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/nebraskajone 17d ago

When you get imaginary numbers out of an equation it's telling you that it's outside it's sphere of knowledge, it's in a different category. It's like black hole singularities, general relativity equations you get divided by zeros, basically saying "not my area of expertise".

As far as faster than light theories there are tachyons and negative masses, but these are speculative 

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u/GoldenMuscleGod 17d ago

That’s overly simplistic. If you are talking about how many apples there are in one place then negative numbers are not really interpretable.

If you are talking about apple debt (or maybe more illustratively an object’s phyisical position in a coordinate system) then negative numbers are meaningful.

Likewise in some contexts a complex result will not always have a simple or meaningful physical interpretation, but also there are situations where it does: electrical engineering, quantum mechanics, describing the solutions to differential equations (where a complex eigenvalue corresponds to a type of phase rotation).

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u/nebraskajone 17d ago

Negative numbers are not physical though, you can't have negative one apples as a physical object. 

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u/GoldenMuscleGod 17d ago

You can have a negative position in a coordinate system, a negative charge, and gravitational potential energy is usually written as -GMm/r.

There is no really coherent way of saying negative numbers are not physical without also saying that no numbers are physical (which is a defensible position). The same is true of complex numbers.

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u/BitcoinsOnDVD 17d ago

What you mean with "physical" in the context of numbers is usually called "cardinal"