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Matter Density and Relativistic Models of Wave Function Collapse |
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| Authors: | Daniel Bedingham Detlef Dürr GianCarlo Ghirardi Sheldon Goldstein Roderich Tumulka Nino Zanghì |
| Affiliation: | 1. Blackett Laboratory, Imperial College, London, SW7 2BZ, UK 2. Mathematisches Institut, Ludwig-Maximilians-Universit?t, Theresienstr. 39, 80333, München, Germany 3. Department of Theoretical Physics, University of Trieste, Trieste, Italy 4. Abdus Salam International Centre for Theoretical Physics, Trieste, Italy 5. Departments of Mathematics, Physics and Philosophy, Rutgers University, Hill Center, 110 Frelinghuysen Road, Piscataway, NJ, 08854-8019, USA 6. Department of Mathematics, Rutgers University, Hill Center, 110 Frelinghuysen Road, Piscataway, NJ, 08854-8019, USA 7. Dipartimento di Fisica dell’Università di Genova and INFN sezione di Genova, Via Dodecaneso 33, 16146, Genova, Italy |
| 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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