I find myself becoming more and more sensitive to this basic mistake: We know relativity is wrong somehow. We know quantum mechanics is wrong somehow. They're both incredibly correct with their predictions but they don't go together, so they can't both be right and in the end they both have to be wrong somehow. Two of the places where they are both clearly somehow wrong are gravity (completely missing from QM, incomp…
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I think this is overly reductive. Indeed, many consequences that follow from the nonexistence or impossibility of a certain thing, event, or effect are brittle to the physical model being refined to include additional effects. But plenty of important consequences follow from existence or possibility and can be directly supported through experimental evidence.
For instance, Newtonian physics predict absolute simultaneity: if one observer measures that two events occurred at the same time, then all other observers will measure likewise, regardless of their relative position or velocity. But special relativity violates this, instead predicting relativity of simultaneity. As long as special relativity's predictions hold to any extent (which, experimentally, they do), then simultaneity is definitely relative and not absolute. There's no way to recover absolute simultaneity short of postulating a grand cosmic conspiracy. And learning that the arrow of time isn't absolute definitely isn't a waste of time!
Also, I think it's unwarranted to say that just because some consequences of nonexistence have historically been invalidated in the past, all the consequences of nonexistence in our current theories are inevitably going to fall over with further evidence. Why should we expect a priori that we haven't yet discovered a single true invariant of our universe? After all, some observed invariants, such as the conservation of energy, have withstood the numerous revisions to our physical models, and it seems odd to blithely assert that they'll be invalidated any year now. In the limit, to say that exceptions will be discovered to every principle ever is to say that the universe doesn't run on any kind of laws.
And if we do concede that at least some of our current models' invariants truly do hold in reality, then it's no longer a waste of time to study their implications, since some subset of our findings will remain just as accurate now matter how far our models are revised.