The wave-function as a multi-field
Open accessThe claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In Everett's theory, there are no point particles, just a wavefunction ψ(x1,...,xN,t) that depends on N position vectors xj.
“However, in this theory (unlike in de Broglie-Bohm mechanics [24]), there are no point particles, just a wavefunction ψ ( x 1 , ..., x N , t ) that depends on N position vectors x j (since ψ is a correlation field, this was identified with a 'webfunction' in [58] and with a 'multi-field' in [59]).”
From An Elementary Proof That Everett's Quantum Multiverse Is Nonlocal: Bell-Locality and Branch-Symmetry in the Many-Worlds Interpretation (2023) · cites this paper as [59]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Wald, R. M. (1984) · doi:10.7208/chicago/9780226870373.001.0001 · Cited by 7,188 · see citing works
Wald, R. M. (1984) · Cited by 6,274 · see citing works
Speakable and Unspeakable in Quatum Mechanics
Bell, J. S., & Mermin, N. D. (1988) · Physics Today · doi:10.1063/1.2811599 · Cited by 2,985 · see citing works
Speakable and unspeakable in quantum mechanics
Whitaker, M. A. B. (1988) · Endeavour · doi:10.1016/0160-9327(88)90092-0 · Cited by 2,106 · see citing works
Schaffer, J. (2009) · Metametaphysics · doi:10.1093/oso/9780199546046.003.0012 · Cited by 1,382 · see citing works
Holland, P. (1993) · Cambridge University Press eBooks · doi:10.1017/cbo9780511622687 · Cited by 1,329 · see citing works
The Undivided Universe: An Ontological Interpretation of Quantum Theory
Böhm, D., Hiley, B. J., & Bell, J. S. (1993) · CERN Document Server (European Organization for Nuclear Research) · Cited by 754 · see citing works
The Undivided Universe: An ontological interpretation of Quantum Theory
Böhm, D., & Stapp, H. P. (1994) · American Journal of Physics · doi:10.1119/1.17695 · Cited by 677 · see citing works
Quantum Mechanics and Experience
Albert, D. Z. (1994) · Harvard University Press eBooks · doi:10.2307/j.ctv1bzfptv · Cited by 588 · see citing works
Elementary Quantum Metaphysics
Albert, D. Z. (1996) · Boston studies in the philosophy of science · doi:10.1007/978-94-015-8715-0_19 · Cited by 351 · see citing works
Quantum Physics Without Quantum Philosophy
Dürr, D., Goldstein, S., & Zanghı̀, N. (2012) · Springer eBooks · doi:10.1007/978-3-642-30690-7 · Cited by 261 · see citing works
Loewer, B., & University of Arkansas Press (1996) · Philosophical Topics · doi:10.5840/philtopics199624112 · Cited by 234 · see citing works
The Ontology of Bohmian Mechanics
Esfeld, M., Hubert, M., Lazarovici, D., & Dürr, D. (2013) · The British Journal for the Philosophy of Science · doi:10.1093/bjps/axt019 · Cited by 165 · see citing works
Albert, D. Z. (2015) · Harvard University Press eBooks · doi:10.4159/harvard.9780674735507 · Cited by 156 · see citing works
Quantum Entanglement, Bohmian Mechanics, and Humean Supervenience
Miller, E. (2013) · Australasian Journal of Philosophy · doi:10.1080/00048402.2013.832786 · Cited by 148 · see citing works
Reality and the Role of the Wavefunction in Quantum Theory
Dürr, D., Goldstein, S., & Zanghí, N. (2011) · Springer eBooks · doi:10.1007/978-3-642-30690-7_12 · Cited by 137 · see citing works
The Nature of the Quantum State*
Maudlin, T. (2013) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780199790807.003.0006 · Cited by 117 · see citing works
Callender, C. (2014) · Synthese · doi:10.1007/s11229-014-0582-3 · Cited by 92 · see citing works
Reality and the Role of the Wave Function in Quantum Theory
Goldstein, S., & Zanghı̀, N. (2013) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780199790807.003.0004 · Cited by 92 · see citing works
What the Humean Should Say About Entanglement
Bhogal, H. K., & Perry, Z. R. (2015) · Noûs · doi:10.1111/nous.12095 · Cited by 92 · see citing works
Quantum states for primitive ontologists
Belot, G. (2012) · European Journal for Philosophy of Science · doi:10.1007/s13194-011-0024-8 · Cited by 89 · see citing works
Dürr, D., Goldstein, S., & Zanghı̀, N. (2012) · Springer eBooks · doi:10.1007/978-3-642-30690-7_1 · Cited by 81 · see citing works
The Theory of (Exclusively) Local Beables
Norsen, T. (2010) · Foundations of Physics · doi:10.1007/s10701-010-9495-2 · Cited by 77 · see citing works
Monton, B. (2013) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780199790807.003.0007 · Cited by 63 · see citing works
Against Radical Quantum Ontologies
Emery, N. (2017) · Philosophy and Phenomenological Research · doi:10.1111/phpr.12444 · Cited by 52 · see citing works
Our Fundamental Physical Space: An Essay on the Metaphysics of the Wave Function
Chen, E. (2017) · The Journal of Philosophy · doi:10.5840/jphil2017114724 · Cited by 41 · see citing works
Relational Holism and Humean Supervenience
Darby, G. (2012) · The British Journal for the Philosophy of Science · doi:10.1093/bjps/axr049 · Cited by 38 · see citing works
Suárez, M. (2015) · Synthese · doi:10.1007/s11229-015-0741-1 · Cited by 36 · see citing works
Norsen, T., Marian, D., & Oriols, X. (2014) · Synthese · doi:10.1007/s11229-014-0577-0 · Cited by 33 · see citing works
Allori, V. (2017) · International Studies in the Philosophy of Science · doi:10.1080/02698595.2018.1424759 · Cited by 28 · see citing works
Our Fundamental Physical Space: An Essay on the Metaphysics of the Wave FunctionPreprint
Chen, E. K. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2110.14531 · Cited by 27 · see citing works
The Universal and the Local in Quantum Theory
Maudlin, T. (2015) · Topoi · doi:10.1007/s11245-015-9301-z · Cited by 13 · see citing works
An Intrinsic Theory of Quantum Mechanics: Progress in Field's Nominalistic Program, Part IPreprint
Chen, E. K. (2017) · PhilSci-Archive (University of Pittsburgh) · Cited by 3 · see citing works
De Broglie-Bohm Pilot-Wave Theory: Many Worlds in Denial?
Valentini, A. (2008) · arXiv · doi:10.48550/arxiv.0811.0810 · cited 1×
“The multi-field interpretation is largely independent of the concrete formulation of the de Broglie–Bohm theory in terms of a first-order formulation (Dürr et al. 2013; Valentini 2010), second-order formulation (Bohm and Hiley 1993), or quantum Hamilton-Jacobi formulation (Holland 1993).”
Method
Flagged first, then by citations
4 of the 38 references couldn’t be matched to a known paper.
Research works printed but not linked: 2
- P. Forrest. Quantum Metaphysics. Oxford: Basil Blackwell, 1988.
- W. Sellars. Empiricism and the philosophy of mind. In Science Perception and Reality, pages 127-96.
Cited by
Sorted by citations
Realism about the Wave FunctionPreprint
Chen, E. K. (2018) · PhilSci-Archive (University of Pittsburgh) · Cited by 67 · see citing works
Quantum Mechanics in a Time-Asymmetric Universe: On the Nature of the Initial Quantum State
Chen, E. (2017) · British Journal for the Philosophy of Science · doi:10.1093/bjps/axy068 · Cited by 59 · see citing works
Realism about the wave function
Chen, E. K. (2019) · Philosophy Compass · doi:10.1111/phc3.12611 · Cited by 50 · see citing works
Romano, D. (2020) · Synthese · doi:10.1007/s11229-020-02737-6 · Cited by 31 · see citing works
Electron Charge Density: A Clue from Quantum Chemistry for Quantum Foundations
Sebens, C. T. (2021) · Foundations of Physics · doi:10.1007/s10701-021-00480-7 · Cited by 27 · see citing works
Understanding quantum mechanics: a review and synthesis in precise language
Drummond, B. (2019) · Open Physics · doi:10.1515/phys-2019-0045 · Cited by 25 · see citing works
Simpson, W. M. (2021) · European Journal for Philosophy of Science · doi:10.1007/s13194-020-00342-5 · Cited by 22 · see citing works
Allori, V. (2021) · Synthese · doi:10.1007/s11229-021-03332-z · Cited by 16 · see citing works
Quantum correlations and the explanatory power of radical metaphysical hypotheses
Emery, N. (2022) · Philosophical Studies · doi:10.1007/s11098-021-01769-z · Cited by 14 · see citing works
The Past Hypothesis and the Nature of Physical Laws
Chen, E. K. (2020) · arXiv · doi:10.48550/arxiv.2008.00611 · Cited by 14 · see citing works
Three arguments for wave function realism
Ney, A. (2023) · European Journal for Philosophy of Science · doi:10.1007/s13194-023-00554-5 · Cited by 13 · see citing works
Time’s Arrow in a Quantum Universe: On the Status of Statistical Mechanical Probabilities
Chen, E. (2019) · Statistical Mechanics and Scientific Explanation · doi:10.1142/9789811211720_0013 · Cited by 19 · see citing works
Allori, V. (2022) · Foundations of Physics · doi:10.1007/s10701-022-00595-5 · Cited by 12 · see citing works
The Past Hypothesis and the Nature of Physical Laws
Chen, E. K. (2023) · Harvard University Press eBooks · doi:10.2307/j.ctv32nxzc6.10 · Cited by 12 · see citing works
Representation of the wave function on the three-dimensional space
Stoica, O. C. (2019) · Physical Review A · doi:10.1103/physreva.100.042115 · Cited by 10 · see citing works
A Puzzle for the Field OntologistsPreprint
Gao, S. (2020) · PhilSci-Archive (University of Pittsburgh) · Cited by 10 · see citing works
Allori, V. (2021) · Crítica (México D F En línea) · doi:10.22201/iifs.18704905e.2021.1292 · Cited by 9 · see citing works
A Puzzle for the Field Ontologists
Gao, S. (2020) · Foundations of Physics · doi:10.1007/s10701-020-00390-0 · Cited by 8 · see citing works
Scientific Realism without the Wave-Function: An Example of Naturalized Quantum MetaphysicsPreprint
Allori, V. (2019) · PhilSci-Archive (University of Pittsburgh) · Cited by 8 · see citing works
Beables, Primitive Ontology and Beyond: How Theories Meet the World
Oldofredi, A. (2022) · Synthese Library/Synthese library · doi:10.1007/978-3-030-99642-0_7 · Cited by 7 · see citing works
Is the Statistical Interpretation of Quantum Mechanics ψ-Ontic or ψ-Epistemic?
Hubert, M. (2022) · Foundations of Physics · doi:10.1007/s10701-022-00651-0 · Cited by 7 · see citing works
The One Magic Wave: Quantum Monism Meets Wavefunction Realism
Calosi, C. (2022) · The British Journal for the Philosophy of Science · doi:10.1086/720523 · Cited by 6 · see citing works
Why Scientific Realists Should Reject the Second Dogma of Quantum Mechanics
Allori, V. (2020) · Jerusalem studies in philosophy and history of science · doi:10.1007/978-3-030-34316-3_2 · Cited by 6 · see citing works
Drezet, A. (2023) · Symmetry · doi:10.3390/sym15061250 · Cited by 5 · see citing works
“,xN , t) that depends on N position vectors xj (since ψ is a correlation field, this was identified with a ‘webfunction’ in [58] and with a ‘multi-field’ in [59]).”
BackgroundThe physics and metaphysics of Tychistic Bohmian Mechanics
Duerr, P. M., & Ehmann, A. (2021) · Studies in History and Philosophy of Science Part A · doi:10.1016/j.shpsa.2021.09.014 · Cited by 5 · see citing works
Classical Logic in the Quantum Context
Oldofredi, A. (2020) · Quantum Reports · doi:10.3390/quantum2040042 · Cited by 5 · see citing works
On the Dual Ontological Structure and Mixed Dynamics of the UniversePreprint
Kahan, D. (2024) · Preprints.org · doi:10.20944/preprints202401.0714.v1 · Cited by 5 · see citing works
The quantum measurement problem: a review of recent trends
Tomaz, A. A., Mattos, R. S., & Barbatti, M. (2025) · The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics · doi:10.1080/14786435.2025.2601922 · Cited by 7 · see citing works
Can de Broglie–Bohm Mechanics Be Considered Complete?
Drezet, A., & Amblard, A. (2025) · Entropy · doi:10.3390/e27040399 · Cited by 4 · see citing works
The Entanglement Problem for Psychological Hylomorphism
Simpson, W. M. R., & Koons, R. C. (2025) · Res Philosophica · doi:10.5840/resphilosophica202541135 · Cited by 4 · see citing works
Cosmic Hylomorphism vs Bohmian Dispositionalism
Simpson, W. M., & Pemberton, J. M. (2022) · Synthese Library/Synthese library · doi:10.1007/978-3-030-99642-0_18 · Cited by 4 · see citing works
The Point of Primitive Ontology
Lazarovici, D., & Reichert, P. (2022) · Foundations of Physics · doi:10.1007/s10701-022-00639-w · Cited by 4 · see citing works
Many-Worlds: Why Is It Not the Consensus?
Allori, V. (2023) · Quantum Reports · doi:10.3390/quantum5010007 · Cited by 4 · see citing works
Wavefunction realism does not ‘privilege position’
Schroeren, D. (2022) · Synthese · doi:10.1007/s11229-022-03525-0 · Cited by 4 · see citing works
Symmetry fundamentalism in quantum mechanics
Schroeren, D. (2021) · Philosophical Studies · doi:10.1007/s11098-021-01634-z · Cited by 3 · see citing works
The Ontology of the Many-Worlds Theory
Arve, P. (2023) · Quantum Reports · doi:10.3390/quantum5010015 · Cited by 2 · see citing works
From Hamilton-Jacobi to Bohm: Why the Wave Function Isn’t Just Another Action
Amblard, A., & Drezet, A. (2025) · Foundations of Physics · doi:10.1007/s10701-025-00865-y · Cited by 1 · see citing works
David Bohm’s philosophy of science in his causal interpretation of quantum mechanics
Kakkuri‐Knuuttila, M. (2025) · Synthese · doi:10.1007/s11229-025-05139-8 · Cited by 1 · see citing works
The Metaphysics of Decoherence
Vassallo, A., & Romano, D. (2021) · Erkenntnis · doi:10.1007/s10670-021-00469-8 · Cited by 1 · see citing works
On The Methodological Arguments for Wave−Function Realism
Matarese, V. (2021) · International Studies in the Philosophy of Science · doi:10.1080/02698595.2021.2024786 · Cited by 1 · see citing works
On the Principles That Serve as Guides to the Ontology of Quantum Mechanics
Matarese, V. (2022) · Synthese Library/Synthese library · doi:10.1007/978-3-030-99642-0_3 · Cited by 1 · see citing works
Quantum Ontology: Out of This World?
Norsen, T. (2022) · Synthese Library/Synthese library · doi:10.1007/978-3-030-99642-0_5 · Cited by 1 · see citing works
On the Galilean Invariance of the Pilot-Wave Theory
Allori, V. (2022) · Foundations of Physics · doi:10.1007/s10701-022-00631-4 · Cited by 1 · see citing works
Can the Ontology of Bohmian Mechanics Consists Only in Particles? The PBR Theorem Says No
Gao, S. (2023) · Foundations of Physics · doi:10.1007/s10701-023-00731-9 · Cited by 1 · see citing works
Simulating Nelsonian Quantum Field Theory
Carosso, A. (2024) · Foundations of Physics · doi:10.1007/s10701-024-00766-6 · Cited by 1 · see citing works
Quantum ontology and intuitions
Allori, V. (2024) · European Journal for Philosophy of Science · doi:10.1007/s13194-024-00595-4 · Cited by 1 · see citing works
Is the Universe Fundamentally a Density Matrix?
Dulani, S., & Ney, A. (2025) · The British Journal for the Philosophy of Science · doi:10.1086/737744 · Cited by 1 · see citing works
The metaphysics of decoherencePreprint
Vassallo, A., & Romano, D. (2021) · PhilSci-Archive (University of Pittsburgh) · Cited by 1 · see citing works
Quantum Cosmology: The Integration of Special Relativity and Quantum Mechanics Part IPreprint
Kahan, D. (2024) · Preprints.org · doi:10.20944/preprints202405.2028.v2
Quantum Cosmology: The Integration of Special Relativity and Quantum Mechanics —Part IPreprint
Kahan, D. (2024) · Preprints.org · doi:10.20944/preprints202405.2028.v4 · Cited by 1 · see citing works
Bohmian Mechanics: Realism and the “Box” Experiment
Yan, C. (2020) · Foundations of Science · doi:10.1007/s10699-020-09661-5
On the Existence of a Preserved Ontology Posited by a High-Dimensional Bohmian Interpretation
Manero, J. (2023) · Foundations of Science · doi:10.1007/s10699-023-09919-8
Quantum Cosmology: The Integration of Special Relativity and Quantum Mechanics - Part IPreprint
Kahan, D. (2024) · Preprints.org · doi:10.20944/preprints202405.2028.v3
A functionalist mixed approach to the ontology of quantum field theories
Yan, C. (2024) · European Journal for Philosophy of Science · doi:10.1007/s13194-024-00599-0
Separability and fundamentality
Calosi, C. (2024) · European Journal for Philosophy of Science · doi:10.1007/s13194-024-00612-6
The Determinacy Problem in Quantum Mechanics
Mariani, C. (2024) · Foundations of Physics · doi:10.1007/s10701-024-00808-z
Burgess and the bucket: the emergence of spacetime in classical theories of gravitation
Cocco, L., & Babic, J. (2025) · Synthese · doi:10.1007/s11229-024-04823-5
The direction of time in Bohmian mechanics
López, C., & Esfeld, M. (2025) · doi:10.1093/oso/9780198901853.003.0011
The pilot-wave theory: a plurality of voices
Oldofredi, A. (2025) · doi:10.1093/oso/9780198901853.003.0001
Antirealism in Sheep’s Clothing
Arroyo, R. W., & Arenhart, J. R. B. (2025) · Foundations of Physics · doi:10.1007/s10701-025-00881-y
Which quantum foundations for the minimalist ontology framework?
Margoni, E. (2026) · Philosophical Studies · doi:10.1007/s11098-026-02485-2
Letertre, L. (2026) · Sciences & philosophie · doi:10.3917/edmat.papal.2026.01.0213
A Three–Dimensional Ontological Formulation of Bohmian Mechanics
Yepes, P. (2026) · Entropy · doi:10.3390/e28040382
The Metaphysics of Field Theory
Matarese, V. (2025) · Elsevier eBooks · doi:10.1016/b978-0-443-40622-5.00039-6
Can active information solve key problems in the Bohm theory?
Pylkkänen, P. (2026) · The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics · doi:10.1080/14786435.2026.2737148
- Authors
- Hubert, M., & Romano, D.
- Affiliations
- University of Lausanne (CH)
- Corresponding author
- Hubert, Mario
- Venue
- European Journal for Philosophy of Science
- Published
- 2018-02-14
- Volume
- 8
- Issue
- 3
- Pages
- 521-537
- ISSN
- 1879-4912 (ISSN-L)
- 1879-4920
- OpenAlex
- W2761065583
- Cited by
- 69
- References
- 38
- Citations by year
- 2026: 5 · 2025: 14 · 2024: 11 · 2023: 7 · 2022: 11 · 2021: 9 · 2020: 6 · 2019: 4 · 2018: 2
- FWCI
- 2.42
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- www.springer.com/tdm (tdm)
- Locations
- European Journal for Philosophy of Science (publishedVersion)
- PhilSci-Archive (University of Pittsburgh) (acceptedVersion)
- arXiv (Cornell University) (submittedVersion)
- PhilPapers (PhilPapers Foundation) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (105212_149650)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Social Sciences › Arts and Humanities › History and Philosophy of Science › Philosophy and History of Science
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Philosophy and Theoretical Science
- Keywords
- Bohmian mechanics, wave functions, physical fields, configuration space, interpretation of quantum mechanics, hidden variables
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review