02 June 1999, “Please Do” You know what I'm really trying to get at here: I want the structure of quantum mechanics to be extremal for some kind of more abstract (i.e., QM-independent) information-disturbance problem. But the first thing that needs to be done is to pin down what quantum mechanics itself has to say. Another thing that keeps coming to mind is that the assumptions behind Gleason's theorem might have something to do with the allegory I presented you with at Charlie and Theo's house. God said, “Ok I will make information gathering invasive, but not so invasive that you will be forever science-less.” The connection is this. I think one can split the assumption behind Gleason up into at least two parts: (1) The questions that can be asked of a quantum system only correspond to orthonormal bases over some vector space, with there being no good notion of measuring two distinct questions simultaneously (there being no good notion of an AND operation). And (2) It is the task of physical theory to give probabilities for the outcomes of those questions, but we can say at least this much about the probabilities. They are context-independent in the sense that, for a given outcome, it does not matter which physical question (which basis) we've associated it with. I.e., the probabilities can be assumed to be of the form of a frame function.
02 June 1999, “Please Do” You know what I'm really trying to get at here: I want the structure of quantum mechanics to be extremal for some kind of more abstract (i.e., QM-independent) information-disturbance problem. But the first thing that needs to be done is to pin down what quantum mechanics itself has to say. Another thing that keeps coming to mind is that the assumptions behind Gleason's theorem might have something to do with the allegory I presented you with at Charlie and Theo's house. God said, “Ok I will make information gathering invasive, but not so invasive that you will be forever science-less.” The connection is this. I think one can split the assumption behind Gleason up into at least two parts: (1) The questions that can be asked of a quantum system only correspond to orthonormal bases over some vector space, with there being no good notion of measuring two distinct questions simultaneously (there being no good notion of an AND operation). And (2) It is the task of physical theory to give probabilities for the outcomes of those questions, but we can say at least this much about the probabilities. They are context-independent in the sense that, for a given outcome, it does not matter which physical question (which basis) we've associated it with. I.e., the probabilities can be assumed to be of the form of a frame function.
June 2000, “References for Gleason” Some relevant references. The important ones are Gleason's paper, Cooke et al .'s paper, and Pitowsky's paper. R. Cooke, M. Keane, and W. Moran, “An Elementary Proof of Gleason's Theorem,” Math. Proc. Camb. Phil. Soc. 98 , 117–128 (1981). A. M. Gleason, “Measures on the Closed Subspaces of a Hilbert Space,” J. Math. Mech. 6 , 885–894 (1957). I. Pitowsky, “George Boole's ‘Conditions of Possible Experience’ and the Quantum Puzzle,” Brit. J. Phil. Sci. 45 , 95–125 (1994). I. Pitowsky, “Infinite and Finite Gleason's Theorems and the Logic of Indeterminacy,” J. Math. Phys. 39 , 218–228 (1998). F. Richman and D. Bridges, “A Constructive Proof of Gleason's Theorem,” J. Func. Anal. 162 , 287–312 (1999). December 2000, “New Ideas and Old Men” Thanks for the new ideas. Let me try to make a few comments. I'm in a smoky hotel bar right now; I wonder how this is affecting my laptop's health? I know it's wreaking havoc on mine. I'm still in Vienna, by the way. I leave Tuesday morning. Unfortunately I haven't gotten an ounce written of what I had hoped to. Renesism 1: This got me thinking about this stuff, and it seems that in some sense what we're gathering information about, when we make measurements, is the ability to predict future measurements . You haven't read my paper with Kurt Jacobs yet, have you? [See quant-ph/0009101.] Come on, at least read the Introduction and Footnote 27.
22 August 1999, “Your Article” I am writing to let you know that I enjoyed your article quant-ph/9812050, “Why Quantum Mechanics is Hard to Understand,” very much. I was in particular very pleased with your Section IV “Dynamics vs. History.” It may interest you to know that Markus Fierz expressed a similar point of view in his article: “Does a physical theory comprehend an ‘objective, real, single process’?” in Observation and Interpretation in the Philosophy of Physics , edited by S. Körner (Dover, NY, 1957), pp. 93–96. I will append the full text below for your enjoyment. [See note to Rüdiger Schack, dated 29 August 1999.] Most importantly, I would like to ask you for the final coordinates of your paper. Was it published somewhere? I would like to cite it in an upcoming paper. 28 August 1999, “Not Much” I don't have a good idea about where to send your paper. I think chances are that AJP will be tougher than FP . In any case, it had an impact on me. My old advisor used to say of our joint papers, “If three people read this paper, we'll be doing OK!” If you know of two others with yours, you're probably doing OK. I like this focus on the concept of “object.” I look forward to anything you might have to say about it. I have some slides that I use as a rallying cry to the idea that quantum information theory may have some impact on quantum foundations. The first is a list of axioms for quantum mechanics.
If you have a restless intellect, it is very likely that you have played at some point with the idea of investigating the meaning and conceptual foundations of quantum mechanics. It is also probable (albeit not certain) that your intentions have been stopped on their tracks by an encounter with some version of the "Shut up and calculate" command. You may have heard that everything is already understood. That understanding is not your job. Or, if it is, it is either impossible or very difficult. Maybe somebody explained to you that physics is concerned with "hows" and not with "whys"; that whys are the business of "philosophy" ---you know, that dirty word. That what you call "understanding" is just being Newtonian; which of course you cannot ask quantum mechanics to be. Perhaps they also added some norms: The important thing a theory must do is predict; a theory must only talk about measurable quantities. It may also be the case that you almost asked "OK, and why is that?", but you finally bit your tongue. If you persisted in your intentions and the debate got a little heated up, it is even possible that it was suggested that you suffered of some type of moral or epistemic weakness that tend to disappear as you grow up. Maybe you received some job advice such as "Don't work in that if you ever want to own a house". I have certainly met all these objections in my short career, and I think that they are all just wrong. In this somewhat personal document, I try to defend that making sense of quantum mechanics is an exciting, challenging, important and open scientific endeavor. I do this by compulsively quoting Feynman (and others), and I provide some arguments that you might want to use the next time you confront the mentioned "opinions". By analogy with the anti-rationalistic Copenhagen command, all the arguments are subsumed in a standard answer to it: "Shut up and let me think"
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.