If there were no matter or energy would there still be time?
In what equation?
This one’s actually a good question.
Ok, let’s see what I can think up…
Assume a certain area in space that just contains vacuum. Let’s say this area was our entire universe, containing no matter or energy (and therefore, also, no life). Time would still exist in a vacuum. Just that nobody would know it, or be able to measure it relative to anything or any event. Each state being exactly the same as the previous state. This is assuming no external interference is possible.
Actually, even though time would exist, it wouldn’t matter. Something like the area outside of our light cone and the time before the big bang. It’s irrelevant to the laws that govern our universe. But a good hypothetical question nonetheless…
I dunno whether I’m right or wrong… these are just my thoughts.
Oh, let’s be fair. this is a legitimate question, even if it is as much metaphysics as physics.
Einstein’s equations say that space and time are not two different things, but two sides of the same coin - spacetime. That’s why people say that time did not exist before the universe came into being. Without space there is no time.
But quantum mechanics says that there can never be nothing. Quantum fluctuations mean that a something, usually called vacuum energy, still exists. (And that’s where the universe comes from, to answer your other question.)
Where the metaphysics come in is in the question of whether vacuum energy is energy in the sense that you use it when you talk about matter or energy. (BTW, you can’t talk about them in our universe as if they are separate things: again, Einstein’s equations says that they are equivalent.) I’m not sure that I have have an answer for that, but I’ll let the legitimate physicists on the Board have fun with it.
One of the early (approximate) models of the Universe was the de Sitter model. In this model, you have a universe without any matter, but which is constantly expanding (or contracting). The math works perfectly well, and there is time in that universe (forward in time being the direction in which space is getting bigger)