**Ask a monkey a physics question thread**

[MadMojoMonkey]

It's not easy finding something reliable on this topic. Those posts are cropped from a discussion asking what the physical significance of the Planck constant is.

I feel like in the latter parts of this post, you've conflated the Planck constant and the Planck length as the same thing.

I agree that there's a lot of misinformation about the significance of the Planck Length. Also, there's a lot of misinformation about the nature of quantum mechanics out there. Sifting through the nonsense to find a single, consistent model isn't easy if the internet is your primary source.

Is he being accurate when he claims that angular momentum is quantised?

100% yes

The quantization of angular momentum is a rather big deal, as it is part of the explanation for why electrons refuse to jump to certain energy levels in atoms. In order to jump, they must absorb or emit a photon, which has angular momentum. This means a electron in a bound system cannot jump to an energy level unless the difference in angular momentum between its start and end differ by exactly the same angular momentum as the photon emitted or absorbed.

All photons have the same angular momentum, and this does not change as they travel through expanding spacetime.

and it's amazing that the law of conservation of angular momentum remains perfectly un-violated in all known, verifiable experiments and observations.

And is he being accurate when he claims that a Planck constant of zero turns a quantum theory into a classical theory?

In this one specific example, yes. But more broadly, no.

If h = 0, then photons have no energy. That's not a classical theory.

Because if those two claims are indeed accurate, then that's pretty solid evidence that we're talking about a constant of nature, not a simple length.

Here, I'm starting to question if you have the Planck constant and the Planck length mixed up.

Whether the larger or smaller Planck Length is considered fundamental, it's a constant of nature either way.
Both are constants of nature, regardless of where they fit into our model.

I think it's easy to get caught up in the "length" aspect of it, in the same way people talk of the speed of light where actually it's not about light, it's about causality. The speed of light emerges from the speed of causality. Likewise, the Planck length emerges from quantum mechanics.

It emerges from a combination of QM and GR. Newton's big-G is in the calculation of the Planck Length, which was absorbed by Einstein's Relativity.

There are many places where QM and GR work well together, but not all. Some of the places they don't work together are so problematic as to motivate many many brilliant physicists to explore strings.

It's not clear if the Planck Length is an appropriate combination of QM and GR, except in that it puts a lower bound on length scales at which our model can no longer produce predictions of the outcomes of experiments. I.e. it don't work there.

If I were to guess which Planck length is "correct", I'd say h-bar because it's smaller, and if we can have a "smaller" length than the smallest length, there's a problem with the entire argument right there. If h is right, then h-bar is meaningless, but the math holds up under theoretical scrutiny as best I'm aware, otherwise they wouldn't use h-bar because the theories would break at these "smaller than h" scales.

But I'm speculating hard here. I don't know the significance of the Planck units. It just seems apparent that there is a major significance there.

Both h and h_bar are meaningful. Which is easiest to use depends on the exact equation you're solving.

Kinda like pi and tau are both equally good, and which is easier to work with depends on what equation you're solving. With pi and tau, what's in question is whether the radius or the diameter of a circle is a better descriptor of a circle. But it's a moot point because both radius and diameter encode the exact same information about the circle.

Pi is used for historical reasons. Ancient people could measure the diameter of a circle and they could measure the circumference. The easy measurability of these made pi the obvious choice for them. circumference / diameter = pi.

Nowadays, mathematicians prefer to describe circles by their radius. Circumference / radius = tau

Which you use is irrelevant. They encode the exact same information about the circle.


Whether or not there is meaning in any Planck units depends on how humans can interpret them. It's not guaranteed that there is meaning in any of them, since they are produced by asking the question, "Can I combine these numbers with gobbledygook units in such a way that I get a number with only 1 unit?" The Buckingham Pi method says, "Yes, you can do that as long as you have enough gobbledygook."

The test of whether those units are meaningful is whether we can reproduce that number using the axioms of the model.