Tachyon increases as its energy decreases

[coolnessitself]

I'm very unfamiliar with them, just curious about the subject, so maybe you can help me out.
I know that the speed of a (hypothetical) tachyon increases as its energy decreases, and that it can't go v <= c.
Assume that by natural processes, the tachyon loses energy, as most things we know that interact do (even if it's interacting with other, similar particles, and not the ones we are familiar with). If would therefore gain speed. What if the energy goes to 0? Would it have infinite speed? Or is there a limit to how low the energy can go, or how high the speed can get?

 

[RyanJ]

Maybe this will help:

http://en.wikipedia.org/wiki/Tachyons

Cheers,

Ryan Jones

 

[Norman]

Hmm... let me try and remember. We had to do a final paper investigating a tachionic field equation for my QFT-1 class. One of the things about tachyons that you find, if memory serves, is that they cannot cross the v=c barrier. So you can never have a tachyon with a velocity of zero. We were investigating the spin zero tachyon field equation- but I don't believe that constraint would be changed by a non spin zero field. If you search Phys. Rev. from the 60s you will find the seminal papers, where they discussed these issues. There are fairly well written and should be accessible to some one who has taken an advanced QM course. Don't trust ANYTHING you find on the internet written about tachyons by someone on their personal page... I found so much rubish when I did my initial lit. search.
Good luck,
Ryan

 

[neutrino]

So you can never have a tachyon with a velocity of zero.

I think the OP was considering the case Energy -> 0.

 

[Swapnil]

That's a good question. I would say that their speed goes to infinity, but don't quote me on this one.

 

[Swapnil]

Also, if tachyons really existed then the principle of special relativity would be false because we would be able to synchronize all the clocks in a particular frame of reference by sending signals at an infinite speed.

 

[selfAdjoint]

Also, if tachyons really existed then the principle of special relativity would be false because we would be able to synchronize all the clocks in a particular frame of reference by sending signals at an infinite speed.

Not so. Nothing says we are able to interact with tachyons in relativity.

Tachyons if detectable would permit communication with the past. See Gregory Benford's novel Timescape for a development of this theme. Benford is a physicst who had at least one refereed paper on the "tachyon telephone".

 

[CarlB]

Tachyons if detectable would permit communication with the past.

Not true. As soon as you find a tachyon, relativity is dead and you can't make Lorentz transforms any more.

See Gregory Benford's novel Timescape for a development of this theme. Benford is a physicst who had at least one refereed paper on the "tachyon telephone".

As it turns out, I went to UC Irvine and knew Benford. Great guy.

Carl

 

[LURCH]

I think the energy of a tachyon is prevented from going to zero by the same constraints that prevent anything else from reaching Absolute Zero. I know they're very different from other, known particles, but I've never heard of anything in their theoretical makeup that would render them immune to that constraint.

 

[dimension10]

I'm very unfamiliar with them, just curious about the subject, so maybe you can help me out.
I know that the speed of a (hypothetical) tachyon increases as its energy decreases, and that it can't go v <= c.
Assume that by natural processes, the tachyon loses energy, as most things we know that interact do (even if it's interacting with other, similar particles, and not the ones we are familiar with). If would therefore gain speed. What if the energy goes to 0? Would it have infinite speed? Or is there a limit to how low the energy can go, or how high the speed can get?

I think that if the tachyon deccelerates to c, it should need infinite enrgy and if energy approaches 0, its speed increases to infinite. I guess these tachyons could be wrong, or probably there's a tachyon constant which a tachyon's speed would be at 0 energy.

 

[JustinLevy]

Not true. As soon as you find a tachyon, relativity is dead and you can't make Lorentz transforms any more.

Nothing in Poincare symmetry forbids faster than light travel. Lorentz transformation will still work fine. Relativity itself is fine.

It is Relativity + Causality that don't fit with tachyons. You can't have both with relativity.
(Whereas Galilean Relativity could have both tachyons and causality.)

Also, if tachyons really existed then the principle of special relativity would be false because we would be able to synchronize all the clocks in a particular frame of reference by sending signals at an infinite speed.

I don't follow your logic here.
Explain the procedure. And explain why you couldn't do the same procedure starting in a different inertial frame to get a different set of synchronized clocks.

Note also that given only rulers and clocks, you can't define a coordinate speed. You also need a clock synchronization convention. So how do you know the tachyon you chose for synchronizing your clocks are infinite in speed? ... You can't. In fact, if in your inertial frame you claim a tachyon is moving at infinite speed, an observer moving relative to you will claim the tachyon is moving slower. The _only_ speed agreed on between all inertial frames is the speed of light (not rest, nor infinite speeds).

 

[CarlB]

JustinLevy, you're right. I'm assuming that the tachyons would operate at some fixed ratio to the speed of light.

The reason for making that kind of assumption is that light (and all other particle waves now known) are transverse waves. In the classic situation of an infinite elastic media, longitudinal waves move faster than transverse waves by a fixed amount $$\sqrt{(\lambda+2\mu)/\mu}$$ if I recall correctly, where lambda and mu are the Lame parameters (see http://en.wikipedia.org/wiki/Lamé_parameters ).

The transverse and longitudinal portions of linear waves in an isotropic elastic media both follow a massless Klein-Gordon equation, but with different "speeds of light". Originally, it was believed that gravity was longitudinal and traveled at the speed of light. This was Newton's theory.

 

[A. Neumaier]

Nothing in Poincare symmetry forbids faster than light travel. Lorentz transformation will still work fine. Relativity itself is fine.

It is Relativity + Causality that don't fit with tachyons. You can't have both with relativity.

Yes. This is discussed at length (and with many references) in the entry ''What about particles faster than light (tachyons)?'' of Chapter A8 of my theoretical physics FAQ at http://arnold-neumaier.at/physfaq/physics-faq.html#tachyons

(Whereas Galilean Relativity could have both tachyons and causality.)

What would a tachyon mean in Galilean relativity, where the speed of light is infinite?
speed>infinity? Or imaginary mass? Or moving backword in time?
Neither of these seems to make sense in a causal Galilean framework.

 

[JustinLevy]

What would a tachyon mean in Galilean relativity, where the speed of light is infinite?
speed>infinity? Or imaginary mass? Or moving backword in time?
Neither of these seems to make sense in a causal Galilean framework.

I just meant particles that travel at faster than the literal speed of light. Yeah, it is a meaningless concept, since the literal speed of light in Galilean relativity isn't special. So I guess that additional comment would have been better to just be left out.

 

[dimension10]

Nothing in Poincare symmetry forbids faster than light travel. Lorentz transformation will still work fine. Relativity itself is fine.

It is Relativity + Causality that don't fit with tachyons. You can't have both with relativity.
(Whereas Galilean Relativity could have both tachyons and causality.)


I don't follow your logic here.
Explain the procedure. And explain why you couldn't do the same procedure starting in a different inertial frame to get a different set of synchronized clocks.

Note also that given only rulers and clocks, you can't define a coordinate speed. You also need a clock synchronization convention. So how do you know the tachyon you chose for synchronizing your clocks are infinite in speed? ... You can't. In fact, if in your inertial frame you claim a tachyon is moving at infinite speed, an observer moving relative to you will claim the tachyon is moving slower. The _only_ speed agreed on between all inertial frames is the speed of light (not rest, nor infinite speeds).

In relativity the imaginary mass things will still work very inversely. To slow down, more energy is required for a tachyon...

 

[dimension10]

Nothing in Poincare symmetry forbids faster than light travel. Lorentz transformation will still work fine. Relativity itself is fine.

It is Relativity + Causality that don't fit with tachyons. You can't have both with relativity.
(Whereas Galilean Relativity could have both tachyons and causality.)


I don't follow your logic here.
Explain the procedure. And explain why you couldn't do the same procedure starting in a different inertial frame to get a different set of synchronized clocks.

Note also that given only rulers and clocks, you can't define a coordinate speed. You also need a clock synchronization convention. So how do you know the tachyon you chose for synchronizing your clocks are infinite in speed? ... You can't. In fact, if in your inertial frame you claim a tachyon is moving at infinite speed, an observer moving relative to you will claim the tachyon is moving slower. The _only_ speed agreed on between all inertial frames is the speed of light (not rest, nor infinite speeds).

I just meant particles that travel at faster than the literal speed of light. Yeah, it is a meaningless concept, since the literal speed of light in Galilean relativity isn't special. So I guess that additional comment would have been better to just be left out.

Galilean relativity is wrong in the first place!

 

[QuantumClue]

Hmm... let me try and remember. We had to do a final paper investigating a tachionic field equation for my QFT-1 class. One of the things about tachyons that you find, if memory serves, is that they cannot cross the v=c barrier. So you can never have a tachyon with a velocity of zero. We were investigating the spin zero tachyon field equation- but I don't believe that constraint would be changed by a non spin zero field. If you search Phys. Rev. from the 60s you will find the seminal papers, where they discussed these issues. There are fairly well written and should be accessible to some one who has taken an advanced QM course. Don't trust ANYTHING you find on the internet written about tachyons by someone on their personal page... I found so much rubish when I did my initial lit. search.
Good luck,
Ryan

Yes, this is right. Tachyons are allowed in relativity, so long as they begin their travels at the speed of light. See, just as a piece of matter possesses an infinite amount of energy at lightspeed, the tachyon which has an imaginary rest mass also has an infinite amount of energy at lightspeed. So likewise for a particle never reaching lightspeed, so is the tachyon never allowed to move past the speed of light and into lower energies and speeds.