I was attempting explain to a co-worker my novice understanding of relativity, I'm was explaining how speed/time/events/etc is relative. My question was could this also lead to a paradoxical/multi-universal(excluding string theory) when two events separated by space are linked?

For example:
I thought about a scenario with which there are two bombs, only 1 bomb could explode (through whatever hypothetical means). A timer is set on both bombs for 10 seconds and 1 person picks up each bomb. Person A stands still, person B travels close to the speed of light close to the speed of light (person A and B can observe each other). Person A, observing person B sees that person B's countdown is going slower (since person B is traveling faster), thus persons A's observes his own bomb going off first which leads to person B's bomb being disengaged (Person B lives).

Person B however, is observing everything else(including person A) moving close to the speed of light in a circle around him (since speed is relative to the observer), thus he observes person A's timer going slower and thus his own explodes first and disengages person A's bomb (Person A lives).

From each perspective, the observer dies and the other lives, which seems to create two conflicting realities, so who actually lives and dies. I feel as though I am misunderstanding something here or am I correct?

  • $\begingroup$ Don't fully understand your question but why don't you just let B travel in a straight path? B orbiting around A is absolute (in SR) and relativity cannot be applied to say that from B's point of view A is orbiting. $\endgroup$ – velut luna Aug 15 '16 at 11:02
  • $\begingroup$ Alrighr i edited my post so B is traveling straight. But what im asking is that from the perspective of each person, the observer's bomb explodes. So after 10 seconds passes, which bomb has exploded? $\endgroup$ – person Aug 15 '16 at 11:07
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    $\begingroup$ The problem here is the 'only one bomb can go off': how do the bombs arrange for that, without FTL communication (hint: they can't). (Please, no-one bring up entanglement: it doesn't help.) $\endgroup$ – tfb Aug 15 '16 at 11:14

The special theory of relativity deals with the inertial observers moving with time-invariant velocities with respect to each other. If you want to analyze a phenomenon from a frame of reference moving with an acceleration with respect to an inertial frame of reference located in the vicinity then you need to invoke principles of the general theory of relativity. Since in your example, the observers are relatively accelerated, the situation can't be dealt purely within the realm of special relativity. But I think that a simpler version of your question can be formulated which carries the essence of your question but relieves us from employing general relativistic arguments.

Assume that the observers are in Linear relative motion instead of a circular one. A mechanism can be used, in each of the frames, to record the information of the events. Your question can be stated as follows: Two bombs - A and B are structurally identical and each of them, as such, explodes in 10 seconds after its trigger is pulled. If through some mechanism, it is ensured that if Bomb A explodes first then Bomb B will never explode and if Bomb B explodes first then Bomb A will never explode and otherwise, the both of them will explode. A and B are, once, at the same location in space-time while they are eternally moving with a constant relative speed with respect to each other. The triggers of the both of them are pulled when they are at the same location in space-time. Now what will happen? Will A explode or will B explode?

The answer is that the mechanism you propose is impossible to construct - at least in the form it is aforementioned. The reason being that the first and the second of one frame is can actually differ from that of many others. So our proposal has an inherent need to specify a frame of reference. Now in this particular frame of reference, we can try to make the proposed mechanism. But one soon realizes that even such a mechanism is not possible because of the finiteness of the maximum possible speed at which any information from one Bomb can be transferred to other.

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  • $\begingroup$ Ahhh, my problem was that i did not know how to word my question for a search engine. After reading your post and the comments, i searched special relatively and acceleration, I believe I was thinking about the twin paradox. which I now have plenty of material to read about. Thanks for answering my novice question, its been on my mind for a while $\endgroup$ – person Aug 15 '16 at 11:41
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    $\begingroup$ It is a common notion that special relativity can't deal with acceleration. But it's not true: it can. See, for instance here. $\endgroup$ – tfb Aug 15 '16 at 11:42
  • $\begingroup$ @sheldonj22 Your question is related to Twin paradox and reading about the same will surely enhance your understanding of the concepts related to the subject. But I would like to point out that your problem has something more than the Twin Paradox - the explicit consideration of the finiteness of the maximum speed of communication. $\endgroup$ – Dvij D.C. Aug 15 '16 at 12:08
  • $\begingroup$ @tfb I agree that acceleration can be dealt with special relativity but accelerated frames of reference can't - at least without the aid of some physical assumptions which are not inherent to the special theory. $\endgroup$ – Dvij D.C. Aug 15 '16 at 12:09
  • $\begingroup$ @Dvij: Accelerated frames are described by, for instance, Rindler coordinates. The criterion for whether SR is applicable or not is whether the spacetime is flat. The particular choice of coordinates / reference frame can't make any possible difference to the physics, any more than it does in Newtonian mechanics: just because the rules look less simple in a non-inertial frame doesn't mean they are not the same rules. I don't want to get into an argument about this, but is simply is not true that you need to use GR for these systems. $\endgroup$ – tfb Aug 15 '16 at 13:46

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