I know there are zillions of questions about faster than light travel, but please hear me out. According to special relativity, it is impossible to accelerate something to the speed of light. However, we can still have objects (like photons) going at speed $c$ if they never had to accelerate in the first place, i.e., if they always go at the speed of light.

What I was wondering is, would it be possible for us to discover some particle that travels faster than the speed of light? Again, I don't mean something that can be accelerated beyond $c$, but rather something that always goes faster than light. Does that contradict relativity?

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Yes, if a particle would be travelling faster than light, it would always travel faster than light. This is what's called a tachyon, and they have in some sense imaginary mass.

The three regimes, time-like, light-like and space-like (i.e. subluminal, luminal and superluminal space-time distances) are invariant under Lorentz transformation. Therefore anything on a super-luminal 'mass-shell' would always stay there and could not be decelerated to light/ or sub-light speed.

The problem is not that it would violate relativity, but rather causality, since with faster than light information propagation one could 'travel back in time', therefore leading to paradoxes.

For an introduction check out Wikipedia

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    $\begingroup$ It's not completely clear whether tachyons would violate causality. There are arguments to the contrary. See, e.g., E. Recami: “Tachyon kinematics and causality: A systematic thorough analysis of the tachyon causal paradoxes”, Foundations of Physics 17 (1987) 239-296, available at dinamico2.unibg.it/recami/scientific.htm $\endgroup$ – user4552 Apr 25 '13 at 23:27
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    $\begingroup$ Is tachyons actually perturbations around an instability? At the quantum level, particles being created and annihilated at events of space-time seems to resolve all the casuality problem. As far as ifyou work out interactions via local fields. $\endgroup$ – Nogueira Oct 30 '16 at 14:49

One of the consequences of the FTL motion is that there is always a reference frame where the object is at different places at the same time. This is opposite to the time-like motion, where there is always a frame where object is at the same place in different times.

Now consider the structure of proton. It is known that the number of observed proton constituents (called quarks) is dependent on the reference frame of the observer. The faster observer moves w.r.t. proton, the more proton constituents are observed. The most natual explanation of this phenomena is that quarks are space-like objects.

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  • $\begingroup$ The most natual explanation of this phenomena is that quarks are space-like objects. That's an awfully big leap in logic. If quarks were tachyons, then they would have to have imaginary masses, which doesn't seem plausible. $\endgroup$ – user4552 Apr 26 '18 at 18:39
  • $\begingroup$ @BenCrowell It has nothing to do with masses. Mass (considered as energy-momentum 4-vector) is always time-like. Observation of proton constituents is conducted in experiments with deep inelastic scattering of electrons on protons. Electrons are scattered on charges, not on masses (unless you assume that charge is always nailed to mass). Charges inside proton demonstrate space-like behavior, not masses. See, e.g. my answer to this question: physics.stackexchange.com/questions/191451/… $\endgroup$ – Murod Abdukhakimov May 3 '18 at 13:06

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