Observables and Unobservables in Quantum Mechanics: How the No-Hidden-Variables Theorems Support the Bohmian Particle Ontology

The paper argues that far from challenging—or even refuting—Bohm’s quantum theory, the no-hidden-variables theorems in fact support the Bohmian ontology for quantum mechanics. The reason is that (i) all measurements come down to position measurements; and (ii) Bohm’s theory provides a clear and coherent explanation of the measurement outcome statistics based on an ontology of particle positions, a law for their evolution and a probability measure linked with that law. What the no-hidden-variables theorems teach us is that (i) one cannot infer the properties that the physical systems possess from observables; and that (ii) measurements, being an interaction like other interactions, change the state of the measured system.

[1]  D. A. Edwards.  The mathematical foundations of quantum mechanics , 1979, Synthese.

[2]  J. Wheeler,et al.  Interaction with the Absorber as the Mechanism of Radiation , 1945 .

[3]  On the Uniqueness of Quantum Equilibrium in Bohmian Mechanics , 2007, 0704.3070.

[4]  Detlef Dürr,et al.  The Ontology of Bohmian Mechanics , 2014, The British Journal for the Philosophy of Science.

[5]  A. Zeilinger,et al.  Speakable and Unspeakable in Quantum Mechanics , 1989 .

[6]  D. Belousek.  Formalism, Ontology and Methodology in Bohmian Mechanics , 2003 .

[7]  Thomas J. McCormack,et al.  The Science of Mechanics: a Critical and Historical Account of its Development , 2019, Nature.

[8]  Henry P. Stapp,et al.  The Undivided Universe: An ontological interpretation of Quantum Theory , 1994 .

[9]  Tim Maudlin,et al.  What Bell did , 2014, 1408.1826.

[10]  Claudio Calosi,et al.  Quantum metaphysical indeterminacy , 2018, Philosophical Studies.

[11]  W. Quine.  The two dogmas of empiricism , 1951 .

[12]  M. Esfeld,et al.  The British Journal for the Philosophy of Science , 1957, Nature.

[13]  B. Hiley,et al.  Bohm's approach and Individuality , 2014, 1405.4772.

[14]  N. David Mermin,et al.  Is the Moon There When Nobody Looks? Reality and the Quantum Theory , 1985 .

[15]  M. Esfeld,et al.  From the Universe to Subsystems: Why Quantum Mechanics Appears More Stochastic than Classical Mechanics , 2016, 1604.00987.

[16]  Matthew F Pusey,et al.  On the reality of the quantum state , 2011, Nature Physics.

[17]  Stefan Teufel,et al.  Bohmian Mechanics: The Physics and Mathematics of Quantum Theory , 2009 .

[18]  Otto Stern,et al.  Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld , 1922 .

[19]  Michael Esfeld,et al.  A Minimalist Ontology of the Natural World , 2017 .

[20]  T. Norsen.  The pilot-wave perspective on spin , 2013, 1305.1280.

[21]  J. Neumann.  Mathematische grundlagen der Quantenmechanik , 1935 .

[22]  Sheldon Goldstein,et al.  Quantum physics without quantum philosophy , 1995 .

[23]  J. Bell.  On the Problem of Hidden Variables in Quantum Mechanics , 1966 .

[24]  S. Goldstein,et al.  On the Common Structure of Bohmian Mechanics and the Ghirardi–Rimini–Weber Theory , 2006, The British Journal for the Philosophy of Science.

[25]  N. Mermin.  Hidden variables and the two theorems of John Bell , 1993, 1802.10119.

[26]  H. Wiseman.  Grounding Bohmian mechanics in weak values and bayesianism , 2007, 0706.2522.

[27]  Dustin Lazarovici.  2 Against fields : The philosophical case , 2016 .

[28]  W. Heisenberg.  Der Teil und das Ganze : Gespräche im Umkreis der Atomphysik , 1969 .

[29]  Martin Daumer,et al.  Naive Realism about Operators , 1996 .

[30]  Eugene P. Wigner,et al.  Review of the Quantum-Mechanical Measurement Problem , 1983 .

[31]  Roderich Tumulka,et al.  What Is Bohmian Mechanics , 2001, Compendium of Quantum Physics.

[32]  W. Quine.  Main trends in recent philosophy: two dogmas of empiricism. , 1951 .

[33]  Federico Laudisa,et al.  Against the ‘no-go’ philosophy of quantum mechanics , 2014 .

[34]  B. Hiley.  The Undivided Universe , 1993 .

[35]  D. Bohm.  A SUGGESTED INTERPRETATION OF THE QUANTUM THEORY IN TERMS OF "HIDDEN" VARIABLES. II , 1952 .