# Relativistic physics of space?

1. Nov 20, 2005

As I understand it the empty space (vacuum) in a relativistic system contracts as well as the matter. I.e. when a wall traveling at relativistic velocities contracts the whole wall shrinks to a smaller size; the wall does not continue to stay the same length and only the bricks shrink:
B=brick
S=vacuum

BBBBSSBBBBSSBBBB

contracts to
BBSBBSBB

and not
BBSSBBSSBB

Now the questions I have are... where does the contraction of vacuum end? I.e. 1 meter form the moving object, directly adjacent to the object, or maybe it tapers off? Also, if one area of space contracts does this mean that another area must expand? I.e. if something is contracted by half what now fills the void where it was expected to be?

Last edited: Nov 20, 2005
2. Nov 21, 2005

### pervect

Staff Emeritus
The contraction never ends - why did you think it would?

If one meter stick contracts, it doesn't mean another one somewhere else expands.

In any non-accelerated frame, the amount of contraction is constant. The amount of contraction changes in an accelerated frame, howver. (The case of an accelerated frame is one that can be handled with advanced SR - some of the techniques of GR are very helpful to handle this case, though. GR itself is not strictly necessary - there's no need for Einstein's field equations, for instance).

There are varioius ways of interpreting the effects of contraction, but it's possible to have the velocity due to this spatial contraction exceed the speed of light for distant objects from the POV of an accelerating frame.

There are other ways of looking at it than your "stretchy space" paradigm, BTW.

3. Nov 21, 2005

Well assuming the wall is of finite length and that an object (i.e. a star) could be behind the wall that was not contracted, because it shares my reference frame, it made since that the contraction must end somewhere.

And what exactly do you mean by the contraction never ends? If the wall is the accelerated object only the wall contracts correct?

For example if I had a huge metal sphere r=1 light year, would its symmetry change if this wall where inside of it? Maybe compare the wall at rest to the wall moving inside the sphere?

Thanks

4. Nov 21, 2005

### Janus

Staff Emeritus
Try not thinking about the space between the bricks as a physical substance that shrinks and more along the line as the distance between the bricks bcomes less as measured by someone moving wrt to the wall.

Reverse your example, and consider the sphere moving with respect to the wall. The sphere contracts but the wall, inside the sphere, does not. (as measured by someone at rest wrt to the wall.)

5. Nov 21, 2005

### pervect

Staff Emeritus
I'm having a hard time following this without a diagram.

http://math.ucr.edu/home/baez/physics/Relativity/SR/barn_pole.html

There is more in the above link, this isn't the complete article...

Anyway, there is no acceleration in this problem at all (which makes things much simpler), and it illustrates how length contraction works in SR. If you could either draw a diagram of your question in ascii, or reprhase it in the "barn/pole" paradigm, I could attempt to answer it.

6. Nov 21, 2005