That's one way to do it. However, you don't have to smash protons to make muons; you can produce them in a vast number of different types of particle collisions as long as there's plenty of energy involved, and you can set experiments up to produce a nice, clean beam of muons moving within a narrow velocity range. After a muon is produced it can also be accelerated by EM fields just like any other charged particle in an accelerator. In fact, dedicated muon colliders are in development right now for certain experiments.
This is consistent with my understanding. I over simplified my question to "protons", as the progenitor particle (if that is even an acceptable phrasing).
The acceleration issue was primarily, focused toward addressing where the muon's final velocity comes from rather than whether they can be accelerated and focused by EM fields.
I should make note of one important QM implication I didn't mention before. We don't have to track a muon from the moment of its creation until decay. Once you start tracking a muon, regardless of where it originally came from or how it got up to speed, the probability of it decaying over a given time period is the same regardless of its past history, so rather than tracking a muon from creation until decay you can track its lifetime after it triggers a clock by some fixed, consistent criteria. The only independent control variable is the velocity of the muons when they trigger the lab's tracking systems.
This I also understood, not the mechanisms involved so much as the functional concept of measurement timing. I think that the OPERA neutrino paper described this, at least in part...
It also addresses the issue that might have involved, when or how the muon is accelerated, as this should at least define the measurement, of its relativistic velocity, to after the initial acceleration. Correct?
Yet the results don't depend on how the lab frame accelerates as the Earth spins, how it shifts velocity as it orbits around the sun, and the sun orbits around the centre of the galaxy, etc. etc. All that matters is the relative velocity of these muons with respect to the lab frame, regardless of the history by which they were produced and accelerated up to whatever velocity, and regardless of the lab frame's own acceleration history. It's easy to show that Relativity requires such a hypothesis to be true, and from a century of extensive testing we know that nothing has yet contradicted Relativity, nor is there any evidence that the Earth and the labs on its rotating surface always happen to live in magically preferred rest frames.
What follows is most likely not phrased well. Try to take it within the whole context, rather than as individual statements.
This is where I begin to have some question, as to the applicability of the results. Not that I do not understand that the data is there, when locally defined in the lab and must be then applicable to the lab's relationship within the Earth's frame of reference.
What I am unsure of is that, when we measure this kind of relativistic situation in the lab, whether we can really assume that all of those levels of inertial and sometimes non-inertial velocities, involve detectable influences on what we observe in the lab. It might be that for practical purposes the Earth and the lab in this case, represent an essentially, at least a partially isolated inertial system, within the greater context, of the galaxy and the universe, as a whole. At least to an approximation beyond our ability to measure the impact of external influences.
In a way we might be able to, define the lab's frame of reference in practice, as representing a flat spacetime consistent with SR. While if we then assume that we can or could accelerate the lab relativistically, we would be doing that within the context of a much larger inertial frame of reference, which can no longer be described, in a similarly limited way, as a flat spacetime. What might then have been trivially undetectable inertial contributions, from the lab's frame of reference in practice, once the lab is moving relativistically, could no longer be associated with the same essentially flat spacetime conditions.
While we know that there are layers of inertial components to our relationship to the universe, these remain trivial to the muon experiment, as we experience it, when compared with the notion of the lab itself having a relativistic velocity within the "universe".
In some respects this, hypotheical vs practical, highlights some of the problems that have been standing in the path of understanding GR from a QM perspective. Relativistic velocities are achievable within particle physics and not so much, within the context of higher orders of scale.
