October 1997, and to Asher Peres, “Premonition?” I was awakened this morning just in the middle of a complicated dream. I only remember very fuzzy fragments, but there is one in particular that I thought you two would enjoy hearing about. Someone walked up and handed me a newspaper clipping. The headline read, “Bill Wootters and World Renowned Teleporter Asher Peres Attain New Heights.” I didn't see the article, but the headline was accompanied by a picture of you two both wearing lederhosen and Alpine hats, smiling at the camera!! July 1998, “Quantum Giggles” I'm sitting at a little sidewalk cafe in Benasque, Spain thinking of you and all your efforts to find a compelling structure underneath quantum mechanics. It's strange, but for me this has turned out to be a very foundation-oriented conference. Carl Caves and I have been working to construct a quantum version of de Finetti's theorem in classical probability theory. de Finetti's theorem gives the “subjectivist” a way to interpret an “unknown probability” within his framework: probability distributions over the probability simplex are nothing more than shorthand for a certain kind of probability assignment (called “exchangeable”) over a large multi-trial space. What is an unknown quantum state? If you take quantum states to be states of knowledge, as we do, then an unknown quantum state is a troublesome concept. We think that it can be fixed up in roughly the same way – one just has to identify the right notion of an “exchangeable density operator.”
October 1997, and to Asher Peres, “Premonition?” I was awakened this morning just in the middle of a complicated dream. I only remember very fuzzy fragments, but there is one in particular that I thought you two would enjoy hearing about. Someone walked up and handed me a newspaper clipping. The headline read, “Bill Wootters and World Renowned Teleporter Asher Peres Attain New Heights.” I didn't see the article, but the headline was accompanied by a picture of you two both wearing lederhosen and Alpine hats, smiling at the camera!! July 1998, “Quantum Giggles” I'm sitting at a little sidewalk cafe in Benasque, Spain thinking of you and all your efforts to find a compelling structure underneath quantum mechanics. It's strange, but for me this has turned out to be a very foundation-oriented conference. Carl Caves and I have been working to construct a quantum version of de Finetti's theorem in classical probability theory. de Finetti's theorem gives the “subjectivist” a way to interpret an “unknown probability” within his framework: probability distributions over the probability simplex are nothing more than shorthand for a certain kind of probability assignment (called “exchangeable”) over a large multi-trial space. What is an unknown quantum state? If you take quantum states to be states of knowledge, as we do, then an unknown quantum state is a troublesome concept. We think that it can be fixed up in roughly the same way – one just has to identify the right notion of an “exchangeable density operator.”
September 1996, “Theorem II” I encountered your “Ithaca Interpretation” paper this morning on the quant-ph archive … and, I must say, I've been walking around with a nice feeling since. There are some things in it that I like very much! Your Theorem II (or a very slight variation of it) has indeed been proven before, by Bill Wootters. I'll attach the citations below along with part of a note Bill once sent me. (Interestingly, one can also make a cut between real, complex, and quaternionic Hilbert spaces based on such a theorem.) About your Theorem I, if I am not mistaken, it also has a history that predates the references you gave. I believe Richard Jozsa once told me that a fellow named Hadjisavvas found it well before HJW and Gisin. If you are interested you can contact Richard directly; his e-mail address is.… As I say, I enjoyed your paper very much! (Presently) I think my only point of departure in what you say is about the issue of “objective probability.” Carl Caves and I (in still another paper cited below which can be found on quant-ph, pp. 22–26 in particular) have advocated the view that even the probabilities of quantum theory should be interpreted in a Bayesian or subjective way. We prefer to say that it is the “indeterminism” of quantum mechanics that is “objective,” and not the probabilities themselves.
June 1997, “Painting My Stripes” I am just returning from the library, where – completely by accident – I ran into and read an entertaining little article: A Peres, “Einstein, Gödel, Bohr,” Foundations of Physics 15 (2), 1985, 201–205. I was especially entertained by your closing line, “Any attempt to inject realism in physical theory is bound to lead to inconsistencies.” Do you have any other writings (beside the AJP paper with Zurek) where you expand upon the ideas presented in this? In connection to this, I have another question. If I recall correctly, you once told me that you finally came to grips (“interpretationally,” that is) with quantum mechanics in 1986. (Perhaps I have the year wrong, but that's part of the question.) Would you be willing to expand upon that point? In particular, was your arrived-at comfort founded upon the line I quote above? I suppose I ask these questions for several reasons, perhaps the strongest of which is a renewed dilettante interest in the foundations of quantum theory. Among other things, I am trying to plan (or dream up!) a talk for the Hull conference in September to be titled something like: “Quantum Information Theory's Implications for the Foundations of the Quantum as a Whole.” My own pet “idea for an idea” (as Wheeler would say) is that the quantum theoretical description – along with its Hilbert-space structure – is forced upon us when the information we have about a physical situation/system is of a certain variety.
February 2000, “The Quantum View” What a really nice article! I read it once this evening with dinner (at a place that served grilled chicken – not so easy to scroll through a computer screen under those conditions!). Now, with my jetlag in distinct control – its 3:30 AM for me – let me read it again and make a few comments here and there. (I just arrived in Haifa yesterday for a visit with Asher Peres; I'll be here a little over a week.) Why don't you write the following for your requested reference: C. A. Fuchs, “The Structure of Quantum Information,” available at […] [Of course, it is no longer available. Instead, see note to Carl Caves, dated 21 December 1997.] I like this view of physics as being like a jig-saw puzzle. Note a typo in this paragraph: you misspelled de Broglie. Ruskai-ism 1: As far as I am aware, there is no evidence that either Heisenberg or Schrödinger was motivated by political or social factors . Actually there is a pretty strong case that these two guys were indeed quite motivated by cultural factors to find an indeterministic element in physics. And that was long before quantum mechanics took a final form. Two important articles to read in this regard are: P. Forman, “Weimar Culture, Causality, and Quantum Theory, 1918–1927: Adaptation by German Physicists and Mathematicians to a Hostile Intellectual Environment,” in Historical Studies in the Physical Sciences, Vol. 3 , edited by R. McCormmach (U. Pennsylvania Press, Philadelphia, 1971), pp. 1–115. […]
November 1997, “The Radical Eye” Let me send you some prep work…while I'm procrastinating from things I really need to be doing. I'll convey the information in my favorite way: quoting/forwarding old emails! The first, an old – kind of poorly written – note “Dreams of a More Ethereal Quantum,” concerns one aspect of the below-the-water stuff: the idea about distilling the MaxEntlooking part out of quantum theory. It doesn't say much more than I said in the proposal…but you can't expect too much, it's still just a vague program for a program. That stuff is at the bottom of the note; the early part of the note says a few – even more sketchy – things about Mermin and Quantum Probabilities…so I thought I would include it for that reason. The only other readable thing (I think) I've written on this aspect of the below-the-water stuff is on pages 22–26 of my paper with Caves, “Quantum Information: How Much Information in a State Vector” (it's on quant-ph). These same pages also contain an extended discussion on probability. The second note, “Rainy Mondays and Consistent Histories,” is a note I wrote Bob Griffiths concerning what I think of his Consistent History stuff. I think it says quite plainly and clearly what I think about probability in quantum mechanics. It's pretty self-contained (i.e., not referring to old conversations, etc.), so you might find it useful reading.
Fifteen years ago, I mused in a Reference Frame column on how different generations of physicists differed in the degree to which they thought that the interpretation of quantum mechanics remains a serious problem. I declared myself to be among those who feel uncomfortable when asked to articulate what we really think about the quantum theory, adding that “If I were forced to sum up in one sentence what the Copenhagen interpretation says to me, it would be ‘Shut up and calculate!’” In the intervening years, I've come to hold a milder and more nuanced opinion of the Copenhagen view, but that should be the subject of another column. The subject of this one is the habit of misquotation or misattribution that afflicts our profession, a rather different example of which I pointed out a few months ago. Given my capacity for intellectual development (“inconsistency,” in the terminology deployed in the current American political season), it's fortunate that I've now reached an age at which I tend to forget about things I've written more than a few years ago. Indeed, I find it downright irritating when somebody asks me questions about papers I wrote a mere half dozen years ago, naively identifying me with the author of those ancient texts. Until quite recently, I had no memory of ever having written such a childishly brusque dismissal of such an exquisitely subtle point of view, much less of having published it in so widely read a venue. This amnesia, combined with the evolution in my thinking that had distanced me from my long-forgotten words, may explain why I was initially somewhat puzzled by the slight sensation of discomfort that passed over me when, browsing the e-print archive earlier this year, I read a characterization of Max Born's probability rule as “the favorite ingredient of what has been nicknamed, after Feynman's famous dictum, the shut up and calculate interpretation of quantum mechanics.” I yield to nobody in my admiration for Richard Feynman's aphorisms on the nature of quantum mechanics. Indeed, long ago I published a poem consisting of nothing more than a resetting as verse of a paragraph Feynman had written about his own attitude toward the quantum theory, in his now (but not then) famous article that launched the whole field of quantum computation. I like to think I have devoured everything Feynman ever wrote on the character of quantum mechanics.
Quantum mechanics is the most useful and powerful theory physicists have ever devised. Yet today, nearly 90 years after its formulation, disagreement about the meaning of the theory is stronger than ever. New interpretations appear every year. None ever disappear. Probability theory is considerably older than quantum mechanics and has also been plagued from the beginning by questions about its meaning. And quantum mechanics is inherently and famously probabilistic. For the past decade, Carl Caves, Chris Fuchs, and Rüdiger Schack have been arguing that the confusion at the foundations of quantum mechanics arises out of a confusion, prevalent among physicists, about the nature of probability [1]. They maintain that if probability is properly understood, the notorious quantum paradoxes either vanish or assume less vexing forms. Most physicists have a frequentist view of probability: Probabilities describe objective properties of ensembles of “identically prepared” systems. Caves, Fuchs, and Schack take a personalist Bayesian view: An agent assigns a probability p to a single event as a measure of her belief that the event will take place [2]. Such an agent is willing to pay less than $ p for a coupon that will pay her $1 if the event happens, and she is willing to underwrite and sell such a coupon for more than $ p . Surprisingly, the standard rules for probability follow from the requirement that an agent should never face certain loss in a single event. (For example, if p exceeded 1, she would pay more than $1 for a coupon that returned at most $1; if p were negative, she would pay somebody to take a coupon from her that might cost her another $1.) Avoiding certain loss is the only constraint on an agent's probability assignments. The probability of an event is not inherent in that event. Different agents, with different beliefs, will in general assign different probabilities to the same event. The personalist Bayesian view of probability is widely held [3], though not by many physicists. It has profound implications for the meaning of quantum mechanics, which Fuchs and Schack call quantum Bayesianism—QBism for short. Since quantum states determine probabilities, if probabilities are indeed assigned by an agent to express her degree of belief, then the quantum state of a physical system is not inherent in that system but assigned by an agent to encapsulate her beliefs about it. State assignments, like probabilities, are relative to an agent.