Thursday, September 7, 2017

quantum mechanics - Do we have any idea why Planck's constant has the value it has?



Since $h$ seems to relate to a fundamental unit of quantization, it only seems right that we should have an idea of why it has the value it has. What do we know?


I understand that to some extent the precise values of universal constants are arbitrary, but when I look at the Bohr model, I see that the angular momentum of electrons comes in discrete levels that appear to be directly proportional to Planck's constant. Which suggests to me that there is something special about this number.



Answer




It has the value that it has because of our choices of the base units for length, time and mass. We can easily make Planck's constant equal to one by choosing different base units. What this tells us is simply that one of the important scales of the universe is not the size of a human but the size of a hydrogen atom. Why humans are so large compared to hydrogen, that is a question that belongs into biochemistry and biology.


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