Relativistic physics of space?

[Wizardsblade]

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?

 

[pervect]

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.

 

[Wizardsblade]

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

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

 

[Janus]

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

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.)

 

[pervect]

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

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

Have you read about the barn and pole "paradox" in SR?

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

A Special Relativity Paradox: The Barn and the Pole

These are the props. You own a barn, 40m long, with automatic doors at either end, that can be opened and closed simultaneously by a switch. You also have a pole, 80m long, which of course won't fit in the barn.

Now someone takes the pole and tries to run (at nearly the speed of light) through the barn with the pole horizontal. Special Relativity (SR) says that a moving object is contracted in the direction of motion: this is called the Lorentz Contraction. So, if the pole is set in motion lengthwise, then it will contract in the reference frame of a stationary observer.

You are that observer, sitting on the barn roof. You see the pole coming towards you, and it has contracted to a bit less than 40m, in your reference frame. (Does it actually look shorter to you? See Can You See the Lorentz-Fitzgerald Contraction? for the surprising answer. But in any case, you would measure its length as a bit less than 40m.)

So, as the pole passes through the barn, there is an instant when it is completely within the barn. At that instant, you close both doors simultaneously, with your switch. Of course, you open them again pretty quickly, but at least momentarily you had the contracted pole shut up in your barn. The runner emerges from the far door unscathed.

But consider the problem from the point of view of the runner. She will regard the pole as stationary, and the barn as approaching at high speed. In this reference frame, the pole is still 80m long, and the barn is less than 20 meters long. Surely the runner is in trouble if the doors close while she is inside. The pole is sure to get caught.

Well does the pole get caught in the door or doesn't it? You can't have it both ways. This is the "Barn-pole paradox." The answer is buried in the misuse of the word "simultaneously" back in the first sentence of the story. In SR, that events separated in space that appear simultaneous in one frame of reference need not appear simultaneous in another frame of reference. The closing doors are two such separate events.

SR explains that the two doors are never closed at the same time in the runner's frame of reference. So there is always room for the pole.

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.

 

[Wizardsblade]

Thanks Janus looking from a pure measurment view makes more since.