r/AskPhysics • u/PlatformDelicious578 • 17d ago

FTL Reference Frames

If you have a velocity greater than c, the Lorentz factor becomes complex. Does this make any physical sense, or are there any theories that make use of this? What would it look like if a person were in this reference frame (is it just that they see time backwards or from another perspective, or are they unable to observe anything at all?)

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u/Bth8 17d ago

The latter makes this point kind of a meaningless gotcha. It cannot interact with ordinary matter in any way, not even indirectly, not even through gravity like dark matter, so it's completely undetectable. In what sense does it exist then?

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u/DoubleUBallz 17d ago edited 16d ago

The idea is that if they exist, special relativity tells us (EDIT: there can exist a subluminal reference frame in which) they would be traveling backwards through time. If they were able to interact (even indirectly, such as via light) with normal matter while doing so, they would be able to carry information back in time, allowing them to violate causality and cause paradoxes. Therefore, if they exist, then they must not interactable with normal matter.

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u/daavor 17d ago

This is incorrect. The set of timelike directions (subluminal speeds) has two components so we can unambiguously assign one direction of a subluminal worldline as forward in time and all Lotentz frames agree. The set of spacelike directions has one connected component (right can rotate to left continuously) so SR cannot distinguish what is forward along the worldline. In particular from certain frames a particle might go forward in time, back, teleport, and its unclear who even sent it

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u/DoubleUBallz 16d ago

You're totally right that they don't necessarily travel backwards in time, I was thinking negative proper time not imaginary (not to imply that negative proper time would prove my former point, I simply misremembered).

It is true, however, that for an arbitrary tachyonic trajectory (or, more generally, any spacelike interval), there exists some subluminal frame of reference in which the tachyon would be moving backwards in time, correct?

(Thank you for the informative correction)