# Is length contraction direction independent?

1. Aug 8, 2012

### phyti

U is the universal rest frame. A and B space ships pass U at t=0, moving at v. Both experience equal length contraction in the x direction.
If length contraction is a result of em deformation in response to acceleration, then length expansion should be the response to deceleration. If the B ship slows to v=0 between t1 & t2, it should recover its original length.
According to SR, if B moves away from A, A should measure a length contraction of B.
So what happens?

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Last edited: Oct 31, 2013
2. Aug 8, 2012

### tiny-tim

hi phyti!
length contraction is a result of the geometry of space, it has nothing to do with electromagnetism

also, the standard length contraction formula, √(1 - v2/c2), depends on relative speed, not acceleration

in A's frame of reference, U is moving away from A, B starts stationary, and from time t1 to time t2 it accelerates away from A until it reaches the same velocity as U, and B's length is contracted increasingly from time t1 to time t2

3. Aug 8, 2012

### ghwellsjr

Just like speed is frame dependent, so is length contraction. A ship will be traveling at different speeds in different frames. Since length contraction is a function of the speed of the object in a particular frame, whenever the ship changes its speed in one inertial frame, it will also change its speed in all other inertial frames. Whether that change in speed is considered an acceleration or deceleration is frame dependent. In those frames in which it is an acceleration, the length contraction will increase. In those frames in which it is a deceleration, the length contraction will decrease, or, as you say, there will be length expansion. In fact, a given change in speed in one frame can result in both an acceleration and a deceleration in another frame resulting in no net change in speed and no net change in length.

4. Aug 8, 2012

### zonde

Yes, A is measuring length contraction of B. And the catch is in relativity of simultaneity i.e. in A's "now" he is longer than B while in B's "now" he is shorter than B. This is best seen in spacetime diagrams. For example like this one:

Now compare length of AC (in "now" of moving object) and AB (in "now" of stationary observer).