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

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

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

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

Refresher: The Double-slit Experiment 5

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

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

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

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

Review of the Alternatives 12

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

The Quantitative Probability Problem for Everettian QM 14

No Similar Problem for Newtonian QM 15

Versus Bohmian Mechanics 16

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

How Many Worlds? 18

The Quantization Condition 19

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

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).

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

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

24 References

End 25

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

An Unnatural Constraint 27

The Orbital 28