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Is the Universe in a Mixed State?

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Abstract

Quantum mechanics with a fundamental density matrix has been proposed and discussed recently. Moreover, it has been conjectured that the universe is not in a pure state but in a mixed state in this theory. In this paper, I argue that this mixed state conjecture has two main problems: the redundancy problem and the underdetermination problem, which are lacking in quantum mechanics with a definite initial wave function of the universe.

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Notes

  1. Dürr et al [4] seem to treat the probabilities as epistemic. Chen [2] suggests taking the probabilities to be those given by the past hypothesis and the statistical postulate, which may be epistemic or ontic depending on how those principles are implemented.

  2. Hartle and Hawking [7]’s no-boundary proposal can be regarded as one example of such a theory. According to this proposal, the wave function of the universe, which obeys the Wheeler-DeWitt equation, is given by a path integral over all compact Euclidean four-dimensional geometries and matter fields that have the three-dimensional geometry and matter field configuration as its only boundary. Recently, Halliwell et al. [6] gave a formulation of the no-boundary wave function directly in terms of a collection of saddle points that satisfy a specific minimal set of criteria, and argued that it determines a unique wave function. Moreover, Feleppa et al. [5] showed that the no-boundary wave function can be obtained in a simple way starting from the Friedmann-Lemaitre-Robertson-Walker line element of cosmological equations for a de Sitter universe.

  3. Here there is a natural speculation on how to solve the puzzle of the arrow of time. It is usually thought that the past hypothesis and the statistical postulate are needed to solve this puzzle (see, e.g. [8]). It is the statistical postulate that motivated the mixed state conjecture [3]. Now it seems that QM with a definite initial universal wave function may solve the puzzle of the arrow of time in a simpler way. In this theory, the statistical postulate is dropped. Moreover, the past hypothesis can be naturally derived: since the universe has only one possible initial wave function, the initial entropy of the universe is zero, which means that the universe begins with the minimum entropy. Penrose’s [9] Weyl curvature hypothesis can be regarded as one example of such a theory.

References

  1. Albert, D.Z.: Time and Chance. Harvard University Press, Cambridge (2000)

    Book  Google Scholar 

  2. Chen, E. K. Quantum States of a Time-Asymmetric Universe: Wave Function, Density Matrix, and Empirical Equivalence. http://philsci-archive.pitt.edu/15658/ (2019)

  3. Chen, E.K.: Quantum mechanics in a time-asymmetric universe: on the nature of the initial quantum state. Br. J. Philos. Sci. 72(4), 1155–1183 (2021)

    Article  MathSciNet  Google Scholar 

  4. Dürr, D., Goldstein, S., Tumulka, R., Zanghi, N.: On the role of density matrices in Bohmian mechanics. Found. Phys. 35(3), 449–467 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  5. Feleppa, F., Licata, I., Corda, C.: Hartle-Hawking boundary conditions as Nucleation by de Sitter Vacuum. Phys. Dark Universe 26, 100381 (2019)

    Article  Google Scholar 

  6. Halliwell, J.J., Hartle, J.B., Hertog, T.: What is the no-boundary wave function of the Universe? Phys. Rev. D 99, 043526 (2019)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  7. Hartle, J.B., Hawking, S.W.: Wave function of the Universe. Phys. Rev. D 28, 2960 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  8. Loewer, B.: The Mentaculus vision. In: Allori, V. (ed.) Statistical Mechanics and Scientific Explanation: Determinism, Indeterminism and Laws of Nature,  pp. 3–30. World Scientific, Singapore (2020)

    Chapter  Google Scholar 

  9. Penrose, R.: On the second law of thermodynamics. J. Stat. Phys. 77, 217 (1994)

    Article  ADS  MathSciNet  Google Scholar 

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Acknowledgements

I wish to thank Eddy Keming Chen, Shelly Goldstein, Tim Maudlin and Rodi Tumulka for helpful discussion.

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  1. Research Center for Philosophy of Science and Technology, Shanxi University, Taiyuan, 030006, People’s Republic of China

    Shan Gao

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  1. Shan Gao
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Gao, S. Is the Universe in a Mixed State?. Found Phys 54, 7 (2024). https://doi.org/10.1007/s10701-023-00742-6

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