# Lorentz contraction question

1. Jun 3, 2010

### Taturana

My question is: why does Lorentz contraction happens?

I have a understanding of this but I don't know if it's correct, so I'll tell what I understand, if I'm wrong please correct me...

Suppose we have two observers A and B. If I say B is moving with respect to A then time is slower to B than to A. Also, if A measures B's dimension, he'll get a smaller measure than if B would do. Right?

So, we have that v = ds/dt, then if we know that B's dt is smaller than A's dt, B's ds should be smaller too so they agree with respect to the velocity. Is that right?

Sorry for my very bad english...

2. Jun 3, 2010

### LostConjugate

I am not sure how to address your way of doing the calculations, however they will not agree with respect to velocity. This is because their velocity has a relative difference.

If B has a coin and lets this coin float next to him/her, the coin will be stationary for B, while A will see the coin with a velocity.

Another way of looking at it is $$x_A = x_B - vt_A$$ where x is position.

If $$x_B$$ is stationary then $$\frac{d}{dt}x_A = -v$$

note: $$t_B = \frac{t_A}{1 - (v/c)^2}$$

Last edited: Jun 3, 2010
3. Jun 3, 2010

### Thought Grind

It would seem to me that the abstract needs another factor for B to see something different than A. Like their relative position in a dynamic space-time. Otherwise they would each see the same thing and wouldn't even notice the compression without a change in velocity.

As to your first question, it depends on the coordinate system used. If you use a coordinate system that has a fixed point of reference relative to the universe within existence, you would not need a flexible system. (Something that doesn't exist at the moment.) If you can find the center of the universe or an equivalent you should have said fixed point of reference. You could make it up, say the Earth is the center, but then you would have to continually change factors to make up for planetary, galactic, and intergalactic contingencies both known and unknown. Thus the existence of Lorentz contraction issues and the like.

Don't take my word for it, go look for yourself.