Consider a rocket traveling at speed v, as shown in Fig. 4. There is an observer O at rest with respect to the rocket and an observer O' riding with the rocket. Two lightbulbs at the ends of the rocket were timed such that their flashes arrive at the observers at the same time. Light from the bulbs traveled towards the observers at the speed of light, c, in the reference frames of both observers. The figure shows how O and O' are lined up when the light arrives.
For O' (on the rocket), the bulbs must have flashed simultaneously because O' is right in the middle. The bulbs are at rest in the frame of O'.
The other observer, O, draws a different conclusion. When the flashes were emitted, the rocket was not centered on O; it was to the left. The pulse from the bulb on the left must have been emitted first; it had farther to travel. Likewise, the pulse from the bulb on the right had a shorter distance to travel. Observer O concludes that the bulbs were not flashed simultaneously.
So, observer O' thinks the events (flashing of the bulbs) were simultaneous while observer O does not. Simultaneity is not independent of reference frame.
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