# The Dynamical Reduction Program: An Example of a Quantum Theory without Observers

## Abstract

After more than 70 years of debate about the difficulties that one encounters in working out a coherent view of physical processes based on the standard formulation of quantum mechanics, there is now a widespread belief that such difficulties do not arise from philosophical prejudices (as has been repeatedly asserted by many of the supporters of *textbook quantum mechanics*) but represent precise mathematical and physical challenges which call for a physical solution. As J.S. Bell appropriately stated^{1} “the way ahead is unromantic in that it requires mathematical work by theoretical physicists, rather than interpretations by philosophers”. It is also encouraging, for those who share this position, to see that now there are explicit proposals indicating possible ways out in which the process of measurement (and more generally all those measurement-like processes^{2} “we are obliged to admit ... are going on more or less all the time, more or less everywhere”) is analysed not in terms of vague assertions or resorting to ill-defined and/or contradictory dualistic evolution processes (the linear and deterministic evolution for microsystems and the nonlinear and stochastic wave packet reduction for the macroscopic ones) but in terms of more fundamental physical concepts. In particular, approaches of this kind, which S. Goldstein^{3} has appropriately denoted as “observer-free formulations of quantum mechanics”, can be grouped in three categories: the pilot-wave theories: the decoherent histories and the spontaneous localization models.

## Keywords

Bohmian Mechanic Standard Quantum Mechanic Dynamical Reduction Mass Density Distribution Property Attribution## Preview

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## References

- [1]John Stewart Bell, “Six possible worlds of quantum mechanics”, in:
*Proceedings of the Nobel Symposium 65: Possible Worlds in Arts and Sciences*, Stockholm, 1986.Google Scholar - [2]John Stewart Bell, “Against measurement”, in: Arthur Miller (Ed.),
*Sixty-Two Years of Uncertainty*,, New York, Plenum Press, 1990, pp. 17–31.CrossRefGoogle Scholar - [3]Sheldon Goldstein “Quantum Theory without Observers”, in:
*Physics Today*,March 1998, pp.4246,*ibid*. April 1998, pp.38–42.Google Scholar - [4]GianCarlo Ghirardi, Alberto Rimini and Tullio Weber, “Unified dynamics for microscopic and macroscopic systems”, in:
*Physical Review*, D 34, 1986, pp. 470–491.Google Scholar - [5]To be precise in the original GRW theory the frequency of the hittings has been assumed to be the same for all elementary particles. However, subsequent investigations
^{6–9}have put into evidence the appropriateness of making the frequency of the spontaneous localizations proportional to the mass.Google Scholar - [6]GianCarlo Ghirardi, Renata Grassi and Alberto Rimini, “Continuous-spontaneous-reduction model involving gravity”, in:
*Physical Review*A, 42, 1990, pp.1057–1064.Google Scholar - [7]P. Pearle, and E. Squires, `Bound state excitation, nucleon decay experiments, and models of wave function collapse“, in:
*Physical Review Letters*,73, 1994, pp.1–5Google Scholar - [8]GianCarlo Ghirardi, Renata Grassi and Fabio Benatti, “Describing the Macroscopic World: Closing the Circle within the Dynamical Reduction Program”, in:
*Foundations of Physics*,25, 1995, pp.5–38.Google Scholar - [9]Alberto Rimini, “Spontaneous localization and superconductivity”, in: Enrico Beltrametti and Jean Marc Levy-Leblond (Eds.),
*Proceedings of the International Course on Advances in Quantum Phenomena*, New York: Plenum Press 1997, pp. 321–333.Google Scholar - [10]John Stewart Bell, “Are there quantum jumps?”, in: C.W. Kilmister (Ed.),
*Schrödinger. Centenary celebration of a polymath*. Cambridge: Cambridge University Press 1987, pp. 41–52.Google Scholar - [11]Philip Penile, “Combining stochastic dynamical state-vector reduction with spontaneous localizations”, in:
*Physical Review*,A 39, 1989, pp.2277–2289.Google Scholar - [12]GianCarlo Ghirardi, Philip Pearle and Alberto Rimini, “Markov processes in Hilbert space and continuous spontaneous localization of systems of identical particles”, in:
*Physical Review*, A 42, 1990, pp. 78–89.Google Scholar - [13]Philip Pearle, “Tales and Tails and Stuff and Nonsense”, in: R.S. Cohen
*et al*. (Eds.),*Experimental Metaphysics*, Dordrecht: Kluwer Academic Publishers 1997, pp. 143–156.Google Scholar - [14]Philip Pearle, “Reduction of the state vector by a nonlinear Schrödinger equation”, in:
*Physical Review*D, 13, 1976, pp. 857–868.Google Scholar - [15]Philip Pearle, “Toward explaining why events occur”, in
*International Journal of Theoretical Physics*,18, 1979, pp.489–518.Google Scholar - GianCarlo Ghirardi, “Macroscopic reality and the dynamical reduction program”, in: M.L. Dalla Chiara
*et al*.,(Eds.),*Structures and Norms in Science*,Dordrecht: Kluwer Academic 1997, pp.221–240.Google Scholar - [17]Abner Shimony, “Desiderata for a Modified Quantum Dynamics”, in: A. Fine, M. Forbes and L. Wessel eds.,
*PSA**1990*, Vol. 2, East Leasing: Philosophy of Science Association 1991, pp. 49–59.Google Scholar - [18]Abner Shimony, “Events and processes in the quantum world”, in:
*Quantum Concepts in Space**and Time*, R. Penrose and C. Isham eds., Oxford University Press 1986, pp. 182–203.Google Scholar - [19]John Stewart Bell, “Towards An Exact Quantum Mechanics”, in: S. Deser and R.J. Finkelstein (Eds.),
*Themes in Contemporary Physics**11*., Singapore: World Scientific 1989, pp. 1–26.Google Scholar - [20]Detlef Dürr, Sheldon Goldstein and Nino Zanghì, “Quantum equilibrium and the origin of absolute uncertainty”, in:
*Journal of Statistical Physics*,67, 1992, pp.843–907 and references therein.Google Scholar - [21]This makes evident the appropriateness of Bell’s remark in the above quoted letter that “even for one particle I think one would have problems with the” matter density interpretation.Google Scholar
- [22]Franca Aicardi, Antonio Borsellino, GianCarlo Ghirardi and Renata Grassi, “Dynamical models for state-vector reduction: do they ensure that measurements have outcomes”, in:
*Foundations of Physics Letters*, 4, 1991, pp. 109–128.Google Scholar - [23]Erwin Schrödinger, “Quantisierung als Eigenwertprohlem”, in:
*Annalen der Physik*,79, 1926, pp.489–527.Google Scholar - [24]Albert Einstein, “Reply to Criticisms”, in: P.A. Schilpp (Ed.),
*Albert Einste*in:*Philosopher-Scientist*, Cambridge: Cambridge University Press 1949, pp. 663–688.Google Scholar - [25]Max Born,
*Briefwechsel*, München: Nymphenburger Verlagshandlung GmbH., 1969.Google Scholar - [26]Philip Pearle, “Toward a relativistic theory of statevector reduction” in: A.I. Miller
*(Ed.)*,*Sixly-two Years of Uncertainity*. New York: Plenum Press, 1990, pp.193–214, “Relativistic model for statevector reduction” in: P. Cvitanovic, I. Percival and A. Wirzba (Eds.),*Quantum Chaos–Quantum Measurement*, Dordrecht: Kluwer Academic Publishers 1992, pp. 283–297.Google Scholar - GianCarlo Ghirardi, Renata Grassi and Philip Pearle, `Relativistic dynamical reduction models: general framework and examples: in:
*Foundations of Physics*,20, 1990, pp.1271–1316; “Relativistic dynamical reduction models and nonlocality” in: P. Lahti and P Mittelstaedt*(Eds.)*,*Symposium on the Foundations of Modern Physics 1990*,Singapore: World Scientific 1991, pp. 109–123.Google Scholar - [28]GianCarlo Ghirardi and Renata Grassi, “Outcome predictions and property attribution: the EPR argument reconsidered”, in:
*Studies in the History and Philosophy of Science*,25, 1994, pp.397423.Google Scholar - [29]GianCarlo Ghirardi, “Properties and events in a relativistic context: revisiting the dynamical reduction program”, in:
*Foundations of Physics Letters*,9, 1996, pp.313–355.Google Scholar