I’m trying to clarify whether empirical evidence has any bearing on your position and thus whether it makes any sense to keep talking about things like the muon experiment.
By anti-realism, I mean that you don’t straightforwardly affirm the existence of things and processes that physicists widely accept based on empirical measurements - such as time dilation. You have a skeptical outlook towards these things, emphasizing the “fundamentally unverifiable” nature of things in reality. I’m not sure what you mean that it is possible to know some things about unverifiable reality. Perhaps you think that it is possible to get knowledge from intuition about them, instead of the senses. In other words, Plato instead of Aristotle.
At this point, the main thing I can say is: yes, physicists working in this field do investigate all sorts of spurious effects that can affect their measuring instruments. I’m from that community, and dealing with these effects (which we call systematic effects) takes up a huge chunk of our time.
Speaking about atomic clocks, physicists are well aware of the various systematic effects that can affect them and study them obsessively when characterizing them. Here, for example, is a well-known 2010 paper (by 2012 Nobel Prize winner Dave Wineland’s group) which saw a frequency difference between two aluminum ion clocks when one clock was elevated by 33 cm relative to the other. This shift they attributed to the gravitational shift predicted by general relativity. Differences in gravitational potential (at different distances from the center of the Earth) causes time dilation.
Now, were these physicists just naive in readily attributing the observed frequency shift to time dilation due to gravity when it could have been something else? No! If you read the paper carefully, they had previously published papers characterizing the various systematic effects which can affect the frequency of the clock. This is one of them. I quote here a table of the different systematic effects they accounted for:
For example, “blackbody radiation shift” refers to the well-known effect that thermal radiation surrounding the clock can affect the energy levels of the aluminum ion, which they had characterized previously in a different paper. The amount of the frequency shift might be different for different transitions in aluminum, which is why you need careful theoretical and experimental characterization. (If you can’t access any of these papers and are interested to read them, PM me.)
To wrap up, I think that you have the epistemic responsibility of learning more about physics and what the evidence actually looks like before making sweeping statements about how much physicists have “verified” about reality. By that I don’t mean that you need to have a PhD in physics; but just learning on your own and asking relevant experts (such as we have in this forum) would be very helpful. What I’m trying to show is that there are relevant bits of technical knowledge that could affect your position, yet from my past interactions with you, you seem averse to actually learning more about the science, preferring to insist that scientists are no better than other people in thinking philosophically, so anyone has a right to do philosophy. If you really care about the truth, then you should try to learn at any opportunity you can. A lot of this information is freely available online, and there are many scientists who would be happy to explain and break it down to you if you are curious.