# Special Relativity

## Homework Statement

Consider two events
$$ct_{1}\; =\; 3\; m,\; x_{1}\; =\; 2\; m,\; ct_{2}\; =\; 5\; m,\; x_{2}\; =\; 6m$$

1. What is the time difference between the two events?
2. Find a reference frame for which the time difference is the negative of the time difference in the original frame.
3. Calculate the invariant interval $$\left( \Delta s \right)^{2}=+c^{2}\left( t_{2}-t_{1} \right)^{2}-\left( x_{2}-x_{1} \right)^{2}-\left( y_{2}-y_{1} \right)^{2}-\left( z_{2}-z_{1} \right)^{2}$$ in both frames.

## The Attempt at a Solution

I honestly don't have any idea what the first question is actually asking. How can I calculate a time difference when I am only given these distance figures with no velocities? It seems like an extremely poorly worded question.

Last edited:

vela
Staff Emeritus
Homework Helper

## Homework Statement

Consider two events
$$ct_{1}\; =\; 3\; m,\; x_{1}\; =\; 2\; m,\; ct_{2}\; =\; 5\; m,\; x_{2}\; =\; 6m$$

1. What is the time difference between the two events?
2. Find a reference frame for which the time difference is the negative of the time difference in the original frame.
3. Calculate the invariant interval $$\left( \Delta s \right)^{2}=+c^{2}\left( t_{2}-t_{1} \right)^{2}-\left( x_{2}-x_{1} \right)^{2}-\left( y_{2}-y_{1} \right)^{2}-\left( z_{2}-z_{1} \right)^{2}$$ in both frames.

## The Attempt at a Solution

I honestly don't have any idea what the first question is actually asking. How can I calculate a time difference when I am only given these distance figures with no velocities? It seems like an extremely poorly worded question.
The first question is just a unit conversion. What does c stand for?

Well c = 3*108 ms-1. So t1 = 1*10-8 s and t2 = (5/3)*10-8 s.

I guess assuming these are both observed from a laboratory frame of reference then the time difference is just t2 - t1 = (2/3)*10-8 s?

It was a simple question, but the obscure way in which it was asked threw me off. Typical me, struggling with the simple stuff but I can much more easily understand the complicated things Thank you for your help. Hopefully I can do the other two problems myself!