Ok this one shows the train and the lightning strikes.
First diagram - you're observer on the train in the middle of the two lightning strikes. In your frame of reference they are
simultaneous.
Second diagram - an observer on the platform adjacent to you at precisely the moment you calculate the lightning strike's occurred.
For the observer the back strike occurred
8.77 seconds ago and the front strike will not occur for another 8.77 seconds.
Alternative approach
He will see your front clock reading -1.2375 seconds of what your back clock says.
This is because Velocity x distance = time 0.99 x 1.25 = 1.2375 train seconds
1.2375 train seconds x gamma =
8.772 observer seconds.
So this is why you see the back and front strikes which he considers simultaneous separated by + / - 8.772 seconds respectively.
Reason
The best way to understand it is that the spacetime interval for any two events is invariant; and that between any two events there exists a Proper distance or a Proper Time, which cannot be reduced by any observer.
The interval is like a sort of unique code between any two events, which all observers will agree on whatever they're inertial frame.
(interval = distance - time)
The moment of the lighting strikes was a space like event. This produces a certain type of interval which is the same for all observers whatever their intertial frame - its not possible for anyone even light, to have been at both space like events. There is a fixed distance gap between the events which cannot be eliminated.For the train the events were simultaneous and therefore it can measure the
Proper Distance.
No other observer in the Universe can possibly measure a lower Proper Distance unless they share the trains frame of reference. Also, no observer can record Less time between the events than the train because... the train measured 0 time between events.
Therefore any other observer must either add time, or add distance to the trains measurement. And, because of the formula they cannot add one without the other otherwise the
interval will increase.
Because the Proper Distance cannot be reduced if any observer wants to use a different reference frame and measurement system the only thing they can do is add extra distance to the train's measurement. This is because the train already has the lowest possible distance and 0 time.
Because
the spacetime interval is the same for all observers and the formula is interval = distance - time. If an observer adds time, then they must also add distance. Alternatively, If they add distance then they must also add time.
For the observer on the platform the train's clocks are not synchronised and so the train moves between lightning strikes. The events are therefore separated by a greater distance than for the person on the train
To keep the interval fixed, the observer must add an appropriate amount of extra time between the events to match the extra distance.
interval = train distance plus the observers extra distance - (train's time (zero)
+ the observer's extra time)
