Abstract
In this paper, I characterize and elaborate on the “Wentaculus” theory, a new approach to time’s arrow in a quantum universe that offers a unified solution to the problems of what gives rise to the arrow of time and what the ontology of quantum mechanics is.
Dedicated to the memory of Detlef Dürr.
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Notes
- 1.
- 2.
The Wentaculus is so named because (1) it is inspired by the Mentaculus, and (2) “W” is sometimes used to denote the fundamental density matrix.
- 3.
For GRW-type theories, the density matrix obeys the stochastic modification of the von Neumann equation described in footnote #22.
- 4.
Albert’s thought experiment relies on certain idealizations about momentum eigenstates. We usually require the particle configuration to be guided by square-integrable wave functions or density matrices with finite traces, which do not include momentum eigenstates. However, as Sheldon Goldstein points out to me, the example can be fixed by considering momentum eigenstates defined on a closed circle instead of on an infinite line.
- 5.
In response to Einstein’s worry about the particle in a box of length L with a real-valued wave function \(\psi (x)=A sin \frac{2\pi n x}{L}\), Bohm points out that ordinary Bohmian mechanics does not “contradict any known experimental facts,” because when we carry out a “momentum measurement,” the wave function (of a stationary state) is transformed and the particle starts to move, even though its original momentum is exactly zero.
References
D.Z. Albert, The foundations of quantum mechanics and the approach to thermodynamic equilibrium. Br. J. Philos. Sci. 45(2), 669–677 (1994)
D.Z. Albert, Elementary quantum metaphysics, in Bohmian Mechanics and Quantum Theory: An Appraisal. ed. by J.T. Cushing, A. Fine, S. Goldstein (Kluwer Academic Publishers, Dordrecht, 1996), pp.277–84
D.Z. Albert, Time and Chance (Harvard University Press, Cambridge, 2000)
D.Z. Albert, After Physics (Harvard University Press, Cambridge, 2015)
D. Z. Albert, Physical laws and physical things (manuscript) (2022)
V. Allori, S. Goldstein, R. Tumulka, N. Zanghì, Predictions and primitive ontology in quantum foundations: a study of examples. Br. J. Philos. Sci. 65(2), 323–352 (2013)
J.S. Bell, Quantum mechanics for cosmologists, in Quantum Gravity 2. ed. by C. Isham, R. Penrose, D. Sciama (Clarendon Press, 1981), pp. 611–637
D. Bohm, A discussion of certain remarks by Einstein on Born’s probability interpretation of the \(\psi \)-function, in Scientific Papers Presented to Max Born (Hafner, 1953), pp. 13–19
C. Callender, Measures, explanations and the past: should ‘special’ initial conditions be explained? Br. J. Philos. Sci. 55(2), 195–217 (2004)
C. Callender, Thermodynamic asymmetry in time, in The Stanford Encyclopedia of Philosophy, ed. by E.N. Zalta (Metaphysics Research Lab, Stanford University, 2011) fall 2011 edition. https://urldefense.com/v3/__. https://plato.stanford.edu/entries/timethermo/__;!!NLFGqXoFfo8MMQ!vprs9m5l_WnJD262YutLOEjrctYKHQxmVxyqMmK3j9jx9VGPMCweSj3h5e1WNlCQJYochYf0E1PwDFXTbQsT4iw7TmlMeLmhMDzemjYoR2fFYoG1$
E.K. Chen, Quantum mechanics in a time-asymmetric universe: on the nature of the initial quantum state. Br. J. Philos. Sci. (2018). https://doi.org/10.1093/bjps/axy068
E.K. Chen, Quantum states of a time-asymmetric universe: wave function, density matrix, and empirical equivalence. Master’s Thesis, Department of Mathematics, Rutgers University, New Brunswick (2019a). arXiv:1901.08053
E.K. Chen, Realism about the wave function. Philos. Compass 14(7) (2019b)
E.K. Chen, Time’s arrow in a quantum universe: on the status of statistical mechanical probabilities, in Statistical Mechanics and Scientific Explanation: Determinism, Indeterminism and Laws of Nature, ed. by V. Allori (World Scientific, Singapore, 2020)
E.K. Chen, From time asymmetry to quantum entanglement: the humean unification. Noûs 56, 227–255 (2022)
E.K. Chen, Fundamental nomic vagueness. Philos. Rev. 131(1) (2022b)
E.K. Chen, Strong determinism. Philosophers’ Imprint, forthcoming (2022c). arXiv:2203.02886
E.K. Chen, The past hypothesis and the nature of physical laws, in The Probability Map of the Universe: Essays on David Albert’s Time and Chance, ed. by B. Loewer, E. Winsberg, B. Weslake (Harvard University Press, 2023)
E.K. Chen, R. Tumulka, Uniform probability distribution over all density matrices. Quantum Stud.: Math. Found. 9(2), 225–233 (2022)
E.Y.S. Chua, E.K. Chen, Decoherence, branching, and the Born rule in a mixed-state Everettian multiverse (2023). arXiv:2307.13218
D. Dürr, S. Goldstein, R. Tumulka, N. Zanghì, On the role of density matrices in Bohmian mechanics. Found. Phys. 35(3), 449–467 (2005)
D. Dürr, S. Goldstein, N. Zanghì, Quantum equilibrium and the origin of absolute uncertainty. J. Stat. Phys. 67(5–6), 843–907 (1992)
D. Dürr, S. Goldstein, N. Zanghì, Bohmian mechanics and the meaning of the wave function, in Experimental Metaphysics: Quantum Mechanical Studies in honor of Abner Shimony (1996)
J. Earman, The “past hypothesis’’: not even false. Stud. Hist. Philos. Sci. Part B: Stud. Hist. Philos. Mod. Phys. 37(3), 399–430 (2006)
S. Goldstein, Boltzmann’s approach to statistical mechanics, in Chance in Physics. ed. by J. Bricmont, D. Dürr, M.C. Galavotti, G. Ghirardi, F. Petruccione, N. Zanghì (Springer, Berlin, 2001), pp.39–54
S. Goldstein, Typicality and notions of probability in physics, in Probability in Physics (Springer, Berlin, 2012), pp. 59–71
S. Goldstein, J.L. Lebowitz, C. Mastrodonato, R. Tumulka, N. Zanghì, Approach to thermal equilibrium of macroscopic quantum systems. Phys. Rev. E 81(1), 011109 (2010)
S. Goldstein, J.L. Lebowitz, R. Tumulka, N. Zanghì, Gibbs and Boltzmann entropy in classical and quantum mechanics, in Statistical Mechanics and Scientific Explanation: Determinism, Indeterminism and Laws of Nature. ed. by V. Allori (World Scientific, Singapore, 2020)
S. Goldstein, S. Teufel, Quantum spacetime without observers: ontological clarity and the conceptual foundations of quantum gravity, in Physics meets Philosophy at the Planck Scale (2001), pp. 275–289
J.L. Lebowitz, Time’s arrow and Boltzmann’s entropy. Scholarpedia 3(4), 3448 (2008)
B. Loewer, Determinism and chance. Stud. Hist. Philos. Sci. Part B: Stud. Hist. Philos. Mod. Phys. 32(4), 609–620 (2001)
B. Loewer, Counterfactuals and the second law, in Causation, Physics, and the Constitution of Reality: Russell’s Republic Revisited, ed. by H. Price, R. Corry (Oxford University Press, 2007)
B. Loewer, Two accounts of laws and time. Philos. Stud. 160(1), 115–137 (2012)
B. Loewer, The Mentaculus vision, in Statistical Mechanics and Scientific Explanation: Determinism, Indeterminism and Laws of Nature, ed. by V. Allori (World Scientific, Singapore, 2020)
O. Maroney, The density matrix in the de Broglie-Bohm approach. Found. Phys. 35(3), 493–510 (2005)
C. McCoy, An alternative interpretation of statistical mechanics. Erkenntnis 85(1), 1–21 (2020)
A. Ney, The World in the Wave Function: A Metaphysics for Quantum Physics (Oxford University Press, 2021)
J. North, Time in thermodynamics, in The Oxford Handbook of Philosophy of Time (2011), pp. 312–350
D. Wallace, The Emergent Multiverse: Quantum Theory According to the Everett Interpretation (Oxford University Press, Oxford, 2012)
D. Wallace, Probability and irreversibility in modern statistical mechanics: classical and quantum, in Quantum Foundations of Statistical Mechanics (Oxford University Press, forthcoming, 2016)
D. Wallace, The logic of the past hypothesis, in The Probability Map of the Universe: Essays on David Albert’s Time and Chance, ed. by B. Loewer, E. Winsberg, B. Weslake, (Harvard University Press, 2023)
E. Winsberg, Can conditioning on the “past hypothesis’’ militate against the reversibility objections? Philos. Sci. 71(4), 489–504 (2004)
Acknowledgements
For helpful discussions, I thank David Albert, Valia Allori, Jeffrey Barrett, Craig Callender, Eugene Chua, Barry Loewer, Katie Robertson, Simon Saunders, Shelly Yiran Shi, David Wallace, audiences in the Oxford Philosophy of Physics Seminar, the Southern California Philosophy of Physics Group, Density Matrix Realism Workshop (FraMEPhys), and editors of this volume. I have learnt much from Detlef Dürr over the years, and I am grateful for his insights, suggestions, and encouragements.
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Chen, E.K. (2024). The Wentaculus: Density Matrix Realism Meets the Arrow of Time. In: Bassi, A., Goldstein, S., Tumulka, R., Zanghì, N. (eds) Physics and the Nature of Reality. Fundamental Theories of Physics, vol 215. Springer, Cham. https://doi.org/10.1007/978-3-031-45434-9_8
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