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.