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I recently asked this question...

When are events frame independent and why?

...on when it is that the simultaneity of events is frame independent. As I understand now, observers in every frame of reference will agree on the simultaneity of two events when those events happened at the same location.

However, besides this being an intuitive observation about our universe, I don't really see why it follows from Einstein's 2 postulates of special relativity:

1. The laws of physics are the same and can be stated in their simplest form in all inertial frames of reference.

2. The speed of light is constant in all frames of reference.

The loss of simultaneity at two different locations for two different reference frames (moving with respect to one another) can be shown with the above two postulates...but, I'm not quite sure how to show the "intuitive" observation above about events at the same location.

I'm definitely wrong...but it seems to me that there should be a third postulate...

3. Observers in every frame of reference will agree on the simultaneity of events that happen at the same location.

If not, what about the first two postulates is to stop observers in from seeing simultaneous events at a specific location in one reference frame, from not being simultaneous when viewed from a different reference frame?

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  • $\begingroup$ Closely related question here. $\endgroup$
    – knzhou
    Commented Jan 12, 2020 at 3:43
  • $\begingroup$ Events are not relative. $\endgroup$
    – m4r35n357
    Commented Jan 12, 2020 at 12:45

2 Answers 2

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I don’t know what counts as “following from the postulates”, but my approach would be:

Take the space-time coordinates shared by the events in frame $S$, and transform them to frame $S’$, and note that the still share the same (transformed) coordinates.

That argument is also the one I would use in Galilean relativity, BTW.

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Physics is about things that really happen in a real universe.

Coordinate systems and reference frames are tools we use to describe and understand those things. But they’re not inherent to that physical universe. We impose them.

Now consider two things that happened at the same time in the same place. That’s a real thing that happened. Nothing we do with coordinate systems is going to change that same time and same place to be different, because the events physically happened together.

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