Does Space exist if there's nothing in it?

I disagree; space would still exist as the set of positions that the object, could occupy.

Could a single object in otherwise empty space have acceleration? I see that it couldn’t have velocity since there is nothing against which relative velocity could be measures, But if it was under acceleration (or under the action of a force which is I believe the same thing) then could that force be hypothetically measured or have effect uppon the lone object?

Yes, modern scientific developments have basically answered this one, but I still think the discussion prior to Einstein is pretty interesting from a historical perspective.

In my opinion, IANA physist, The fact that the event (particle, movement of a singel object, etc…) was observed at all would qualify it as measureable. For something to be observed, there would then be two things in the “space” the object in question and the observer, otherwise how could it be observed. Right there would give you distance. Point A to Point B (observer to object). There would also then be time. The length of the observer observing the object. If there is no observer, then how could you prove there was an object in the first place?
Sorry about grammer and spelling. I am nearing the end of my shift and getting very tired.

The Zero Point. Isn’t that where Dr. Tom Beardem gets zero point energy?
Or taps into the free energy of the vacuum to solve the world’s energy deficit? :slight_smile:

Never mind. Just couldn’t resist adding a bit of ? humor ?
I’ll leave and not be back here.

Interesting, possibly. IMHO, such discussion should be set out as tangential to the OP, which didn’t ask what people thought about whether space existed, but whether or not it does exist without “anything” in it.