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In a very recent post here I recently learned that simultaneity has no meaning in general relativity; I can accept the answer and explanation that was given for that question.

But then Harry Johnston replied to my comment saying that the concept of simultaneity also has no place in special relativity - that it's just a pedagogical tool.

Is that right - simultaneity - what I take as two observers in separate reference frames not necessarily agreeing on when events happen, or even the order in which they happen - is just a pedagogical tool?

To what end? How does that prepare them for understanding general relativity?

I only have a cursory understanding of both SR and GR - but now I'm really confused.

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  • $\begingroup$ simultaneity has different meanings according to the authors. Some consider the raw measures and others do distances corrections. $\endgroup$ – user46925 Jun 4 '15 at 22:57
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    $\begingroup$ Note how harry stated "im my opionion," in abbreviation ("IMO"). Perhaps it has something to do with his understanding of the word. $\endgroup$ – Cicero Jun 5 '15 at 0:19
  • $\begingroup$ I like to think I know something about relativity, and I don't agree that the concept of simultaneity has no place in special or general relativity. Events occur at some place in some sequence. Two spaceships crash because they are at the same place at the same time. Simultaneously. The motion of observers doesn't change this one bit. They can argue about two separated spaceships, but their motion doesn't change those spaceships at all. $\endgroup$ – John Duffield Jun 5 '15 at 6:52
  • $\begingroup$ I disagree that it's just a pedagogical tool. It is, at the end of the day, a computational tool that brings calculations down to Earth. $\endgroup$ – FenderLesPaul Jun 5 '15 at 21:25
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In most introductions to Special Relativity, students learn a special procedure for setting up coordinates which involves synchronizing clocks with light pulses. This leads to a natural definition of simultaneous events as events which occur at the same coordinate time. The notion of simultaneity basically stems from a preference for a particular set of coordinates.

Its a fundamental principle in Relativity that the choice of coordinates is arbitrary (so long as you preserve the space time interval). The whole point of the subject is that there isn't a preferred reference frame. There is no coordinate invariant notion of simultaneity, so it doesn't make sense to talk about it in from this perspective, except to emphasize that its not a thing.

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  • $\begingroup$ "There is no coordinate invariant notion of simultaneity ..." So I think I understand now . There is however a notion in a specific coordinate frame - one that we normally perceive. So therefore no simultaneity in either SR or GR since the theories are both developed from generalized coordinates. Thanks! $\endgroup$ – docscience Jun 5 '15 at 14:13
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While I'm not a relativist I think that the notion is perfectly well defined (if frame dependent). After all, Einstein told us how to synchronize space-like separated clocks presuming that they are mutually at rest and that these clocks define the time coordinate for that frame.

Thus I don't see how you can avoid the conclusion that simultaneity is defined. Perhaps harry just means that the frame dependence renders the notion less generally useful than it is in Galilean relativity.

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Here's the original comment:

@docscience: IMO, simultaneity has no real meaning in SR, either. It is only used for pedagogical purposes - basically, to explain SR to someone who is used to thinking in Newtonian terms. By the time you get to explaining GR, the student is expected to be knowledgeable enough to cope without it. – Harry Johnston

What Harry meant was that the concept of absolute simultaneity--that is, every observer agrees on whether event A happened before, after, or simultaneously with event B--is a useful idea to contrast with relativistic notions of observers in different reference frames. A common teaching technique is to take a familiar concept (absolute simultaneity) and show how the concept to be learned (relativity) is different.

In Galilean relativity (and our everyday life), absolute simultaneity exists. A student first learning relativity needs to learn that, for different observers, event A happening before event B and B happening before A can both be correct observations for different observers. Furthermore, there is no correct truth of the matter. Both observers are correct in their conclusions.

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