Hello Everything. I have a proposal for a common-sense justification of the Born Rule for QM. The idea was motivated with the Many-World Interpretations in mind, but it also works for QM-with-collapse, if that is ever found to be true.
It would be great if you respond with any comment, objection, contribution, or question. Or you can direct me to another discussion forum. My current draft of the Introduction is at the following link (to save "bandwidth"): https://drive.google.com/file/d/1CE_qkit5PnS-rzKKmlOoDReBJVN1T0kA/view?usp=sharing To give you an idea, I paste here just the Abstract and the first subsection of the Introduction. ~~~~ An argument for workability of QM leads to the Born Rule, for QM without collapse and for QM with collapse George Kahrimanis [, ...] 6 April 2022, incomplete work ABSTRACT Any interpretation of QM without collapse (a.k.a. a MWI) crucially needs to produce (not assume) an Everettian analogue of the Born Rule, indispensable not only in practical decisions but also for testing a theory. Related proposals have been controversial. The proposal introduced here is based on an argument for workability of QM and on the old notion of Moral Certainty (formulated by Jean Gerson, cited by Descartes and many others). There are consequences for the foundations of decision theory because chance is undefined for any single outcome, so that Maximisation of Expected Utility is meaningless as a fundamental rational rule, therefore a different decision theory is needed. 1- INTRODUCTION 1.1- Comparison with other derivations of the Born Rule, either in MWI or with collapse The present study is based on an assessment (not an assumption, strictly speaking) regarding workability of QM (its usability and testability); that is, an argument for workability is presented and the assessment is up to the reader. It avoids a tacit assumption of certain derivations in MWI, developments of the one by [Deutsch 1999], declaring the utility of a bet as a single value, rather than a pair (corresponding to a buying value and a selling value) or an interval -- however, an Everettian agent may well be unwilling to admit a single value, in view of the diversity of outcomes in branching futures. Despite this disagreement, we share an essential common trait: we address the problem outside of pure epistemology, by studying how QM can be a guide to practical applications. Another difference is that the present study is based solely on the status of QM as a workable theory, but Deutsch's derivation also introduces claims about rational behaviour (with which I agree, except for the one mentioned above). Other derivations not assuming collapse (for example, Zurek's), nonetheless invoke the concept of probability in the interpretation, on the basis of various arguments [Vaidman 2020]. In contrast, the present study adopts a restriction: probability proper will be considered only for outcomes of a randomising process. (It is not enough to know that a black box contains just ten black and ten white balls, or that there are only four aces in a deck of fifty two cards: the cards must be shuffled and the balls stirred, with specifications tailored to the game.) In a single-world interpretation assuming collapse, randomisation is a required assumption (albeit derided as "God plays dice") so that we may legitimately speak of probability; in a MWI though, randomisation makes no sense. Therefore the present study does not invoke a ready concept of probability; it rather discovers what quantum-mechanical quasi-probability is (and what it is not). The results are relevant also to the interpretation of non-QM probability, regardless if it may be ultimately based on QM. There are derivations of the Born Rule assuming collapse with randomisation, along with some special assumption. (The first such derivation was Gleason's theorem, assuming "non-contextuality" of measurements; for references, see [Vaidman 2020] and [Masanes, Galley, Müller].) These special assumptions are deemed more plausible than assuming the Born Rule directly, because they are qualitative properties rather than quantitative ones; nonetheless any special assumption needs justification, whether on experimental grounds or by some theoretic argument. The present study shows that we can replace both randomisation and the additional special assumption by workability. So the Born Rule is derived from workability alone, whether we assume collapse or not. 1.2- About Moral Certainty [...] -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAOvf70b7XgCj0MuqSWktJ3UU_rk6pUg4X_T01rSnmsEiJxZ-MQ%40mail.gmail.com.
