What is the Planck Constant?

Recently, the Planck constant was mentioned in the news due to an agreement to change the definition of the kilogram.  Rather than returning to the reference kilogram mass, the kilogram is now to be determined based on the value of the Planck constant, which is now a defined value in the same way as the speed of light is a defined value.

The question that is a little difficult to find the answer to in all the new reports is “what precisely is the Planck constant?”  Of course you could go and ask Google, but when you’re reading an article, you sort of want all your answers in one place.

I did see one article which tried to address the question, with the following:

The Planck constant is the amount of energy released in light when electrons in atoms jump around from one energy level to another, explained physicist Tim Bedding of Sydney University.

Well, yes, sort of.  I am pretty sure that this is a journalist error rather than a physicist error.

The Planck constant (h) can be used to work out the energy of a photon, when we know its wavelength or its frequency: E=h.f=h/λ.  But that’s not all.  The Planck constant is often used as part of a sort of exchange rate, allowing you to convert from everyday units like seconds, metres and kilograms into quantum level units: Planck units like Planck time, Planck length and Planck mass.

A particularly useful thing about using natural units, like Planck units, is that fundamental constants resolve down to unity, that is, they equal 1.  For example, using Planck units:

•         Speed of light, c = 1
•         Gravitational constant, G=1
•         Coulomb constant, k_e=1
•         Boltzmann constant, k_B=1

As it is, the Planck constant itself is not a fundamental constant that resolves to unity, but the reduced Planck constant is and does – meaning that the value of the Planck constant in Planck units is 2π, so the reduced Planck constant is ħ=h/2π.  There are two other key constants, the permittivity and permeability of free space, or the electric constant and the magnetic constant, ε₀ and μ₀, which don’t quite resolve down to 1 either, but these resolve down to ε₀=1/4π and μ₀=4π, so you could have a raised permittivity and a reduced permeability of ε₀-bar=1 and μ₀-bar=1.

In an earlier article, I wrote about how it is possible to resolve even the fine-structure constant and the gravitational coupling constant (which are both dimensionless) to 1.

None of this would be possible without the Planck constant, so the added role of defining the kilogram should not be too much for it to bear.

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I thought I might add here that for many purposes in physics what matters more is angular frequency rather than just frequency per se.  That is to say its not just how many whatevers per unit of time, but how many rotations per unit of time.  A full rotation is 2π radians so the relationship between vanilla frequency (f) and angular frequency (ω) is ω=2π.f which means that there is another equation for the energy of a photon, E=(h/2π).ω=ħ.ω.  There is an argument that the unreduced Planck constant is only used for historical reasons and that the reduced Planck constant is that one that we should be using primarily.

I'll go into this a bit more in a later article.