On spontaneous wave function collapse and quantum field theory
Open accessAbstract
One way of obtaining a version of quantum mechanics without observers, and thus of solving the paradoxes of quantum mechanics, is to modify the Schrödinger evolution by implementing spontaneous collapses of the wave function. An explicit model of this kind was proposed in 1986 by Ghirardi, Rimini & Weber (GRW), involving a nonlinear, stochastic evolution of the wave function. We point out how, by focusing on the essential mathematical structure of the GRW model and a clear ontology, it can be generalized to (regularized) quantum field theories in a simple and natural way.
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Assumption (Q) is manifestly violated by theories that postulate a modification of standard quantum mechanics, such as spontaneous and gravity-induced collapse models.
“Assumption (Q) is manifestly violated by theories that postulate a modification of standard quantum mechanics, such as spontaneous16–20 and gravity-induced21–23 collapse models (cf. 24 for a review).”
From Quantum theory cannot consistently describe the use of itself (2018) · cites this paper as [19]
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Quantum theory cannot consistently describe the use of itself
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Eternal inflation and collapse theories
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InfluentialA Proposal for a New Kind of Spontaneous Collapse Model
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“The idea of modifying quantum theory by adding to it a mechanism for explicit dynamical reduction has a long history The existing work in this direction includes : GRW [7], Pearle [8], Diósi [2], Penrose [1], Bassi [9] (where its worthwhile noting some recent advances towards making collapse theories compatible with s…”
MethodQuandt-Wiese, G. (2017) · arXiv (Cornell University) · Cited by 3 · see citing works
Why Uncertainty Is Essential for Consciousness: Local Prospect Theory vs. Predictive Processing
Heylighen, F., & Beigi, S. (2025) · Entropy · doi:10.3390/e27020140 · Cited by 2 · see citing works
“This is similar to the collapse of the wave function in quantum mechanics, where an observation reduces the uncertainty of the variable that was observed (e.g., the position q of a particle), thus “collapsing” the probability distribution to the value that was measured [76,77].”
Hybrid classical-quantum Newtonian gravity with stable vacuum
Piccione, N., & Bassi, A. (2025) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ae1540 · Cited by 2 · see citing works
“The GRW model, however, is not applicable to identical particles and fields without modifications; such generalizations exist [38, 44] and we denote them as Poissonian Spontaneous Localization (PSL) models.”
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“In [ 36 , 37] the GRW model has been generalized so as to apply not only to quantum mechanics, but also to quantum field theory (see also [38] for a recent comparison between the two approaches).”
MethodToward relativistic generalization of collapse models
Gundhi, A., Diósi, L., & Carlesso, M. (2026) · Physical Review A · doi:10.1103/g7xn-bwfs · Cited by 1 · see citing works
Applications of quantum entanglement
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Introduction to Dynamical Wave Function Collapse
Pearle, P. (2024) · doi:10.1093/oso/9780198901372.001.0001 · Cited by 1 · see citing works
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Primitive ontology and quantum state in the GRW matter density theoryPreprint
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Annex: Basic mathematical tools of quantum mechanics
Laloë, F. (2012) · Cambridge University Press eBooks · doi:10.1017/cbo9781139177160.013
Experiments: quantum reduction seen in real time
Laloë, F. (2012) · Cambridge University Press eBooks · doi:10.1017/cbo9781139177160.011
Relativistic Model for Gravity-Induced Quantum State ReductionPreprint
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MethodImpossibility of superluminal communication
Laloë, F. (2012) · Cambridge University Press eBooks · doi:10.1017/cbo9781139177160.019
Quantum measurements at different times
Laloë, F. (2012) · Cambridge University Press eBooks · doi:10.1017/cbo9781139177160.020
The influence of pair selection
Laloë, F. (2012) · Cambridge University Press eBooks · doi:10.1017/cbo9781139177160.018
Manipulating and preparing additional variables
Laloë, F. (2012) · Cambridge University Press eBooks · doi:10.1017/cbo9781139177160.021
Maximal probability for a state
Laloë, F. (2012) · Cambridge University Press eBooks · doi:10.1017/cbo9781139177160.017
Present situation, remaining conceptual difficulties
Laloë, F. (2012) · Cambridge University Press eBooks · doi:10.1017/cbo9781139177160.004
The theorem of Einstein, Podolsky, and Rosen
Laloë, F. (2012) · Cambridge University Press eBooks · doi:10.1017/cbo9781139177160.005
Models for spontaneous reduction of the state vector
Laloë, F. (2012) · Cambridge University Press eBooks · doi:10.1017/cbo9781139177160.023
Mental content of the state vector
Laloë, F. (2012) · Cambridge University Press eBooks · doi:10.1017/cbo9781139177160.014
Consistent families of histories
Laloë, F. (2012) · Cambridge University Press eBooks · doi:10.1017/cbo9781139177160.024
Bohmian field theory on a shape dynamics background and Unruh effect
Dündar, F. S., & Arık, M. (2018) · Annals of Physics · doi:10.1016/j.aop.2018.03.011
ψ-Ontology, or, Making Sense of Quantum Mechanics
Boge, F. J. (2018) · European studies in philosophy of science · doi:10.1007/978-3-319-95765-4_6
Other Inequalities, Cirelson’s Limit, Signaling
Laloë, F. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108569361.008
Attractive Schrödinger Dynamics
Laloë, F. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108569361.028
Mental Content of the State Vector
Laloë, F. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108569361.017
Manipulating and Preparing Additional Variables
Laloë, F. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108569361.024
Laloë, F. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108569361.003
Models for Spontaneous Reduction of the State Vector
Laloë, F. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108569361.026
Attempting to Construct a “Separable” Quantum Theory
Laloë, F. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108569361.019
Correlations and Trajectories in Bohmian Theory
Laloë, F. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108569361.025
Various Interpretations and Reconstructions of Quantum Mechanics
Laloë, F. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108569361.014
Laloë, F. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108569361.012
The Theorem of Einstein, Podolsky, and Rosen
Laloë, F. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108569361.006
Quantum Measurements at Different Times
Laloë, F. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108569361.023
Applications of Quantum Entanglement
Laloë, F. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108569361.011
Maximal Probability for a State
Laloë, F. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108569361.020
Present Situation, Remaining Conceptual Difficulties
Laloë, F. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108569361.005
Laloë, F. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108569361.009
The Influence of Pair Selection
Laloë, F. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108569361.021
- Authors
- Tumulka, R.
- Affiliations
- University of Tübingen (DE)
- Corresponding author
- Tumulka, Roderich
- ORCID
- Tumulka, Roderich
- Venue
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Publisher
- The Royal Society
- Published
- 2006-03-24
- Volume
- 462
- Issue
- 2070
- Pages
- 1897-1908
- ISSN
- 1364-5021 (ISSN-L)
- 1471-2946
- OpenAlex
- W2171676563
- Semantic Scholar
- f38d4feb837d3751b34a795211435f04bb0dd89c
- Cited by
- 144
- References
- 32
- Citations by year
- 2026: 4 · 2025: 6 · 2024: 30 · 2023: 3 · 2022: 5 · 2021: 4 · 2020: 1 · 2019: 30 · 2018: 6 · 2017: 6 · 2016: 2 · 2015: 3 · 2014: 6 · 2013: 3 · 2012: 18
- FWCI
- 3.66
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- spontaneous wave function collapse, quantum field theory, measurement problem, quantum ontology, regularization
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