# Action Duality: A Constructive Principle for Quantum Foundations

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## Abstract

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## 1. Introduction

## 2. The Action Duality

Feynman Integral Symmetry Hypothesis (FISH):For any two experiments with an action duality (a well-defined spacetime transformation that maps the classical Lagrangian density of one experiment onto the classical Lagrangian density of the other), any realistic ontology must also map between the two experiments under the same spacetime transformation.

## 3. Action Duality under Time Reversal

## 4. Action Duality for Entangled Systems

## 5. Generalizations

#### 5.1. Single Quantum Systems

#### 5.2. Entangled Systems

## 6. Discussion

## Acknowledgements

## References

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**Figure 1.**Experiment A1: a double Mach–Zehnder interferometer for a single photon input at C. The circle represents a phase delay element E set to a phase delay angle $\alpha $.

**Figure 2.**Experiment A2: a double Mach–Zehnder interferometer for a single photon input at A. The circle represents a phase delay element E set to a phase delay angle $\alpha $.

**Figure 3.**Experiment B1: A two-photon source Z (constrained to emit in opposite directions only), sends one photon to the detectors at $A/B$ and the other to the detectors at $C/D$. The circles represent phase delay elements E and F set to phase delay angles $\alpha $ and $\beta $ respectively.

**Figure 4.**Experiment B2: An interferometer for a single photon input at C. The circles represent phase delay elements E and F set to a phase delay angles $\alpha $ and $\beta $ respectively; the photon will pass through exactly one of these.

**Figure 5.**Two generic, action-dual experiments; time runs vertically, one spatial dimension is horizontal, the other spatial dimensions are suppressed. (

**a**) An initially-entangled bipartite system $|\Phi \rangle $ is spatially separated, with each subsystem measured at a later time; (

**b**) A single system is subject to a unitary evolution before being measured. See text for further details.

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**MDPI and ACS Style**

Wharton, K.B.; Miller, D.J.; Price, H.
Action Duality: A Constructive Principle for Quantum Foundations. *Symmetry* **2011**, *3*, 524-540.
https://doi.org/10.3390/sym3030524

**AMA Style**

Wharton KB, Miller DJ, Price H.
Action Duality: A Constructive Principle for Quantum Foundations. *Symmetry*. 2011; 3(3):524-540.
https://doi.org/10.3390/sym3030524

**Chicago/Turabian Style**

Wharton, Ken B., David J. Miller, and Huw Price.
2011. "Action Duality: A Constructive Principle for Quantum Foundations" *Symmetry* 3, no. 3: 524-540.
https://doi.org/10.3390/sym3030524