The Shtetl Optimizer informs me that there has not been enough contemplation of Quantum Quandaries for his taste recently. Since there has not been a lot of interesting foundational news, the only sensible thing to do is to employ the usual blogger’s trick of cut, paste, link and plagiarize other blogs for ideas.

Scott recently posted a list of papers on quantum computation that a computer science student should read in order to prepare themselves for research in quantum complexity. Now, so far, nobody has asked me for a list of essential readings in the Foundations of Quantum Theory, which is incredibly surprising given the vast numbers of eager grad students who are entering the subject these days. In a way, I am quite glad about this, since there is no equivalent of “Mike and Ike” to point them towards. We are still waiting for a balanced textbook that gives each interpretation a fair hearing to appear. For now, we are stuck trawling the voluminous literature that has appeared on the subject since QM cohered into its present form in the 1920’s. Still, it might be useful to compile a list of essential readings that any foundational researcher worth their salt should have read.

Since this list is bound to be several pages long, today we will stick to those papers written before the outbreak of WWII, when physicists switched from debating foundational questions to the more nefarious applications of their subject. This is not enough to get you up to the cutting edge of modern research, so more specialized lists on particular topics will be compiled when I get around to it. I have tried to focus on texts that are still relevant to the debates going on today, so many papers that were important in their time but fairly uncontroversial today, such as Born’s introduction of the probability rule, have been omitted. Still, it is likely that I have missed something important, so feel free to add your favourites in the comments with the proviso that it must have been published before WWII.

- P.A.M. Dirac, The Principles of Quantum Mechanics, Oxford University Press (1930).
- J. von Neumann,
*Mathematical Foundations of Quantum Mechanics*, Princeton University Press (1955). This is the first English translation, but I believe the original German version was published prior to WWII. - W. Heisenberg,
*Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik*, Zeitschrift für Physik,**43**, 172-198 (1927). The original uncertainty principle paper. - A. Einstein, B. Podolsky, and N. Rosen, Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935).
- N. Bohr,
*Can quantum-mechanical description of physical reality be considered complete?*, Phys. Rev.**48**, 696 (1935). - N. Bohr,
*The Philosophical Writings of Niels Bohr (vols. I and II),*Oxbow Press (1987). It is a brave soul who can take this much Bohrdom in one sitting. All papers in vol. I and about half of vol. II were written prior to WWII. There is also a vol. III, but that contains post 1958 papers. - E. Schrödinger, Discussion of probability relations between separated systems, Proceedings of the Cambridge Philosophical Society.
**31**, 555-562 (1935). - E. Schrödinger,
*Die Gegenwärtige Situation in der Quantenmechanik*, Die Naturwissenschaften.**23**, 807-812; 824-828; 844-849 (1935). Translated here. - Birkhoff, G., and von Neumann, J., The Logic of Quantum Mechanics,
*Annals of Mathematics***37**, 823-843 (1936).

Many of the important papers are translated and reproduced in:

- J. A. Wheeler and W.H. Zurek (eds.),
*Quantum Theory and Measurement,*Princeton University Press (1983).

Somewhat bizzarely it is out of print, but you should find a copy in your local university library.

I am also informed that Anthony Valentini and Guido Bacciagaluppi have recently finished translating the proceedings of the 5th Solvay conference (1927), which is famous for the Bohr-Einstein debates, and produced one of the most well-known photos in physics. It should be worth a read when it comes out. A short video showing many of the major players at the 1927 Solvay conference is available here.

**Update:** A draft of the Valentini & Bacciagaluppi book has just appeared here.

Copyright © 2006 Matthew Leifer. All Rights Reserved.

“John von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton University Press (1955).”

Shouldn’t there be like a special mark or something here to warn people of the hidden variable mistake in this book?

It’s not the only mistake in that book!

von Neumann did make a mistake or two, but the book is more “correct” than anything else that had appeared at the time, in the sense of mathematical rigour and the recognition that there were interpretational difficulties. It’s not as if the other texts in the list don’t contain assertions that we would regard as naive from a modern point of view, so I don’t see any reason to single him out for special attention.

The no-hidden variables mistake is major, but at least he tried to give an explanation for why they were impossible rather than just asserting it, as some others did at the time. This started the whole tradition of no-go proofs, which eventually led us to Bell’s theorem and the Kochen-Specker theorem.

von Neumann is my scientific hero you know. I switched from Feynman when I realized that there is more to life than being able to play the bongos and tell cute stories about yourself. Besides, I could never identify with the most popular kid in class.

I didn’t realize that von Neumann was your Hero. Too bad he’s my Bad Guy. I’m not sure whether he actually invented the chimera of an evolving quantum state, but he certainly set it in stone with his

Mathematical Foundations.Quantum states are probability algorithms. They allow us to calculate the probabilities of possible measurement outcomes on the basis of actual outcomes. Consequently and most importantly, a wave function’s dependence on time is not the time dependence of an evolving state of affairs but a dependence on the time of the measurement to the possible outcomes of which the wave function serves to assign probabilities. Treat it as an evolving instantaneous state, and you are faced with the mother of all pseudo-problems: why two modes of evolution rather than one? It is a pseudo-problem because the true number of modes of evolution is zero. One gratuitous solution gives rise to other pseudo-problems and other gatuitous solutions, and the end result is that no “one understands quantum mechanics” (Feynman) or that “quantum mechanics makes absolutely no sense” (Penrose).

PS: watching the Feynman video The Pleasure of Finding Things Out should help you to a more balanced view of Feynman.

I’m not sure that the vN no-hidden variables proof was really so very major a mistake. Since it is an *axiom* of vn N’s formulation of QM that states are additive, even over non-commuting observables, criticism of this “assumption” in his no-HV proof seems misplaced. Whether the additivity axiom is well motivated or not is an entirely different question.

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koantum,

Believe me, I have consumed a large amount of Feynman material, including that video. I didn’t intend anything I wrote to be disparaging towards him.

Whilst I appreciate your criticism of the “state vector as state of reality” point of view, I think it is unfair to pin even most of the blame for this on von Neumann. He is not responsible for what later textbook writers have chosen to read into his work. After all, he was never satisfied with the Hilbert space formulation of QM set out in his book, which motivated his later work on quantum logic and operator algebras. From this later point of view, it is much clearer that the quantum state can be viewed as a “probability-like” object instead of a “state-of-reality-like” object. In my view, the book is best appreciated as a rather successful attempt to bring a mathematical rigour to quantum theory that was lacking in earlier formulations. I think we can all appreciate this as the main contribution of his work on quantum theory, even if we disagree about how to interpret it.

I quite agree with you there. Perhaps your hero became my villain because he is also Stapp’s hero. After the motto, the friend of my enemy is my enemy. (I once published a paper in Foundations of Physics subtitled “The 18 errors of Henry P. Stapp”, quant-ph/0105097.)