# Spacetime Interval

1. Jun 20, 2012

### Monster007

1. The problem statement, all variables and given/known data

The spacetime interval between the origin in frame S and an event, A, is found to be r = 8
lightseconds. In frame S' moving in Standard orientation with respect to S at speed v =
0.5c event A is measured at a distance r' = 6 lightseconds from the origin.

(a) What is the time interval between the origin in S' and event A?

(b) Could an event at the origin and event A be causally related? Explain your answer

2. Relevant equations

3. The attempt at a solution

I am studying for upcoming exam so the solution isnt as important as understanding the question, but as far as i know the spacetime interval is invariant which is throwing me way off here, I'm certain if i can get part a i understand part b but am completely at sea with part a) any help will be greatly appreciated, cheers.

2. Jun 22, 2012

### BruceW

Yes, the spacetime interval is invariant. Question (a) asks for the time interval, not spacetime interval.

3. Jun 22, 2012

### collinsmark

Also, in addition to what BruceW mentioned,

I suspect that when the problem statement said,
"...distance r' = 6 lightseconds..."
it's not asking for the spacetime interval to A, but really asking for the x' component of r. In other words, the distance from the origin to the projection of A onto the x' axis.

It probably would have been clearer if the problem statement was worded, "measured at a distance x' = 6 lightseconds."

In other words, the spacetime interval from the origin to A is 8 lightseconds (true whether one is in S or S', since spacetime intervals are invariant). And in S', the spacial distance (not spacetime distance) from the origin to A is 6 lightseconds. Still in other words, this "6 lightseconds" vector lies along the x' axis itself.

That's my guess as to what the problem statement is trying to say.