Talk:Quantum mechanics

Quantum Relativity

I have just published a new theory I call Quantum Relativity on Wiki. You may wish to review my new theory in order to gain deeper insight into the topic. Feedback left at the Quantum Relativity discussion is also appreciated. Michael Stahl 12 September 2011 02:03, 12 September 2011 (UTC) — Preceding unsigned comment added by Michael.stahl (talk • contribs)

The lead is a mess

The lead is a disorganized mess, likely to put anyone off who tries to read this article. It was much better in an earlier version. I propose going back to that version (for the lead, not the whole article) and building on it. RockMagnetist (talk) 00:01, 30 November 2011 (UTC)

I contributed to that lede, so I figured that if I put your suggestion into play, then other editors could do their part by adding the deleted paragraphs into the body of the article. Thanks for your suggestion. --Ancheta Wis (talk) 00:37, 30 November 2011 (UTC)

I'm glad that someone who contributed to the lede is willing to do this. RockMagnetist (talk) 00:43, 30 November 2011 (UTC)

Suggestions for body

There is a discussion going on at WikiProject Physics and a deletion discussion for Basic concepts of quantum mechanics about how many articles should be devoted to quantum mechanics at different levels of explanation. In my opinion, multiple articles would not be needed if this one did its job better. The editors of this article should read Make technical articles understandable, particularly this rule of thumb: "Put the most understandable parts of the article up front". Then look at the first three sections of this article: 1. History 2. Mathematical formulations 3.Interactions with other scientific theories. Is this what readers are most interested in? Hardly.

Here are some of the subjects that ought to be prominently featured near the front:

• the uncertainty principle
• wave-particle duality
• the Pauli exclusion principle
• some interesting experiments like the photoelectric effect and the Stern-Gerlach experiment.

Do this, and there will be less call for simpler articles. RockMagnetist (talk) 01:06, 30 November 2011 (UTC)

The history section can still lead off the article, but it should look much more like Basic concepts of quantum mechanics, with concrete examples like hydrogen spectra. RockMagnetist (talk) 01:18, 30 November 2011 (UTC)

I basically have a problem with 'in your face' formulations of QM. The 4 topics listed above can be derived logically from the right set of basics, just as Newtonian mechanics can be derived logically from point masses, ordinary geometry and the laws of force. Otherwise, the 4 topics are just random items which are not derivable from Newton's POV, but basically reduce down to prejudices: "Do you know A? You don't? Aha, gotcha ...". It is much more helpful to state the basic framework of the physics, and to then derive the topics as consequences. This is more useful to students, than lists of facts, for example. I admit that it is easier for an article to consist of lists of facts bagged under a name.

• the uncertainty principle is derivable from systems with dual descriptions.
• wave-particle duality was historically meaningful in the evolution of viewpoints from Newton, Young, Einstein, ... The thing is for physicists to be trained to be able to switch viewpoints, to get to a better representation, as needed.
• Pauli exclusion principle, like many other 'principles' has got to be a theorem, a consequence of more basic ideas. That doesn't mean denigrate the principles, but elevate or tag them so that the hidden assumptions are exposable in the future.
• photoelectric effect, etc. again are consequences. The issue there is experimental: what theory was just shown to be deficient by the experimental result?

--Ancheta Wis (talk) 04:30, 30 November 2011 (UTC)

Your preferred approach might be appropriate for a full-semester course on quantum mechanics, as long as the students are mathematically strong. But you can't expect to "train" students with an encyclopedia article. Anyway, even serious students usually take a series of increasingly deep courses on quantum mechanics.

I don't think the approach I suggest needs to be a "gotcha" approach. Look at the way Feynman does it in volume 3 of his lectures. In chapter 1 he describes a few experiments, then some basic laws of superposition and, yes, the uncertainty principle. Before he mentions the Hamiltonian, he develops the physics of bosons and fermions (and therefore the exclusion principle); emission and absorption of photons; the blackbody spectrum; and even liquid helium! In this article, the exclusion principle isn't even mentioned. RockMagnetist (talk) 05:20, 30 November 2011 (UTC)

And Feynman asserts that the double-slit experiment has all the elements of QM, so yes, I would have no problem with that experiment as the basis, with the other gotchas as 'Oh by the way', if you are trying to grab the reader's attention. But then there needs to be a statement of a QM framework, with Ehrenfest's theorem (the idea of gigantic averages) to show how some abstract QM framework (for example Heisenberg picture) connects with macroscopic people who live in spacetime and who use lasers, magnets, and other technology to connect with the microscopic world. --Ancheta Wis (talk) 12:18, 30 November 2011 (UTC)

Certainly the framework should be there too - just later in the article. RockMagnetist (talk) 16:24, 30 November 2011 (UTC)

"Mathematical formulations" section badly needs rewriting

The first paragraph of the Mathematical formulations section is as follows:

"In the mathematically rigorous formulation of quantum mechanics developed by Paul Dirac[9] and John von Neumann,[10] the possible states of a quantum mechanical system are represented by unit vectors (called "state vectors"). Formally, these reside in a complex separable Hilbert space (variously called the "state space" or the "associated Hilbert space" of the system) well defined up to a complex number of norm 1 (the phase factor). In other words, the possible states are points in the projective space of a Hilbert space, usually called the complex projective space. The exact nature of this Hilbert space is dependent on the system; for example, the state space for position and momentum states is the space of square-integrable functions, while the state space for the spin of a single proton is just the product of two complex planes. Each observable is represented by a maximally Hermitian (precisely: by a self-adjoint) linear operator acting on the state space. Each eigenstate of an observable corresponds to an eigenvector of the operator, and the associated eigenvalue corresponds to the value of the observable in that eigenstate. If the operator's spectrum is discrete, the observable can only attain those discrete eigenvalues."

This needs rewriting in so many ways.

First of all "defined up to a complex number of norm one" is meaningless unless the arithmetic operation is specified. Presumably this is multiplication.

But then, the quotient of a vector space V (over the complex numbers) by the equivalence relation that v ~ cv where c is a complex number of absolute value 1 is not "projective space". (The projective space P(V) of a vector space over a field F is the quotient space of V^* by the equivalence relation v ~ cv, where v is any member of V^* and c is any nonzero element of F. Here V^* denotes all the nonzero vectors of V.)

Third, how about a hint as to why "the state space for position and momentum states is the space of square-integrable functions" ? (On what are they square-integrable?) Also: Does this mean the state space for the position states -- and the state space for the momentum states -- are each the space of square-integrable functions? Or is this a reference to the state space for combined position-and-momentum states?

Next, "the state space for the spin of a single proton is just the product of two complex planes" certainly doesn't appear to be defined "up to [multiplication or any other arithmetic operation by] a complex number" (of norm one or otherwise).

While "observable" has an intuitive meaning -- so perhaps it need not be defined rigorously -- the concept of an "eigenstate" of an observable has no such intuitive meaning without further explanation. So that just stating here that "Each eigenstate of an observable corresponds to an eigenvector of the operator" has no mathematical meaning. The article may as well read that "every mxyzptlk corresponds to an eigenvector" of that operator. Not. Helpful. (Or is the entire content of this statement that "eigenstate" is another word for an eigenvector of this operator?)Daqu (talk) 17:17, 25 December 2011 (UTC)

Daqu (talk) 17:17, 25 December 2011 (UTC)

Most accurate?

Not any more! See the article by Penrose that says that quantum field theory has been tested to one part in 10¹¹ while an aspect of General Relativity has been tested to one part in 10¹⁴! — Preceding unsigned comment added by RockMagnetist (talk • contribs) at 17:18, 15 January 2012

Understandable?

This is one of the most un-understandable English texts in the world! Unless you have a degree in physics and English , you won't understand this article.We need an expert to rewrite it or at least the lead in a way that is understandable to more people. Arminale (talk) 14:23, 21 February 2012 (UTC)

OK. I copyedited a little, but QM is for a realm which is outside our ordinary experience. The objects of classical mechanics are larger than an atomic nucleus, hotter than nanoKelvin temperatures, slower than GPS satellites, and smaller than the cosmos. QM is not for your ordinary realm.

I have to say that it takes more than two years of study in physics to understand the one-sentence statement of QM, according to Richard Feynman, so perhaps you might clarify on this talk page just where the English prose in the lede is starting to lift off beyond the grasp of the layman. If you could do so, then we might start to add more items to the introduction to quantum mechanics. --Ancheta Wis (talk) 15:28, 21 February 2012 (UTC)