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Quantum Mechanics as Classical Physics Charles Sebens University of Michigan July 31, 2013

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Dirk-André Deckert Michael Hall Howard Wiseman UC Davis Griffith University Griffith University 2

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A Strange Interpretation of QM This is a development of the hydrodynamic interpretation, originally proposed by Madelung (1927) and developed by Takabayasi (e.g., 1952) among others. 3

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Outline I.A Series of Solutions to the Measurement Problem I.The Many-worlds Interpretation II.Bohmian Mechanics III.Prodigal QM II.Newtonian Quantum Mechanics III.A Strength: Probability IV.A Weakness: Non-quantum States 4

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Refresher: The Double-slit Experiment 5

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Solution 1: Everettian QM What there is (Ontology): The Wave Function What it does (Laws): Schrödinger Equation 6

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Solution 2: Bohmian QM Ontology: The Wave Function Particles Laws: Schrödinger Equation Guidance Equation 7

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Solution 3: Prodigal QM Ontology: The Wave Function Particles (in many worlds) Laws: Schrödinger Equation Guidance Equation 8 This is a significantly altered variant of the proposal in Dorr (2009).

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Worlds are distributed in accordance with psi-squared: The Schrödinger equation: The guidance equation: From the following facts one can derive the double boxed equation below. The quantum potential Q. 10

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Ontology: Particles (in many worlds) Law: Newtonian Force Law Solution 4: Newtonian QM 11

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Review of the Alternatives 12

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The Wave Function in Newtonian QM Worlds are distributed in accordance with psi-squared The guidance equation is obeyed 13

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The Quantitative Probability Problem for Everettian QM 14

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No Similar Problem for Newtonian QM 15

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Versus Bohmian Mechanics 16

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Avoiding Anomalous Statistics In Newtonian QM, it is also possible that one’s own world does not exhibit quantum statistics. However, it is necessarily true that the majority of worlds in any universe satisfy the quantum equilibrium hypothesis since (by definition of Ψ ). Thus, one should always expect to be in a world that is in quantum equilibrium. So, one should expect to see Born Rule statistics in long-run frequencies of measurements (see Durr et al. 1992). 17

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How Many Worlds? 18

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The Quantization Condition 19

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Limitations of Newtonian QM Yet to be extended to relativistic quantum physics Yet to be extended to multiple particles with spin We don’t yet have the fundamental law(s) The state space is too large in two ways: States that violate the Quantization Condition States with too few worlds to use the hydrodynamic limit 20

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Neat Features of Newtonian QM Wave function is a mere summary of the properties of particles No superpositions No entanglement No collapse No mention of “measurement” in the laws All dynamics arise from Newtonian forces The theory is deterministic Worlds are fundamental, not emergent (so avoids the need to explain how people and planets arise as structures in the WF) Worlds do not branch (so avoids concerns about personal identity) No qualitative probability problem No quantitative probability problem Immune to Everett-in-denial objection,* not in denial 21 * See Deutsch (1996), Brown & Wallace (2005).

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Neat Features of Newtonian QM Wave function is a mere summary of the properties of particles No superpositions No entanglement No collapse No mention of “measurement” in the laws All dynamics arise from Newtonian forces The theory is deterministic Worlds are fundamental, not emergent (so avoids the need to explain how people and planets arise as structures in the WF) Worlds do not branch (so avoids concerns about personal identity) No qualitative probability problem No quantitative probability problem Immune to Everett-in-denial objection, not in denial 22

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Neat Features of Newtonian QM Wave function is a mere summary of the properties of particles No superpositions No entanglement No collapse No mention of “measurement” in the laws All dynamics arise from Newtonian forces The theory is deterministic Worlds are fundamental, not emergent (so avoids the need to explain how people and planets arise as structures in the WF) Worlds do not branch (so avoids concerns about personal identity) No qualitative probability problem No quantitative probability problem Immune to Everett-in-denial objection, not in denial 23

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24 References

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End 25

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Ontological Options Option 1: World-particles in Configuration Space Option 2: World-particles in Configuration Space and 3D Worlds Option 3: Distinct 3D Worlds Option 4: Overlapping 3D Worlds Shown below for two particles in one dimensional space… 26

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An Unnatural Constraint 27

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The Orbital 28

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