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Dec 12, 2022 at 22:34 comment added asmaier "Since proper time is the time measured on the wristwatch of an inertial observer who is present at both events, an imaginary proper time means that it is impossible for an observer to be present at both events. In other words, nothing could move fast enough to be present at both events. Not even light. And if light isn't fast enough to be present at both events, then there can be no causal connection between them." (phys.libretexts.org/Courses/Skidmore_College/…)
Sep 18, 2021 at 21:09 comment added J.G. @asmaier No, it means a proper distance of $\sqrt{d\vec{x}^2-c^2dt^2}$.
Sep 18, 2021 at 20:50 comment added asmaier I'm wondering, does a complex proper time then maybe have the same physical meaning as a complex speed of light (I mean like a complex phase velocity, which means the amplitude of a wave will decay)?
Sep 16, 2021 at 19:54 history answered J.G. CC BY-SA 4.0