This is an appeal to some sort of imperative that demands the Born Rule because the counterfactual lack this certainty. This is a sort of "It must be true" type of argument.
LC On Thursday, April 7, 2022 at 5:06:08 PM UTC-5 [email protected] wrote: > 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/f3adaf68-311e-400a-8d14-b18816209321n%40googlegroups.com.
