Is it known if space:
1. is "grainy" or smooth ?,
2. has singular points ?,
3. is like R^3 ?
the physical space i think is amazing, you know its exist but sometimes it is so abstract!
Remember that space is an element/subset of space-time.
For all intents and purposes, space-time is very smooth. On the smallest scales, we don't know; its possible that space-time is riddled with vacuum fluctuations just like quantum fields. We might need a quantum theory of gravity to find out.
General relativity (GR) says that space-time does have singular points, but most people believe thats just a sign of GR's incompleteness---and once we have a good quantum theory of gravity, those singularities will be smoothed out.
I'm not sure what you mean here. If you mean, is space euclidean---then the answer is 'asymptotically yes', but locally no---thats why we need general relativity.
If you're asking if it has three dimensions, then---at least macroscopically---yes. But there may be 'hidden' microscopic dimensions.
Thank you both for the replies.
Sorry question 3 wasn't specific enough.
Could physical space have a different topology than the usual R^3 ?
Yes, the simplest of them being a 3-torus.
Yeah; well, apparently its invisible, transparent to light, and even weightless ! And even though it is very hard to grasp, I have managed to get some excellent samples of deep space for further experimentation.
I found space to be very stiff. Nevertheless I was able to make massive objects pass right through it unhindered ! and was even able to make it appear to bend in a graviational field ! ;))
So you can have hours of fun and experimentation....we are offering these excellent untouched samples of space for the unheard of low low price of $12.95 per cubic centimeter...(plus s & h).
Call 1-800-vacuum; hurry before the supply runs out. :)
How does this interplay with measurements of flatness? The universe is flat to some high percentage, so does that place limits on the curvature of such a torus (i.e. analogous to the toroidal radius of a 2-torus)? Then, if such limits were placed, would that provide limits on the size of the universe?
The 3-Torus is actually spatially flat everywhere, so the measurements of flatness only support such a theory. One idea of how to place limits are whether or not we see radiation running along the compactified dimensions of the torus, i.e. multiple images of the same objects. This of course gives you only an lower limit to the 'radius' of the torus, but I don't know of any actual experimental bounds on this from CMB data, for example.
Aw man... so much for my conceptions of understanding.
I'm going to start a new thread on this; would appreciate if you continued the conversation there Nabeshin.
Separate names with a comma.