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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:

Example from Fundamentals of Physics by Halliday, Walker, and Resnick

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?

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    $\begingroup$ The important part is that, after obtaining the best information and deducing backwards from all the observed facts, the two observers would disagree on whether two events happened at the same time or not. There is no such disagreement in old Newtonian physics. Sound waves are just not fundamental to the universe, and you could explain the discrepancy in sound waves by the properties of the medium in which sound waves travel. $\endgroup$
    – naturallyInconsistent
    Commented May 9, 2023 at 4:05
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    $\begingroup$ I do not like this graphic. Is it really from HRW? It makes it sound as if the issue of simultaneity is a result of light waves chasing moving observers relative to stationary ones. The simultaneity issue works when light is not involved at all. The simultaneity issue is baked into the geometry of the universe. Light is not needed. There is an issue of light propagation, but that is different, and it is piled on top of the geometrical aspect. $\endgroup$
    – garyp
    Commented May 9, 2023 at 4:54
  • $\begingroup$ @garyp I think the original problem did not include the light, it was just a question of mine. Perhaps I could have rephrased the question as, "Why is simultaneity unique to special relativity, do we not already see it in classical mechanics?" $\endgroup$
    – Ayush Kumar
    Commented May 9, 2023 at 5:04
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    $\begingroup$ Why is relativity of simultaneity so special? - Because it is Special relativity? ;) $\endgroup$
    – Roger V.
    Commented May 9, 2023 at 7:11
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    $\begingroup$ It’s not at all “a common phenomenon that we experience every day”, because (unless we’re astronomers) we are never moving at a significant fraction of lightspeed relative to events in which we are interested. $\endgroup$
    – Mike Scott
    Commented May 10, 2023 at 4:00

2 Answers 2

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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.

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For one thing, in the sound example the pressure waves are moving through the air or some fluid medium. You could choose a reference frame where the bulk motion of the fluid with respect to the observer is zero (no "headwind") and say that is the "true reference frame" in which to measure the times and order of events. With light, Einstein shows that there is no underlying medium which is "absolutely at rest" (e.g. ether), and both the "stationary" and "moving" frames are equally valid. Indeed, you cannot tell which is a "moving frame."

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