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Journal of Statistical Physics

, Volume 154, Issue 1–2, pp 623–631 | Cite as

Matter Density and Relativistic Models of Wave Function Collapse

  • Daniel Bedingham
  • Detlef Dürr
  • GianCarlo Ghirardi
  • Sheldon Goldstein
  • Roderich Tumulka
  • Nino Zanghì
Article

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.

Keywords

Ghirardi–Rimini–Weber (GRW) theory of spontaneous wave function collapse Relativistic Lorentz invariance 

Notes

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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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Daniel Bedingham
    • 1
  • Detlef Dürr
    • 2
  • GianCarlo Ghirardi
    • 3
    • 4
  • Sheldon Goldstein
    • 5
  • Roderich Tumulka
    • 6
  • Nino Zanghì
    • 7
  1. 1.Blackett LaboratoryImperial CollegeLondonUK
  2. 2.Mathematisches InstitutLudwig-Maximilians-UniversitätMünchenGermany
  3. 3.Department of Theoretical PhysicsUniversity of TriesteTriesteItaly
  4. 4.Abdus Salam International Centre for Theoretical PhysicsTriesteItaly
  5. 5.Departments of Mathematics, Physics and PhilosophyRutgers University, Hill CenterPiscatawayUSA
  6. 6.Department of MathematicsRutgers University, Hill CenterPiscatawayUSA
  7. 7.Dipartimento di Fisica dell’Università di Genova and INFN sezione di GenovaGenovaItaly

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