The Evolution from the Law of Gravitation to General Relativity

Albert Einstein’s field equation lies at the core of general relativity. However, it did not emerge solely from thought experiments; rather, it represents the culmination of scientific advancements across multiple fields, shaped by the contributions of many great thinkers. By tracing the progression from Newton’s law of gravitation, we can gain valuable insight into how Einstein formulated the field equation. This historical perspective not only deepens our understanding of the underlying physics but also enhances our appreciation of the groundbreaking contributions made by both Newton and Einstein. This article begins by exploring Newton’s discovery of the law of universal gravitation. Inspired by this groundbreaking work, Coulomb and his contemporaries formulated a corresponding law describing the electrostatic force between electric charges. Both Newton’s law and Coulomb’s law express the force between interacting bodies as inversely proportional to the square of the distance separating them. Building on these foundational principles, mathematicians developed Gauss’s law of field flux, which later became a cornerstone of Maxwell’s equations in electromagnetism. Further abstraction of these force fields led to Poisson’s Equation, which relates potential fields to the density of the matter that generates them. Ultimately, Einstein’s field equation can be viewed as a profound generalization of Poisson’s equation.