2

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.

Qmechanic
  • 201,751
Alan Gee
  • 245
  • 5
    Possible duplicate of Why do universal constants have the values they do? – David Hammen Aug 14 '16 at 11:25
  • 2
    Some countries still use English units. In such a system, with mass in pounds mass, force in pounds force, and acceleration in feet/second$^2$, Newton's second law becomes $F=kma$ as opposed to $F=ma$. Your question is exactly the same as asking about the physical significance of the $k$ in $F=kma$. There is none. That $k$ has to exist in English units simply means that English units are a bit goofy. The exact same reasoning applies to $h$, $c$, and $G$ in SI units. Those constants are just conversion factors. – David Hammen Aug 14 '16 at 12:05
  • Energy travels around the universe in discrete units, I just want to know if anyone has discovered why these discrete chunks are the size that they are. Forget Planck if you like. – Alan Gee Aug 14 '16 at 12:16
  • 1
    @AlanGee: Energy is not quantized, as far as we know. You can have any amount of it that you like. – CuriousOne Aug 14 '16 at 12:17
  • In the same way as $c$, $h$ is not at all a mere conversion factor. One instructive example is the use of $ ħ$ within the solutions of Schrödinger equation. $e^{i ħ}$ is describing a helix with the radius $ħ$. In this sense, $h$ is describing the size of the components our world is made of. I recommend to reformulate the question such that everybody understands. – Moonraker Aug 14 '16 at 12:47
  • @AlanGee I am sorry that I had vote to close your question, but it - in its original form - was really a duplicate which was already answered very well in the dupe. My suggestions: 1) Accept CuriousOne's answer if you find it acceptable to the original question, and 2) Make a new question about which this time already contains the more wide details. As little effect I can make with my votes, I will try to help you in that. – peterh Aug 14 '16 at 12:52

1 Answers1

0

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.

CuriousOne
  • 16,318
  • please see my update. – Alan Gee Aug 14 '16 at 11:34
  • 1
    @AlanGee: What's special about the kg prototype in Paris? It's a chunk of metal that some folks in the late 19th century declared to be the unit of mass in one system of physical units. The only reason why you think that there is something special about the scale of the hydrogen atom is because you aren't living on it. You can ask a more meaningful question about why some forces are strong and others are weak, because those ratios are not impacted by the choice of units. – CuriousOne Aug 14 '16 at 11:39
  • 1
    If that Kg prototype could only be broken into bits of a certain size, I would be curious as to why that size happened to be what it was. – Alan Gee Aug 14 '16 at 11:42
  • @AlanGee: Because some people chose 1kg as the base unit about 200+ years ago. Why did they do that? Because 1l of water is a pretty good thing to have, as a human. If we were the size of mice, we would probably have chosen a ml of water and 1g as the base unit and something 1cm or an inch for distances and maybe a fraction of a second for time, which would have changed the size of MousePlanck's constant by a couple orders of magnitude. You are still comparing the wrong things against each other. Ask why gravity is weak compared to electromagnetism and you got yourself a question. – CuriousOne Aug 14 '16 at 11:48
  • 1
    I have already made it clear that I understand the arbitrary nature of universal constants. What I am trying to understand is why the discrete energy bands in an atom have the separation units that they have. – Alan Gee Aug 14 '16 at 11:53
  • @AlanGee: Because of the mass and charge of the electron and proton (and with that of the other nuclei). Where do they come from? Nobody knows, but that is not connected to the size of Planck's constant in SI units. – CuriousOne Aug 14 '16 at 12:00