# Special Relativity vs. Curled up spacial dimensions

1. Jan 8, 2010

### Zula110100100

Special Relativity vs. "Curled up" spacial dimensions

To be more specific I mean the 3 familiar spacial dimensions not extra ones(unless I guess they are large enough for SR to be effective). Anyway, I was reading a book on Superstring Theory(Which is why I say not extra ones it proposed extra culred dimensions which if were sub-planck length would not be detectable to us), I don't have it with me to cite to author, but it said it hasn't been proven or disproven that the familiar spacial dimensions are or are not curled upon themselves. And so in theory you could return at the same point by going to a straight line.

From what I know of SR and the constant motion clock examples two people with clocks floating in opposite directions through space would feel to be at rest with the other moving relative to them causing the slowing of time for each other but on a symmetrical basis so the paradox is negated due to the fact logistically it could not be compared accurately enough by either accelerating back causing the one accelerating to have agreed upon tile slowing, or a signal sent at light speed making up for the lag.

So if we had an empty path(No gravitational influence or at least negligible) through the universe that was curled upon itself the two clock would eventually meet back up, each observer expecting the other to be behind theirs and find the clocks reading the same time. Since SR has been proven in many instances this should either disprove the theory of curled up spacial dimensions in which SR is at play...or there is more I don't know as I am I would say amatuer at best.

2. Jan 13, 2010

### tiny-tim

Welcome to PF!

Hi Zula110100100! Welcome to PF!

Take a 3D version of the screen of the "Asteroids" video-game …

if you go off one edge, you immediately come back at the opposite edge.

This is a flat space, with only 3 dimensions, all curled-up.

… would SR in such a space produce a paradox, thereby proving the impossibility of SR in such a space?

Seems plausible

anyone else have any thoughts?

3. Jan 13, 2010

### atyy

4. Jan 13, 2010

### marcus

Re: Special Relativity vs. "Curled up" spacial dimensions

I was not aware of the Barrow Levin paper. It's a fascinating non-intuitive result.
Thanks for spotting it!

Here is a more recent paper that goes over similar ground and which I find in some respects easier to read:
http://arxiv.org/abs/gr-qc/0503070
Here the result is proven in the case where there one compact spatial dimension, as in a cylinder.
I still have a hard time believing the Barrow Levin claim that a compact spatial topology gives a preferred frame.

Maybe it depends on having the compact space be non-expanding. Could this be?

The paradox seems to arise when one or both make a full circuit along a geodesic. If space is compact and non-expanding this can happen. But in an expanding universe like ours, even if space is compact, one cannot circumnavigate. One cannot go fast enough. One would have to freeze the expansion in order to make a circuit.

Last edited: Jan 13, 2010
5. Jan 14, 2010

### tiny-tim

So two of those three papers show that, in a non-expanding 3D space with one curled-up dimension, you can have SR only if you have a preferred frame of reference.

Also Couolmb's law (1/r2 field from a point electric charge) is different.
So before inflation in our universe, there was a preferred frame?

6. Jan 14, 2010

### arivero

Re: Special Relativity vs. "Curled up" spacial dimensions

Yep it is a issue of General Relativity, no need of extra dims to think about the problem.