Gravitation and the Noise Needed in Objective Reduction Models

doi:10.1017/CBO9781316219393.026

24 - Gravitation and the Noise Needed in Objective Reduction Models

from Part IV - Nonlocal Realistic Theories

Published online by Cambridge University Press: 05 September 2016

Stephen L. Adler

Edited by

Mary Bell and

Shan Gao

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Stephen L. Adler: Affiliation:
The Institute for Advanced Study, Princeton
Shan Gao: Affiliation:
Chinese Academy of Sciences, Beijing

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Abstract

I briefly recall intersections of my research interests with those of John Bell. I then argue that the noise needed in theories of objective state vector reduction most likely comes from a fluctuating complex part in the classical spacetime metric; that is, state vector reduction is driven by complex-number-valued “space–time foam.”

Introduction

My research interests have intersected those of John Bell three times. The first was when I found the forward lepton theorem for high-energy neutrino reactions, showing that for forward lepton kinematics, a conserved vector current (CVC) and a partially conserved axial vector current (PCAC) imply that the neutrino cross section can be related to a pion scattering cross section [1]. This led to an exchange of letters and discussions with Bell during 1964–5, which are described in the Commentaries for my selected papers [2]. The second was in the course of my work on the axial-vector anomaly [3], when I had further correspondence with John Bell, as described both in the Commentaries [4] and in the volume of essays on Yang–Mills theories assembled by 't Hooft [5]. The third time was a few years after Bell's death in 1990, when I became interested in the foundations of quantum theory and the quantum measurement problem, in the course of writing my book on quaternionic quantum mechanics [6]. Foundational issues in standard, complex quantum theory had preoccupied Bell for much of his career and led to his best known work. However, my correspondence with Bell in the 1960s never touched on quantum foundations, and I only read his seminal writings on the subject much later on. In this article I focus on this third area of shared interests.

Objective Reduction Models

There is now a well-defined phenomenology of state vector reduction, pioneered by the work of Ghirardi, Rimini, andWeber (GRW) and of Philip Pearle, and worked on by many others. John Bell was interested in this program from the outset.

Type: Chapter
Information: Quantum Nonlocality and Reality
50 Years of Bell's Theorem
, pp. 390 - 399

DOI: https://doi.org/10.1017/CBO9781316219393.026 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2016

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References

[1] S.L., Adler, Tests of the conserved vector current and partially conserved axial-vector current hypotheses in high-energy neutrino reactions, Phys. Rev. 135 (1964), B963– B966.Google Scholar

[2] S.L., Adler, Adventures in Theoretical Physics: Selected Papers with Commentaries (Singapore: World Scientific, 2006), section on “Forward lepton theorem,” pp. 6–8.

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[6] S.L., Adler, Quaternionic Quantum Mechanics and Quantum Fields (Oxford: Oxford University Press, 1995). See especially pp. 520–25, which deal with the quantum measurement problem in the context of quaternionic quantum theory.

[7] J.S., Bell, Are there quantum jumps? In Schrödinger, Centenary of a Polymath. (Cambridge: Cambridge University Press, 1987). This article is reprinted in S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge: Cambridge University Press, 1987), pp. 201–12; M. Bell, K. Gottfried and M. Veltman (eds.), Quantum Mechanics, High Energy Physics and Accelerators: Selected Papers of John S Bell (with Commentary) (Singapore: World Scientific, 1995), pp. 866–86; M. Bell, K. Gottfried and M. Veltman (eds.), John S. Bell on the Foundations of Quantum Mechanics. (Singapore: World Scientific, 2001), pp. 172–92. For an 398 Gravitation and the Noise Needed in Objective Reduction Models appreciation byG.C.Ghirardi of Bell's paper, see G.C.|Ghirardi, John Stewart Bell and the dynamical reduction program, in R.A. Bertlmann and A. Zeilinger (eds.), Quantum [Un]speakables: From Bell to Quantum Information (Berlin: Springer, 2002), pp. 287–305.

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[10] S.L., Adler, D.C., Brody, T.A., Brun and L.P., Hughston, Martingale models for quantum state reduction, J. Phys. A: Math. Gen. 34 (2001), 8795–820.Google Scholar

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[15] Shan, Gao, Does gravity induce wavefunction collapse? An examination of Penrose's conjecture, Stud. Hist. Philos. Mod. Phys. 44 (2013), 148–51. In addition to a reviewof work suggesting a relation between state vector reduction and gravitation, this article gives a critique of the Diosi–Penrose proposal, as does Shan Gao, On Diosi–Penrose criterion of gravity-induced quantum collapse, Int. J. Theor. Phys. 49 (2010), 849–53.Google Scholar

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[26] S.L., Adler,Adensity tensor hierarchy for open system dynamics: Retrieving the noise, J. Phys. A. Math. Theor. 40 (2007), 8959–90. See citations [5] and [6] of this paper for earlier related work of Mielnik, and Brody and Hughston.Google Scholar

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