2019/02/12 by Eddy Keming Chen
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Arrow of time #Classical mechanics #Density matrix #Entropy (arrow of time) #Mathematics #Open quantum system #Physics #Quantum #Quantum Mechanics and Applications #Quantum mechanics #Quantum operation #Quantum state #Quantum statistical mechanics #Randomness #Statistical Mechanics and Entropy #Statistical physics #Statistics #Theoretical physics #Universe #Wave function #Wave function collapse #gr-qc #physics.hist-ph #quant-ph
paper · pdf · doi:10.1142/9789811211720_0013
published as Valia Allori (ed.), Statistical Mechanics and Scientific Explanation: Determinism, Indeterminism and Laws of Nature. World Scientific, May 2020 · Forthcoming in Valia Allori (ed.), \emph{Statistical Mechanics and Scientific Explanation: Determinism, Indeterminism and Laws of Nature}, World Scientific
arxiv created 2019/02/12 · openalex publication_date 2020/04/21 · arxiv updated 2021/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 (the Statistical Postulate). 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 (normalized) projection operator onto the Past Hypothesis subspace (of the Hilbert space of the universe). 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 (1989) of a strongly deterministic universe.