Causality in Discrete Time Physics Derived from Maupertuis Reduced Action Principle

Area of Science:

• Physics
• Theoretical Physics
• Philosophy of Science

Background:

• Causality, the relationship between cause and effect, is fundamental but not explicitly a law in classical or relativistic physics.
• The time-symmetric nature of physical laws has led to challenges regarding the existence of causality.
• Existing theories preserve causality but do not define it as a core principle.

Purpose of the Study:

• To redefine causality within a physical framework.
• To establish causality as a derivable concept from fundamental principles.
• To explore the implications of a discrete dynamical time for causality.

Main Methods:

• Utilizing the reduced action and Maupertuis' least action principle.
• Introducing a discrete dynamical time to yield an arrow of time.
• Defining causality as the partial spatial derivative of the reduced action.

Main Results:

• Causality is defined as a position- and momentum-dependent quantity.
• This definition necessitates the presence of space for causality to exist.
• The system evolves step-by-step without explicit reliance on time, which can be reconstructed.

Conclusions:

• A novel, physics-based definition of causality is proposed.
• This definition integrates causality with concepts of action and space.
• The framework allows for a discrete, reconstructed time, offering new insights into temporal evolution.