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By "real space" I mean a space in which physical particles move.

Consider a color sphere and let a bunch of objects "move" on its surface. "Move" means "change colors". Let there be some rules governing the changes of color, maybe giving rise to something like inertness or collisions. .

Under which conditions will we be willing or forced to think of the movements as real movements in real space?

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Please stop with this "philosophy" tag: either your question is a valid question about physics as a science and it doesn't need this tag or this is not a valid question and it should be closed. – Cedric H. Nov 17 '10 at 12:03
This doesn't really seem like physics to me, I'm afraid. Mathematics, at best. It's not a very well-specified problem though, even. – Noldorin Nov 17 '10 at 14:22
This is possibly an interesting problem but you have to make it clear what exactly you are after. For one thing, try to formulate it mathematically. "Color" doesn't really tell me anything. What I read is that you have foobars moving by the means of foobar laws. This has no mathematical content (not to mention physical). Also, what precisely is real movement and real space? – Marek Nov 17 '10 at 14:42
@Hans: I've never encountered the term "real space" before, but it seems to just be 3-dimensional Euclidian space. The whole idea of colours in confusing me though. It sounds like you're describing a scalar field. – Noldorin Nov 17 '10 at 14:42
The idea of Euclidian space is very much tied in with the physical reality. Newtonian physics only works in a Euclidian space, and GR talks about differential manifolds that reduce to Euclidian space on a small-enough scale. – Noldorin Nov 17 '10 at 15:34

The answer to your question is that the way we perceive reality is governed by physical laws as well. In your coloured sphere model, the coloured sphere people would perceive the changing of colour as we perceive movement.

In fact, it is quite customary in physics to think using completely abstract representations of space, and only ultimately reduce the equations to real space. In other words there are representations of the universe which do not resemble real space, but are equally as valid.

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