### [Fis] Logarithm

For entropy we do need the log, because the chemists already knew that it is additive, whereas probability and "the number of ways", are multiplicative. Hans Christian von Baeyer ___ Fis mailing list Fis@listas.unizar.es http://listas.unizar.es/cgi-bin/mailman/listinfo/fis

### [Fis] A curious tale and QBism

Thank you Pedro for mentioning my new book. Actually, there is a connection between my book and the curious tale. QBists look at the future as a web of interlaced personal, numerical probability estimates, with no certainties anchored in REAL mechanisms. The probability that CERN will blow up the world is small enough to be negligible for most people, but not for all. The thing QBists reject as *in principle *unattainable is ABSOLUTE certainty, which many lay people and some physicists (Einstein was among them) continue to long for. Hans Christian von Baeyer ___ Fis mailing list Fis@listas.unizar.es http://listas.unizar.es/cgi-bin/mailman/listinfo/fis

### [Fis] Pedro's trinity

It seems to me that Pedro himself incarnates the third element of his AP. What undoubtedly accounts for most of the success, and certainly for the longevity of FIS, is his profound, utter, and unshakeable KINDNESS -- a virtue that may not be as deep as compassion or love, but that has a much broader reach. If human society were shaped by the forces of reason, justice, and kindness, what a paradise this world would be! Hans Christian von Baeyer ___ Fis mailing list Fis@listas.unizar.es http://listas.unizar.es/cgi-bin/mailman/listinfo/fis

### [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

### [Fis] New Year Lecture wrap-up

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 they make to natural science. In return he hopes that they will listen to physicists who bring news from the furthest reaches of nature. My most intense experience in connection with the New Year Lecture was the writing of it. The first challenge was brevity: The letter I have written today is longer than usual because I lacked the time to make it shorter quipped Blaise Pascal. In order to introduce QBism to you, I had to explain the Q and the B. How to do that within the allotted length? The distinction between Bayesian and frequentist probability is an old subject among mathematicians, so I was able to steal from them. (Schreiben ist Borgen, writing is borrowing, according to the aphorist G.C. Lichtenberg.) But in order to talk about the Q, I had to show succinctly what's so special about quantum mechanics. At this point I was considerably aided by the GHZ prediction and its fairly recent corroboration, because, unlike all previous experiments, GHZ is a one-shot deal, rather than a subtle statistical effect. Like finding a single white raven to falsify the claim that all ravens are black. But even so, although I could easily demonstrate the WRONG classical prediction, I was not able to show those of you who are not trained in theoretical physics how the correct quantum mechanical prediction for GHZ comes about. Unfortunately I would need a semester for that! In any case, by keeping to the prescribed format of the lecture, I was able to clarify my own thinking and to streamline my presentation of the unfamiliar topic. My timing was very fortunate in that two unusually accessible articles about QBism appeared in November and December 2013 -- both available for free at arxiv.org. (ID numbers 1311.5253v1 and 1312.7825.) What a welcome coincidence! It reassured me that the topic I had chosen for my lecture is emerging from its niche in quantum foundations research and slowly seeping out into the broader community. From the subsequent discussion I discovered several important things that are new to me. I learned that there is the possibility, by means on non-Kolmogorovian probabilities, to avoid the troublesome certainty of probability 0 and 1 -- in particular via Logic in Reality. I learned about the interesting concept of feed-forward, in contrast to feedback, which corrects for disruptions of a system BEFORE the disrupting influence kicks in. (In order to do that, the mechanism has to make use of an accurate model of the system's performance, so that it can PREDICT how the system will react. I think it's an exaggeration to call this maneuver inverting the cause-and-effect sequence, but it comes close.) I learned about instrumentalism, and will try to understand how it relates to pragmatism. I was surprised when the conversation on the list veered from probability and epistemology to communication and information. But I shouldn't have been. The QBist point of view divides science into two realms. On the one hand each individual agent assembles the totality of her experiences (experimenting, reading, talking, calculating...) into a web of probability assignments that is as coherent and comprehensive as possible. That's the easy part, and, as usual, physicists have picked it as their domain. But the hard part is the effort of agents to correlate their private experiences -- i.e. to communicate with each other in order to develop a common scientific worldview. Agent A's description of an experience serves as input for updating B's personal probability assignments via Bayes' law. And this is done through language as well as math. Niels Bohr more clearly than any of the other pioneers of quantum mechanics realized the importance of language

### [Fis] First harvest after the New Year Lecture

Dear friends -- Pedro had suggested that the mini-session of responses to my New Year Lecture should last about two weeks. I think that the lesson of QBism for FIS is indirect. In order to make sense of quantum mechanics, which has been spectacularly successful, the interpretation of probability should be Bayesian. If we want a unified worldview to include both quantum physics and classical physics, we should adopt a Bayesian philosophy for ALL of science. From this point ion, quantum mechanics itself can be left out of the debate. So what are the implications of Bayesianism for the definition of the term information? It was surprising to me that the discussion veered off to ancient concepts like Shannon information and entropy, but I suppose that's what FIS is all about. Bob Logan and Rafael helped to tighten the discussion by putting it into its into historical context. Gordana linked the philosophical outlook of personalist Bayesians to that of instrumentalists. I hope that this connection will be further explored by philosophers of science. On the more technical level, I was very pleased to read Robert Ulanowicz's statement: So Bayesian forms of Shannon indices are far more useful about gauging information than most realize. In this way Bayesianism can help to put meaning back into the information concept, from which Shannon summarily, but effectively, banished it. The aspect of probability theory with which QBists have the most trouble is the treatment of certainty -- i.e. probabilities 0 and 1. QBist struggle to define those by insisting that probability 1 for an event does not mean that the event is a fact, or an Einsteinian element of reality -- only that an individual agent is very, very sure that the event will occur. Loet goes in the opposite direction by excizing the probabilities 0 and 1 from the normal, Kolmogorovian closed range from 0 to 1. This approach (Logic in Reality) is too new to me to comment on, but it does offer an interesting alternative. Hans ___ fis mailing list fis@listas.unizar.es https://webmail.unizar.es/cgi-bin/mailman/listinfo/fis

### [Fis] Isms

Physicists generally don't spend much time on distinguishing among philosophical isms. However, since my New Year lecture was on an ism, I can't very well avoid them! Gordana speaks of Instrumentalist Epistemology and Epistemological Instrumentalism. As I understand it, instrumentalism was a term preferred by Dewey to pragmatism, which I called the philosophy most closely related to QBism. So I would agree that pragmatism/instrumentalism is a good framework for exploring both the implications of QBism beyond quantum mechanics, and, conversely, for understanding the claims of QBism itself -- especially in contrast to realism. A new ism was introduced by David Mermin in a short paper submitted on the eve of my New Year Lecture (arxiv.org paper id 1312.7825.) But since his point of view, by his own admission, is that of QBism *tout court*, I won't dwell on his new term. Mermin shows that the philosophy of QBism solves the Problem of the Now, which has nothing to do with quantum mechanics or probability. The question, which frustrated Einstein, is: Why can physics not deal with the universal human experience of the unique moment called NOW? Mermin answers that the problem arises from a fundamental mistake. Since the time of the Greeks we have banished the subject (me -- myself) from any description of the object (the rest of the universe.) Since NOW is a personal experience, it therefore played no role in physics. QBism, on the other hand, puts personal experience front and center in any description of the world. The NOWs of several people coincide only when they are in the same place -- another universal human experience. With this realization Mermin reconciles the personalist Weltanschauung of the QBist with the insights of special relativity. By way of a detour through atomic physics, QBism goes a long way toward healing the subject/object split, which has been effective for physical science, but has also impeded progress toward a more inclusive, holistic understanding of the world. Since Pedro and many other members of the FIS community are biologists, I hope that this conversation will help to bring physical scientists and life scientists closer to each other. Joseph seeks to defend QBism against the charge of ignorantism. Thank you! When physicists calculate observed properties of the electron to nine decimal points, they are hardly ignorant. But QBists insist that we incapable of knowing the real essence of what an electron is. What's a rainbow? I can't tell you in fewer than 300 words. I can't tell you without telling you a story about light, water, eyes, reflection, refraction, dispersion etc. Why should an electron (or a piece of chalk) be simpler? One of my favorite quotes is by the American poet Muriel Rukeyser who said (approximately): The universe is made of stories, not of atoms. And the stories are about experiences, mine and those of all the the scientists who came before me. Hans ___ fis mailing list fis@listas.unizar.es https://webmail.unizar.es/cgi-bin/mailman/listinfo/fis

### [Fis] Responses

Dear friends -- Pedro informs me that as lecturer I'm allowed four responses per week. Not having kept track very well, I take this opportunity to answer some questions, and will start a fresh count on Monday -- if that's OK. Gordana -- l am out of my depth in a discussion of phenomena/noumena/Dinge-an-sich. But when I agree that the Higgs exists out there in the world, I am sure it's not an object like a marble, but a symbol for a collection of experiences that many people have had, and have discussed, and codified, so that if they perform another experiment where it might play a role, they can be prepared with betting odds for what they might experience next. Joseph -- the electron is a point means that no experiment to date has found evidence for a finite size. In the theory (quantum electrodynamics) there is no room for any parameter with dimensions of length, although there are mass, charge, spin, and magnetic moment. When you introduce a finite size into the theory, it makes wrong predictions. (This is not true for protons, for example.) The gravitational field lives in 3D was not supposed to deny that Einstein's elegant formulation treats time as a fourth dimension. But a quantum field is an altogether different and much more complicated beast which lives in infinite dimensions, and has no analog whatever in our everyday human world. Stan -- Is quantum mechanics meaningless? Not if it is regarded as a recipe for manipulating nature successfully for good or ill. The philosophical attitude that is most close to QBism is probably pragmatism: Truth is what works. Lars -- How does QBism differ from Copenhagen? This is a crucial question. It differs not at all in the formalism, and only subtly in the interpretation. Many users of quantum mechanics regard the wavefunction as a real property of an electron. They talk about the wavefunction in the same way you might say the speed of the car. They must then deal with perennial problems such as action-at-a-distance and the collapse of the wavefunction. QBists regard the wavefunction the way Bruno de Finetti regarded probability, when he wrote, in caps, PROBABILITY DOES NOT EXIST. I think he meant that the probability of a coin falling heads is not a measurable property of a coin. All it is is a personal belief of how much an agent should bet. And that belief changes instantly and locally when you make a measurement, or hear that someone else has made one. Some people call the he Copenhagen wavefunction ontic, the QBist one epistemic. Thank you for making me think these things through -- though it's hard work! Hans ___ fis mailing list fis@listas.unizar.es https://webmail.unizar.es/cgi-bin/mailman/listinfo/fis

### [Fis] Social constructivism

Stan asks: Would we be justified in viewing QBism the latest venture of [social] constructivism? WOW, I sure hope not! While it is true that there are fads in science, and that the direction of research is influenced to some degree by the society that funds it and consumes its fruits, I think that the underlying methodology distinguishes socially constructed models of reality from scientific ones. Social constructions use arguments that play no role in any account of the scientific method as it applies to the Natural Sciences (as opposed to the Social Sciences). Some examples: Deutsche Physik referred to the ethnicity of scientists, Lysenkoism adduced ideological goals; Creationism appeals to scripture; Feminist Science Studies consider the gender of scientists. QBism does not change any of the impressive successes of quantum mechanics. It simply says that quantum mechanics is a very complex, abstract encoding of the experiences of generations of scientists interacting with atomic systems. It disenfranchises a physicist from knowing what an electron spin, for example, REALLY is, while celebrating her ability to predict correctly, albeit probabilistically, what to expect in the next experiment. She and her predecessors have created an abstract model, and validated it by appeal to experiments, without appeal to any of the other considerations listed above. In conversation with Joseph Brenner and others I have used the rainbow as a metaphor. The rainbow is a phenomenon that everyone experiences slightly differently, but that we all agree on. The scientific model that explains it is very complicated and highly abstract. Is the rainbow real? It certainly does not exist when nobody is looking. It is, in the end, a personal experience. For me the experience is enhanced considerably by my understanding of the scientific model of it, because it allows me to look for and discover details I had never noticed, but I would not presume to say I know what YOUR experience of it is. Maybe you are thinking of Iris or Noah, and feeling awe or curiosity, and remarking on its (apparently) immense size and variable brightness. QBism suggests that we look at the world as consisting of rainbows -- an ensemble of complex phenomena about which we know some things, but whose essences we cannot capture. The QBist says: I don't know what the world is. All I know is what I experience in my interactions with the world, as they are illuminated and modified by what I have learned from other people, past and present, who have had similar experiences and encoded them in the succinct language of mathematics. Hans ___ fis mailing list fis@listas.unizar.es https://webmail.unizar.es/cgi-bin/mailman/listinfo/fis

### [Fis] Logic in Reality and QBism

Dear Joseph, Jerry, Pedro, and all: 1. QBism seems not to consider the option of using non-standard, non-Kolmogorivian probabilities to describe quantum and non-quantum nature, that is, with values 0 but 1. It is difficult enough to get physicists to consider the standard interpretation of probability offered by Bayesianism, without straying off into the unknown territory in which probabilities 0 and 1 are excluded! However, it is true that those two cases do present special difficulties, and it might be interesting to see what happens when they are forbidden. The paper by Fuchs et al. strains to establish the case of probability 1, which is called a fact, as nothing more than a very,very strong belief. (I enjoy astonishing my students by proving that even though most of them believe that 0.999...1 it actually equals 1.) If a non-standard formalism is used, I would guess that a special category of probabilities very close to 0 and 1 would still have to be singled out, because we have been so thoroughly brainwashed that we parse the world around us in terms of absolute certainties, i.e. of probabilities 0 and1. 2. It excludes the case, impossible by classical logic, but basic to physics and LIR, of a dynamic interaction between the subject and the object which allows both views (belief and facts) to be partly true or better operative at the same time or at different times. I don't know enough about LIR to understand what is meant by the word fact in that context. The interaction between subject and object is a central concept in QBism. It takes the place of the measurement of the older literature, which has the connotation of revealing something objective, real, and pre-existing. An interaction, on the other hand, changes both the external world, and the agent's belief. It creates brand-new facts that did not pre-exist the interaction. Thus we humans participate in tiny ways in the ongoing creation of the world. 3. Since the QBism interpretation does not deal with points 1. and 2. above (also in the Fuchs, Mermin, Shack paper), it leaves the door open to an anti-realist interpretation not only of quantum mechanical reality, but of reality /tout court/ which must be based on and reflect the quantum 'situation'. Right! QBism seeks to establish a new worldview in which the entire material universe is quantum mechanical and described in terms of Bayesian probability -- even those things we think of as real, objective, and factual. Pedro wrote: What I most like of this new quantum approach is the radicalism regarding meaning, experience, knowledge, science... This is good news for the people who sees information science as an occasion to contemplate anew the relationship of the individual with the increasing stock of knowledge accumulated by our civilization, where the ratio of our individual experience to the total is acceleratedly approaching zero!, and where the blind spots of collective intelligence are shining in too many areas of global life... It is healthy that the explicit limitation of the individual is also a message contained in QBism, at least in my understanding. I agree wholeheartedly. The way I see the interaction between the QBists and FIS evolving is this: The physicists are busy trying to rewrite all of quantum mechanics (not just its interpretation) along QBism-inspired lines. This means principally re-casting the entire formalism in terms of probabilities rather than wavefunctions. If they succeed (and the jury is still out on that) they will have created an entirely new theory that is mathematically equivalent to the Schroedinger-Heisenberg theory, but looks completely different. Meanwhile others, including members of FIS, can study the implications of QBism for a new worldview. By the success of quantum theory, nature seems to be urging us into a more personalist, anti-realist view of the world, a view that focuses on individual experience. As Pedro implies, communication with other persons -- information exchange -- is a key component of this experience. I see that tree out there myself, and I can even feel its bark, but the overwhelming majority of what I think and do is triggered by my experience of reading and listening and learning about the experiences of others. In this way information and communication continue to be crucial concepts. Another concept Pedro touches on is human limitation. I find it very liberating to feel that there is no such thing as a grand Theory of Everything -- only little patches of understanding of relationships encoded in rules of thumb with names like Relativity, The Standard Model, Quantum Field Theory, Evolution... With the help of the experiences of generations of scientists I can incorporate these rules in my own personal ordering and surveying of the world around me. So I don't worry, as the Greeks did, about what the world really, really is. It's good to talk to you all, as wee say in Virginia. Hans

### [Fis] New Year Lecture

*Quantum Bayesianism (QBism): An interpretation of quantum mechanics based on quantum information theory* Hans Christian von Baeyer, Professor of Physics, emeritus College of William and Mary, Williamsburg, Virginia January 2014 I am honored and proud to be asked by Pedro to inaugurate the tradition of “New Year Lecture” to the FIS community, in the spirit of the Royal Institution’s “Christmas Lectures”, which have been presented in London almost every year since 1825. Those shows were originally intended for a “juvenile audience”, but have always captivated young and old alike. My electronic lecture is not for children, but like many of its famous predecessors it features a mind-boggling experiment. In spite of the scholarly nature my topic – the interpretation of quantum mechanics – my principal message is simple, and I hope relevant to our quest for the meaning of information. I look forward to a lively discussion after my virtual lecture! QBism (with a capital B) is a radical new interpretation of quantum mechanics that resolves many of the paradoxes that have bedeviled the theory since its invention. The technical successes of quantum theory are unchanged and undisputed -- only the meaning of the formalism is re-appraised. The revision has far-reaching implications for the scientific worldview in general. The crucial move for QBism, inspired by quantum information theory, is very simple. It consists of revising the predominant interpretation of probability. Most physicists accept the frequentist interpretation of probability as “favorable outcomes/all possible outcomes”. Even though this definition becomes rigorous only in the unrealistic limit of an infinite number of trials, it is claimed to be objective. QBism is based instead on the older Bayesian interpretation, which defines probability as “degree of belief.” Specifically, the probability that an event will occur is an agent’s personal assignment of betting odds for the occurrence of the event. It is based on all the information available to the agent, and is explicitly subjective. Bayesian probability, unlike frequentist probability, is meaningful for a single, unrepeatable event. Bayesianism is more general than frequentism. In many cases, such as normal laboratory practice, Bayesian probability can be *measured *by conventional frequentist procedures, but the *meaning *of the result remains Bayesian. (Similarly, temperature is measured by a thermometer, but its meaning runs much deeper.) Bayesianism thus absorbs the successes of frequentism. By combining Bayesian probability with conventional quantum mechanics, QBism locates the result of a calculation in the mind of the agent who makes it. The Schrödinger wavefunction, which is a compendium of information about a quantum system, and in turn yields probabilities for the outcomes of future experiments, becomes subjective as well. Input for assigning betting odds comes from the experiments the agent performs herself, added to information she gathers from the written and oral records of science, i.e. from the totality of her personal experiences. Since wavefunctions are not real in this scheme, the problems associated with such phenomena as the “collapse of the wavefunction” (when probability snaps into certainty as a result of a measurement), Schrödinger’s cat, nonlocality, and Bell inequalities, issues that were interminably debated during the twentieth century, all dissolve. The notorious problem of wavefunction collapse, for example, which defies both mathematical description and the relativistic speed limit, is interpreted as the modification of a probability assignment by a measurement. It is a straightforward application of Bayes’ Law (also known as Bayes’ Theorem or Rule) for updating a probability upon the acquisition of new information. In this way QBism provides a natural and convincing explanation of the mysterious collapse. Apparent nonlocality is displayed most dramatically in an experiment suggested in 1989 by Daniel Greenberger, Michael Horne, and Anton Zeilinger (GHZ). The spin of a “spin 1/2 particle” (such as an electron) can be measured along one axis at a time -- say pointing up or down (U/D) along the z axis, or, alternatively, right or left (R/L) along the x axis. Three identical particles are brought into close contact, and prepared in the special GHZ configuration, in which they are said to be “entangled.” They are then separated by large distances and it is found that whenever two of them point in the same horizontal direction, the third one points UP. (DOWN, if the first two point in opposite directions.) Thus LLU, RRU, RLD and LRD are found among the measurement results, but LLD, RRD, RLU and LRU never occur. A mnemonic: If your two index fingers point in the same horizontal direction, one thumb (representing the third particle,) points up. If they