Relativity Tunnel

In the above diagram, I've indicated the variation of mass of a particle with its velocity using the solid curve for $v < c$ and using the long dashed lines (which lie in the complex plane) for $v > c$.

I know the particle cannot be accelerated to $v >= c$ as its mass reaches infinity when $v$ approaches light speed, but I was just wondering, if it's possible for the particle to somehow "tunnel" into the tachyon world bypassing the barrier (indicated by the curved arrow), especially when the rest mass is low?

If this is, well, physically feasible, what physical process/condition would be a possible candidate that enables such a transition?

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    $\begingroup$ We prefer to avoid the old concept of relativistic mass on this site. Please see physics.stackexchange.com/q/133376/123208 $\endgroup$
    – PM 2Ring
    Commented Aug 14, 2021 at 16:02
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    $\begingroup$ But anyway, the problem isn't just that $\gamma\to\infty$ as the particle approaches lightspeed. As your question alludes to, $\gamma$ becomes imaginary for $v>c$. How do you tunnel to such a state? $\endgroup$
    – PM 2Ring
    Commented Aug 14, 2021 at 16:06
  • $\begingroup$ @PM2Ring Well, to be honest, I don't have an answer to how such a transition can happen. I can't visualize how an object with imaginary mass would look like or behave; nor guess what would happen to the "real" part of the mass after the transition. What I'm trying to understand here is whether any factor(s) outside relativity (such as QM effects) can play a role on the process and allow anomalous behavior (particularly for very low masses, as I hinted in the question). $\endgroup$
    – nav
    Commented Aug 14, 2021 at 16:30
  • $\begingroup$ @PM2Ring Thanks for the link. $\endgroup$
    – nav
    Commented Aug 14, 2021 at 16:31
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    $\begingroup$ @PM2Ring : Imaginary gamma can be understood at least in 1+1 dimensions as exchanging the spatial and temporal axes of the reference frame, i.e. "space becomes time and time becomes space". However, this doesn't work as nice in 3+1 dimensions, so I'm not sure. That said, it only matters if we want to define a "reference frame" for tachyons, versus considering observing them from our own. $\endgroup$ Commented Aug 16, 2021 at 23:02

1 Answer 1


Remember, speed is relative: no matter how fast a particle is going relative to you, in its own rest frame its speed is $0$ and the speed of light is $c$. So your hypothetical "tunneling" would, in the initial rest frame of the particle, consist of a particle spontaneously changing from being at rest to being a tachyon. This would appear to violate conservation of momentum, at the very least.

  • $\begingroup$ But could a bradyon-tachyon pair swap velocities — the bradyon becoming a tachyon and the tachyon becoming a bradyon — without interacting, thereby conserving momentum and energy? $\endgroup$ Commented Aug 18, 2021 at 1:10
  • $\begingroup$ Such an exchange would be an "interaction". Would it be possible? I suppose you could arrange it so that momentum, energy, and appropriate quantum numbers are conserved. I think experimental evidence (from the LHC and from proton decay experiments) would indicate that such interactions must be, at best, extremely unlikely. $\endgroup$
    – Eric Smith
    Commented Aug 18, 2021 at 23:13
  • $\begingroup$ It is hard to define a rest frame for particles that go beyond the speed of light. Unless you accept that causality is wrong and or your metric changes completely (including being completely 0) $\endgroup$ Commented May 24 at 9:35
  • $\begingroup$ Note that I said the "initial" rest frame of the particle, i.e. while it was still moving slower than light. Indeed it would be difficult to define a rest frame for tachyons. $\endgroup$
    – Eric Smith
    Commented May 24 at 18:40

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