[Paper Review] Quantum Clocks and the Origin of Time in Complex Systems

Scott M. Hitchcock|ArXiv.org|Feb 16, 1999

Earth Systems and Cosmic Evolution1 references3 citations

TL;DR

This paper proposes that time in complex systems emerges from networks of quantum clocks—unstable quantum configurations whose lifetimes define temporal evolution. Using Feynman path integrals and instantons, it models the universe's origin as a quantum clock, showing that temporal phase transitions give rise to classical time, irreversibility, and thermodynamic arrows of time.

ABSTRACT

The origin and nature of time in complex systems is explored using quantum (or 'Feynman') clocks and the signals produced by them. Networks of these clocks provide the basis for the evolution of complex systems. The general concept of 'time' is translated into the 'lifetimes' of these unstable configurations of matter. 'Temporal phase transitions' mark the emergence of classical properties such as irreversibility, entropy, and thermodynamic arrows of time. It is proposed that the creation of the universe can be modeled as a quantum clock. Keywords: the problem of time, the arrow of time, time asymmetry, the many-body problem, cellular networks, complexity, the Wheeler-DeWitt equation, quantum cosmology, and instantons.

Motivation & Objective

• To address the foundational problem of time's origin in quantum gravity and complex systems.
• To resolve the 'problem of time' in canonical quantum gravity by modeling time as emergent from unstable quantum configurations.
• To explain the emergence of classical time, irreversibility, and thermodynamic arrows from quantum dynamics.
• To provide a quantum cosmological model where the universe's creation is interpreted as a quantum clock event.
• To unify concepts from quantum mechanics, general relativity, and complexity theory through the lens of quantum clocks.

Proposed method

• Uses Feynman path integrals to model the evolution of quantum clocks as unstable, decaying configurations.
• Applies the Wheeler-DeWitt equation to describe a timeless quantum state of the universe, from which time emerges dynamically.
• Introduces networks of quantum clocks as the fundamental substrate for complex system evolution.
• Employs instanton solutions in Euclidean quantum gravity to model tunneling processes that initiate time evolution.
• Analyzes temporal phase transitions in the clock network to identify the emergence of classical time properties.
• Translates the general concept of 'time' into the measurable lifetimes of quantum clocks, linking quantum decay to temporal flow.

Experimental results

Research questions

• RQ1 How can time emerge from a fundamentally timeless quantum theory of gravity?
• RQ2 What mechanism underlies the transition from quantum coherence to classical time with an arrow?
• RQ3 How do networks of quantum clocks give rise to thermodynamic irreversibility and entropy increase?
• RQ4 Can the origin of the universe be modeled as a quantum clock event within a path integral framework?
• RQ5 What role do instantons and non-perturbative quantum effects play in the emergence of time?

Key findings

• Temporal phase transitions in networks of quantum clocks mark the emergence of classical time, irreversibility, and thermodynamic arrows.
• The lifetime of unstable quantum clocks serves as a fundamental measure of time, replacing the need for an external time parameter.
• The model realizes a solution to the problem of time by deriving time from quantum dynamics rather than imposing it.
• The universe's creation is modeled as a quantum tunneling event via instantons, analogous to a quantum clock initiating time.
• The Wheeler-DeWitt equation's solutions are interpreted as timeless, but time emerges through the collective behavior of quantum clocks.
• The framework provides a consistent quantum mechanical basis for the thermodynamic arrow of time through irreversible decay processes.