I've heard it said that relativity formally permits tachyons and that we don't believe they exist merely because there is no empirical evidence of them. However, since a tachyon's speed exceeds c, its γ must be imaginary. The t-component of the particle's 4-velocity is, depending on definition, either γ or γc, which in either case will be imaginary for a tachyon. This means that the 4-velocity is not a vector in ℝ[itex]^{4}[/itex]. My understanding is that spacetime is ℝ[itex]^{4}[/itex] (equipped with a metric that solves the Einstein field equation). Formally, this seems to imply that a particle cannot have a 4-velocity with an imaginary component. Am I correct in concluding then that relativity in its present formulation doesn't in fact allow tachyons?(adsbygoogle = window.adsbygoogle || []).push({});

Extending the theory to make spacetime ℂ[itex]^{4}[/itex] seems like it would be a nontrivial change, as it would become effectively 8-dimensional.

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# Does relativity permit tachyons given that they have negative gamma?

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