Talk:Proper length

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spacelike?

... spacelike events in a frame of reference in which the events are simultaneous.

Doesn't it mean timelike? If I remember correctly, spacelike events can be in the same spot, but not at the same time. Timelike events, however, can be at the same time, but not in the same place.

You don't remember correctly. Timelike events can be related through time. So they can be at the same place but not at the same time. Similartly spacelike events can be related only through space. --EMS | Talk 20:17, 3 July 2007 (UTC)[reply]

Is this formula correct?

$\Delta \sigma ={\sqrt {\Delta x^{2}+\Delta y^{2}+\Delta z^{2}-c^{2}\Delta t^{2}}}$

Looking at this formula, where $\Delta t^{2}>0$ (meaning the events took place at different times), it appears that the only time it produces a real, non-zero result is when the events occur at places that are too far from each other for light to travel from the place of the earlier-occurring event at the time the earlier-occurring event occurs, to the place of the later-occurring event by the time the later-occurring event occurs. And in this case, the distance is "spacelike" rather than "timelike".

Did I get that right?--Beneficii (talk) 21:34, 2 February 2017 (UTC)[reply]

Almost right. First, the events took place at different times for an observer using coordinates (x,y,z,t), but not for some observer for whom the events are simultaneous. There can be such an observer if the formula produces a real, non-zero result. For that observer the distance between the events is indeed Δσ. Second, it's not distances that are spacelike, lightlike or timelike, but intervals—see Spacetime#Spacetime intervals. The interval is Δσ², which in this case, for this particular observer, happens to be the square of the distance Δσ.

For further questions you should probably go to the wp:Reference desk/science, as here on the article talk page we can only discuss modifications to the article, not the subject itself—see wp:Talk page guidelines. - DVdm (talk) 22:37, 2 February 2017 (UTC)[reply]