My feeling is that this post is mixing up cause and effect. There are plenty of non-commuting operators that not easily described as "The end result of this time evolution rule is that blobs of particle-presence appear to race around in physical space.", such as Sx and Sy, the different components of spin. On the other hand, different components of the momentum operator commute. I cannot see how you can hand-wave the difference from the fuzzy picture presented in this post.
Indeed, as most QM students learn, the uncertainty relation comes from the quantum equivalents of the Poisson bracket, so one can probably intuit the quantum results from the classical cases, contrary to what the post posits.
First off, your 'The end result' quote does not appear on this page, so the inaccuracy of that statement doesn't really seem to me a defect of the page.
But backing up, I do not see how cause and effect are mixed up - the relationship between position and momentum is the Fourier transform, as the post says, and that is why they have a nonzero Poisson bracket, and that is why they don't commute. Yes, it only speaks of the position-momentum case, and it doesn't consider more than one dimension, and it leaves out a highly technical middle step. At this level of discussion, I seriously doubt that going further is fruitful. This gets across an important point. That there is way more that could be said does not weaken it in the least.
And... 'plenty'? You gave the spin operators as an example. What's another? Energy-time, if you're working in QFT and you measure some spacetime region selected out by some other operator, against a timelike-oriented tensor... and in that case, a very similar Fourier transform reasoning applies.
At this level of discussion, I seriously doubt that going further is fruitful. This gets across an important point.
Unfortunately, it also gives an illusion of understanding, since it does not explain that this is only one example out of many (why do different components of momentum commute, but different components of angular momentum do not?). As for the Fourier transform, arguably this can be presented as a result of position and momentum being conjugate variables/canonical coordinates. Speaking of which, any pair of classical canonical variables probably translates into a version of uncertainty relation, even such unusual ones as action/angle, fluxes of electric and magnetic fields, etc.
Good catch on angle/angular momentum. Obvious now that you point it out.
"Illusion of understanding" - I don't see what's so illusory about understanding one case - the most commonly met case, the one people hear about and get confused by.
If one has looked into quantum mechanics enough to know about the other cases, and understands the position/momentum connection, but can't figure out the nature of the relationship of these other cases... such a person is sufficiently black-swan-ish that I don't believe failure to account for em when writing the sequence was really a deficiency.
"Illusion of understanding" - I don't see what's so illusory about understanding one case - the most commonly met case, the one people hear about and get confused by.
What I mean is that the position-momentum case is explained so well and so convincingly by EY (took me quite a bit of thinking to convince myself that the other examples are not covered by his explanation), that an uninitiated reader gets an illusion of understanding the general principle, not just this one specific case. And a misled disciple is the worst kind.
What would fix it for you? A brief disclamer, "This is a sample for the most common case of the HUP; related but non-identical processes apply to other cases."??
But as an aside -
How is the angle/action case not meaningfully connected to the momentum/position case, such that really getting one doesn't hands you the other one on a silver platter? After all, momentum/position is the special case of angle/action where the origin of rotation is placed at infinity (at least, classically - you can't make angular momentum eigenstates without enveloping the origin of rotation).
I doubt that a disclaimer would dissuade an aspired non-expert reader from proudly proclaiming her deep understanding of the uncertainty principle and looking down at those who cannot see the proverbial forest for the (QM math) trees.
The only honest position, in my opinion, is to expressly declare that the whole QM sequence is pop-science, not real science, and, while an engaging read, has no meaningful connection to the rest of the sequences.
As for angle/action vs momentum/position vs components of spin, they all are rather different beasts, originally corresponding to different spacetime symmetries to begin with, so I would not feel comfortable trying to salvage a flawed explanation by stretching an analogy.
(taking this in reverse order)
The separate symmetries that underly linear momentum and angular momentum themselves have a deep connection.
Components of spin are definitely a separate issue. I did not (mean to?) imply that it was the same thing.
The only honest position, in my opinion, is to expressly declare that the whole QM sequence is pop-science, not real science...
If by this you mean, "This is the general idea. If you don't push too hard on it, it will serve you well, but a lot has been left out, so don't go extending the arguments too far, because you could easily reach a point where yet more of your fundamental assumptions are wrong." Then yes, that would be a good thing to have put back in "Quantum Explanations", and maybe repeated at the top of each page.
If you mean, "This is basically bullshit", well, no.
... and, while an engaging read, has no meaningful connection to the rest of the sequences.
It connects directly to zombies and addresses anti-realist positions. Both of these are well within the 'solid' portions of the sequence. It also connects to the nature of probability, which is a core issue for Bayesian inference of real situations (as opposed to general theories).
I doubt that a disclaimer would dissuade an aspired non-expert reader from proudly proclaiming her deep understanding of the uncertainty principle and looking down at those who cannot see the proverbial forest for the (QM math) trees.
I'm having a hard time coming up with an objectionable statement that reading this (this article in particular) would produce in someone who read it at all carefully. This article hit the main point on the head, which is that the HUP is totally consistent with physical realism. It gave a correct account of the HUP for position and momentum, and showed exactly where it was skipping the work.
Someone who doesn't understand Fourier already isn't going to read this explicit 'here be technicals I'm not covering' and think 'Aha! I know it all!" unless they're the kind of person who's basically out to do what you're describing anyway, in which case this hasn't made matters any worse.
"This is the general idea. If you don't push too hard on it, it will serve you well, but a lot has been left out, so don't go extending the arguments too far, because you could easily reach a point where yet more of your fundamental assumptions are wrong."
Basically, yes. This is what pop-sci means to me: providing some understanding of the concepts, without the ability to calculate anything of value.
It connects directly to zombies and addresses anti-realist positions... It also connects to the nature of probability
Are you saying that in a fully classical universe, with a random number generator instead of QM, p-zombies are OK and Bayes is invalid? If yes, feel free to explain, if no, you don't need this sequence.
This article hit the main point on the head, which is that the HUP is totally consistent with physical realism. It gave a correct account of the HUP for position and momentum, and showed exactly where it was skipping the work.
Having looked through it again, I suppose I agree with that. I just wish it gave explicit examples of what was left out.
Today's post, The So-Called Heisenberg Uncertainty Principle was originally published on 23 April 2008. A summary (taken from the LW wiki):
Unlike classical physics, in quantum physics it is not possible to separate out a particle's "position" from its "momentum". The evolution of the amplitude distribution over time, involves things like taking the second derivative in space and multiplying by i to get the first derivative in time. The end result of this time evolution rule is that blobs of particle-presence appear to race around in physical space. The notion of "an exact particular momentum" or "an exact particular position" is not something that can physically happen, it is a tool for analyzing amplitude distributions by taking them apart into a sum of simpler waves. This uses the assumption and fact of linearity: the evolution of the whole wavefunction seems to always be the additive sum of the evolution of its pieces. Using this tool, we can see that if you take apart the same distribution into a sum of positions and a sum of momenta, they cannot both be sharply concentrated at the same time. When you "observe" a particle's position, that is, decohere its positional distribution by making it interact with a sensor, you take its wave packet apart into two pieces; then the two pieces evolve differently. The Heisenberg Principle definitely does not say that knowing about the particle, or consciously seeing it, will make the universe behave differently.
Discuss the post here (rather than in the comments to the original post).
This post is part of the Rerunning the Sequences series, where we'll be going through Eliezer Yudkowsky's old posts in order so that people who are interested can (re-)read and discuss them. The previous post was Decoherence, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.
Sequence reruns are a community-driven effort. You can participate by re-reading the sequence post, discussing it here, posting the next day's sequence reruns post, or summarizing forthcoming articles on the wiki. Go here for more details, or to have meta discussions about the Rerunning the Sequences series.