Does the Lorentz equation preserve causality?

[silenzer]

Homework Statement

Observer S' moves at a speed u compared to observer S in x-direction. Two events happen on the x-axis of S, with the coordinates x1 and x2 at times t1 and t2 measured in S. Let L = x2-x1 and T = t2-t1.

a) If the events happen at the same time in S, does the same apply to S'? b) What relationship must there be between L and T for the order of the events become switched? c) Let there be a causal relationship between the events. Can the order seem different in S'?

Homework Equations

The Lorentz equation t = (gamma) * ( t' + x' * u / c^2 )

The Attempt at a Solution

a) The answer to this is no, because they happen at varying units of x. If they had happened at the same location, the answer would be yes.

b) Not really sure, other than to have the product on the right in the parentheses be larger than t', resulting in a negative time for t. Only thing is, I don't know what that means in terms of the Lorentz equation...

c) Obviously no.

 

[voko]

Let's assume that T > 0. Then, in (b), T' < 0. Find what T' is, and see what it takes for it to be negative, assuming T is positive.

 

[Chestermiller]

You need to use both Lorentz equations, not just one of them. And you need to use the version where x' and t' are expressed in terms of x and t (rather than the other way around).

Chet

 

[vela]

c) Obviously no.

I think you're meant to show that the Lorentz transformation preserves causality.