Special Relativity simultaniety

1. Sep 18, 2016

PhysicsInNJ

1. The problem statement, all variables and given/known data
Two events occur in an inertial system K as follows.
Event 1: x1 = a, t1 = 2a/c, y1 = 0, z1 = 0
Event 2: x2 = 2.6a, t2 = 1.9a/c, y2 = 0, z2 = 0

What is the velocity of the frame K' in which these events appear to occur at the same time? Express the velocity vector using the variables a and c and the unit vectors, i, j, and k; for example, 2*i + 2*j is a vector which bisects the x and y axes.
2. Relevant equations
Lorentz equations

3. The attempt at a solution

First I assumed that I could use the time dilation, T0=T/Ɣ with T (the observed time) being zero but that obviously will not work. I likewise tried it with length contraction.

I dont know where else to go from here.

2. Sep 18, 2016

Simon Bridge

HInt: "simultaniety" and "Lorentz transformation".

3. Sep 18, 2016

PhysicsInNJ

So the K' would have to travel the distance between event 1 and 2, in the amount of time between the events?

4. Sep 18, 2016

TSny

Wouldn't this make the two events occur at the same place in K' rather than occur at the same time in K'?

5. Sep 18, 2016

Simon Bridge

You know the space-time coordinates for the events in K.
Use the Lorentz transformation to get equations for the space-time coordinates in another reference frame.

6. Sep 19, 2016

Staff: Mentor

PhysicsInNJ: Please write down for us the Lorentz equations for $\Delta x'$ and $\Delta t'$ in terms of $\Delta x$ and $\Delta t$.