# what is the kinematics of a particle with complex mass?

• particles with real-mass have time-like kinematics ($ds^2 > 0$).
• particles with zero-mass have light-like kinematics ($ds^2 = 0$).
• particles with imaginary-mass have space-like kinematics ($ds^2 < 0$) (tachyons).

So the question is pretty simple:

What would be the kinematics of a particle with both non-zero real and imaginary parts?

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Maybe such a particle is decaying or being born? – Vladimir Kalitvianski Oct 26 '11 at 18:54
This is something people doing PT quantum mechanics study. Complex classical mechanics is a field which is about 5 years old. – Ron Maimon Oct 30 '11 at 19:57

## 2 Answers

I think the question has no meaningful answer, at least in our universe. If you look at $$E^2 - p^2 = m^2$$ then if $m$ is complex with non-zero real and imaginary components, then $m^2$ is also complex with non-zero real and imaginary components and therefore either $E$ or $p$ (or both) must also be complex with non-zero real and imaginary components. I don't think there is any meaningful description of the kinematics of a particle with complex energy or momentum.

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thanks for the answer. Yeah i've thought this as well, since in the lorentz transform expression, fixing the $\beta=\frac{v}{c}$ factor and $E$ to be real implies that $m$ must be either real or immaginary, but since in twistor geometry one might want to study complexified poincare geometries (where the above asumptions about $\beta$ and $E$ being real do not necessarily hold anymore), i wondered if in a twistor description a complex mass would have a meaningful kinematics – lurscher Oct 31 '11 at 3:41

In AWT (dense aether model) all particles have complex mass terms due the quantum fluctuations. A the case of photons and neutrinos the complex mass becomes pronounced. With respect to high density of atom nuclei the mesons are have complex mass too. These particles are doing tachyonic "jumps" in space-time and they undergo quantum decoherence and oscillations.

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