And then you have the Planck units, defined through the Planck constant.
I'm ready to (partially) finish that blogpost now.
At a very small scale, things don't have much energy, which makes sense, as they typically have little mass. Take a photon, for instance. It's a particle that came about through a debate on whether light was a wave or a particle. Turns out it's both, oddly enough. And its energy can be calculated with this formula:
E = hf
where E is the energy, f is the frequency of the photon, and h is the Planck constant, or about 6.63x10-34 Js.
h
Planck stumbled across the constant when formulating a different law, relating to the distribution of radiation of a black body, which states that energy is distributed in quanta, or small packets of particles. The problem he found with black bodies were that they absorbed all energy but didn't emit it equally, and his work ended up with him breaking physics and starting quantum theory. And, almost hidden amongst the other letters in the equation he derived when working on the problem, is h.
Planck's work was built upon by Albert Einstein, who came up with the photoelectric effect in his miracle year of 1905 - essentially, electrons would only be emitted from a metal by light under certain frequencies, greater than the threshold frequency, f0. Many physicists assumed it was the intensity of light that influenced this emission, but experimental research proves this isn't the case. This was one of the first instances of photons being defined - they're the quanta which light would use to carry energy - and so h comes up again. In fact, h is the smallest quantum of energy available in a photon, which somewhat makes sense - the earlier equation shows its energy is proportional to its frequency.
I suppose the main question is why is h so small? It's not the smallest constant we know of - the cosmological constant is eighteen magnitudes smaller - and indeed it's hard to understand how we got to this position, aside from the fact you can calculate h through experiments. The fact it's so mysterious as well as being ridiculously small makes h quite beautiful in my opinion - it's some random decimal (to most people) that just so happens to help dictate how light functions.
That's not even mentioning how it's now the principal way to define the kilogram. Instead of using a mass that was said to be 1kg, now you can use h as it's already defined in SI units as kg m s-1, with greater precision too.
ħ
The reduced Planck constant is h/2π, or about 1.05x10-34 Js, and is represented as ħ. This version of h defines it in terms of radians instead of hertz, and is used in relation to quanta in angular momentum. It only really came about because it was far more intuitive to discuss angular momentum with radians, so physicists always wrote down h/2π, until ħ caught on - 2π rad is equal to one wave cycle.
It also appears in Heisenberg's Uncertainty Principle, this time divided by 2, but that's beyond the scope of this blogpost (simply put, you can't know an electron's momentum and position simultaneously without loss of accuracy in either to a point).
I could go on to discuss the Planck length and Planck time, amongst other constants, but I'd rather touch upon them in a different blogpost, because they're quite different from h and bear no similarity to it. Either way, I may just go on to write about them - quantum physics is certainly quite fascinating.
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