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The curious thing about space is that it seems to have certain definite properties of its own. For example, it is three dimentional. If it is just nothing, why can't you erect as many mutually perpendicular axes as you like?
How exactly would "nothing" expand or contract?
The problem with the term "space" is that it has no specified physical meaning in GR theory to begin with. GR theory describes "spacetime" geometry which in turn is *caused* by the concentration of mass/energy. The term "space" isn't even physically defined in GR.
The curious thing about space is that it seems to have certain definite properties of its own. For example, it is three dimentional. If it is just nothing, why can't you erect as many mutually perpendicular axes as you like?
I would say the properties you observe are not properties of "space", but of the material occupying that space.
Also, theorectically, you can create more than 3 perpendicular axes. I was heavily influenced by Flatland and my father (a mathematics teacher), and for a long time held the view that infinite dimensions exist, but we can only perceive 3. I've since changed that view. I still believe infinite dimensions are possible, but only because I see them as a mathematical description of the material, and so a dimension is not a thing. It's a property of the material.
Space is what you get when you fix the time coordinate, and take a three dimensional slice of spacetime; just as a circle is what you get when you fix one coordinate, and take a two dimensional slice of a sphere.
Mathematicians, and even physicists, can find uses for spaces with an infinite number of dimensions, but again, they are not supposed to represent physical space, which only seems to have three dimensions.
The problem with the term "space" is that it has no specified physical meaning in GR theory to begin with. GR theory describes "spacetime" geometry which in turn is *caused* by the concentration of mass/energy. The term "space" isn't even physically defined in GR.
How are you physically differentiating then between ordinary distance and what you're calling "space"?
You're missing my point. When you construct these 3 perpendicular axes, what are you constructing them from? You seem to be insisting that we speak of demonstrable things. I doubt you could build anything from "space". When you construct 3 perpendicular axes, you have constructed a thing from materials.
We're talking about space. As such, there are multiple ways to describe space, and not all of them use 3 dimensions.
Conceptually they don't need to be made out of anything. They can be three field lines.
This thread is not about any kind of exotic spaces. It is about the kind of space we live in - i.e. Euclidean space.
Dimensionality is determined by the number of linearly independent vectors you can have in a space. And in physical space that equates to the number of mutually orthoganol axes.
Actually, I think modern physics says we live in a Riemannian space, not a Euclidean space. I'm saying it's neither.
So are we talking about conceptual spaces or real spaces?
We are talking about the space we live in.
Actually, I think modern physics says we live in a Riemannian space, not a Euclidean space. I'm saying it's neither. You're not describing a space, but the objects in space. A Cartesian coordinate system is an object in a space used to locate points according to a Euclidean model.
If you are talking about Special Relativity, we live in Minkowski Space. If you are talking about General Relativity, we live in whatever weird geometry the distribution of matter throws up. None of which alters the fact that there are three spatial dimensions.
Don't bother dragging in string theory, because it wouldn't answer the question about something which is apparently "nothing" can have any properties at all.
Are you saying that a mechanism with 3 rotational joints and 1 slider joint doesn't have 4 independent degrees of freedom? It's not a mechanism that describes an exotic space. It fits quitely nicely into the physical space where we live.
I am saying that the dimensionality of a vector space is DEFINED as being the number of linearly independent vectors it can play host to.
We are talking about the space we live in.
Don't bother dragging in string theory, because it wouldn't answer the question about something which is apparently "nothing" can have any properties at all.
Let us finish with a question resembling a Buddhism-Zen `koan': in an empty universe, what is expanding?
The curious thing about space is that it seems to have certain definite properties of its own. For example, it is three dimentional. If it is just nothing, why can't you erect as many mutually perpendicular axes as you like?
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