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This study introduces a unified action function to describe object motion in spacetime under various forces. This framework simplifies dynamics across electromagnetic, gravitational fields, and media interactions.

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Area of Science:

  • Theoretical Physics
  • Classical Mechanics
  • Spacetime Dynamics

Background:

  • Describing object motion in force fields and media traditionally involves separate frameworks.
  • A unified approach is needed to simplify the understanding of complex dynamics.

Purpose of the Study:

  • To define a universal action function for describing object motion.
  • To ensure observer and parametrization independence in the action formulation.
  • To unify the description of motion in electromagnetic, gravitational fields, and media.

Main Methods:

  • Defined a Lorentz-invariant and positive homogeneous action function L(x, u).
  • Ensured the action function is independent of observer frame and world-line parametrization.
  • Utilized two four-potentials for the simplest form of L(x, u).

Main Results:

  • The derived action function L(x, u) successfully unifies dynamics.
  • The model accurately describes motion in electromagnetic and static gravitational fields.
  • It also accounts for combined fields and propagation in isotropic media.

Conclusions:

  • A single action principle can describe diverse physical phenomena.
  • The method simplifies dynamics by defining potentials directly from sources.
  • This unified approach offers a powerful tool for theoretical physics.