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Matter Density and Relativistic Models of Wave Function Collapse

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Abstract

Mathematical models for the stochastic evolution of wave functions that combine the unitary evolution according to the Schrödinger equation and the collapse postulate of quantum theory are well understood for non-relativistic quantum mechanics. Recently, there has been progress in making these models relativistic. But even with a fully relativistic law for the wave function evolution, a problem with relativity remains: Different Lorentz frames may yield conflicting values for the matter density at a space-time point. We propose here a relativistic law for the matter density function. According to our proposal, the matter density function at a space-time point x is obtained from the wave function ψ on the past light cone of x by setting the i-th particle position in |ψ|2 equal to x, integrating over the other particle positions, and averaging over i. We show that the predictions that follow from this proposal agree with all known experimental facts.

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Acknowledgements

G.C.G. and N.Z. are supported in part by INFN, Sezioni di Trieste e Genova. D.D., S.G., G.C.G., and N.Z. are supported in part by the COST-Action MP1006. R.T. is supported in part by NSF Grant SES-0957568 and by the Trustees Research Fellowship Program at Rutgers, the State University of New Jersey. S.G. and R.T. are supported in part by grant No. 37433 from the John Templeton Foundation.

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Authors and Affiliations

  1. Blackett Laboratory, Imperial College, London, SW7 2BZ, UK

    Daniel Bedingham

  2. Mathematisches Institut, Ludwig-Maximilians-Universität, Theresienstr. 39, 80333, München, Germany

    Detlef Dürr

  3. Department of Theoretical Physics, University of Trieste, Trieste, Italy

    GianCarlo Ghirardi

  4. Abdus Salam International Centre for Theoretical Physics, Trieste, Italy

    GianCarlo Ghirardi

  5. Departments of Mathematics, Physics and Philosophy, Rutgers University, Hill Center, 110 Frelinghuysen Road, Piscataway, NJ, 08854-8019, USA

    Sheldon Goldstein

  6. Department of Mathematics, Rutgers University, Hill Center, 110 Frelinghuysen Road, Piscataway, NJ, 08854-8019, USA

    Roderich Tumulka

  7. Dipartimento di Fisica dell’Università di Genova and INFN sezione di Genova, Via Dodecaneso 33, 16146, Genova, Italy

    Nino Zanghì

Authors
  1. Daniel Bedingham
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  2. Detlef Dürr
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  3. GianCarlo Ghirardi
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  4. Sheldon Goldstein
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  5. Roderich Tumulka
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  6. Nino Zanghì
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Corresponding author

Correspondence to Roderich Tumulka.

Additional information

Dedicated to Herbert Spohn on the occasion of his 65th birthday.

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Bedingham, D., Dürr, D., Ghirardi, G. et al. Matter Density and Relativistic Models of Wave Function Collapse. J Stat Phys 154, 623–631 (2014). https://doi.org/10.1007/s10955-013-0814-9

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  • DOI: https://doi.org/10.1007/s10955-013-0814-9

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