Hi Eckhard,
my personal answer to your question is, that for the case of a simulation concerning quantum microscopic behaviour, be it in a computer or a human mind, one has at first to discriminate such a simulation from what nature really does.
The reason for this is grounded in correcting a huge misunderstanding. Because independent from what John Bell said or thought or not said and not thought, for coming to a conclusive result that could be valid for the whole scientific community, one has to present a fully fledged theory of ones underlying assumptions which have gone into the mathematics and therefore also into the simulation.
1) If such a fully fledged alternative theory cannot predict something different and testable against the established theory, no infinity of wordings can decide who is wrong or right.
2) If such a fully fledged theory CAN predict something different and testable against the established theory, BUT those experiments have not yet been conducted, THEN they should be conducted, of course.
3) Until these experiments have been actually performed, one should not use wordings that suggest that the proposed theory MUST and IS inevitably true. Nonetheless doing so merely MIRRORS some bad habits even professional theorists have when talking about their hypothesis, right?
4) When the mentioned experiments deliver a negative result for the new theory, this does not mean that other possible theories must necessarily also deliver negative results. We simply cannot know in advance, right?
Since the proponents of locally realistic hidden-variable theories usually not only hope that somedays their own or another such theory can deliver a positive experimental result, but heavily claim it as if it were an already established truth, I think it is perfectly fair that I am allowed to claim that not one of those possibly formulizable theories will ever yield the desired positive result. In a reply above to Andrew Beckwith I gave a description for the reasons why I believe that this must be the case. In my own essay as well as in my subsequent comments on it on my essay page and on other essay pages, I argue for the possibility that nature isn't fully formalizable by mathematics - in opposition to the philosophical prejudice that it nonetheless should. If my claim would be true, it would explain why a mathlab simulation is totally non-conclusive to decide whether or not a violation of Bell's inequalities necessarily indicates non-locality and the like. Because if nature is indeed not totally formalizable (especially regarding nature's behaviour at the quatum level), then no software program that tries to mathematically catch nature's behaviour has to fail - since this behaviour would not be mathematically formalizable. Hence, the underlying maths of such a simulation has nothing to do with what is going on in nature. As I outlined to Andrew Beckwith above, one cannot have one's cake and at the same time eat it. If one labels oneself to be a Realist, one has to accept logic, and hence Gödel's results, and hence physically realized undecidability - and face the possibility that nature may not fully follow the philosophical prejudice of determinism and complete formalizability.
I think the huge misunderstanding I spoke of lies in the fact that it is possible to formulate locally realistic hidden-variable theories - what means nothing but that one can simulate such a theory - either in a computer or in a human mind, but does in no way a priori necessitate that nature has to behave according to the formulated theories. In this sense the fact that it is possible to formulate such theories which may or may not disprove some of Bell's *logical* assumptions, does not suffice to establish any truth of the new theory without an experimental test. Because Bell's assumptions may well be non-conclusive - concerning what nature really does.
Even being able to conclusively identify such false assumptions, be it in Bell's work or in others, this would be totally non-conclusive regarding the question who is wrong or right about nature's real behaviour.
You and me, we are both longstanding essay authors here on fqxi. We both - at least I for myself - know very well that these contests aren't at all exclusively only about TRUTH, but extensively often also about opinions, camouflaged as already established facts. Therefore there is no need for anyone here to argue that one is a Realist and therefore one's own statements about nature's behaviour must inevitably be necessarily true - when one isn't willing to correctly communicate the own approach *realistically*, namely as a possible truth instead of a necessary truth.
Of course, even the realist has emotions. And therefore he illogically values his approach higher than all others. But mixing the logical with the illogical regularily results in an inconsistency, the OPPOSITE OF REALISM, and hence the "Realist" confuses this paraconsistent logics to self-confirm the absolute priority of his own approach. Don't misunderstand me, my words here aren't adressed only to 'hidden-variable' proponents, but also to professional scientists working in the departments of theoretical physics. I know what will be the consequences of this comment here. It will not be a logical answer, but an emotionally answer - expressed in scoring points. But I am a Realist and consider it as necessary and worth to comment the way I did it here. Therefore there is also really no reason for Robert to be disappointed since we know what these contests are all about, they are in much cases not primarily about stringent logical arguments, but rather about personal emotional musings, the latter not even loosely related to the contest's genuine theme. Therefore most of them can be considered 'not even wrong', to cite Pauli.
Best wishes to you - Stefan.
