# Lorentz transformation Problem, Confused on setting it up

1. Sep 16, 2012

### sealsix14

So this is my first course in upper level physics, and i'm still trying to figure out special relativity.

The problem:

Two events occur at the same place in a certain inertial frame and are separated by a time interval of 4sec. What is the spatial separation between these two events in an inertial frame in which the events are separated by a time interval of 6 sec?

I know the problem states that the two events occur in a certain inertial frame (frame S), and have a dt = 4. but I'm confused as to what It is exactly asking, is it asking what the d would be in another inertial frame where the dt = 6? I'm Just confused on setting up the problem and feel stupid.

2. Sep 16, 2012

### jfy4

I'm always rusty with this stuff too. SR is the hardest thing, don't believe people if they tell you otherwise ;) I would think that the total spacetime interval in both frames has to be the same, that is $(\Delta s)^2$ is the same in all frames. so lets use
$$(\Delta s)^2 = (\Delta t)^2 - (\Delta \vec{x})^2$$
In the first frame we know that
$$(\Delta s)^2 = (4)^2\$$
since there is no spatial change. But in the other frame it is
$$(\Delta s)^2 = (6)^2 - (\Delta \vec{x})^2$$
Now the kicker is that $(\Delta s)^2$ is the same for both frames. The question is then, what does $(\Delta \vec{x})^2$ have to be to make that true? I hope this helps/is right.

3. Sep 16, 2012

### Staff: Mentor

This problem seems to be designed to give you a little experience in applying the Lorentz Transformation. In addition to the method that jfy4 described, you can also solve this directly by using the Lorentz Transformation. Lets say that the two events occur in the S frame of reference. According to the problem description, what is the difference in spatial positions between the two events (Δ x) and what is the difference in times of the two events (Δt)? Now, from the Lorentz Transformation, what are the corresponding quantities (Δx') and (Δt') for the S' frame of reference (expressed in terms of the relativity factor γ and v/c)? Since the problem statement already tells you what Δt' is in the S' frame of reference(6 sec), you can use one of the LT equations to solve for γ, and then v/c. You can then substitute into the other equation to get Δx'. The result you get should match what jfy4's method gives.

4. Sep 16, 2012

### sealsix14

Thanks, I'll give this a try and see If I get anywhere with it.