If simultaneity is relative; meaning that for each any events A and B and we can find a reference frame in which two events A and B occur in inverse order, how does our notion of 'causality' withholds?
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3$\begingroup$ Keep in mind that your first sentence only applies if events A and B are space-like separated. For time-like separated pairs there is a well defined ordering in time. $\endgroup$– dmckee --- ex-moderator kittenCommented Aug 5, 2019 at 16:40
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3$\begingroup$ Possible duplicate of Causality and Simultaneity in special relativity $\endgroup$– Luke PritchettCommented Aug 5, 2019 at 16:48
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$\begingroup$ I've marked this as a duplicate. You might also find this question helpful: physics.stackexchange.com/q/100448 $\endgroup$– Luke PritchettCommented Aug 5, 2019 at 16:50
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2 Answers
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Spacetime causality holds within the light cone. Only events within the past light cone can affect the present event (the here-and-now at the vertex of the light cone). The present event can affect only the future light cone. Events outside the light cone can neither affect nor be affected by the present event.
Lorentz transformations can change the temporal ordering of events outside the light cone relative to the present event, but they cannot change the temporal ordering of events inside the light cone relative to the present event. All events in the past light cone are temporally before the present event in all Lorentz frames, and all events in the future light cone are temporally after the present event in all Lorentz frames.
The essence of the events inside the light cone are that they are closer in space than they are in time to the present event, so signals traveling at the speed of light or less can travel from those in the past light cone to the present event or from the present event to those in the future light cone. To get to or from events outside the light cone would require traveling faster than light.
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1) If there exists a frame in which B precedes A, then A cannot cause B.
2) That having been said, the whole notion of "causality" is a little slippery to begin with in a deterministic theory where all the laws are time-reversible.
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$\begingroup$ I think you mean "in which B precedes A". $\endgroup$ Commented Aug 5, 2019 at 16:48
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