Physical Determination of the Action

TL;DR

This paper aims to establish a physical foundation for mechanics by operationally defining basic observables, revisiting classical and relativistic kinematics, and reformulating energy, momentum, and action from a measurement-based perspective.

Contribution

It offers a new physical interpretation of mechanics rooted in measurement operations, revisiting classical and relativistic concepts without altering their mathematical formalism.

Findings

Operational definitions of observables are used to derive equations of motion.

A relativistic revision of energy, momentum, and inertial mass is proposed.

The approach provides a deeper physical understanding aligned with Einstein's thought experiments.

Abstract

The objective is a foundation of physics from the operationalization of its basic observables. We begin with classical and relativistic kinematics. Seizing on a programmatic proposal by Heinrich Hertz we arrive via quantification of energy-momentum at the equations of motion and the action functional. Finally we present a relativistic revision of energy, momentum and inertial mass. The goal is not primarily to change or improve the mathematical structure of mechanics, but to gain a deeper physical understanding of mechanics like Einstein with his gedanken experiments on relativistic kinematics. Starting from undisputed measurement operations and natural principles the mathematical formalism is only created and thus shown in a new light. This work is in the same context as current efforts to the "foundation of quantum mechanics", just with respect to the interpretation of the classical and relativistic calculuses.