Quantum foundations before WWII





Many of the important papers are translated and reproduced in:





Creative Commons License
Quantum foundations before WWII by Matthew Leifer, unless otherwise expressly stated, is licensed under a Creative Commons Attribution-Noncommercial 3.0 Unported License.

8 Responses to Quantum foundations before WWII

  1. “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? :)

  2. It’s not the only mistake in that book!

  3. 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.

  4. 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.

  5. 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.

  6. Pingback: Quantum Theory at the Crossroads Conference « physics musings

  7. 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.

  8. 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.)

Leave a Reply