User talk:Sbyrnes321/Archives/2007

Kevins Note

Hi.

Your rewrite is much better, but I think it still don’t address some issues. I can’t say that I agree that the product of statistical standard deviations imply anything about the measurement of an individual event. To actually calculate a standard deviation, say of x, one needs to have a measurement error much less than the standard deviation for the calculation to make sense. Measurement error, δp and δq, is not the same as standard deviations, and in fact can not be related.

e.g. http://plato.stanford.edu/entries/qt-uncertainty/#2.3,

to wit:

• quote

“A solution to this problem can again be found in the Chicago Lectures. Heisenberg admits that position and momentum can be known exactly. He writes:

"If the velocity of the electron is at first known, and the position then exactly measured, the position of the electron for times previous to the position measurement may be calculated. For these past times, δpδq is smaller than the usual bound. (Heisenberg 1930, p. 15)

Indeed, Heisenberg says: "the uncertainty relation does not hold for the past". “ etc…

And, according to Ballentine, deltaQ and deltaP are not even calculated at the some instant in time. I’ll just paste some stuff in, and see what you think

1Ballentine "Quantum Mechanics, A Modern development" P.225- P.226 (reference to graphs of delta_x and error_x, showing them not the same)

"...One must have a repeatable preparation procedure corresponding to the state p which is to be studied. Then on each one of a large number of similarly prepared systems, one performs a single measurement (either Q or P). The statistical distributions of the results are shown as histograms, and the root mean square half-widths or the two distributions deltaQ and deltaP, are indicated in fig. 8.2. The theory predicts that the product of these two half-widths can never be less then hbar/2, no matter what state is considered."

"To the reader who is unfamiliar with the history of quantum mechanics, these remarks may seem to belabor the obvious. Unfortunately the statistical quantities delta_q and delta_p in(8.33) have often been misinterpreted as the errors of individual measurements. The origin of the confusion probably lies in the fact that Heisenberg's original paper on the certainty principle, published in 1927, was based on early work that predates the systematic formulation and statistical interpretation of quantum theory. Thus the natural derivation and interpretation of (8.33) that is given above was not possible at the time. The statistical interpretation of the indeterminacy relations was first advanced by K.R. Popper in 1934." (8.33) - delta_x.delta_p >=1/2|<C>|, the result hold for any operators that satisfy [A,B]=iC"

2Ballentine "Quantum Mechanics, A Modern development" P. 225-226

"Jauch (1993). The rms atomic momentum fluctuation, delta_p is directly obtained from the temperature of the crystal, and hence gives a lower bound to delta_q, the rms vibration amplitude of an atom. The value of delta_x can be measured by neutron diffraction, and at low temperature it is only slightly above its quantum lower bound, hbar/2delta_p. Jauch stresses that it is only the rms ensemble fluctuations that are limited by (8.33). The position coordinates of the atomic cell can be determined with a precision that is two orders of magnitude smaller then the quantum limit on delta_q".

Jauch (1993) - Heisenberg's Uncertainty Relation and Thermal Vibrations in Crystals, Am. J. Phys. 61, 929-932 —Preceding unsigned comment added by Kevin aylward (talk • contribs) 13:48, 15 September 2007 (UTC)

Thanks for the message! If I'm reading right, I absolutely agree with that, and in fact your quote from Ballentine conveys precisely the same message as the section on the observer effect. (And as Ballentine says, Heisenberg himself didn't understand the HUP in the same way modern physicists do.) The standard-deviation-not-measurement error issue is certainly a worthwhile nuance to get straight (hence the whole "observer effect" section), and if you find anywhere that confuses the issue, or anywhere where it could be explained better, I hope you go ahead and do that. Or tell me and I'll do it. --Steve 23:09, 15 September 2007 (UTC)

Measurement in quantum mechanics

hello. i noticed you were cleaning up that article, which was degenerating into something not good. thanks. hope you don't mind me making couple suggestions. the article still contains some funny statements. in particular, some statements referring to the mathematical formulation doesn't quite make sense. perhaps better to rewrite the whole thing in physicist's language without the pretense of rigor. also, seems to me couple sections of the article could be removed in their entirety. thanks again and hope to see you around. Mct mht 02:44, 23 October 2007 (UTC)

Thanks for the message! Unfortunately I'm not at all knowledgable regarding interpretations of quantum mechanics, and only a little knowledgable about decoherence. So I'm unlikely to edit anything after the (current) first section. If the rest of the article is to be fixed up (and it should), it won't be my doing. Feel free to do it yourself though!

I deleted one full section. I was also thinking of deleting the "example" section, but rewrote it instead. It's still potentially deleteable though, I wouldn't be offended. Since your message, there was one place (Hermitian operators not always having complete eigenbases) where I tried to brush aside some mathematical details without actually making any incorrect statements. I think that should be the goal, and if there's other places where you see opportunity to do the same, go for it. --Steve 00:56, 24 October 2007 (UTC)

Update: I revised the rest of the article, notwithstanding my lack of expertise. Could use a few more references and detail, I suppose. Also, the "von Neumann measurement scheme" is a bit unreadable, but seemingly worth keeping in...don't really know what to do with that. --Steve (talk) 07:17, 20 November 2007 (UTC)

hi again, Steve. you seem to be doing a lotta clean up. quantum state is in much improved state after the contributions of you and User: B. Wolterding. may i suggest you consider taking a look at bra ket notation? Mct mht (talk) 02:46, 27 November 2007 (UTC)

Electron is a magnet

Can you explain by what nature an 'electron is by its nature a magnet?' I think this statement under Magnetism needs to be supported or if it can't, should go. John 06:35, 13 November 2007 (UTC)

I think that "see electron magnetic dipole moment" is a reasonable enough justification in this context. The electron has a magnetic moment, it's equal to 9× 10^-24 J/T, and it's just a property of every electron in the universe. There isn't really any deeper explanation. I guess you could say it has a magnetic moment because it has a nonzero spin, but why does it have a nonzero spin? Because that's the way it works out in the standard model. In any case, having a magnetic moment is undoubtedly and uncontroversially part of the "nature" of an electron. If you think a reference is called for, any book on quantum mechanics will do.

By the way, despite the name "spin", the electron is not literally rotating about an axis. A much better explanation is that it's just an intrinsic property of the electron. Again, any quantum-mechanics book written since 1950 will tell you that. --Steve 18:00, 13 November 2007 (UTC)

Then could it state that it has a magnetic property because of the quantum mechanical spin property? I think this needs something for laymen assessability. John 19:04, 13 November 2007 (UTC)

Hmm...Well no one would think twice about saying that the reason an electron has a charge of -1.6*10^-19 Coulombs is that "it just does" or "it's a property of the electron". Nor would anyone require a deeper explanation of the fact that the electron's mass is 10^-30 kg. I'm proposing that we say something analogous regarding the electron's magnetic moment. Why should that be any different?

My view is that bringing up spin in this context doesn't add any illumination. A lay reader can be prodded to accept that an electron has a certain magnetic moment just like it has a certain electric charge, just because that's what an electron is. But saying that it has a magnetic moment because of something called spin doesn't help matters at all: First, the reader needs to look up the article spin; second, the reader won't understand how the spin gives rise to a magnetic moment (and won't understand it without QED), and third, the reader will wonder...why does the electron have spin? And the answer is: Just because that's what an electron is. (So you're still stuck with an unjustified assertion about the nature of the electron, only this time it's one which is harder to understand.) --Steve 21:43, 13 November 2007 (UTC)

I claim magnetism is different because it is not a fundamental property, is a derrived property, charge, mass and (maybe) spin aren't; ...and magnetism is what this article is about, after all. To cite that a derrived property 'just is' is a little misleading in that it implies the representation that it is a fundamental property. If we don't know what it is derrived from, then lets admit it. Would an electron with no spin have a magnetic moment? To answer that in the negative implies a pair of monopoles in it. I think we should call a spade a spade here. John 20:54, 14 November 2007 (UTC)

Mass is widely accepted to be a derived property, a consequence of the Higgs mechanism. But the article mass, for good reason, doesn't mention this bit of quantum field theory. Charge is also a derived property, derived from the more fundamental electroweak theory. Moreover, according to string theory (for example), my understanding is that the electron itself is a derived particle, coming from more fundamental interactions with strings and vaccuums.

I guess what I'm saying is, there's different levels of explanation. A biology article can say a metabolic pathway functions because these two chemicals react. A chemistry article can say two chemicals react because of electron orbital interactions. A general physics article can say electrons have orbitals because of the Pauli exclusion principle. An article on the Pauli exclusion principle can talk about the spin-statistics theorem derived from quantum field theory. And so on, and so on. The purpose of this particular paragraph is explaining magnetism in materials, and the most important cause of this is that electrons have magnetic moments. Readers interested in the more fundamental question of why electrons have magnetic moments are explicitly redirected to the article electron magnetic dipole moment, where they can learn lots about it. The article doesn't imply that there's no deeper explanation of the dipole moment; on the contrary, it makes it very easy to find that explanation. I think that should be the goal.

By the way, an electron with no spin isn't an electron. An electron which didn't interact with photons wouldn't have charge, and that wouldn't be an electron either. --Steve 23:01, 14 November 2007 (UTC)

Vector (spatial)

Hi Steve, this is one of those articles that gets a lot of little edits by hacks (like me) and ends up getting fragmented. Articles like this need periodic copyedits or rewrites. I saw your note on the talk page - go for it - be bold - the article could use some TLC. --Duk 20:33, 30 November 2007 (UTC)

Thanks for the encouragement :-) Happy holidays! --Steve 20:42, 30 November 2007 (UTC)