Different frames of reference and particle production? a contradiction maybe?

[jeebs]

Hi,
Second time I'm writing this question, the first one seems to have been lost in cyberspace but sorry if it somehow comes back and appears twice.

Anyway, you know how kinetic energy depends on velocity, so that the energy of a particle collision will be different for two frames of reference moving relative to one another?
And also, how when particles collide with sufficient energy, a new particle can be created if the rest mass can be reached?

Well, what if one observer is moving such that he sees a collision with just barely enough energy to produce this new particle, and it is produced, but another observer is moving such that the collision does not have enough energy to produce this new particle, what happens then?
Surely if a particle exists in the universe, either everyone can see it or no one can?
What's the deal here?

thanks.

 

[jtbell]

Well, what if one observer is moving such that he sees a collision with just barely enough energy to produce this new particle, and it is produced, but another observer is moving such that the collision does not have enough energy to produce this new particle, what happens then?

Can you set up a specific numeric example to illustrate this?

 

[humanino]

If I understand jeebs correctly, his concern is about heavy particles productions. But to answer, I think it is helpful to begin with the decay of a single heavy particle into two (or more) lighter ones. The decay is best thought of in the rest frame of the heavy particle where the decay products have the minimal kinetic energy. Going to another reference frame will just give them more kinetic energy. The same thing happen when you collide two light particles to create heavier ones. You can always think of them being produced from an initial state which looks like the decay of a system from far away enough. The final decay products have minimal energy in the center-of-mass frame of the initial incoming particles. Transforming to another referential just gives them more kinetic energy.

The problem is with :

another observer is moving such that the collision does not have enough energy

This is an impossibility. There is no such observer or referential. In particular

if one observer is moving such that he sees a collision with just barely enough energy to produce this new particle

in this frame, the new particle is produced at rest.

 

[jtbell]

Now that I think of it, for a particular collision, the energy available for production of new particles is independent of reference frame (i.e. it's a Lorentz invariant), isn't it?

In the reference frame in which the total momentum of the incoming particles is zero, all this "available energy" can be used to produce new particles, in which case the new particles are at rest.

If we now switch to a reference frame in which the total momentum is not zero, the incoming particles have more kinetic energy than in the zero-momentum frame; but this "extra" KE is not available for producing new particles. The outgoing particles must now also have KE, which comes from the "extra" KE of the incoming particles.

 

[humanino]

Now that I think of it, for a particular collision, the energy available for production of new particles is independent of reference frame (i.e. it's a Lorentz invariant), isn't it?

Yes, it is usually written s

I think jtbell explained it better than I did