# Relativity along an axis in an inertial frame

1. Jun 6, 2013

### ZanyCat

Suppose that two events occur on the x axis of an inertial frame, Δx apart with a time interval between the events of Δt.
a) the proper time interval between the events is...?
b) the proper distance between the events is...?

I think I'm just getting confused by the wording. I imagined that I was in the same frame of reference, and therefore the answers are Δt and Δx. But evidently, I'm wrong. Do I need to set the speed of the frame to 'v' and do something with simultaneous equations to remove that variable?

Thanks!

2. Jun 6, 2013

### ZanyCat

OK, so I defined a stationary reference frame as S, and defined the frame in the question as S'. S' is moving wrt S at a velocity v.
So the proper time is the Δt observed in S', and the proper length is the Δx observed in S'.

I think I've worked out a, but struggling with b. I'm using the length contraction formula as one equation, and the Lorentz coordinate transformation as the second equation, but when I solve them simultaneously I can only achieve v=0.

3. Jun 6, 2013

### voko

Start with definitions. What are proper time and distance?

4. Jun 6, 2013

### ZanyCat

Proper length is measured distance in the FOR where the objects are at rest, i.e. in frame S'.

I'm using the equations L' = L/gamma and x' = gamma(x-vt) and trying to solve these simultaneously, am I on the right track?
I can't determine whether L' = x' and L = x, or L' = x and L = x', though...

5. Jun 6, 2013

### voko

What are the "objects" in the case? Are they at rest as stated? In what reference frame are they at rest?

6. Jun 7, 2013

### ZanyCat

The objects are two arbitrary points situated along the x axis of S', and are at rest in frame S', thus always separated by delta x.

7. Jun 7, 2013

### voko

If you measure distance between two arbitrary points, you get arbitrary results. I do not think this is what the problem is about. Connect "objects" with the description of the problem.

8. Jun 7, 2013

### HallsofIvy

Staff Emeritus
Given the information as stated, with everything motionless in an inertial frame, why would the "proper time interval" not be $\Delta t$ and the "proper distance" $\Delta x$.

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