Modeling the Arrows of Time with Causal Multibaker Maps.

Area of Science:

• Theoretical physics
• Dynamical systems theory
• Philosophy of time

Background:

• The emergence of time's asymmetry (arrows of time) is a fundamental question in physics.
• Existing models often link time's arrows to thermodynamics.
• Causal relationships are crucial for understanding temporal directionality.

Purpose of the Study:

• To investigate emergent time asymmetries using a novel theoretical model.
• To establish the causal arrow of time as fundamental.
• To derive other time arrows from the causal arrow.

Main Methods:

• Introduction of the causal multibaker maps, a class of reversible discrete-time dynamical systems.
• Imposition of an initial condition (Past Hypothesis) and coarse-graining.
• Analysis of emergent causal structures and record-keeping systems.

Main Results:

• The causal multibaker maps model generates a Pearlean locally causal structure.
• The causal arrow of time is shown to be fundamental, distinct from the thermodynamic arrow.
• The thermodynamic and epistemic arrows of time are derived from the causal arrow.
• Records, defined as systems encoding past states, are shown to exist for the past but not the future.

Conclusions:

• The causal arrow of time provides a foundational basis for understanding temporal asymmetries.
• The model successfully derives other time arrows, including thermodynamic and epistemic.
• The concept of records highlights the asymmetry in information storage about past versus future events.