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We know that order in time between two events with causal relation is invariant under relativistic transformation. Now if order in time between two events is invariant under every relativistic transformation, must there be causal relation between the two events?

updat given any two event $p$, and $q$, $ds^2=(x_p-x_q)^2+(y_p-y_q)^2+(z_p-z_q)^2+(ict)^2\leq 0$ and it is invariant that $p$, is before $q$ or simultaneous with $q$ under relativistic transformation. must there be causal relation between $p$ and $q$ the two events??

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    $\begingroup$ No. Things can be in the past of an event without causing that event. $\endgroup$
    – Chris
    Commented Nov 4, 2017 at 3:38
  • $\begingroup$ @Chris, But we can find a relativistic transformation which can change the time order between the two event. So I think they must have causal relation. $\endgroup$ Commented Nov 4, 2017 at 3:51
  • $\begingroup$ The question can be asked in another way, can any time order between two events without causal relation be changed by some relativistic transformation? $\endgroup$ Commented Nov 4, 2017 at 3:54
  • $\begingroup$ Causality is distinct from time ordering. $\endgroup$ Commented Mar 24 at 13:38
  • $\begingroup$ @AlbertusMagnusa, any example, theory, or experiment to refute ? $\endgroup$ Commented Mar 24 at 13:53

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