[Paper Review] The Universal Arrow of Time II: Quantum mechanics case

Oleg Kupervasser|arXiv (Cornell University)|Jun 30, 2011

Quantum Mechanics and Applications23 references3 citations

TL;DR

This paper extends the universal arrow of time concept to quantum mechanics, showing that thermodynamic time arrows align in closed quantum systems due to weak subsystem interactions and the impossibility of observing entropy decrease during introspection. It resolves foundational quantum paradoxes—such as wave function collapse, Wigner's friend, and the measurement problem—by unifying the many-worlds and Copenhagen interpretations through decoherence and time-asymmetric observation.

ABSTRACT

This paper is a natural continuation of our previous paper arXiv:1011.4173 . We illustrated earlier that in classical Hamilton mechanics, for overwhelming majority of real chaotic macroscopic systems, alignment of their thermodynamic time arrows occurs because of their low interaction. This fact and impossibility to observe entropy decrease at introspection explain the second law of thermodynamics. The situation in quantum mechanics is even a little bit easier: all closed systems of finite volume are periodic or nearly periodic. The proof in quantum mechanics is in many respects similar to the proof in classical Hamilton mechanics - it also uses small interaction between subsystems and impossibility to observe entropy decrease at introspection. However, there are special cases which were not found in the classical mechanics. In these cases one microstate corresponds to a set of possible macrostates (more precisely, their quantum superposition). Consideration of this property with use of decoherence theory and taking into account thermodynamic time arrows will introduce new outcomes in quantum mechanics. It allows to resolve basic paradoxes of quantum mechanics: (a) to explain the paradox of wave packet reduction at measurements when an observer is included in the system (introspection) (paradox of the Schrodinger cat); (b) to explain unobservability of superposition of macroscopic states by an external observer in real experiments (paradox of Wigner's friend); (c) to prove full equivalence of multi-world and Copenhagen interpretations of quantum mechanics; (d) to explain deviations from the exponential law at decay of particles and pass from one energy level to another (paradox of a kettle which will never begin to boil).

Motivation & Objective

• To extend the universal arrow of time concept from classical to quantum mechanics.
• To explain the emergence of thermodynamic time arrows in quantum systems despite periodicity.
• To resolve foundational quantum paradoxes (e.g., Schrödinger's cat, Wigner's friend) using introspection and decoherence.
• To demonstrate equivalence between the many-worlds and Copenhagen interpretations in quantum mechanics.
• To account for deviations from exponential decay laws in quantum transitions.

Proposed method

• Adapts the classical proof of time arrow alignment to quantum systems using weak interactions between subsystems.
• Applies the principle that entropy decrease cannot be observed during introspection to enforce time asymmetry.
• Uses decoherence theory to explain the transition from quantum superpositions to classical-like macrostates.
• Analyzes systems with finite volume, where all states are periodic or nearly periodic, to derive time-asymmetric behavior.
• Introduces a formalism where a single microstate can correspond to a superposition of macrostates, enabling time arrow resolution.
• Combines thermodynamic time arrows with quantum measurement theory to resolve observer-dependent paradoxes.

Experimental results

Research questions

• RQ1 How does the thermodynamic arrow of time emerge in quantum systems despite their inherent periodicity?
• RQ2 Why is the superposition of macroscopic states unobservable in practice, even though it is theoretically allowed?
• RQ3 Can the measurement problem be resolved when the observer is part of the quantum system (introspection)?
• RQ4 What is the relationship between the many-worlds and Copenhagen interpretations in the context of time-asymmetric observation?
• RQ5 How do deviations from exponential decay laws arise in quantum transitions, and what explains the 'kettle that never boils' paradox?

Key findings

• In quantum mechanics, thermodynamic time arrows align across subsystems due to weak interactions and the impossibility of observing entropy decrease during introspection.
• The paradox of wave function collapse during measurement is resolved when the observer is included in the system, as decoherence prevents macroscopic superpositions from being observed.
• The unobservability of macroscopic superpositions (Wigner's friend paradox) is explained by the time-asymmetric nature of observation and decoherence.
• The many-worlds and Copenhagen interpretations are shown to be fully equivalent when time-asymmetric observation and decoherence are properly accounted for.
• Deviations from exponential decay laws are explained by the time-asymmetric alignment of thermodynamic arrows and the structure of quantum superpositions.
• The paper provides a consistent framework where quantum mechanics and thermodynamics cohere through the universal arrow of time, even in finite-volume systems.