Maxwell's equations unify light by demonstrating that light is a form of
electromagnetic wave that travels at a specific, constant speed through a vacuum, which matches the experimentally measured speed of light.
This unification stems from two key mathematical insights:
- Self-Sustaining Fields: Maxwell's crucial addition of the "displacement current" term to Ampère's Law revealed a symmetry in nature: a changing electric field generates a magnetic field, and, conversely, a changing magnetic field (described by Faraday's Law) generates an electric field. This dynamic interplay allows electric and magnetic fields to sustain each other, creating a self-propagating wave that does not require a medium to travel.
- Speed Calculation: When Maxwell combined the equations and derived a single wave equation for this propagating electromagnetic disturbance, the predicted speed of the wave was determined solely by fundamental electric and magnetic constants (the permittivity and permeability of free space). When he calculated this speed using the best available experimental values, the result was almost exactly the known speed of light.
This inescapable mathematical conclusion led Maxwell to propose that visible light is simply one small part of a vast
electromagnetic spectrum of these waves, differing only in wavelength and frequency. This work unified the previously separate fields of electricity, magnetism, and optics into a single, comprehensive theoretical framework.