Can physical 3D space exist at all?

[p764rds]

I have read about how space-time is shaped by gravity - fine.
Is there an underlying assumption that 3D space exists in the first place? (because that's where we live).

If I were to place a 3D sphere of radius 1 billion miles into nothingness - would it hold up?
I mean there is nothing to define its boundary or its relative length measurement - its empty space (no time added!) - it appears to be an illogicality as I cannot understand how it could exist at all. It would not rush out at the speed of light surely - why would it?

(I am trying to show that 3D space is made in information - an easy task - and impossible in "real physical space" i.e. there isn't any)

Really grateful for knowledegable reply especially if there is an undelying assupmption about its existence in the first place.

 

[Mentz114]

In GR, where the gravitational field is in the space-time curvature, it doesn't matter whether there is anything physical that corresponds to curvature. The theory works in any case.

So the answer to your question 'is there an assumption of existence' is 'no'.

Space is generally thought of as separations or extents (information). So you need one extended thing, or at least two points for 'distance' to have meaning ( for there to be distance information).

 

[VKint]

The relevant question here is, "what do you mean by 'exist?' " For example, you point out that the concept of "space" without a line element or notion of distance is absurd. You are quite right; in fact, in GR, spacetime is essentially defined by the line element (called the metric). Thus, in the context of GR, this observation is tautological. Another problem is your implicit assignment of a boundary to your hypothetical bubble of space. In GR, spaces don't have boundaries; when they appear, they are the result of poorly chosen coordinates, and great effort is expended to find more suitable coordinates. All of this stems (probably) from the fact that your physical intuition depends on the geometric notion of an embedding. In other words, you seem to implicitly visualize your spatial bubble as "existing" in some larger manifold (this is seen, for example, in the fact that you freely endow it with a "diameter," presumably inherited from the line element of some larger space); your question, however, concerns its existence independent of any such embedding. This conflict seems to be the source of some of your confusion.

The situation you're probably thinking of is somewhat different. At any given moment, we appear to inhabit a three-dimensional space sitting inside, well, nowhere; superficially, this appears to be analogous to the situation you propose. In fact, as I'm sure you're aware, scientists even propose that "space," in this sense, does indeed have a boundary. The problem, however, is that this three-dimensional space is in fact not "in the middle of nowhere," but is sitting inside a larger manifold called spacetime. In fact, the very notion of "now" or "the present moment" is only locally defined; there is no way to tell, in general, if an event occurring at Proxima Centauri happened before, after, or concurrently with an event on Earth (for example). The fact that space has a boundary presents no difficulty because spacetime does not (well, it kind of does, but it is expected that quantum gravity will help sort out issues with singularities); the "boundary" of space is unreachable by anything in the universe, and so it really isn't a "boundary" at all in the space-time sense.

At a deeper level, though, there's a semantic issue with your question. The notion of space, or spacetime, is meaningless if it is completely empty; in other words, the "existence" of space is defined by the presence of something therein. A statement about the possible existence of a completely content-free space or spacetime is thus entirely vacuous. The question of existence is thus ill-posed when asked concerning an object such as "empty space."

 

[marcus]

In GR, where the gravitational field is in the space-time curvature, it doesn't matter whether there is anything physical that corresponds to curvature. The theory works in any case.

So the answer to your question 'is there an assumption of existence' is 'no'.

Space is generally thought of as separations or extents (information). So you need one extended thing, or at least two points for 'distance' to have meaning ( for there to be distance information).

I like Mentz's answer a lot.
I was going to say the same thing. GR has no assumption that space exists. In fact Einstein expicitly said that his theory "deprives space of the last shred of physical reality". Specifically it was the principle of general covariance.

So the whole line of investigation that p764rds starts off with here does not make sense to me.

I have that quote in German somewhere, it is from 1915 or 1916. Nice aphoristic utterance.

What I think he is referring to is after you take the diffeo equivalence class there is no more manifold, there is only the gravitational field itself (the geometry).
A bit like the smile after the cat disappears. Anyway GR doesn't assume that points in spacetime have any objective reality. Only material events---objects, observers etc.
Of course these have geometric relations between them. (Like Mentz says that is "information".)

Here's the Einstein quote:
https://www.physicsforums.com/showpost.php?p=2126131&postcount=111

 

[Naty1]

I am trying to show that 3D space is made in information

(I don't see how this relates to the rest of your post, so I'll just tackle this piece. You likely won't get many answers here under 'relativity'...)

You can read a little about information based physics at

http://en.wikipedia.org/wiki/Information#Information_as_a_property_in_physics

Or a lot more in DECODING THE UNIVERSE BY Charles Seife...

If you are not familiar with black hole horizons, you might also read about them as holographic representations of our universe in information based terms...

and the other item that comes to mind is entropy as a special case of information...for example, quantum entanglement and entropy might be different manifestations of an information based universe...an information bit per pixel...at the Planck scale...

all these ideas point to the possibility that information based casuality is the basis of our universe...not so much the apparent physical manifestations which appear so different to us...like mass, energy,time,space, and so forth...instead of atoms, or strings, for example, being a commonality, its really information that is common to all...
you are, after all, just a computer replicating your information (DNA)...