Light and waves
1865
Light is electromagnetism
James Clerk Maxwell
What is light, actually?
Maxwell wrote electricity and magnetism as one set of equations. They predicted waves of electric and magnetic field travelling at a speed he could calculate from lab measurements. It matched the speed of light. Light was an electromagnetic wave.
- Flow out through the edge ∮F·n ds
- -1.06e-5
- Sources added up inside ∬div F dA
- 0
- Agree?
- ✓ Yes, as the theorem promises
Draw any closed loop. Arrows on the edge show flow leaving (green) or entering (pink). Inside, green dots are sources and pink dots are sinks. What flows out through the edge always equals what is created inside: the divergence theorem in two dimensions.
How they figured it out
Michael Faraday imagined invisible lines of force filling space, but he had little mathematics. James Clerk Maxwell took Faraday’s picture seriously, and in 1861 built a strange mechanical model of space: tiny spinning vortices separated by “idle wheels”, like ball bearings.
From that model he calculated how fast a wave would travel through it: about 310,700 km/s, using electrical measurements made in a lab. The measured speed of light was about 315,000 km/s. Maxwell wrote that “we can scarcely avoid the inference that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena”. Later he threw the wheels away and kept the equations.
The equation
The speed of light follows from two numbers measured with magnets and electric charges.
See it in real life
Measure the speed of light with chocolate
Take the turntable out of a microwave, put in a plate of chocolate and heat it briefly. Melted spots appear about 6 cm apart: half a wavelength. Multiply the wavelength (12 cm) by the frequency printed on the back (2.45 GHz) and you get about 300,000 km/s.
Where engineers use it
Everything wireless
Antennas, Wi-Fi, mobile networks and radar are designed with Maxwell’s equations.
Motors and transformers
Changing magnetic fields making currents is how every motor and transformer works.
Worked example: The speed of light from the lab
- ,
- m/s.
Where it came from
- The invention of calculus 1665–1684
Built on
Maxwell’s equations are calculus applied to fields filling space.
- Stokes’ theorem 1850–1854
Built on
Maxwell sat the exam with Stokes’ question; his equations switch between edge and inside forms using Stokes’ theorem.
- The divergence theorem 1813–1826
Built on
Gauss’s law for electric charge, one of Maxwell’s four equations, is the divergence theorem.
What it led to
- The experiment that found nothing 1887
Led to
If light is a wave, what is waving? Michelson and Morley tested for the ether and found nothing.
- Special relativity 1905
Built on
Einstein’s 1905 paper begins with Maxwell’s theory: light’s speed is the same for everyone.
- Hearing black holes merge 14 September 2015
Analogy only
Gravitational waves travel at the speed of light, like Maxwell’s light waves.
Where the comparison stops: Light is a wave in electric and magnetic fields. Gravitational waves stretch space itself, and are far, far weaker.