Yesterday’s equation was the first real result of quantum theory, Max Planck’s formula for the black-body spectrum. Planck never really liked the quantum basis of it, though, and preferred to think of it as just a calculational trick. It wasn’t until 1905 that anybody took the idea really seriously, leading to today’s equation:
From the year, you can probably guess the guy responsible: Albert Einstein. Einstein realized that if you took Planck’s idea and ran with it, you could explain the photoelectric effect very neatly. Where Planck had viewed the quantized radiation as a fictitious property of the black-body emitting light, Einstein applied it to the light itself. Light was not a continuous wave, but a stream of “light quanta” (now called “photons”), little particles of light, each carrying an amount of energy equal to Planck’s constant (h) multiplied by the frequency of the light (represented by a Greek letter nu (ν), for what reason I can’t say). You can also write this has Planck’s constant times the speed of light divided by the wavelength of the light, which is more convenient in some circumstances.
So, why is this important?
Well, why isn’t it important? It was arguably the most revolutionary thing Einstein did in his career (Pais quotes Einstein calling it the only really revolutionary thing he did; relativity can be seen as simply putting existing physics on a more solid theoretical and philosophical foundation), and it was the one accomplishment specifically mentioned in his Nobel Prize citation, awarded “for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect.”
This is the step that puts the “quantum” in “quantum mechanics,” telling us that energy comes in discrete chunks, not a continuous range of values. It’s the theoretical explanation for the photoelectric effect, which in turn is the basis for all manner of light sensors– basically anything that converts a light signal into an electrical signal.
The discrete photon energy, when combined with Einstein’s relativity, also implies that photons carry momentum. This, in turn, has a number of technological applications: the scattering force that arises from atoms absorbing photons of light is the basis for laser cooling, which serves as the starting point for all manner of experiments investigating ultra-cold matter, including ultra-precise atomic clocks. At a much higher energy density, radiation pressure from light scattering plays a major role in making a hydrogen bomb work, and is used in laser-ignited fusion experiments as well.
And speaking of lasers, the operating principle of a laser is most easily understood using photons. And lasers are everywhere these days– you wouldn’t be able to read this without the telecom lasers that carry the Internet over fiber-optic transmission lines. And while most laser technologies involve huge numbers of coherent photons, laser technology also makes it possible to make single-photon sources, and sources of entangled pairs of photons, which can be used to do quantum teleportation and quantum cryptography, and maybe someday form the backbone of a “quantum internet” carrying quantum information between quantum computers (and, presumably, quantum spam from quantum scammers in quantum Nigeria).
So, take a moment today to appreciate Einstein’s most revolutionary contribution to physics. And come back tomorrow for the next revolutionary development as we continue our countdown to Newton’s birthday.