Tachyons

[Enola Straight]

When exploring the various Grand Unified/supergravity/superstring/M theories, theoretical physicists willdiscard a theory if it proposes the existence of tachyons; theoretical (and unobserved) superluminal particles with imaginary mass.

Now, I prefer my universe with balance and symmetry; if you have massless luxons in the middle of the velocity scale going at a constant c, and tardyons on one side always going at a velocity slower than light, why NOT have tachyons on the other side always going faster than light?

[FireNexus]

Because there isn't a shred of experimental evidence for the existence of tachyons? And because tachyons, from my understanding, would essentially falsify special relativity?

[King Kong]

From what I have vaguely heard of tachyons, their 'rest state' is moving at an infinite velocity, at least from our vantage point. Therefore, a force would need to act on a tachyon to get it to slow down to a finite speed. However, just as tardyons cannot move faster than the speed of light, tardyons cannot move slower than c.

*looks up info on google*

Tachyons are consistent with the equations of special relativity, but they do have the potential to falsify special relativity by transmitting information faster than the speed of light (creating a preferred reference frame).

This, fortunately, is not possible, as explained by a man smarter than I:

The bottom line is that you can't use tachyons to send information faster than the speed of light from one place to another. Doing so would require creating a message encoded some way in a localized tachyon field, and sending it off at superluminal speed toward the intended receiver. But as we have seen you can't have it both ways: localized tachyon disturbances are subluminal and superluminal disturbances are nonlocal.

Link to the mathematical basis of that explanation and a brief overview of tachyons.

In this overview, he does explain some methods for observing tachyons, but notes that none have been observed.

While it is puzzling that the universe does not show this symmetry, it is important to remember that many symmetries that seem possible from pure equations (such as time independence) are impossible due to other properties of the universe (in this case, entropy). A very bad explanation, I'll admit, but I doubt that anyone (at present) would be able to answer such fundamental questions about the nature of the universe.

[Kuroneko]

Charged tachyons are ruled out by the Cherenkov effect, so only neutral particles need be considered. I recall discussing much the same effect with a friend. Although initially we reached the same conclusion as Mr. Chase, the situation is a bit more complicated than that. Rather than relying on the Klein-Gordon equation, it is possible to modify the Dirac equation to have a negative mass-squared, although with a non-Hermitian Hamiltonian. The result is a spin-1/2 particle that has the same helicity in every refererance frame.

There is some evidence that this matches the behavior of the neutrino--it also has the same handedness in every reference frame. I know of a researcher at a local university that's pushing this conclusion, which is how I first became aware of it. The tachyonic neutrino hypothesis doesn't seem to be very popular among physicists, but some believe they can make it work. (I think I mentioned this before.)

[King Kong]

Wouldn't a non-Hermitian Hamiltonian mean that the tachyons are not observable? Since neutrinos have been observed, this would mean that they are not described by the Hamiltonian you mention. Or am I missing something?

I do recall something about a complex non-Hermitian Hamiltonian that would be observable if a certain space-time symmetry applies; is this a similar situation?

[drachefly]

No, a non-hermitian Hamiltonian would mean that total energy is not observable.

Also, there are various ways tachyons can work; and only some have infinite velocities. Others max out at 2c.