Chen, Eddy Keming (2019) Time's Arrow in a Quantum Universe: On the Status of Statistical Mechanical Probabilities. [Preprint]
|
Text
IPH-Prob 2.pdf Download (287kB) | Preview |
Abstract
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.
| Export/Citation: | EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL |
| Social Networking: |
| Item Type: | Preprint | ||||||
|---|---|---|---|---|---|---|---|
| Creators: |
|
||||||
| Additional Information: | Forthcoming in Valia Allori (ed.), \emph{Statistical Mechanics and Scientific Explanation: Determinism, Indeterminism and Laws of Nature}, World Scientific | ||||||
| Keywords: | time's arrow, Past Hypothesis, Statistical Postulate, the Mentaculus Vision, typicality, unification, foundations of probability, quantum statistical mechanics, wave function realism, quantum ontology, density matrix, initial condition of the universe, strong determinism | ||||||
| Subjects: | General Issues > Determinism/Indeterminism Specific Sciences > Probability/Statistics Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Statistical Mechanics/Thermodynamics |
||||||
| Depositing User: | Dr. Eddy Keming Chen | ||||||
| Date Deposited: | 12 Feb 2019 15:22 | ||||||
| Last Modified: | 12 Feb 2019 15:22 | ||||||
| Item ID: | 15736 | ||||||
| Subjects: | General Issues > Determinism/Indeterminism Specific Sciences > Probability/Statistics Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Statistical Mechanics/Thermodynamics |
||||||
| Date: | 11 February 2019 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/15736 |
Monthly Views for the past 3 years
Monthly Downloads for the past 3 years
Plum Analytics
Actions (login required)
 |
View Item |
![[feed]](http://philsci-archive.pitt.edu/style/images/feed-icon-32x32.png){kind=icon}