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Entanglement and the Path Integral

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Abstract

The path integral is not typically utilized for analyzing entanglement experiments, in part because there is no standard toolbox for converting an arbitrary experiment into a form allowing a simple sum-over-history calculation. After completing the last portion of this toolbox (a technique for implementing multi-particle measurements in an entangled basis), some interesting 4- and 6-particle experiments are analyzed with this alternate technique. While the joint probabilities of measurement outcomes are always equivalent to conventional quantum mechanics, differences in the calculations motivate a number of foundational insights, concerning nonlocality, retrocausality, and the objectivity of entanglement itself.

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Notes

  1. This rule, and the other rules below, can be motivated by Eq. (1); squaring this amplitude gives the stated 50% probability for each possibility.

  2. A third option, superdeterminism, posits a common cause of both \(\lambda\) and the settings.

  3. Just as we would naturally say that such normal modes were caused by all of the adjustable mirror positions, the solution of an all-at-once calculation is caused by all of the controllable boundaries on the problem, both past and future.

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Acknowledgements

The authors would like to thank N.Argaman for bringing the intriguing features of the triangle network to our attention (and other useful advice), H. Price for encouraging us to think more carefully about entanglement swapping, E. Adlam for very useful insights, and of course N. Tyagi for her work on which this paper was based.

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Authors and Affiliations

  1. Department of Physics and Astronomy, San José State University, One Washington Sq., San José, 95192-0106, CA, USA

    Ken Wharton & Raylor Liu

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  1. Ken Wharton
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  2. Raylor Liu
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Contributions

KW wrote the main manuscript text and RL designed the general entangled measurement, performed calculations, and prepared the figures and equations. All authors reviewed the manuscript.

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Correspondence to Ken Wharton.

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Wharton, K., Liu, R. Entanglement and the Path Integral. Found Phys 53, 23 (2023). https://doi.org/10.1007/s10701-022-00664-9

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