It can be easily shown that if we have two time-like separated events which are not simultaneous in one frame then they cannot be made simultaneous by Lorentz transformation. But, if those events are simultaneous in one frame then they can be made non-simultaneous by Lorentz transform, which contradicts the previous statement because we can Lorentz transform back to the original frame making it simultaneous again? Am I missing something?
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1$\begingroup$ Understanding the difference between timelike and spacelike separations $\endgroup$– mmesser314Jun 14, 2021 at 3:39
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1$\begingroup$ You have proved by contradiction that distinct timelike-separated events cannot be simultaneous in any frame. $\endgroup$– WillOJun 14, 2021 at 4:36
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if we have two time-like separated events...But, if those events are simultaneous in one frame then they can be made non-simultaneous by Lorentz transform
If two events are both time-like separated and simultaneous then the two events have the same spacetime coordinates and will be simultaneous in all frames.
Furthermore, if the two events are simultaneous in one frame but not in another then the events cannot be time-like separated.
So there is no contradiction. In the second scenario you either have to drop time-like separation or drop that there is a frame where the events are not simultaneous; you can't keep both.
answered Jun 14, 2021 at 3:24
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$\begingroup$ oh yeah. Thanks a lot. I just realised that simultaneous events at distinct locations have to be spacelike seperated, where it is possible to convert a simultaneous event into non-simultaneous by lorentz transform and vice versa. A S C E N D I N G $\endgroup$– GaganJun 14, 2021 at 5:23