Relativity and Spatial Dimension

[ajjjja]

If mass influences the 'shape' of three dimensional space plus time, does that require a further or higher spatial dimension, or is that unnecessary?

 

[Neo_Anderson]

If mass influences the 'shape' of three dimensional space plus time, does that require a further or higher spatial dimension, or is that unnecessary?

Mass doesn't determine the structure of spacetime; matter does. Mass is simply defined as, "a resistance to a change in motion" and nothing more.
BTW, why don't three spatial dimensions work just fine? Why an additional spatial dimension?

 

[Jolb]

General Relativity states that the presence of mass/energy changes the geometry of spacetime. We have three (noneuclidean) spatial dimensions and one time dimension--for a total of 4, and that's it for general relativity.

You might be intrigued by something called "Kaluza-Klein" theory. By incorporating another spatial dimension into general relativity, Kaluza managed to derive the laws of electromagnetism.

M-theory's up to 11 or so, last I heard...

 

[diazona]

If mass influences the 'shape' of three dimensional space plus time, does that require a further or higher spatial dimension, or is that unnecessary?

If I correctly understand what you're asking, no, an extra dimension is not necessary.

You may be thinking of curved 2D surfaces as an example. For example, a sphere. I'm guessing that you can't imagine how one could have a 2D surface that is curved like the surface of a sphere without there being some higher-dimensional space for the full sphere to live in. Am I on the right track?

If so, I don't blame you, since this is a tricky idea to get used to, but it is in fact possible to have, say, a spherically curved 2D surface without there being a whole 3D sphere. You can actually measure the curvature of a surface without leaving the surface itself. The method for doing so is, roughly speaking, to measure how the distance between two points depends on the path you take between those points. Alternatively, you can measure the ratio of the diameter of a circle to its circumference, or the sum of the angles of a triangle, or other geometric things like that. In "flat" space they have the normal values we're used to (pi, or 180 degrees, respectively), but in "curved" (I prefer "distorted") space you will notice some different numbers. Still, these sorts of measurements are based only on the space itself, so there's no need to have any higher dimension.