Stress Tensor for Quantized Random Field and Wave Function Collapse

Abstract

The continuous spontaneous localization (CSL) theory of dynamical wave function collapse is an experimentally testable alternative to non-relativistic quantum mechanics. In it, collapse occurs because particles interact with a classical random field. However, particles gain energy from this field, i.e., particle energy is not conserved. Recently, it has been shown how to construct a theory dubbed "completely quantized collapse" (CQC) which is predictively equivalent to CSL. In CQC, a quantized random field is introduced, and CSL's classical random field becomes its eigenvalue. In CQC, energy is conserved, which allows one to understand that energy is conserved in CSL, as the particle's energy gain is compensated by the random field's energy loss. Since the random field has energy, it should have gravitational consequences. For that, one needs to know the random field's energy density. In this paper, it is shown how to construct a symmetric, conserved, energy-momentum-stress-density tensor associated with the quantized random field, even though this field obeys no dynamical equation and has no Lagrangian. Then, three examples are given involving the random field's energy density. One considers interacting particles, the second treats a "cosmological" particle creation model, the third involves the gravity of the random field.

16 pages. To be published in Phys. Rev. A78. Changes are in response to referee comments, and include an example involving the gravitational interaction of the random field's energy density with the particle energy density

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• Relativistically Invariant Markovian Dynamical Collapse Theories Must Employ Nonstandard Degrees of Freedom
• Generally covariant dynamical reduction models and the Hadamard condition
• Relativistic quantum field theory of stochastic dynamics in the Hilbert space
• Relativistic consistency rules out GRW-Pearle collapse schemes
• Dark energy from quantum wave function collapse of dark matter