Re: [Fis] Fw: Responses
The reason of being of information, whatever its content or quantity, is to be used by an agent (biological or artificial). Dear Christophe, In making this restriction you are limiting the domain of information to communication and excluding all information that inheres in structure per-se. John Collier has called the latter manifestation enformation, and the calculus of IT is quite effective in quantifying its extent. Perhaps John would like to comment? Cheers, Bob U. ___ fis mailing list fis@listas.unizar.es https://webmail.unizar.es/cgi-bin/mailman/listinfo/fis
[Fis] New Year Lecture wrap-up
Dear Hans, Thank you very much again for your lecture and your subsequent comments and replies. I dare posting a new comment as an aftermath to your wrap-up and to Pedro's official closure. But I am sure you agree with me, that the matter cannot be settled yet and that a continuation of the discussion is a sign of the fruitfulness of your lecture. As a matter of fact, when I received Pedro's official closure announcement I was a little disappointed because I had been gathering some evidence in support of a previous comment of mine, which probably was not clear enough. I would not like to bother you any more, but since you mention the usefulness of a philosophical outlook, here is a philosophical observation I was able to find. According to Jules Vuillemin (*Necessity or Contingency*, Stanford CA, CSLI Publications, 1996), “probability in the classical sense,” as is well known, is “relative to our ignorance only” (p. 261), but “probability amplitude is something altogether different” (264). For “when physicists today make reference to [...] probability amplitudes [...] they indeed allude to second order probabilities” (167). Therefore, the distinction “between a probability and a probability amplitude” entails a “new distinction in the history of modal notions,” a distinction that Vuillemin describes in the following way: “Classical physics was content with the opposition 'This particle passes through A' versus 'This particle has the probability π of passing through A'. This opposition has nothing to do with ontology: it incorporates what is due to our ignorance into the determination of natural phenomena. Instead of attributing a property or magnitude to a physical system, we attribute it a disposition or propensity to have that property or magnitude. Probability measures that disposition or propensity that belongs to the system in act. A probability amplitude is something altogether different. We can compare it to an embryonic probability as the inventors of the infinitesimal calculus compared the moment of motion to an embryonic motion that an integration would bring to a state of whole motion. But the comparison limps. For the probability amplitude, which is generally a complex quantity, does not figure among the elements of reality. To obtain a probability we must multiply two conjugated probability amplitudes. This means that, when we attribute that amplitude to a system, it is attributed neither as an actual property or magnitude nor as an actual disposition or propensity to having such property or magnitude, but as a purely virtual disposition or propensity to having it. The second- order potentiality, as it were, thus put into play is no longer the measure of an ignorance that might have some chance of being only provisional. It is physical. It describes nature.” (264-65) This is just the conclusion of a long-winded argument, but if Vuillemin is right, then, the interpretation of a superposition of probability amplitudes cannot be Bayesian, or “relative to our ignorance only.” (261) As S. Barry Cooper observes ( *Definability in the Real Universe*, http://arxiv.org/abs/1109.1416 ), “the Laplacian model has a deeply ingrained hold on the rational mind. For a bromeliad-like late flowering of the paradigm we tend to think of Hilbert and his assertion of very general expectations for axiomatic mathematics. Or of the state of physics before quantum mechanics.” From this point of view, QBism might be described, to use Barry Cooper's own words, as “a defensive response to an uncompleted paradigm change” (p. 4). Kind regards, -dino buzzetti On 18 January 2014 18:47, Hans von Baeyer henrikrit...@gmail.com wrote: Dear Friends: In keeping with the message of my lecture, that knowledge of the world is based on the ensemble of individual experiences, more than on assumed objective, actual properties of an external reality, I will tell you about my experiences of writing and discussing the New Year Lecture. I enjoyed the entire process enormously, and wish once more to applaud Pedro for inventing this new tradition! Even as I started this email I learned something that piqued my interest. Gregory Bateson was quoted: Kant argued long ago that this piece of chalk contains a million potential facts (Tatsachen) but that only a very few of these become truly facts by affecting the behavior of entities capable of responding to facts. Google.de informed me that Tatsache is probably an 18th century translation of the English matter of fact. Tat is a deed, a factum, something done or performed, while Sache means a thing or a matter. This tenuous etymology connects factuality with action rather than with some intrinsic essence. Kant's words affecting, behavior and responding are QBist to the core. More and more I realize that philosophy matters. Chris Fuchs, the chief spokesman for QBism, is among the rare physicists who give credit to philosophers for the contributions
[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 https://webmail.unizar.es/cgi-bin/mailman/listinfo/fis
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 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 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
