## Special Relativity: Find the reference frame in which two events are Simultaneous

1. The problem statement, all variables and given/known data
events A(ct,x)=(1m, 2m) and B(ct,x)=(3m,4m) are separated in a lightlike interval. I need to find the velocity of a seperate reference frame in which they BOTH occur at the same time.

Next I need to find the velocity of the frame where they will occur at the same LOCATION.

2. Relevant equations
t=(gamme)t'

3. The attempt at a solution
To solve for this, I need to find where the t' for both events is equal. But when i set tb'=ta', everything cancels out and I end up getting 1=3. Is there any other way of doing this that I am missing? I am getting the same problem with the location part as well.

 Or am I just doing this completely wrong?
 Recognitions: Science Advisor This problem appears to have been designed to force you to think about the physical situation it describes before you jump into the equations and formulas. Think about why we use the word "lightlike" to describe some intervals.

## Special Relativity: Find the reference frame in which two events are Simultaneous

Hmmm... Well Lightlike means they are only in a causal relationship if you use light. So would the frame of reference have to moving at speed c? I thought you can't have a frame moving at speed c?

Recognitions:
Gold Member
 Quote by khfrekek92 Hmmm... Well Lightlike means they are only in a causal relationship if you use light. So would the frame of reference have to moving at speed c? I thought you can't have a frame moving at speed c?
That's a bingo!
 Oh! Duh, why didn't I think of that? So if they were in a spacelike interval, you still wouldn't be able to have them happen at the same time, would you?

Recognitions:
 Quote by khfrekek92 Hmmm... Well Lightlike means they are only in a causal relationship if you use light. So would the frame of reference have to moving at speed c? I thought you can't have a frame moving at speed c?
A better description of lightlike separation might be that a flash of light could have been emitted at one event and absorbed at the other... But this definition will bring you to the same result.
 Remember that ds^2 is an invariant. This means that if ds^2=0 in one frame, then it is 0 in all frames. Further, this means that ds^2 can never change signs. 2 events which occur at the same time must have ds^2<0 (assuming metric (+ - - -)), and 2 events which occur at the same point in space must have ds^2>0.

Recognitions: