Popper School Methodological Disproof of Quantum Logic Steve Meyer Tachyon Design Automation San Francisco, CA 94111 smeyer@tdl.com Presented August 6, 2015 CLMPS Helsinki Slides and addition references will posted on my web page www.tdl.com/ smeyer
Context - why did Felix Bloch and David Bohm write this? And I chose Utrect I think that was partly also Pauli s influence, maybe also partly Heisenberg s. Both were somewhat critical of Goettingen spirit; that is, Born s school and approach were considered highly formal and mathematical (Kuhn s 1964 AHQP interview, p.29 1930 decision). I had the impression that group theory is something tremendously import. Later on, I didn t think so much of it any more, but at the time I did. AHQP, p.34 on 1929-1931 research). KP archive letter D. Bohm to KP 26 Feb. 1969: My advice to you is Never entangle yourself with buzz saws, cobras, and Von Neumann s articles on physics.
Overview Presentation changed from abstract because of discussions at HQ-4. 1. What is quantum logic (QL) and history of Grete Hermann s and Karl Popper s falsification by finding flaws in John Von Neumann s mathematical proof. 2. Post 1964 Bell inequality transition discussion, change to modern terminology. Different views of metaphysics. 3. Modern use of QL in discourse and interpretation of experiments. Niels Bohr s and Paul Feyerabend s use of conceptual analysis in quantum theory construction: complementarity, uncertainty principle, exclusion principle etc.
Overview continued... 4. Show how QL is currently being used to interpret experiments using formalized axiomatic QL to discover quantum properties such as entanglement, non locality, observer dependence, quantum computers and other philosophical properties. 5. Discussion uses just Feyerabend s Hidden variables and the argument of Einstein, Podolsky in Feyerabend s collected works Vol. 1 (denoted PKF-EPR).
Von Neumann/Birkoff Quantum Logic references Von Neumann s formalization of QM first appeared in his 1932 book Mathematical Foundations of Quantum Mechanics. but most modern discussions use the axiomatization from a 1936 paper written with Garret Birkhoff The Logic of Quantum Mechanics in Ann. Math. 37(4), 823-843.
What is Von Neumann/Birkoff Quantum Logic QL is an axiomatization of a formalized statistical structure that is claimed to not change if new physical hidden parameters (variables) are discovered. Theorem has been used to eliminate theories that combine descriptions (possibly causal in some sense) of the wave aspects of light and the particle aspects. An example is De Broglie/Bohm combination of statistical particle dynamics and wave functions (usually called pilot waves).
Reaction to QL Einstein rejected both statistical properties and complementarity (wave and particle dual and separate properties) as just an indication of incomplete reality (another basic undiscovered type of field will be found, say). The Bohr school believed in constructing theories using conceptual analysis so obviously opposed QL. The Bohr school interpreted QM s statistical nature (different from Born s) and complementarity as experimentally proven facts.
Reaction to QL continued... I think Von Neumann himself did not take QL as seriously as current mathematical physicists. In the Warsaw 1936 New Ideas in Physics Conference Proceedings discussion Bohr was able to get Von Neumann to agree QL was problematic. In 1974, Patrick Suppes writing in Popper s Schlipp volume (Vol. 14, 767-774) seems to agree that quantum logic is wrong or at least poorly defended, but still maintains only axiomatized theories of physics are possible and suggests some as yet undiscovered axiomatization of QM will solve the problems with quantum logics.
Hermann s and Popper s ignored falsification of QL Grete Herman showed that Von Neumann s proof was circular. Proof assumed the conclusion. Popper showed that the Von Neumann proof used incorrect corollaries of the statistical structure. I think Hermann s falsification is better, but both were ignored. Popper s paper was rejected. After a long exchange of referee rejections and Popper replies, in 1968 Popper was able to get a short note published in Nature (Vol. 219, 682-685) that was then answered in a long paper in BJPS (Vol 25, 1974, 319-332).
Rest of talk considers modern uses of QL I planned to just focus my presentation on the two falsifications but ran into some problems. QL has become an axiom in itself justifying any philosophical interpretation of QM experiments. There is a problem with context. Explanations filtered from Hermann s original 1930s work to her colleague Richard Von Weizsaecker to Feyerabend to Jammer in one thread and Heisenberg to Pauli to Vienna Circle to Popper in another. There is renewed interest in Hermann s work. For example Elise Krull is about to release a book on Hermann.
Transition slide - definitions of term metaphysics Bohr definition: metaphysics is anything that is neither mathematical nor empirical (PKF-EPR 314 note 47). Born s definition: anything that is not axiomatized mathematics. Modern definition: metaphysics is a positive term applying to anything used in the abstract debate between realism and anti-realism.
Einstein explaining transition problem To begin with I refer to the essays of Wolfgang Pauli and Max Born... For only those who have successfully wrestled with the problematic situations of their own age can have a deep insight into those situations; unlike the later historian, who finds it difficult to make abstractions from those concepts and views which appear to his generation as established, or even as self-evident (1949 Schlipp Vol. 665).
Phrase substitution I use I use this phrase substitution to make current terms used in philosophy of physics understandable using physics style analysis. Substitute Shannon-Fano code for information. Substitute physical field for structural realism. Substitute thought experiment for metaphysics.
PKFs criticism of QL allows different explanation of experiments Following Bohr, complementarity is an experimentally established fact. Separate dual wave and particle properties. Moving an experimental apparatus may simply create a new experiment that measures one property rather than the other (I am working on detailed analysis of experiments). Modern use of QL avoids any need to analyze how an experiment relates to the complex and strange experimentally established properties of QM by converting first into formal mathematics and then into formulas with a separate existence - in American vernacular an end run.
Problem with formalization continued... QL formalization is used to convert a conceptual situation into a formula. Various experiments are then used to assign numerical values to various terms and sides of the formula. Experment variations often just change collision/reflection angle. It is this use of formalization that Feyerabend criticizes as non empirical and Popper criticizes as not falsifiable in principle so Popper falsifies the Von Neumann proof using Imre Lakatos method of quasi-empirical math. This is documented in Lakatos archive by late 1960s letters from Feyerabend.
Modern six sigma and empirically verified properties of QM Scientific American magazine articles going back at least to the 1990s justify the experiments proving philosophical properties of quantum effects by arguing semiconductors work. Builders of quantum computer qbits can t assume entanglement but must either show their machine is consistent with complementarity or show complementarity and possibly other properties of QM are incorrect. The six sigma discovery of the Higgs Boson are related to this. The existence of the Boson is verified to a 6 sigma confidence level because the entire measuring system is validated to six sigma - the various measuring apparatus, the background removal monte carlo simulations, the software, the event detectors etc.