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## Main Question or Discussion Point

Are tachyons force Particles/messenger particles ? Is so do they act messenger between two entangled particles and allow faster than light information exchange? Thank for the answer.

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Are tachyons force Particles/messenger particles ? Is so do they act messenger between two entangled particles and allow faster than light information exchange? Thank for the answer.

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But "hypothetically" since they have mass -1 maybe?

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Drakkith

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Are tachyons force Particles/messenger particles ? Is so do they act messenger between two entangled particles and allow faster than light information exchange? Thank for the answer.

But "hypothetically" since they have mass -1 maybe?

No, there is no evidence for any of the above and no reason to think they do.

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DrDu

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I thougt they had ##m^2=-1##.But "hypothetically" since they have mass -1 maybe?

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My bad their m=√-1I thougt they had ##m^2=-1##.

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Or do they? Higgs field before symmetry breaking can be thought of as a tachyon field with ##m^2<0##. Nevertheless, it does not propagate faster than ##c##. It has been discussed in more detail in

https://www.physicsforums.com/threads/do-tachyons-exist.827961/

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martinbn

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What is the precise definition of a tachyon? (This is a B thread so I can ask clarifying questions, right? )Or do they? Higgs field before symmetry breaking can be thought of as a tachyon field with ##m^2<0##. Nevertheless, it does not propagate faster than ##c##. It has been discussed in more detail in

https://www.physicsforums.com/threads/do-tachyons-exist.827961/

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Tachyons are objects with ##m^2<0##, but the meaning of the parameter ##m## depends on the context. It may be the "mass" of theWhat is the precise definition of a tachyon? (This is a B thread so I can ask clarifying questions, right? )

In the particle case, ##m## defines the relation between energy ##E## and 3-momentum ##{\bf p}## through

$$E^2-{\bf p}^2=m^2$$

In the field case, one considers a field ##\phi(t,{\bf x})## which can be Fourier transformed in terms of plane waves ##e^{-i(\omega t- {\bf k}\cdot{\bf x})}##. Here ##m## defines the relation between frequency ##\omega## and wave 3-vector ##{\bf k}## through

$$\omega^2-{\bf k}^2=m^2$$

Is that precise enough?

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Can you clarify what you are referring to here?Higgs field before symmetry breaking can be thought of as a tachyon field with ##m^2<0##

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They don't have to have ##m^2 = -1##. They just have ##m^2 < 0##.I thougt they had ##m^2=-1##.

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Thanks I needed this kind of an answer.Or do they? Higgs field before symmetry breaking can be thought of as a tachyon field with ##m^2<0##. Nevertheless, it does not propagate faster than ##c##. It has been discussed in more detail in

https://www.physicsforums.com/threads/do-tachyons-exist.827961/

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martinbn

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The particle case is clear to me because it connects with the causal structure. It's what I thought tachyons are. In the field case it is not clear to me why that should be called tachyons (or anything at all), and how does the definition go in a general space-time?Tachyons are objects with ##m^2<0##, but the meaning of the parameter ##m## depends on the context. It may be the "mass" of theparticleor the "mass" of thefield.

In the particle case, ##m## defines the relation between energy ##E## and 3-momentum ##{\bf p}## through

$$E^2-{\bf p}^2=m^2$$

In the field case, one considers a field ##\phi(t,{\bf x})## which can be Fourier transformed in terms of plane waves ##e^{-i(\omega t- {\bf k}\cdot{\bf x})}##. Here ##m## defines the relation between frequency ##\omega## and wave 3-vector ##{\bf k}## through

$$\omega^2-{\bf k}^2=m^2$$

Is that precise enough?

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I am referring to the Higgs potentialCan you clarify what you are referring to here?

$$V(\phi)=-\frac{\mu^2}{2}\phi^2+\frac{\lambda}{4}\phi^4$$

where ##\mu^2>0## and ##\lambda>0##. For small ##\phi## you can ignore the ##\lambda##-term, so what remains is a "mass" term with a wrong sign. Does it help?

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$$V'=\phi (-\mu^2+\lambda \phi^2)=0,$$

i.e., around ##\phi_0=\mu/\sqrt{\lambda}##.

You can, to a certain extent, define QFTs of tachyons. See, e.g.,

J. Dhar, E.C.G. Sudarshan, Quantum Field Theory of interacting tachyons, Phys. Rev. 174, 174 (1968)

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I guess you know that quantization of fields leads to quantum states that can be interpreted as quantum particles. If they are states with definite energy and momentum, then their energy and momentum satisfies the same relation as that for the corresponding classical particles. That explains why such fields are called tachyon fields.In the field case it is not clear to me why that should be called tachyons (or anything at all), and how does the definition go in a general space-time?

Concerning general spacetime, it's much easier to write down the partial differential equation which the fields satisfy. This is the Klein-Gordon equation

$$(\nabla^{\mu}\nabla_{\mu}+m^2)\phi(x)=0$$

in general spacetime with metric signature ##(+,-,-,-)##, where ##m^2<0## for tachyon fields.

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Well, it depends on what do you mean by "doesn't make sense". Mathematically, it makes sense if you are studying a regime in which ##\phi## is close to zero. It is certainly not easy to satisfy this condition in an LHC experiment, but in principle it is not impossible. Initial conditions are, in principle, arbitrary, so there is no physical principle which would forbid ##\phi(t=0)=0##. For a short time after such initial condition, the system would behave as a tachyon field.But the point is that for this potential pertubation theory around ##\phi=0## doesn't make sense, because it's a maximum of the potential rather than a minimum.

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Neither do I. That's one of the reasons for

https://www.physicsforums.com/threads/experimental-physics-for-theoreticians.883789/

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DrDu

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Terms luke "soft modes" and " glass transition" come to my mind.

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Ah, ok. @vanhees71 has already raised the points I would make.I am referring to the Higgs potential

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Can you be more explicit?Terms luke "soft modes" and " glass transition" come to my mind.

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DrDu

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They do, though. As Demystifier pointed out, they show up whenever you are perturbing around an unstable vacuum. What is true is that no particles which travel faster than light (for a reasonable definition of "travel") can exist in any reasonable quantum field theory. But a particle can be a "tachyon" (an imaginary mass solution of the linearized equations of motion around an unstable vacuum) and still travel no faster than light, respecting causality. See e.g. http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html and http://physics.stackexchange.com/questions/166095/do-tachyons-move-faster-than-light . Look especially at Qmechanic's excellent answer.

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Drakkith

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I'm pretty sure Peter was saying that tachyons, in the context of FTL particles that the OP was asking about, do not exist.They do, though. As Demystifier pointed out, they show up whenever you are perturbing around an unstable vacuum.

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