February 1998, “Law Without Law…Or Something Like That”

This morning I read one of the papers you gave me last week (“Information is Inevitably Physical”) and was reminded of your interest in the idea that the laws of physics may not be written in stone once and for all…but instead may be contingent upon the particular details of the universe itself…and indeed may be evolutionary à la Peirce, Wheeler, Lee Smolin, etc. At least one version or other of this kind of thing has intrigued me for some time (essentially since meeting John Wheeler in 1985). It's been sort of a hidden hobby, somewhat connected with separating the wheat from the chaff in quantum mechanics. My personal writings on the subject are now pretty voluminous, though not yet tight enough in substance that I show them to too many: most are in the form of emails to colleagues such as you.

Anyway, if you're interested, perhaps I'll compile a small compendium and send it your way when I get back from Tokyo March 15 – I'm travelling essentially every moment until then. May be this will help us open a dialog to pinpoint where some real progress might be made.

In the meantime let me tip you off to another article on the subject that I ran across recently: S. S. Schweber: “The Metaphysics of Science at the End of a Heroic Age,” in Experimental Metaphysics, edited by R. S. Cohen, M. Horne, and J. Stachel (Kluwer, Dordrecht, 1997), pp. 171–198.

February 1996, “QM is a Law of Thought”

By the way, did you ever read the paper Carl and I wrote titled “Quantum Information: How Much Information in a State Vector?” In it we talk at some length about this idea of “Quantum Mechanics as a Law of Thought” and other Bayesian sounding things. (We even quote Gertrude Stein?!”!) Of course, all the ideas are loose now, but one day they'll be tight.

September 1996, “Silly Latin”

Allow me to continue my tradition of writing you only when I need something translated!! I've decided on an epithet for myself. Either:

What do you think? (…and don't tell me I'm plagiarizing Boole!) Anyway, the problem is that I would like to have these translated as closely as possible into Latin. Do you think you're up to the task? I would appreciate it so much.

I can't wait to see you in Japan; I really miss the old gang.

Rüdiger's First Reply: 19 September 1996

I like “Quantum Mechanics is a Law of Thought” better, but I can't give a good reason for that.

January 1999, “The (Un-)Detached Observer”

Yesterday I ran across your paper “On the Interpretation and Philosophical Foundation of Quantum Mechanics” posted on the web, and was very much impressed with its depth. Most importantly, however, I am sad to say, it reminded me that I still owe you some papers.

I have remedied that now by sending you a pile of things that I have written on the relation between information gain and quantum state disturbance. These are relevant to your request above, and, I think, even more relevant to the thoughts in your paper. I am in great agreement with the idea that there may be a deeper foundation to quantum mechanics, one along the lines that Pauli and Wheeler attempted to sketch. Quantum mechanics, it seems to me, is an expression of the best we can say in a world where the observer is not detached (to use Pauli's phrase). Recognizing and appreciating that lack of detachedness is the most exacting tool we have for peering into the greater future of quantum theory. This I think is the ultimate role of quantum information theory. (For the opposite point of view, however, you may be interested in having a look at John Preskill's paper “Quantum Information: Its Future Impact on Physics” at http://theory.caltech.edu/~preskill/.)

I hope you will enjoy the things I have sent you; it is always my attempt to be as clear as I possibly can be when I write.

May 2000, “History Reduced to Eight Pages”

Dear friends and family who have written or called with concern over the Los Alamos fires,

I apologize at the outset for sending a mass mailing like this. All of you hold a unique place in my mind, but time is scarce at the moment.

Sometime Wednesday or Thursday last week, the Cerro Grande fire invaded our home in Los Alamos and took essentially all that was in it. The only exceptions were our car, a couple of suitcases of clothes and memories, and most importantly, our lives. Kiki, Emma, and I are all physically well. So are our “boys,” the golden retrievers Albert and Wizzy. The last few days we have received shelter and comfort in Albuquerque in the home of Carl Caves and Karen Kahn. The boys have been in the foster care of Chris Hains (where they likely view themselves as having a resort vacation).

We saw the remains of our home Sunday: all that was left solid was the chimney. The thought of it makes us quite sad at times. I count as my greatest loss all the “intellectual property” that never made it or could not make it into my computer – my thousands of pages of meticulous calculation, my sad poems from sad times and my pre-electronic correspondence, my collection of over 700 physics, math, and philosophy books.

25 December 1996, “Reality Steaks”

Holiday cheers! I'm sitting in Geneva, connected to my machine at Caltech, thinking about an old fart in Massachusetts. I was just reading an article (in the New Yorker) about Woody Allen and came across the most wonderful quote: “I hate reality, but, you know, where else can you get a good steak dinner?” Like it? Quantum mechanics everywhere you turn.

17 February 1997, “Prophetic Herberts”

This is the second time you've intrigued me with a phrase or two: I'm not letting you off the hook this time. Please explain in more detail what you mean by the following. The first quote comes from 25 December 1996:

Herbal Treatment 1:Actually that Austrian reaction to enhancing classical communication was probably part of a reality-loving or at least a quantum-preferring inclination which is some-thing beneficial to the reality-seekers amongst us – if everyone were so crazed about measurement and what-all, Charlie would never have figured out that it wasn't the knowing of an answer which introduced the irreversibility; it was the erasure of the “garbage” produced in the calculation. And without all the fuss over reversible classical computation, we wouldn't have had so much fun with quantum comp.

The second quote comes from 12 February 1997:

Herbal Treatment 2:I was impressed similarly by Charlie's hint that thinking beyond the “big deal” everyone since Szilard seemed to make of measurements was crucial to his realization that the entropy generated by Maxwell's demon for a 1-molecule gas came from forgetting which side of the door it was on.

On 18 September 1996 I received email that began

Dear Dr. Mermin,

Although I didn't really know my correspondent, it was clear from what followed that he had thought hard – probably harder than I had – about many of the matters I was trying to address. His scholarship and intelligence were so evident that I started walking around with a nice feeling myself at having received unsolicited praise from so thoughtful a source.

Little did I know that those heartwarming words of appreciation were just bait to lure me into a long critical exchange which, to my pleasure and enlightenment, has been going on ever since. A part of my subsequent education (there have also been several invariably instructive and delightful real-life meetings) can be found in Chapter 18 below.

If Chris Fuchs (rhymes with “books”) did not exist then God would have been remiss in not inventing him. Foundations of quantum mechanics is a unique blend of poetry and analysis. Without the poetic vision the analysis tends to chase its own tail into more and more convoluted realms of intricate triviality. Without the analysis the poetry easily degenerates into self-indulgent doggerel.

June 2000, “References for Gleason”

Some relevant references. The important ones are Gleason's paper, Cooke et al.'s paper, and Pitowsky's paper.

1. R. Cooke, M. Keane, and W. Moran, “An Elementary Proof of Gleason's Theorem,” Math. Proc. Camb. Phil. Soc.98, 117–128 (1981).

2. A. M. Gleason, “Measures on the Closed Subspaces of a Hilbert Space,” J. Math. Mech.6, 885–894 (1957).

3. I. Pitowsky, “George Boole's ‘Conditions of Possible Experience’ and the Quantum Puzzle,” Brit. J. Phil. Sci.45, 95–125 (1994).

4. I. Pitowsky, “Infinite and Finite Gleason's Theorems and the Logic of Indeterminacy,” J. Math. Phys.39, 218–228 (1998).

5. 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.

April 1996, to Michiel van Lambalgen, “Thesis”

About myself (in case you are wondering) I am a physicist. My research specialty is “quantum information theory,” a field that concerns a hodgepodge of things including quantum cryptography, quantum computing, and statistical inference problems having to do with quantum mechanical systems. You may have heard of some of these things through Paul Vitanyi or André Berthiaume (Vitanyi's postdoc). I am presently a postdoc working for Gilles Brassard and Claude Crépeau in Montréal; starting October, I will have a three year position at Caltech.

I was once interested in the mathematics of randomness because, though I am Bayesian through and through for all other uses of probability, I believed that probabilities for quantum mechanical measurement outcomes were something different…in fact something more akin to the frequentist conception. Thus I put a lot of effort into studying von Mises, Church, Kolmogorov, Martin-Löf, Chaitin, etc. (I didn't find your papers until I had pretty much abandoned this belief, though I'm not sure that I am completely over it!) I had hoped that there might be some mathematical connection between the structures found in quantum theory (vector spaces, positive-operator valued measures, etc.) and the structures required to formalize the notion of random sequences…at least that was my motivation.

30 August 1998, “Desiderata”

I just read over your four desiderata for an acceptable “über-quantum theory” for the third time. (When I finish this note, I'll read them over for the fourth time … at the very least for simile's sake.) They're not so uninspired! (… to use your words, that is.) But I do hope you will keep your promise of writing a longer exposition.

In the mean time, let me ask you for one point of clarification about the connection between your Desideratum #1 and my latest happy thoughts.

Kentism 1:1. A theory in which some elementary, and precisely defined, components constitute the basic statements from which propositions about an external and objective reality can be built. Maybe trajectories à la Bohm, maybe collapse events à la GRW, maybe events of more general form à la consistent historians, maybe the evolution of the classical gravitational field in some (unknown) theory that links classical metric and quantum matter. Maybe something quite different from any of the above. But, at any rate, something which allows us to talk about what happened in the past, in the absence of observers, and which allows us to resolve the measurement problem by replacing the vague notion of measurement by something precise.

03 April 2000, “Foundations in the Light of Information”

Below is a slightly modified version of the invitation letter I sent everyone. (The only change is an update on the attendance.) Looking forward to seeing you again. (BTW, I hope you'll take the problems list seriously.)

Dear friends,

Gilles Brassard and I are organizing a little meeting in Montréal from Wednesday May 17 through Friday May 19 on the subject of “Quantum Foundations in the Light of Quantum Information and Cryptography.” We hope you can come. Mainly the purpose of the meeting is to gather a group of our friends who think that some aspects of quantum foundations are a little more mysterious than they ought to be and, importantly, are intrigued by the idea of applying quantum information to the task of cleaning things up. The atmosphere of the meeting should be quite relaxed with plenty of time for discussion and/or private brooding: we only ask that you be prepared to give a 20 to 30 minute talk (though longer talks are welcome too) expressing your point of view and any avenues for progress you foresee. Attendants are also encouraged to compile and share a list of concrete problems whose solution would tell us something novel about the quantum foundations.

February 1996, “Goo-Losh”

Mmm, goulash…is that how you spell it? Thanks for the tip. I haven't heard the reaction of Bennett and company on this business yet, but when I do, I'll send a report your way.

I've been thinking about Kochen–Specker theorems lately; they're very nice you know…especially the ones with small numbers of vectors. Implications for “quantum information”? There must be! In particular, why can't one go much further in this effort to prove the theorem with smaller and smaller numbers of vectors? Why is there no proof of this property (i.e., no noncontextual hidden variables for the outcomes of standard von Neumann measurements), the very second you admit a measurement that is nonorthogonal to the others? Just food for late night thoughts.

March 1996, “The Commitments”

It's a good movie; did you ever see it?

Suppose you need some cash and so you go to your Automated Teller Machine (ATM). You insert your bank card and the machine asks you for your Personal Identification Number (PIN). It does this for the obvious reason that it wants to know that you are indeed who you say you are before it hands over the money. That's a good safeguard. However suppose, as really did happen a year or two ago, someone had set up a fake ATM in place of the real one.

18 November 1997, “Bolt from the Blue”

I saw Adrian Kent's four papers on the server early this morning, and I was reminded of Léon Rosenfeld's description of Bohr's reaction to the EPR paper:

I suspect the air in Montréal will be just as this when you all awake today. How I wish I were there to see the excitement!

I hope for the sake of our field, and a generally more exciting world, that Kent is right! As you all know, this sceptical physicist (i.e., me) was always a little wary of the Mayers–Lo–Chau strong claim of having considered all possible quantum protocols. I would like to hear the Montréal verdict once it is in.

A good day to all!

31 August 1999, “Subliminal Messages”

Quantum Foundations in the Light of Quantum Cryptography

Quantum Foundations in the Light of Quantum Cryptography

Quantum Foundations in the Light of Quantum Cryptography

Quantum Foundations in the Light of Quantum Cryptography

November 1997, “Martha White and Her Flour”

[Note: Words supplied by Greg Comer. See notes to Asher Peres, dated 17 October 1997, Greg Comer, dated 25 November 1997, and Carlton Caves, dated 21 December 1997.]

October 1998, “Oh Magic Eight Ball”

Democritus said, “All the world is but Atom and Void.” I've decided (with Kiki's help) that I much more like the metaphor, “All the world is but Magic Eight Balls and Questions.” See the resemblance? You couldn't have atom without void; but you could have void without atom. You couldn't have Questions without Magic Eight Balls; but you could have Magic Eight Balls without Questions. The sole remainder of archaic atomism is that “atoms” be “repositories.” Not repositories of “properties.” But repositories of answers to the questions we might ask. To keep these sentences from being contradictory, those answers can't exist before we ask them (else they be properties).

April 1999, “Thinking Kantian Thoughts?”

The other day I wrote the little essay below [cf. “Fuchsian Genesis” addressed to Greg Comer, dated 22 April 1999] for myself, and then searched up a reason to send it to my friend Greg Comer. It would have been better to send it to you I think. It strikes me as sounding a little Kantian, though with an extra twist: namely, that we are even further removed from the “ding an sich” than he had imagined. On my view, we know that the quantum formalism CANNOT correspond to reality (whatever it may be). My understanding of Kant is that he would have said that classical physics may or may not be a reflection of the real thing, but we can never know. It does form part of the categories of understanding and is therefore necessary to make sense of the world; but correspondence to reality is a different issue – in fact, one that cannot be decided. In the case of the quantum world, I think it is (reasonably) safe to assume that the terms in quantum theory cannot be mapped to any sort of “ding an sich.” That's why it strikes me as a still stronger form of Kantianism.

Am I way off track here? Any thoughts?

Jon's Reply

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:

1. 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.

2. […]

February 1999, “From Gleason to Pitowsky”

You'll note that I've forwarded you three emails from my correspondence with Itamar. [See note to Pitowsky dated 13 October 1998 (Other Letters).] I'd be keen to hear any further thoughts you might have on Gleason or Kochen and Specker. My email is always an open door when it comes to better understanding the quantum …

May 1999, “SD and KS” and “Even More Relevant”

How about we plan on my dropping by sometime during the week of May 24–28. You guys choose the exact dates (either one or two nights, as you said). I'll probably bring my wife and little girl down with me. They'll drop me off to play with you, and go off to play a little on their own.

I have a question about your rational-point anti-KS result. I'm starting to wonder how robust the idea is. The way you pose the problem is to consider the points on the sphere with rational cartesian coordinates. But are you sure that nothing changes under rather natural coordinate changes? For instance, imagine working in spherical coordinates for vectors on the unit sphere in R3. If we restrict ourselves to rational angles θ and φ, the cartesian coordinates so generated will almost always be irrational. And this discrete set of vectors is not just a rigid rotation of the ones you consider.

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 Physics15(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, “Your Project”

(Please remind me of our conversation in Italy. I remember your name, but I can't quite picture you.)

Your proposal sounds interesting: it wasn't too bold. Why don't we carry on just as you suggested. I'd be happy to supervise a project of yours (or perhaps collaborate)…as long as the work concerns something that interests me. Presently most of my interest is in quantifying different aspects of the trade-off between information and disturbance in quantum mechanics. This includes deriving various properties for some information functions that have little coverage in the existing literature so far. If we could find something that pleases us both in that general area, I think it'd be great. (Presently I'm not too interested in tackling entanglement questions: I can't see the forest for the trees in that subject.)

About collaborations, I only have one hard and fast rule at the outset: that is that author ordering be alphabetical. I place my form letter concerning this issue below. If you feel that this would hurt you, we can agree to keep MY role in the project in a strictly supervisory capacity.

Let me know what you think: I'm always within email contact.

17 January 2001, “First Contact”

I am writing this letter to find out if you are interested in attending a conference in Växjö, Sweden this summer titled “Quantum Theory: Reconsideration of Foundations.” I do this because I have read a few of your papers and parts of your book on Bohr, and I have been extremely impressed. By trade, I am a practitioner of the new field of quantum information theory and computing – and indeed the main session I am organizing at the Växjö meeting will be about quantum foundations reconsidered in that light – but your description of Bohr's thought meshes so well with what I'm seeking in physics that I'd like to get you there too. PLEASE NOTE that this is not exactly a real invitation yet: I am still lobbying for a more philosophical contingent at the meeting. But, I would very much like to hear your reaction just as soon as possible. If things work out, and you would like to come, I will recontact you very soon with further details.

The main reason I want you at our meeting is that I have this “madly optimistic” (Mermin called it) feeling that Bohrian–Paulian ideas will lead us to the next stage of physics. That is, that thinking about quantum foundations from their point of view will be the beginning of a new path, not the end of an old one.