In a recent paper [e-print quant-ph/0101012], Hardy has given a derivation of “quantum theory from five reasonable axioms.” Here we show that Hardy's first axiom, which identifies probability with limiting frequency in an ensemble, is not necessary for his derivation. By reformulating Hardy's assumptions, and modifying a part of his proof, in terms of Bayesian probabilities, we show that his work can be easily reconciled with a Bayesian interpretation of quantum probability.
http://dx.doi.org/10.5007/1808-1711.2008v12n2p121 O objetivo deste trabalho é discutir e desenvolver o diagnóstico que efetua van Fraassen (1987, p. 110) da lei de Hardy-Weinberg, de acordo coo qual esta: 1) não pode ser considerada uma lei a ser utilizada como un axioma da teoria genética de populações, pois é uma lei de equilíbrio que só vale sob certas condições especiais, 2) só determina uma subclasse de modelos, 3) sua generalização resulta vácua e 4) variantes complexas da lei podem ser deduzidas para (...) pressupostos mais realistas. A discussão e desenvolvimento deste diagnóstico será levada a cabo tomando como base noções propostas por outra das concepções semânticas afim daquela desenvolvida por van Fraassen, a saber: a concepção estruturalista das teorias, e uma reconstrução da genética clássica de populações no marco de uma tal metateoria, também apresentada neste trabalho. (shrink)
A so called “weak value” of an observable in quantum mechanics (QM) may be obtained in a weak measurement + post-selection procedure on the QM system under study. Applied to number operators, it has been invoked in revisiting some QM paradoxes (e.g., the so called Three-Box Paradox and Hardy’s Paradox). This requires the weak value to be interpreted as a bona fide property of the system considered, a par with entities like operator mean values and eigenvalues. I question such (...) an interpretation; it has no support in the basic axioms of quantum mechanics and it leads to unreasonable results in concrete situations. (shrink)
There is another sort of ‘defense’ of relativism that I mention in conclusion. Sometimes one finds the view that one is rightly punished for a crime only if they admit committing it, and that it was a crime — something wrongly done: ‘punishment conditional on confession’ is the rule proposed. It might seem that this would give impunity to a criminal hardy enough to deny the fact, or the evil, of her deed; so it would, unless it was also (...) understood that if a person was proved by accepted standards to be the perpetrator of an action agreed to be wrong, the opportunity to admit guilt would extend from open questioning through beating to exquisite torture until confession was extracted (cf. the Chinese customs reflected in the Judge Dee stories of Robert Van Gulik). More often, one finds the view that a person is not refuted unless he admits this, and a view is not refuted — and so is not properly dismissed — unless its proponents concede defeat. A similar view is that all really telling philosophical criticism must be internal or else non-neutral (a view we discussed above).If one can in principle produce a conceptual system from a list of all propositions by following the recipe: for any proposition P include P, or else include not-P, in S, then (providing one adds no constraints concerning consistency) there will be no proposition that will appear in all conceptual systems. If what it is for a proposition to be neutral is for it to appear in all conceptual systems, then no proposition is neutral. But of course, the same recipe that produces this result produces the result that the proposition (P) Some proposition is both true and false appears in some conceptual system which (since the denial of (P) appears in less than all systems and hence is not neutral) is (allegedly) none the worse for that. And the proposition (P1) Conceptual relativism is false appears in some conceptual systems which (since the denial of (P1) appears in less than all systems and hence is not neutral) is none the worse for that. But then what remains of the claim that conceptual relativism is true?Sometimes refuted is used in a person-independent manner: Proposition P is (and always was) refuted by the fact that F uses P is refuted in such a way that it does not entail There is someone who refuted P. Sometimes, of course, it is so used that P is refuted does have that entailment. Even in the latter case, refutation is an epistemological notion, and Person S is refuted does not entail S knows that S is refuted and is compatible with S believes that S is not refuted. The recommendation that we add a psychological component of ‘admits to’ to the epistemological notion ‘being refuted’ seems to have no other ground than the arbitrary one that if we do we shall then be able better to defend relativism.While the recipe for constructing conceptual systems suggested above may seem useful to a relativist — it gives one clear content to ‘neutral proposition’ — it has what must surely seem a defect to the relativist, namely that given it (even with consistency constraints added) there will be no translational incommensurability. For if P is contained in system S, then not-P is expressible in S, and conversely. And the recipe yields the result that for any proposition P, and any system S, S contains either P or else not-P.This, of course, brings out an ambiguity in ‘contains’. In one sense, a system ‘contains (1)’ whatever can be expressed in it. In another, it ‘contains (2)’ whatever, according to it, is true. If it is a complete system without suspense of judgment it contains (1) twice the propositions it contains (2). Further, a system contains (1) lots of propositions it (or its proponent) does not regard as true, and so the fact that a proposition P appears in system S does not mean that P favors S. One often at least can state the conditions of S's falsehood in S, and even prove in S that S is false, where “in” is used in the sense of “contains (1).”Sophisticated relativism, then, seems no more plausible, no more free from inconsistency, and no less open to devastating critique than are its less cultured relatives. Relativism, at least in the varieties discussed here, seems to live up to its unsavory reputation. Since not even translation incommensurability seems to entail lack of cognitive competitiveness, it seems that it will have to be admitted that, regarding apparent disagreement on basic matters — including fundamental religious disagreement — the appearance is also the reality. People do uneliminably disagree, and short of conversion or (what will seem from within the religious perspective in question) some other ‘failure in faith’ (e.g., coming to reject all religious views) will continue to do so. Whatever can be done in terms of common understanding and common humanitarian endeavors must be done without denying the many basic disagreements that there are. And whatever notion of inter-faith dialogue is other than espitemically defective will have to face that fact; for significant dialogue based on self-deception or on falsehood seems not a terribly promising enterprise. (shrink)
A paradigmatic shift in the foundations of quantum mechanics is recorded, from interpreting to reconstructing quantum theory. Examples of reconstruction are analyzed, and conceptual foundations of the information-theoretic reconstruction developed. A concept of intentionally incomplete reconstruction is introduced to mark the novel content of research in the foundation of quantum theory. ‡Many thanks to Lucien Hardy, Jeff Bub and Bill Demopoulos for their comments. This research was supported through the ANR grant ANR-06-BLAN-0348-01. Part of this research was held at (...) the Perimeter Institute for Theoretical Physics. Research at Perimeter Institute for Theoretical Physics is supported in part by the Government of Canada through NSERC and by the Province of Ontario through MRI. †To contact the author, please write to: CEA-Saclay, 91191 Gif-sur-Yvette, France; e-mail: email@example.com. (shrink)