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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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Related: – David Z Mar 4 '13 at 23:25
up vote 12 down vote accepted

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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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 – Ben Crowell Apr 25 '13 at 23:27

It is a fact of physics that no massive particle can travel at speeds greater than or equal to the speed of light. It is a sub-fact that no massive particle can be accelerated to the speed of light.

Massless particles can travel at the speed of light, but no particle, not even massless particles, can travel faster than the speed of light (at least if causality is to be preserved) See What are some scenarios where FTL information transfer would violate causality?.

Edit. I want to be clear that I'm not claiming that relativity itself forbids the existence of tachyons.

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What about a particle with zero mass? – Javier Mar 4 '13 at 23:21
@JavierBadia See additions. – joshphysics Mar 4 '13 at 23:25

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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protected by Qmechanic Apr 25 '13 at 21:57

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