Would GR apply to a universe without any matter or energy? Would such a universe have time?
Yes, it would apply in a hypothetical universe in which it applies.
What is a universe without matter and energy? No theory would apply.
-- in this geddenaken -- GR alone applies. Can GR make sense without any matter or energy? What would a universe described by GR but no matter or energy
Physics only describes this universe and this universe has matter and energy.
GR is a theory that explains the interaction of matter and space. It is insensible to apply it to any Universe that does not contain both. That is the reason GR breaks down at the Big Bang. Time also is an insensible concept without motion. No matter.. no motion.. no time.
It is nonsense to try to apply any physical theory in another universe. We have no empirical data about such universes, no reason to suppose that any postulate of physics holds. If you are inventing fantasy universes there is no reason why you can't invent one that has matter and energy where GR doesn't apply and there is no reason why you can't invent one that has no matter and energy where GR does apply. It is pure fiction, so choose any story you like.
There's no time without clocks. There's no clocks without massive particles.
GR does have a "flat" solution (Minkowski space-time) in which no matter/energy is present...but that's like saying does Newton's law: F=ma apply in a universe with no acceleration? Yes you can set a=0 but then the whole theory is pretty useless...
Of course the GR theory applies to this situation.
This solution of Einstein's equations is flat space-time.
This is the most commonly used solution of Einstein's equations !!!
"Day-to-day physics" simply neglects the influence of mass and energy on the structure of space-time.
This is the same as assuming the universe is approximately empty.
Further assuming that no test-mass would even exist is of course more like brain-washing that thinking physics.
Sorry for this engineer, non-philosophycal, grass-root and uneducated, comment.
But that is what the OP asks. Physics makes predictions about observations. If there is nothing to observe, physics makes no predictions. Does this mean that physics still applies? It is at least not wrong. It predicts nothing and there is nothing.
Not approximately empty, but approximately flat. This solution serves to calculate (estimate) the matter and radiation behavior. The flat ST is widely used in SR. As soon as there is no matter/radiation, this solution or whatever else is just not practiced.
The converse: "GR does not apply to a universe with no matter or energy"- is certainly not true, as there is nothing wrong with simply putting a load of zeroes into the EM tensor and coming up with the Minkowski metric.
It's a trivial solution, but not an invalid one..
The other thread has the reason why I asked
Emergence of General Relativity from Loop Quantum Gravity
Chun-Yen Lin (University of California at Davis)
7 pages, 2 figures
(Submitted on 3 Dec 2009)
"I show that general relativity emerges from loop quantum gravity, in a relational description of gravitation field in terms of coordinates defined by matter. Local Dirac observables and coherent states are constructed for an explicit evaluation of the dynamics. The dynamics of large scales conforms with general relativity, up to the corrections near singularities."
with the reply
"He makes the problem easier by introducing matter.
That is not necessarily bad, but it makes the problem different. But that said, it does change the problem. He solved an easier problem than the one you seem to be talking about.
I think it's great, but I don't see any way I can answer on your poll. There is no place where it says he solved an easier version of the problem."
and reply is that since the universe contains matter, isn't the easier version of the problem the only one that matters as far as physics is concerned?
LQG + Matter = GR + matter (with quantum corrections in planck sector)
LQG = no derivable semiclassical limit
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