An Ahistorical Approach to Elementary Physics

TL;DR

This paper proposes a modern, wave-based perspective on elementary physics, replacing traditional concepts like energy and momentum with wave parameters, thereby unifying classical mechanics through spacetime wave phenomena.

Contribution

It introduces a wave-centric framework that simplifies and unifies classical mechanics, replacing archaic concepts with modern wave parameters and spacetime invariants.

Findings

Classical mechanics can be derived from wave phenomena in spacetime.

Energy, momentum, and action correspond to wave parameters.

Mass emerges as a real-space effect of reciprocal-space invariants.

Abstract

A goal of physics is to understand the greatest possible breadth of natural phenomena in terms of the most economical set of basic concepts. However, as the understanding of physics has developed historically, its pedagogy and language have not kept pace. This gap handicaps the student and the practitioner, making it harder to learn and apply ideas that are `well understood', and doubtless making it more difficult to see past those ideas to new discoveries. Energy, momentum, and action are archaic concepts representing an unnecessary level of abstraction. Viewed from a modern perspective, these quantities correspond to wave parameters, namely temporal frequency, spatial frequency, and phase, respectively. The main results of classical mechanics can be concisely reproduced by considering waves in the spacetime defined by special relativity. This approach unifies kinematics and dynamics, and introduces inertial mass not via a definition, but rather as the real-space effect of a reciprocal-space invariant.