Postulating the Unicity of the Macroscopic Physical World
Abstract
:1. Introduction
1.1. Our World Is Unique…
1.2. … But Is It Classical and/or Quantum?
2. Overview of the Construction of Non-Fully Unitary QM
2.1. Introduction and Motivation
2.2. The Proposed Construction
- P
- Unicity of the macroscopic world —There is a unique macroscopic physical world in which a given measurement yields a single result.
- D
- Contexts, systems, and modalities—Given a microscopic physical system, a modality is defined as the values of a complete set of physical quantities that can be measured in this system. This complete set of physical quantities is called a context, and a modality is attributed to a system within a context. Contexts are concretely defined by the settings of macroscopic measurement devices.
- P
- Predictability and extravalence—Once a context is defined and the system is prepared in this context, modalities can ideally be predicted with certainty and measured repeatedly in this system. When changing the context, modalities change as a general rule, but some modalities belonging to different contexts may be connected with certainty; this property is called extracontextuality, and it defines an equivalence class between modalities, called extravalence [14,15].
- P
- Contextual quantisation—For a given system and context, there exist at most D distinguishable modalities that are mutually exclusive: if one modality is realised in an experiment, yielding a result in the macroscopic world, the other ones are not realised. The value of D, called the dimension, is a characteristic property of the quantum system and is the same in all relevant contexts.
- P
- Changing context—Given P and P, the different contexts relative to a given quantum system are related to each other through continuous transformations (e.g., rotating a polarisation beamsplitter), which are associative, have a neutral element (no change), and an inverse. Therefore, the set of context transformations has the structure of a continuous group, which is generally non-commutative.
- P
- Projective probabilities—In a given context , each exclusive modality of a system is represented by a projector in a Hilbert space of dimension D, with all ’s being orthogonal.
- D
- Observables as operators—From the orthogonal rays generated by the s, Hermitian operators on a D-dimensional Hilbert space can be constructed by considering each as an eigenspace associated with , the corresponding eigenvalue. If corresponds to a single observable quantity, this yields an operator . If is a tuple of several observable quantities, a tuple of operators can be constructed in a similar way.
2.3. Discussion
2.4. The Crucial Role of Unitary Transformations
3. Higher-Level Implications
3.1. Is Infinity Acceptable at All?
- (1)
- The breakdown into non-unitarily equivalent orthogonal sectors that correspond to an infinite number of changes in the elementary subsystem states.
- (2)
- The fact that sectors are not connected by operators in the ring built as an extension to the full ITP of operators that act on elementary subsystem Hilbert spaces, their products, sums, and topological completions.
- (1)
- If and in are not in the same sector when , for any , one can find a finite set of M indices s, all distinct, so as to build and , such that
- (2)
- Assume is a bounded operator in . If and are not in the same sector when , for any , one can find a finite set of M indices s, all distinct, so as to build and as above, and the restriction of to , such that .
- There is a mapping between concepts in the representation (that can be expressed in mathematical language) and the target elements of reality.
- This mapping allows conducting surrogate reasoning [35] on the concepts to yield (falsifiable) claims on the elements of reality they are meant to describe.
3.2. Unitarity Relevance and Multiverse Interpretation
- For it to be a scientific statement, it would need to yield a falsifiable experimental prediction, much like Bell’s inequalities for local hidden variables. Such a prediction is not yet available. Actually, this idea only arises as a consequence of extrapolating the type-I quantum formalism by carelessly applying it to macroscopic systems and then to the whole Universe. This is the difference between the round and moving aspects of the Earth, which quickly led to many practical predictions, e.g., sailing around it, that have largely been vindicated.
- The above considerations regarding ITP show (if the model holds) that there is no reason to expect any unitarity whatsoever at a macroscopic scale, and thus the very motivation for parallel universes collapses.
3.3. Reductionism vs. Dualism
4. Conclusions: QM for Engineers and Beyond?
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Uniqueness vs Unicity: Unraveling Commonly Confused Terms. Available online: https://thecontentauthority.com/blog/uniqueness-vs-unicity (accessed on 15 November 2023).
- Laloë, F. Do We Really Understand Quantum Mechanics? Cambridge University Press: Cambridge, UK, 2012. [Google Scholar]
- von Neumann, J. On infinite direct products. Compos. Math. 1939, 6, 1–77. Available online: http://www.numdam.org/item/CM_1939__6__1_0/ (accessed on 15 November 2023).
- Murray, F.J.; von Neumann, J. On Rings of Operators IV. Ann. Math. 1943, 44, 716. [Google Scholar] [CrossRef]
- Emch, G.G. Algebraic Methods in Statistical Mechanics and Quantum Field Theory; Dover: New York, NY, USA, 2000; (Reprint of the Wiley-Interscience 1972 Edition). [Google Scholar]
- Landau, L.D.; Lifshitz, E.M. Quantum Mechanics. 1965. Available online: https://archive.org/details/ost-physics-landaulifshitz-quantummechanics (accessed on 15 November 2023).
- The Feynman Lectures on Physics, Volume III: Quantum Mechanics, Millenium Edition. Available online: https://www.feynmanlectures.caltech.edu/ (accessed on 15 November 2023).
- Cohen-Tannoudji, C.; Diu, B.; Laloë, F. Quantum Mechanics; (3 Volumes); John Wiley & Sons: Hoboken, NJ, USA, 2019. [Google Scholar]
- Peres, A.; Zurek, W.H. Is quantum theory universally valid? Am. J. Phys. 1982, 50, 807. [Google Scholar] [CrossRef]
- Stanford Encyclopedia of Philosophy. Available online: https://plato.stanford.edu/search/searcher.py?query=quantum+mechanics (accessed on 15 November 2023).
- Coppo, A.; Pranzini, N.; Verrucchi, P. Threshold size for the emergence of classical-like behavior. Phys. Rev. A 2022, 106, 042208. [Google Scholar] [CrossRef]
- Zeh, H.D. On the Interpretation of Measurement in Quantum Theory. Found. Phys. 1970, 1, 69–76. [Google Scholar] [CrossRef]
- Zurek, W.H. Emergence of the Classical World from within Our Quantum Universe. In From Quantum to Classical. Fundamental Theories of Physics, Vol. 204; Kiefer, C., Ed.; Springer: Cham, Switzerland, 2022. [Google Scholar]
- Auffèves, A.; Grangier, P. Revisiting Born’s rule through Uhlhorn’s and Gleason’s theorems. Entropy 2022, 24, 199. [Google Scholar] [CrossRef] [PubMed]
- Auffèves, A.; Grangier, P. Extracontextuality and extravalence in quantum mechanics. Phil. Trans. R. Soc. A 2018, 376, 20170311. [Google Scholar] [CrossRef]
- Grangier, P.; Auffèves, A. What is quantum in quantum randomness? Phil. Trans. R. Soc. A 2018, 376, 20170322. [Google Scholar] [CrossRef]
- Auffèves, A.; Grangier, P. Deriving Born’s rule from an Inference to the Best Explanation. Found. Phys. 2020, 50, 1781–1793. [Google Scholar] [CrossRef]
- Grangier, P. Contextual inferences, nonlocality, and the incompleteness of quantum mechanics. Entropy 2021, 23, 1660. [Google Scholar] [CrossRef]
- Grangier, P. Completing the quantum formalism in a contextually objective framework. Found. Phys. 2021, 51, 76. [Google Scholar] [CrossRef]
- Van Den Bossche, M.; Grangier, P. Contextual unification of classical and quantum physics. Found. Phys. 2023, 53, 45. [Google Scholar] [CrossRef]
- Van Den Bossche, M.; Grangier, P. Revisiting Quantum Contextuality in an Algebraic Framework. J. Phys. Conf. Ser. 2023, 2533, 012008. [Google Scholar] [CrossRef]
- Allahverdyana, A.E.; Balian, R.; Nieuwenhuizen, T.M. Understanding quantum measurement from the solution of dynamical models. Phys. Rep. 2013, 525, 1–166. [Google Scholar] [CrossRef]
- Rovelli, C. Relational quantum mechanics. Int. J. Theor. Phys. 1996, 35, 1637. [Google Scholar] [CrossRef]
- Jarrett, J.P. On the physical significance of the locality condition in the Bell arguments. Noûs 1984, 18, 569. [Google Scholar] [CrossRef]
- Budroni, C.; Cabello, A.; Gühne, O.; Kleinmann, M.; Larsson, J.-A. Kochen-Specker contextuality. Rev. Mod. Phys. 2022, 94, 045007. [Google Scholar] [CrossRef]
- Khrennikov, A. Contextuality, Complementarity, Signaling, and Bell Tests. Entropy 2022, 24, 1380. [Google Scholar] [CrossRef]
- Svozil, K. Extending Kolmogorov’s axioms for a generalized probability theory on collections of contexts. Entropy 2022, 24, 1285. [Google Scholar] [CrossRef]
- Uhlhorn, U. Representation of symmetry transformations in quantum mechanics. Ark. Fys. 1962, 23, 307–340. [Google Scholar]
- Semrl, P. Wigner symmetries and Gleason’s theorem. J. Phys. A Math. Theor. 2021, 54, 315301. [Google Scholar] [CrossRef]
- Gleason, A.M. Measures on the Closed Subspaces of a Hilbert Space. J. Math. Mech. 1957, 6, 885. [Google Scholar] [CrossRef]
- Cooke, R.; Keanes, M.; Moran, W. An elementary proof of Gleason’s theorem. Math. Proc. Camb. Phil. Soc. 1985, 98, 117. [Google Scholar] [CrossRef]
- Thiemann, T.; Winkler, O. Gauge field theory coherent states: IV. Infinite tensor product and thermodynamical limit, section 4. Class. Quantum Grav. 2001, 18, 4997. [Google Scholar] [CrossRef]
- Earman, J. Quantum Physics in Non-Separable Hilbert Spaces. Available online: http://philsci-archive.pitt.edu/18363/ (accessed on 15 November 2023).
- Available online: https://plato.stanford.edu/entries/scientific-representation/ (accessed on 15 November 2023).
- Swoyer, C. Structural representation and surrogative reasoning. Synthese 1991, 87, 449–508. [Google Scholar] [CrossRef]
- Laloë, F. Introduction to Continuous Symmetries: From Space-Time to Quantum Mechanics; Blackwell Verlag GmbH: Berlin, Germany, 2023. [Google Scholar]
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Van Den Bossche, M.; Grangier, P. Postulating the Unicity of the Macroscopic Physical World. Entropy 2023, 25, 1600. https://doi.org/10.3390/e25121600
Van Den Bossche M, Grangier P. Postulating the Unicity of the Macroscopic Physical World. Entropy. 2023; 25(12):1600. https://doi.org/10.3390/e25121600
Chicago/Turabian StyleVan Den Bossche, Mathias, and Philippe Grangier. 2023. "Postulating the Unicity of the Macroscopic Physical World" Entropy 25, no. 12: 1600. https://doi.org/10.3390/e25121600