Dear Joseph, you are going toward quantum probability theory where probabilities are determined by vectors; moreover, the vectors belong to complex Hilbert space, i.e., roughly speaking each probability has not only the direction but even the phase, andrei

Andrei Khrennikov, Professor of Applied Mathematics, International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science Linnaeus University, Växjö-Kalmar, Sweden ________________________________________ From: fis-boun...@listas.unizar.es [fis-boun...@listas.unizar.es] on behalf of Joseph Brenner [joe.bren...@bluewin.ch] Sent: Wednesday, January 22, 2014 8:54 AM To: Dino Buzzetti; Hans von Baeyer; fis Subject: Re: [Fis] Probability Amplitudes Dear Hans and Dino, This is a direct question to both of you, to which I have not found a clear answer: are value and amplitude the only parameters that have been assigned to probability? In my theory, the changing value of actuality and potentiality of specific antagonistic process elements are probability-like in not including 0 and 1, as I have said. Can, in addition, probabilities have some vector-like properties, that is, include a /direction/? This concept would be moving toward (and past) Dino and away from Hans . . . Your comments and those of others would be welcome. Best wishes, Joseph ----- Original Message ----- From: Dino Buzzetti<mailto:dino.buzze...@gmail.com> To: Hans von Baeyer<mailto:henrikrit...@gmail.com> ; fis<mailto:fis@listas.unizar.es> Sent: Wednesday, January 22, 2014 3:53 AM Subject: Re: [Fis] Probability Amplitudes Dear Hans, Thank you for your explanation about probability amplitudes, that clarifies a lot. My only worry was about the *epistemological* implications of quantum mechanics in its standard formulation, that in my opinion point to a paradigm shift, which is felt not only in this domain, but in all fields where *emergent* phenomena are accounted for—a process that I thought was hinted to by Wheeler's famous words "It from Bit," that I remember reading for the first time precisely in your book on information. That's the ground for expressing my worry that reverting to classical probability theory might entail a drawback to this decisive epistemological turn. But I might misunderstand the whole story, that is certainly not over yet :-) -dino On 22 January 2014 00:21, Hans von Baeyer <henrikrit...@gmail.com<mailto:henrikrit...@gmail.com>> wrote: Dear Dino and friends, thanks for bringing up the issue of probability amplitudes. Since they are technical tools of physics, and since I didn't want to go too far afield, I did not mention them in my lecture. The closest I came was the wavefunction, which, indeed, is a probability amplitude. In order to make contact with real, measurable quantities, it must be multiplied by its complex conjugate. This recipe is called the Born rule, and it is an ad hoc addition to the quantum theory. It lacks any motivation except that it works. In keeping with Einstein's advice (which he himself often flouted) to try to keep unmeasurable concepts out of our description of nature, physicists have realized long ago that it must be possible to recast quantum mechanics entirely in terms of probabilities, not even mentioning probability amplitudes or wavefunctions. The question is only: How complicated would the resulting formalism be? (To make a weak analogy, it must be possible to recast arithmetic in the language of Roman numerals, but the result would surely look much messier than what we learn in grade school.) Hitherto, nobody had come up with an elegant solution to this problem. To their happy surprise, QBists have made progress toward a "quantum theory without probability amplitudes." Of course they have to pay a price. Instead of "unmeasurable concepts" they introduce, for any experiment, a very special set of standard probabilities (NOT AMPLITUDES) which are measurable, but not actually measured. When they re-write the Born rule in terms of these, they find that it looks almost, but not quite, like a fundamental axiom of probability theory called Unitarity. Unitarity decrees that for any experiment the sum of the probabilities for all possible outcomes must be one. (For a coin, the probabilities of heads and tails are both 1/2. Unitarity states 1/2 + 1/2 = 1.) This unexpected outcome of QBism suggests a deep connection between the Born rule and Unitarity. Since Unitarity is a logical concept unrelated to quantum phenomena, this gives QBists the hope that they will eventually succeed in explaining the significacne of the Born rule, and banishing probability amplitudes from quantum mechanics, leaving only (Bayesian) probabilities. So, I'm afraid dear Dino, that the current attitude of QBists is that probability amplitudes are LESS fundamental than probabilities, not MORE. But the story is far from finished! Hans _______________________________________________ fis mailing list fis@listas.unizar.es<mailto:fis@listas.unizar.es> https://webmail.unizar.es/cgi-bin/mailman/listinfo/fis ________________________________ _______________________________________________ fis mailing list fis@listas.unizar.es https://webmail.unizar.es/cgi-bin/mailman/listinfo/fis _______________________________________________ fis mailing list fis@listas.unizar.es https://webmail.unizar.es/cgi-bin/mailman/listinfo/fis