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My question is the following:

Is it possible that an event which is in my past light cone is currently in another observer's future light cone?

(i.e. for an observer sitting at a point in the set of coordinates $(x, t = 0)$ for a spacetime diagram in my reference frame, where I occupy the origin $(0, 0)$)

In plain English, is it possible that something which happened to me has not 'happened' yet in every possible reference frame (and thus not happened yet for some hypothetical observer), or have things that 'happened', like an explosion or an earthquake, occured in some fundamental sense, and are therefore in every observer's past ( 'every observer' meaning every possible reference frame associated to points $(x, 0)$ in my reference frame, i.e. observers which are in my current present).

Apologies for the convoluted form of the question, I'd gladly accept simplifications to it.

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  • $\begingroup$ Someone that is standing in front of me and looking in the same direction as me relative to the Earth is in my future-oriented light cone. $\endgroup$
    – Daddy Kropotkin
    Jan 27, 2021 at 13:41
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    $\begingroup$ What do you mean 'currently'? Sounds like you're trying to define simultaneity, take a look at en.wikipedia.org/wiki/Relativity_of_simultaneity $\endgroup$
    – Eletie
    Jan 27, 2021 at 13:42

2 Answers 2

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Is it possible that an event which is in my past light cone is currently in another observer's future light cone?

No. Any frame’s definition of “currently” means “outside the light cone” or in other words “spacelike separated”.

For any two spacelike separated events, the intersection between one event’s past light cone and the other event’s future light cone is empty.

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  • $\begingroup$ Thank you. I edited out 'light cone'- I just want to know whether it can be in their future (even if it is non accessible future for them) $\endgroup$
    – Noam
    Jan 30, 2021 at 16:19
  • $\begingroup$ @Noam Tamarin it is against the site policy to edit a question after it has received answers in a way that invalidates the answers received. I have reverted your edit. Please post a separate question instead, and you may want to link to this one and explicitly identify the difference between this question and your new one. $\endgroup$
    – Dale
    Jan 30, 2021 at 16:24
  • $\begingroup$ Hi Dale, okay, although I did clarify in the edit to the question exactly what I edited out... So it doesn't really invalidate your answer. Anyway, I am totally fine with keeping the question as it was- would you mind answering here as a comment, the edit I wrote above? $\endgroup$
    – Noam
    Jan 30, 2021 at 16:36
  • $\begingroup$ Yes, that is possible $\endgroup$
    – Dale
    Jan 30, 2021 at 16:44
  • $\begingroup$ To clarify: Supposing someone you know passes away and that constitutes an event now in your past. You are saying it is possible that there is an observer, such that in your current present, the event "person X passed away", in your past, is currently in someone else's (inaccessible) future? I know there is no causality paradox here, but this feels somewhat philosophically problematic $\endgroup$
    – Noam
    Jan 30, 2021 at 16:55
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For the original version of the question (involving light cones) the answer is "no", as Dale answered. If you leave out light cones, then it depends on your definition of "future" and "past". If you just mean coordinate future and past, then yes, because of the relativity of simultaneity. But really this is an artificial definition of future and past, since it is coordinate dependent. The light cones are the invariant things that all observers agree on.

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