Time Dilation & Bosons: Decay Rate Changes?

[Andrew Wright]

Hi,

It is easy to find discussions about time dilation and muon Half-Life. Is it meaningful to discuss whether bosons capable of pair production can have their decay rate changed if they pass through material?

 

[Vanadium 50]

it meaningful

I didn't understand what you said, so probably not.

 

[PeterDonis]

time dilation

pass through material?

What does passing through a material have to do with time dilation?

 

[Nugatory]

Is it meaningful to discuss whether bosons capable of pair production can have their decay rate changed if they pass through material?

One could imagine some physical interaction between particle and medium which affects the particle in some way. However there is zero evidence or reason to think that such a hypothetical interaction might change the decay rate…. and even if such a thing were possible it would be unrelated to relativistic time dilation. An easy way to see this is to use a frame in which the particle is at rest and the medium is moving - there is no time dilation in that frame.

 

[Andrew Wright]

I was thinking of light slowing down when it passes through a medium. People have told me that this is due to interactions that happen to bend and slow the light. It feels odd that a bunch of particle interactions happen to make light refract like a water wave. It always felt like it should not just pop out of particle interactions because it looks like wave behaviour.

 

[Ibix]

If you're talking classically, light is slowed and refracted because it's an EM wave and it interacts with the EM fields of the medium. If you're talking quantum mechanically I think that basically the same thing is true; it's a mistake to think of a photon as a pointlike particle because it has no position operator - it's always spread out and wavelike. But you should probably wait for an answer from someone who's a bit better at QFT than me!

In terms of entering the medium changing decay rates, I'd think that the interactions with the matter change the decay channels available and their relative cross-sections anyway, and it would be hard to separate that from any supposed relativistic effects.

 

[vanhees71]

Indeed, you can just use relativistic QFT as well in many-body theory. You get the "properties of an in-medium photon" through calculating the self-energy (or propagator) in the medium. For a very good introduction to this physics, see

J. I. Kapusta and C. Gale, Finite-Temperature Field Theory;
Principles and Applications, Cambridge University Press, 2
edn. (2006).

or

M. LeBellac, Thermal Field Theory, Cambridge University
Press, Cambridge, New York, Melbourne (1996).