# 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 $\Delta t$.