Dear Andrei, Hans and all I agree with Andrei. And why make quantum theory more complex than it is? One may use all kinds of mathematical tools in a scientific theory, and the more these tools simplify calculations the better. I see no reason to avoid using amplitudes or matrices in quantum theory. Using a mathematical concept for making calculations doesn't entail that I accept that that concept represent a physical property.

To Hans: Where exactly did Einstein wrote that one should avoid unmeasurable concepts in the description of Nature? I can't remember having read that. The issue is how we should interpret quantum theory, in particular the wave function, i.e., probability amplitudes; are they just mathematical tools, or do they describe real physical features of quantum systems? I believe the latter alternative is true and so did Schrödinger. But there are formidable difficulties to give a realistic interpretation of wave functions, and Schrödinger didn't succeed. But I think the difficulties can be overcome and I have published my views about these things (Lars-Göran Johansson: Interpreting Quantum Mechanics. A realist view in Schrödinger's vein, Ashgate, Aldershot 2007). Lars-Göran 22 jan 2014 kl. 10:59 skrev Andrei Khrennikov <andrei.khrenni...@lnu.se<mailto:andrei.khrenni...@lnu.se>>: Dear Hans, I would like just to point that 99,99% of people working in quantum theory would say that the complex amplitude of quantum probability is the main its intrinsic property, so if you try to exclude amplitudes from the model you can in principle do this and this is well known long ago in so called quantum tomographic approach of Vladimir Manko, but in this way quantum theory loses its simplicity and clarity, yours, 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<mailto:fis-boun...@listas.unizar.es> [fis-boun...@listas.unizar.es<mailto:fis-boun...@listas.unizar.es>] on behalf of Hans von Baeyer [henrikrit...@gmail.com<mailto:henrikrit...@gmail.com>] Sent: Wednesday, January 22, 2014 12:21 AM To: fis@listas.unizar.es<mailto:fis@listas.unizar.es> Subject: [Fis] Probability Amplitudes 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 -------------------------------------------------- Lars-Göran Johansson professor filosofiska institutionen Uppsala Universitet 0701-679178

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