# Does Space exist if there's nothing in it?

And by nothing I mean no seething quantum flux, full of potential universes, no particles, zilch. Can there be said to be anything there at all? If I suddenly appeared in it could I move through it? (In other words, does it have dimension?)

And another thing. Would Time exist in such a state of affairs, with no events at all?

I think it exists as the distance between things that do exist.

aldiboronti: Alessan hit on the important aspect of space as you have defined it: It only exists as the distance between objects. Thus, if you have one object or zero objects space does not exist.

Time is simply space in a different dimension, and thus only exists if something is changing. If your universe is absolutely steady-state, with no entropy or other change, the idea of time is not meaningful.

What about a universe with only one object in it (an indivisible one). Any Space?

If an object is moving, can you consider space to be the distance between where it was and where it is, even if it’s the only object in the universe?

Ah, but could there be any such thing as motion in a one-object universe? Motion relative to what?

Relative to itself, it could spin or twist. Assuming the object could detect acceleration, this would be measurable. Also, if one object exists their is space between one side of it and the other (it has “extent”) so in the case of one object space and time exists.

If the object is a point charge, or some other dimensionless entity, then I’m less sure. I have a sense that such objects can “spin” in a sense, and that it’s wave function gives it a spatial extent, but you’ll need a quantumn physicist in here to tell us if I’m right.

A completely empty 4-D universe would still have time and space; it’s just that there would be nothing to distinguish one point in it from another.

Could you actually have a space with nothing in it? Even given zero energy, doesn’t the uncertainty principle mandate flucuations around the zero point that would give rise to virtual particles and potential real ones?

And if you could appear in such a space, then by definition it has dimensions as well as time.

Spacetime, under GR, is a thing in and of itself. There are many “toy universes” with no “matter” in them. They’re the solutions to Einstein’s vacuum equations (the stress-energy tensor vanishes and the Einstein tensor is identically zero). In 3+1-dimensional spacetime there are gravitational wave solutions, which are certainly as much “things” as electromagnetic waves are.

Brian Greene’s the elegant universe has a lot about this as a thought experiment that has lurked beneath many cosmological theories.

First of all, space is not empty.

Actually, no. That would be multiple objects. Each particle counts as an object.

Let’s try this. (Apologies if it’s a dumb question. I just love speculating on stuff like this.)

There are two objects in the universe. Particle A and, an indeterminate distance away, Particle B. A starts moving towards B at a constant rate, B moves directly away from A at a constant and equal rate.

How would this differ from both particles remaining motionless? Could it be established that the particles are in motion or does it make no sense to speak of motion in these circumstances? (Clearly, accellerated motion would be a whole different kettle of fish.)

Well fair enough, then I still hold the particle’s wave function would have a certain extent that could be measured, and space would be meaningful.

Also, the particle could move at constant velocity in a circle, measure the centrifical force it was experiencing, find the diameter of the circle it was moving in and thus how much space it was covering.

As you’ve written it, particles A and B start moving at some point, so there is acceleration. Once the acceleration becomes zero, you’ve got constant velocity, and so there’s no indication of motion.

I’m not understanding whether you’re saying this to indicate that truly empty universes can exist or can’t exist. IOW, do the “things” make it not empty?

And what then is the relationship between solutions to GR and the quantum mechanical findings about spacetime? Are these still incompatible until a ToE exists? Do they answer the OP’s questions in different ways?

What I’m saying is that the OP is ill-founded. The very fact that there is a universe means there’s something (spacetime itself) in it.

Such geniuses as Newton and Leibniz have disagreed on this very question. They didn’t know about General Relativity, of course.

(see this wikipedia article. Or for further reading, here are some books I’d recommend. Although, to be honest, those are the only three books I’ve read on the subject – I was taking a class – so I can’t say if they’re the best, only that I enjoyed them and found them fairly accessible, even as someone without much philosophical background.)

I should clarify: Those are books on the philosophy of space and time in general – the question of whether space is just the relationships between objects or whether it exists as an independent thing is just one of the topics covered.

If GR is accurate, spacetime obviously is a thing in and of itself. If the spacetime manifold is an epiphenomenon of some other model (as in various quantum gravity theories) then those are things in and of themselves. The stage has joined the actors irrevocably.