While watching this video, at around 5:00, the man mentions a certain type of particle having imaginary mass. He also says that these kind of particles can go faster then light. But how it is possible that a mass is imaginary? For me, this make no sense. And also what does this even mean? For example, how would you calculate a gravitational force involving particles having imaginary masses? The result of the force will also be imaginary. Or will it interact gravitationally with other objects?

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    $\begingroup$ This is talking about pathological solutions of Einstein's mass-energy relation. It doesn't mean that these kinds of particles actually "exist"... they're just mathematically possible. $\endgroup$ Jun 5 '13 at 13:12
  • $\begingroup$ Related: physics.stackexchange.com/q/16227/2451 and physics.stackexchange.com/q/41947/2451 $\endgroup$
    – Qmechanic
    Jun 5 '13 at 13:21
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    $\begingroup$ These questions that refer to a video are not very useful. The video is time-consuming for anyone else to watch and to get enough context to understand what's being presented. The video will probably not be on the internet at the same location in 10 years. There is a reason that writing was invented. $\endgroup$
    – user4552
    Jun 6 '13 at 0:45
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    $\begingroup$ I think that I wrote down the necessary information to answer the question. I've linked the video for persons that are interested or needs additional informations. So even if the video won't be available or people don't watch it, they will be able to understand and answer to the question. $\endgroup$
    – moray95
    Jun 6 '13 at 6:10

The idea at the most simplest level comes from the relation $E^2-p^2c^2=m^2c^4$. This is the Einstein relation $E=mc^2$ for a particle of mass $m$ traveling with relativistic momentum $p$. The idea is that if $m^2<0$, and therefore $m$ is imaginary, that $E^2-p^2c^2 < 0$ or $E^2<p^2c^2$. With real mass this relation is the other way around and corresponds to $v^2<c^2$, this results in the idea that imaginary $m$ yields $v^2>c^2$.

This isn't very physical, as you have noted with your confusion over implications of imaginary mass. It usually means that there is an instability in your theory, for example, in Quantum Field Theory, you are not expanding around the correct vacuum.

If you want to search for more discussion on the topic, we call these "particles" tachyons. See for example http://en.wikipedia.org/wiki/Tachyon.


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