I am currently learning about relativity of simultaneity right now, and I feel like this is a common phenomena that we experience every day (question at end). The example from Fundamentals of Physics by Halliday, Walker, and Resnick is as follows: "Suppose that one observer (Sam) notes that two independent events (event Red and event Blue) occur at the same time. Suppose also that another observer (Sally), who is moving at a constant velocity v with respect to Sam, also records these same two events. Will Sally also find that they occur at the same time?" Here is a picture of the problem below in which the two observers are Sam and Sally:
The answer to this question is that Sally will find that these two events do NOT occur at the same time. In a different scenario, instead of a light pulse being released as a result of the event occurring, a sound wave is released. Wouldn't Sam and Sally still record the same results as in the example above? What makes simultaneity so different in special relativity?
Best Answer
The crucial mistake you are making is to focus on the reception of the signals, not the events that generated them. Clearly Sally receives the blue and red signals at different times, and that would be true whether we were talking of light or sound. The difference is that the speed of light is constant in Sally's frame, so if the two signals arrive at different times, having travelled the same distance, they must have been emitted at different times. However, with sound, the speed of sound coming from the front of the train will be higher than the speed coming from the back of the train (assuming the sound is travelling through the air outside the train), so although the signals arrive at two different times, the events that caused the sound to be emitted can still be considered simultaneous.