# The principle of inertia and hypothetical FTL particles

Hello,

A recent paper by Cohen and Glashow argued recently that FTL neutrinos would quickly lose energy by pair creation (in vacuum).

Starting from the principle of inertia, I had a hard time trying to understand that.
According the principle of inertia, the physics should be the same in any frame of reference.
Therefore, it should not depend on the speed of the neutrinos, except for the mere coordinate transformation to/from the reference frame of a fast neutrino. So, on this basis, the fast decay would simply be the result of a slower decay in the proper frame of the neutrino converted in a faster decay in the laboratory frame. (except that the neutrino frame of reference is FTL!)

However, the decay rate calculated by Cohen and Glashow are not obvioulsy related to such a simple change of coordinate. They are not covariant, maybe only because of approximations in the derivation.

Therefore, I would like to understand if the principle of inertia could be compatible with the Cohen and Glashow scheme where physics is different for FTL particles?
What am I missing?
How should covariance be understood when there is FTL side in the story?

Thanks for teaching me a few things,

Michel

Why did I say "principle of inertia" ?
I obviously wanted to say "principle of relativity" !

ghwellsjr
Gold Member
Well, why don't you just edit it and fix it before it's too late?

ghwellsjr
Gold Member
Well then did you mean "relativity" every time you put "inertia", including in the title?

PeterDonis
Mentor
the physics should be the same in any frame of reference.
Therefore, it should not depend on the speed of the neutrinos, except for the mere coordinate transformation to/from the reference frame of a fast neutrino.

A particle traveling faster than light does not have a "reference frame" in this sense. It is traveling on a spacelike worldline, and the idea of "reference frame" can't be applied to this case; you can't do the kind of "coordinate transformation" you're describing. You can describe the motion of an FTL particle using any standard frame of reference, but there will be *no* such frame in which the particle is at rest.

The paper you link to is pretty short and does not give explicit derivations of most of the formulas, so I can't tell for sure, but I strongly suspect, from what it says on page 2 about general cases of superluminal propagation, that their formulas, even though they don't look manifestly covariant, are derived from covariant expressions that depend only on the assumption that the particle is FTL, i.e., that its worldline is spacelike. That characteristic is independent of the frame of reference chosen.