Help understanding a SR equation

[Reikoku]

Hi all, I'm currently a stage 1 Physics student at uni; and in the process of learning Special Relativity.

I was reading my textbook and came across this in the Time and Space section:

Suppose an observer in frame S measures two flashbulbs going off at the same time t but at different x-coordinates x1 and x2. Then an observer in frame S` would measure the time interval t`1 - t`2 between the flashbulbs going to be:

t`1 - t`2 = $\gamma$((x2-x1)*(u/c)^2)

I was wondering why it's t`1 - t`2 instead of the usual t`2 - t`1. I assume it's to prevent the final answer being negative? I feel like I'm being stupid asking this :|

 

[Doc Al]

It's just to get rid of a minus sign. The full transformation is:
$$\Delta t' = \gamma(\Delta t - v\Delta x/c^2)$$

Since Δt = 0, you get:
$$\Delta t' = -\gamma(v\Delta x/c^2)$$

Where Δt' is the usual t'₂ - t'₁. But if you switch the order you can get rid of the minus sign on the right hand side.

 

[Reikoku]

Yeah that makes sense now, cheers! :D