Yes. We would be able to set up experiments where one interpretation would assign non-zero chance to an outcome that has zero quantum amplitude. Run the experiment and observe the outcome enough times and if the positive-chance-but-zero-amplitude event ever happens, then quantum states are merely a calculational tool. If the zero-amplitude event never happens, then as the number of repetitions goes to infinity, you can be as close to certain that the quantum state is real as you’d like. It’s worth mentioning that almost all physicists would believe the latter is more likely, i.e. that Born’s rule will keep holding up under experiment. But few want to carry that to further conclusions. This paper adds another layer of difficulty in believing the amplitude rule but not believing that amplitude is physically real.
Yes. We would be able to set up experiments where one interpretation would assign non-zero chance to an outcome that has zero quantum amplitude. Run the experiment and observe the outcome enough times and if the positive-chance-but-zero-amplitude event ever happens, then quantum states are merely a calculational tool. If the zero-amplitude event never happens, then as the number of repetitions goes to infinity, you can be as close to certain that the quantum state is real as you’d like. It’s worth mentioning that almost all physicists would believe the latter is more likely, i.e. that Born’s rule will keep holding up under experiment. But few want to carry that to further conclusions. This paper adds another layer of difficulty in believing the amplitude rule but not believing that amplitude is physically real.