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.
I love (hate?) the idea of quantum spam, but it really seems unlikely thanks to the No Cloning theorem!
Spam is obviously quantized. have you ever seen only 1/2 can of spam?
One thing that never seemed clear to me was the at the time strange assumption that it was the light that was coming in discrete chunks. My understanding of the photoelectric effect is that it could be explained just as well with a classical field with the assumption that it is simply the absorption and radiative processes that occur discretely. In this way, the photoelectric effect is not without semi-classical loopholes. What made Einstein say it was the light not the oscillators in the material that were quantized in the photoelectric effect?
Chris @3: The key point is that the photoelectric effect has a threshold. Light whose wavelength is a certain length *or shorter* can produce photoelectrons in a given metal. Light whose wavelength exceeds this maximum value does not produce photoelectrons. The threshold value, we now know, corresponds to the amount of energy needed to extract an electron from the metal. So the idea that light comes in packets with a discrete amount of energy which is inversely proportional to its wavelength is not so strange once Planck introduced the idea. At least, it's no stranger than your idea that the absorption/radiation processes are what is discretized (and I suspect that if you tried to create a formal theory based on this hypothesis, it would at best be mathematically equivalent to assuming light is discretized).
The link to an old post in #5 is the best explanation of the situation, but for those too lazy or busy to click through: It's perfectly true that you can explain the photoelectric effect without describing light in terms of photons-- this was worked out in detail in the 60's-- and for this reason, the existence of photons remained somewhat debatable until 1977. Einstein's explanation of the photoelectric effect with photons is simpler to understand, though, and since 1977, there have been numerous experiments demonstrating unambiguously that photons are real, so there's no reason not to use the photon model.
Thanks for the link. It looks like it was produced on a typewriter! I am glad to live in a time when LaTeX and other typesetting programs exist. It is also interesting that Dr. Lamb is one of the primary authors of the paper considering he won the nobel a full decade earlier for using QED to predict the energy shift that now bears his name.
The only reason why I asked is because I am a physics undergraduate in the process of completing my senior project. It has to do with theoretical quantum optics and during my final presentation I fully expect to be doggedly questioned about historical and current evidence for a quantized electromagnetic field by the reviewers.