vanhees71 said:
What do you mean by "heuristic fashion"? All a physical theory as a physical theory and only a physical theory has to provide is a description of the measured and observable phenomena. The fact that there are incompatible observables and that thus not all observables can take determined value is an observed fact you have to accept. Science is about observed facts and the prediction of possible yet unobserved predictions of new facts. If the latter turn out to be wrong, the theory is wrong. Otherwise it's a success, and so far QT is a great success.
If the focus in the practice of physics is on getting or matching experiment, then heuristics are acceptable; this is true for experimentalists and applied physicists, as well as those theorists whose theoretical focus are in close proximity to their contemporary state of experimental physics. In other words, heuristic arguments are only acceptable for non-fundamental research; most sciences aren't mathematical in their foundations so they do not have to directly address this problem.
Physics however is mathematical, not only in its daily practice, but even way down in its foundations, i.e. the subject of physics is about physical laws which are as far as we can tell properties or aspects of nature which have or can be given a mathematical form. Because of this, the foundations of physics necessarily requires the same level of rigour as that required in the practice of mathematics, therefore heuristic arguments are clearly foundationally unacceptable.
Changing the meaning of what a science is - i.e. insistence on the new philosophy of science about observables invented by the pioneers of QM - is fully a heuristic argument which was made in the 20th century only to forget about foundational issues and pursue new available experiments; this is the correct approach if there are new available experiments to explain, which was the case for much of the 20th century until the completed construction of the Standard Model during the 70s.
Trying to reform the foundations based on heuristic arguments such as the operational success of QFT is not even wrong; all that such often made suggestions demonstrate is an immense ignorance of what foundations research is among those making the suggestion, i.e. most contemporary physicists. This is actually something which is to be expected because there aren't any practicing physicists who are still alive and were already practicing before, during and after the last completed foundational change i.e. the SR/GR revolutions; to make matters worse the practice of mathematics is still divorced from that of physics.
The foundational revolution for QT was never completed, but its completion just ignored for heuristic reasons. In other words, the heuristic argument was a good argument for physics until the 70s. Thereafter however the heuristic argument becomes the wrong approach, precisely because there aren't any more experiments to explain, yet there have remained glaring mathematical inconsistencies in the foundations of the still ongoing revolution, which moreover get exacerbated when trying to theoretically merge fundamental theories.
In physics, w.r.t. QT we are today obviously in this theory crisis situation at the moment, meaning both theoreticians and mathematicians are needed to resolve the problems in the foundations of QT. Any theorist who doesn't see this has actually stopped pursuing the theoretical practice of fundamental physics, but instead has for practical reasons chosen to disregard mathematics as the ultimate method for engaging in fundamental physics and instead settle for heuristics i.e. for philosophy instead.
This heuristic attitude among physicists actually seems to be imparted during the training of students (shut up and calculate), which contemporary physicists of course learned from their own teachers, because it was adequate for that period in history of physics when there were experiments to analyze; unluckily, this attitude has become educational dogma which doesn't change even when change is needed.
Today we don't have the excuse of unfinished experiment anymore and we have through the professionalized educational system managed to remove practically all aspiring foundational physicists from physics, leaving us unable to complete the QT revolution even if we desperately want to finish it. This mental inertia among physicists is incidentally also why I chose to leave physics after getting my degree and instead just continue to pursue theoretical and mathematical physics from outside the academic establishment, next to medical practice and applied mathematical research.