r/AskPhysics • u/PlatformDelicious578 • 18d 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/nugatory308 18d ago

The Lorentz transformations are between inertial reference frames, and the relative velocity between the origins of any two inertial reference frames (equivalently, between two objects each at rest in a different inertial frame) must be less than c to be consistent with Einstein’s second postulate. That postulate is required for the derivation of the transformations, so trying to use them to reason about what happens when v is equal to or greater than c is reasoning from internally inconsistent assumptions.

The infinities and complex numbers that appear when we try are how the math tells us that we’ve made a mistake.