Time's Arrow in a Quantum Universe: On the Status of Statistical Mechanical Probabilities

In Valia Allori (ed.), Statistical Mechanics and Scientific Explanation: Determinism, Indeterminism and Laws of Nature. World Scientific. pp. 479–515 (2020)
  Copy   BIBTEX


In a quantum universe with a strong arrow of time, it is standard to postulate that the initial wave function started in a particular macrostate---the special low-entropy macrostate selected by the Past Hypothesis. Moreover, there is an additional postulate about statistical mechanical probabilities according to which the initial wave function is a ''typical'' choice in the macrostate. Together, they support a probabilistic version of the Second Law of Thermodynamics: typical initial wave functions will increase in entropy. Hence, there are two sources of randomness in such a universe: the quantum-mechanical probabilities of the Born rule and the statistical mechanical probabilities of the Statistical Postulate. I propose a new way to understand time's arrow in a quantum universe. It is based on what I call the Thermodynamic Theories of Quantum Mechanics. According to this perspective, there is a natural choice for the initial quantum state of the universe, which is given by not a wave function but by a density matrix. The density matrix plays a microscopic role: it appears in the fundamental dynamical equations of those theories. The density matrix also plays a macroscopic / thermodynamic role: it is exactly the projection operator onto the Past Hypothesis subspace. Thus, given an initial subspace, we obtain a unique choice of the initial density matrix. I call this property "the conditional uniqueness" of the initial quantum state. The conditional uniqueness provides a new and general strategy to eliminate statistical mechanical probabilities in the fundamental physical theories, by which we can reduce the two sources of randomness to only the quantum mechanical one. I also explore the idea of an absolutely unique initial quantum state, in a way that might realize Penrose's idea of a strongly deterministic universe.

Similar books and articles

Quantum Mechanics in a Time-Asymmetric Universe: On the Nature of the Initial Quantum State.Eddy Keming Chen - 2021 - British Journal for the Philosophy of Science 72 (4):1155–1183.
Statistical mechanics and the ontological interpretation.D. Bohm & B. J. Hiley - 1996 - Foundations of Physics 26 (6):823-846.
Measurement in Bohm's versus Everett's quantum theory.H. -D. Zeh - 1988 - Foundations of Physics 18 (7):723-730.
Time asymmetry and quantum equations of motion.T. E. Phipps - 1973 - Foundations of Physics 3 (4):435-455.
Probabilistic Time.C. Wetterich - 2012 - Foundations of Physics 42 (11):1384-1443.
Quantum mechanics without the projection postulate.Jeffrey Bub - 1992 - Foundations of Physics 22 (5):737-754.
Everett and evidence.Hilary Greaves & Wayne Myrvold - 2010 - In Simon Saunders, Jonathan Barrett, Adrian Kent & David Wallace (eds.), Many Worlds?: Everett, Quantum Theory & Reality. Oxford University Press.
Is - kTr( ln ) the entropy in quantum mechanics.Orly Shenker - 1999 - British Journal for the Philosophy of Science 50 (1):33-48.


Added to PP

591 (#27,972)

6 months
153 (#18,324)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Eddy Keming Chen
University of California, San Diego

References found in this work

The metaphysics within physics.Tim Maudlin - 2007 - New York: Oxford University Press.
Time and chance.David Z. Albert - 2000 - Cambridge, Mass.: Harvard University Press.

View all 72 references / Add more references