# Does space have a structure? [duplicate]

I’m sorry to ask such a vague question as I’m not able to put into words a certain question that I have in mind. I will do my best to describe this question. If I was to create a vacuum inside a box making it devoid of any form of matter or radiation , what will the resulting space inside the box consist of? More specifically, how is this space different from a computer simulated 3 dimensional space?

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• I think you will find duplicates of this question if you use Google and include PSE in the search terms. My own inexperienced hand wavy " understanding" is that so far we have found nothing to indicate that space has a discrete structure. But our efforts to add gravity to the standard model (quantum gravity), might cause us eventually to see an aspect of space-time that we currently are unaware of. – user178231 Dec 14 '17 at 12:16
• -1 Not clear what you are asking. The properties of a computer simulated 3D space are those which it has been programmed to have, plus any emergent properties which arise from programmed properties. – sammy gerbil Dec 14 '17 at 12:36

Space does indeed have structure. There are three structure that are immediately visible when we think of it as a manifold.

1. Continuous structure
2. Smooth structure
3. Metric structure

The first says that curves in space are continuous; the second says that they have no kinks; and the third says we have a distance function between points.

They are in order of increasing strictness; for example, a metric structure determines a smooth and continuous structure.

Since relativity up-ended our notions of space and time we ought not to speak of space and time separately but together - spacetime. The above still holds but now we can add a time orientation. One might think that here we have an additional structure - causality. But this in fact is implicit in the metric structure.

And also since QM up-ended our notions of what physics means at small distances there has been a further revolution in our understanding of space. Contemporary thinking supposes space has a discrete structure.

For example, in Loop Quantum Gravity, the area and volume operators have a discrete spectrum; this means that area and volume comes in discretely sized blocks. This is taken as a starting point in causal set theory where spacetime evolves in discrete jumps.

There is a long history attached to the conceptualisation of space. Even as far back as Aristotle, this is two and a half millenia ago he pointed out that space was a thing, it was a place which could be occupied by a thing; he pointed this out to dismiss the atomists conceptualisation of space as a void; for him, there was no such thing as void, and he argued that the atomists void was better conceptualised as place.

• While you're correct about the implications (metric implies smooth implies continuous) people need to be aware that those terms might not mean what they think. For instance you can put a metric on a discrete lattice of points and it will correspond to a topology, but it's a mostly useless one (the discrete topology). – tfb Dec 14 '17 at 21:09
• @tfb: I wasn't intending to go into that kind of detail... – Mozibur Ullah Dec 14 '17 at 22:17
• Yeah, I realise, and your answer is good I think: I just wanted to add a slight caveat. – tfb Dec 14 '17 at 22:52