can find an empty universe in which to test this hypothesis (which is unlikely). The best we can do is to observe how spacetime behaves in our own universe at locations in intergalactic space that are far away from any concentrations of mass/energy - and we do this by measuring how the light from distant galaxies is affected as it travels through these "empty" regions. It is from these observations that we discovered the cosmological constant.
