**1. Suppose the space time co-ordinates of two events in inertial frame S are as follows:**

Event 1:

x1=x0, t1=x0/c y1=z1=0

Event 2:

x2=2x0, t2= x0/2c y2=z2=0

Show that there exists an inertial frame s' in which these events occur at the same time (i.e t1'=t2') and find the value of time for which these events occur in this reference frame.

Event 1:

x1=x0, t1=x0/c y1=z1=0

Event 2:

x2=2x0, t2= x0/2c y2=z2=0

Show that there exists an inertial frame s' in which these events occur at the same time (i.e t1'=t2') and find the value of time for which these events occur in this reference frame.

**2. You may assume that: (Δx)^2+c^2Δt^2=(Δx’)^2 + (Δt’)^2**

**3. I think I have a solution but annoyingly have not used the above asssumption which I want to do as it is given in the question. Anyway I did the following:**

Firstly I set t1'=t2' from this it follows that γ(x0/c - ux0/c^2)=γ(x0/2c-2ux0/c^2) (by the lorentz x co-ordinate transformations) rearranging gives that u=-0.5c. Indeed u=-0.5c seems to work giving t1'=t2'=√3x0/c. However, I am unhappy with my answer in that firstly I seem to have assumed it rather than proved it and secondly I did not use the above assumption. Any guidance would be very welcome.(By the way this is not assesed work merely revision so feel free to give as much help as you deem appropriate).Firstly I set t1'=t2' from this it follows that γ(x0/c - ux0/c^2)=γ(x0/2c-2ux0/c^2) (by the lorentz x co-ordinate transformations) rearranging gives that u=-0.5c. Indeed u=-0.5c seems to work giving t1'=t2'=√3x0/c. However, I am unhappy with my answer in that firstly I seem to have assumed it rather than proved it and secondly I did not use the above assumption. Any guidance would be very welcome.(By the way this is not assesed work merely revision so feel free to give as much help as you deem appropriate).

Last edited: