You'll not be surprised to find that when Einstein abandoned absolute time and fixed space, the idea of "at the same time" lost some of its absolute character.
It is all tied very directly to accomodating Maxwell's Laws that say that the speed of light is always 186,000mi/sec.
Imagine that you are standing on a railway platform and a railway car passes along the track from left to right in a thunderstorm.
Suddenly, lightning strikes both the front and the rear of the railway car simultaneously, at the same time.
The light from these strikes moves toward the center of the railway car, and if it really is the center, the light from the front and the back should reach there at the same time.
Oh? Well not so! Assume the railway car is moving quite fast, let's say one tenth the speed of light. Then the "center" of the railway car will have moved to the right some distance while the light beams converge to the half-way point between the lightning strikes.
So, if you are inside the car, the light from the front of the car will reach you before the light from the back, and since from your point of view you are still in the center of the car, you conclude that the lightning struck the front of the car first, and the rear of the car slightly later.
You might think you ought to draw a different diagram for yourself inside the car, with the light coming at you in the center from the two ends of the car, and you would be clever to think of that. Clever, but wrong. Because the lightning strikes were simultaneous as seen from the platform, it is only in that frame of reference that one can assume that the light beams meet half way between the lightning strikes.
In the frame of reference of the railway car with the person in the center with arms outstretched, the light from the strikes can not be assumed to move inward from the ends of the car starting at the same time. Yes, light travels at a speed of 'c' in that frame of reference, but because the strikes don't occur simultaneously, the light beams do not meet in the middle.
It is precisely because we know where the light beams meet, and it isn't in the middle of the railway car, that we conclude that in the railway car frame, the strike at the front occurred first.
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