WMdeMuynck

{{help me}}

I am presently editing the `Bohr model' page. On the `Talk: Bohr model' page there is an entry `12 Correspondence principle', signed by Likebox, which I would like to comment on. How and where should this be done so as to be sure that the comment reaches Likebox, in order to discuss changes to be made in text that probably is his?

It's up to you, really. I'd probably add the comments on Talk:Bohr model to begin with at least - just edit the Correspondence Principle section of the talk page. Regular editors of the page may well have it watched, in which case they'll be alerted to your changes. If there's no response after a few days, or if what you want to add is a message specifically for the attention of Likebox, then start a new thread at User talk:Likebox. Don't forget to sign your comments with ~~~~. All the best, Gr1st (talk) 22:23, 3 April 2008 (UTC)

Html editing

While editing the Kochen-Specker page I would like inline v to have the same (italic) font as in the displayed equation. Can someone tell me how this can be done?WMdeMuynck (talk) 22:16, 3 June 2008 (UTC)

Problem solved.WMdeMuynck (talk) 22:01, 25 September 2008 (UTC)

Categories

Please see my reply at User talk:Biscuittin. Biscuittin (talk) 08:24, 13 June 2008 (UTC)

Interpretations of Quantum Mechanics

May I suggest you look at this article which has serious deficiencies. I gave up on that article quite a while back. The first statement is very confusing. An interpretation I suppose is a statement of some kind, but I think it is more accurate to think of it as a correspondence between mathematical structures and something else (operational processes? physical processes? "Things"?...who knows). In any case I have been unable to find a satisfactory definition to replace the one that is there now.

Maybe you have some ideas. You might also want to look at the article history. Some previous states were better in my opinion.--CSTAR (talk) 03:57, 23 October 2008 (UTC)

Please see reply on my talk page.--CSTAR (talk) 15:51, 23 October 2008 (UTC)

I know you've stated your reluctant to intervene, but I do think that the existing intro to Interpretations of QM needs to be rewritten. Basically my problem is pretty simple: I know how to provide a reasonable beginning to an introductory sentence:

An interpretation of quantum mechanics is a correspondence between mathematical structures and.... X

What follows? What should we put in as X? "Reality"?, physical objects?, Soccer balls?--CSTAR (talk) 21:09, 5 December 2008 (UTC)

I would say: "an interpretation of a physical theory is a mapping from the mathematical formalism of that theory into physical reality". But different interpretations may correspond to different mappings. For instance, realist and empiricist interpretations of (the mathematical formalism of) quantum mechanics are thought to map into microscopic reality, respectively into the macroscopic reality of preparation procedures and measurement procedures within the domain of application of quantum mechanics. You may find this worked out on my web site, to which a link is provided on my User page.WMdeMuynck (talk) 15:51, 7 December 2008 (UTC)

I don't think there is much dispute about the sentence "different interpretations may correspond to different mappings." However, the word "reality" or "physical reality" in your preceding sentence "an interpretation of a physical theory is a mapping from the mathematical formalism of that theory into physical reality" is far more controversial. I certainly prefer a term with a more constrained meaning such as "soccer balls". However, given that quantum mechanics isn't about soccer balls (Fluminense!!) I would settle with something such as "the purported universe of objects of the theory". I know it's a mess. The Stanford Encyclopedia of Philosophy unfortunately didn't offer much help last time I checked.--CSTAR (talk) 19:31, 7 December 2008 (UTC)

Don't you think physics is about physical reality? Of course, a particular physical theory is about a particular part of physical reality. Quantum mechanics is about the microscopic part of physical reality, consisting of the elementary particles (like electrons, photons, protons and neutrons, or even buckeyballs) and their interactions. As far as my experience goes there is no controversy on that matter among physicists. There is controversy on the question of whether quantum mechanics just describes the phenomena observed in this domain (empiricist interpretation) or whether it describes the reality behind the phenomena (realist interpretation).WMdeMuynck (talk) 19:54, 7 December 2008 (UTC)

Reply Re: Don't you think physics is about physical reality? Isn't everything about physical reality? I suppose one could argue theology isn't about physical reality, but let's leave that aside for now (is it about unphysical reality or physical unreality?). Maybe I'll have to accept that your definition (i.e. your answer to my X) is probably as close to any grammatically correct sentence about what an interpretation of QM is. I am, however, profoundly unhappy with it. "Whenever I hear the word "reality" I reach for my...bottle of aspirin."--CSTAR (talk) 17:38, 9 December 2008 (UTC)

I think that bottle of aspirin is a part of reality. Physicists are nowadays (ontological) realists, believing that reality is there independent of their own existence (I think that Einstein's question "Is the moon there when nobody looks?" was just meant as a joke, referring to 19th century worries). Probably the last physicist who worried seriously about the old realism-idealism dichotomy was Ernst Mach. Whether electrons or soccer balls are involved does not make much difference (although we may be less sure of an object's reality if we only have indirect evidence of its existence: for instance, we are not sure that the Higgs particle exists). For this reason we should not believe every theory we are able to think of. What exactly is an electron is unknown (this incidentally holds as well for the soccer ball and aspirin, since electrons are parts of it). Sorry if this answer is not sufficient to replace your aspirin.WMdeMuynck (talk) 00:46, 10 December 2008 (UTC)

Oh I'm all gung-ho for reality. It's just that when I try putting my mind around it, so to speak, my cranium starts pounding.--CSTAR (talk) 01:28, 10 December 2008 (UTC)

Abiding with Einstein's following advice may help: "If you want to find out anything from the theoretical physicists about the methods they use, I advise you to stick closely to one principle: don't listen to their words, fix your attention on their deeds. To him who is a discoverer in this field, the products of his imagination appear so necessary and natural that he regards them, and would like to have them regarded by others not as creations of thought but as given realities." (A. Einstein, On the Method of Theoretical Physics. The Herbert Spencer Lecture, delivered at Oxford, 10 June 1933).WMdeMuynck (talk) 14:42, 10 December 2008 (UTC)

Advice requested

I've been trying to work out the details of Heisenberg's matrix mechanics since I have been rather dissatisfied with the secondary source materials I have found. It is clear to me how Heisenberg could calculate quantum theoretical predictions for hydrogen bright lines frequency values, the related energy values, etc. I have your Sources of Quantum Mechanics and a few articles that comment on Heisenberg's 1925 paper, but the amount of detail involved, the various ways of symbolizing the same things, etc., have me very confused.

Is there one place that tells in unambiguous terms how the transition amplitude for any pairs of energy states were calculated?

Young readers need to have explanations that are clear to the extent possible without a university education, that do not create false impressions, and that do not involve any waving of the magic wand.

Thank you. P0M (talk) 15:44, 21 May 2009 (UTC)

If your intention is to give a simple account of the way transition probabilities are calculated in quantum mechanics I do not think Heisenberg's 1925 paper to be a good starting point. We should remember that when this paper was written quantum mechanics did not yet exist. The paper is a first attempt at developing something in this direction. It is therefore understandable that it does not give as clear an account as one would like to have. Thus, it only treats harmonic oscillators and therefore is not applicable to, for instance, the hydrogen atom.

In quantum mechanics textbooks simple derivations are given of such transition probabilities by means of perturbation theory (this is to make the calculation mathematically tractable). Thus, starting from an eigenstate of the unperturbed atom as an initial state, the state is calculated at a later time after the atom has been perturbed by an electromagnetic wave. When this state is written as a superposition of eigenstates of the unperturbed atom it is possible to calculate transition probabilities between the eigenstates from the coefficients in this superposition, their absolute squares being the probabilities of finding the atom in the corresponding eigenstate.WMdeMuynck (talk) 19:20, 21 May 2009 (UTC)

It is my understanding that before Heisenberg's paper of 1925, the main thing about the hydrogen spectrum that could not be predicted on a quantum theoretical basis was the intensity of each of the lines. Heisenberg promised to work only with what were observable quantities, so to come even close to that promise he had to be able to compute the amplitudes on a theoretical basis that would, when squared, give him the values for the intensities.

In his paper of 1925, he says "In order to complete the description of radiation it is necessary to have not only the frequencies but also the amplitudes. The amplitudes may be treated as complex vectors, each determined by six independent components, and they determine both the polarization and the phase. As the amplitudes are also functions of the two variables n and α, the corresponding part of the radiation is given by the following expressions:" [p.263f in your book}

I am puzzled by what he means by "the corresponding part of the radiation." I assume that he means: "The amplitude of the radiation is given by the following expressions."

He then gives a quantum theoretical expression without defining symbols. My guesses:

R symbolizes (Rydberg constant?)

e symbolizes (charge of one electron?)

ω symbolizes the frequency of radiation associated with that transition

t symbolizes time

Re={U(n,n-α)e exp(iω(n,n-α)t)}

On 266 he says that "formulae of the type (7) (8) should quite generally also suffice to express the interaction of the electrons in an atom in terms of the characteristic amplitudes of the electrons." Both (7) and (8) involve expressions comparable to

{U(n,n-α)e exp(iω(n,n-α)t)}

I'm not sure of my old German alphabet. Maybe that should have been an "A" rather than a "U." Possibly it signifies amplitude.

Thank you. P0M (talk) 02:36, 22 May 2009 (UTC)

Let me first correct a misunderstanding. The book you refer to is by B.L. van der Waerden, it is not mine. I have a copy of the book, though, so I can try to answer your questions.

Let me start, however, with some remarks additional to my former ones. First, Heisenberg started from Kramer's dispersion theory which he had himself contributed to in a paper with Kramers. His discovery of matrix mechanics has nothing to do with his professed empiricism, but follows naturally from dealing with the classical radiation emitted by an electron represented in the 1925 paper by the electric field (first formula in the paper) using Fourier theory: when you represent x(t) by a Fourier expansion then you stumble into matrix multiplication automatically when calculating $\scriptstyle x(t)^{2}$ (this term pops up when calculating the classical intensity from the amplitude of the classical electric field). There is nothing quantum mechanical to this: it is simple classical analysis. The difference between classical and quantum-theoretical comes in via the different ways addition of frequencies is conceived on p. 263/264 when calculating the amplitude of the electric field at the Bohr frequency (something different from classical had to be done because classical theory did not work properly outside the classical limit).

There is also nothing empiricist in this. Heisenberg was a very pragmatic scientist who adopted any idea that seemed advantageous for selling his ideas. With the same ease he adopted empiricist ideas he adopted Einstein's very anti-empiricist one that the theory determines what can be measured (this was used by Heisenberg to push his uncertainty relation).

Let me now answer some of your questions (as far as necessary).

By "the corresponding part of the radiation" is meant the amplitude of the part of the radiation having the Bohr frequency (in his general treatment he started from a Fourier representation of the field in which all frequencies are present in principle).

Probably your question about the meaning of symbols refers to eq. (1) on p. 264. In this expression Re stands for the `real part of' the amplitude of the electric field at the Bohr frequency (which in the theoretical treatment is a complex quantity with amplitude (German) A); e is the base of the natural logarithm, $\scriptstyle e^{i\omega t}$ representing the phase of the field. In eq. (7) by (German) B is meant the intensity of the radiation at the Bohr frequency.

Let me once more repeat, however, that the paper hardly deals with quantum mechanics as nowadays is practiced (I even never read the Heisenberg-Kramers paper). So, I wonder whether it serves your purpose to provide explanations to young readers that are clear to the extent possible without a university education (actually, the Heisenberg-Kramers theory has not been part of my university education).WMdeMuynck (talk) 11:32, 22 May 2009 (UTC)

I find that when I am writing about something (or, in this case, trying to improve what other people have written), it is better to have too much information to start with. I could list a few books that have sections on matrix mechanics that I find very disappointing because they will lead readers well off the path or at least leave them dangling in the air over the path. Almost all of these descriptions jump on matrix mathematics as the marvelous discovery that did everything when the fact is that Heisenberg did not even know about matrix mathematics in the beginning. The stepping off point was, instead, the idea that started in the Kramer dispersion paper -- that one needs to use the "combination relations" on p. 263 (as you noted above).

In describing the history of this first departure from the old quantum physics I want to be able to bring readers to the point that Heisenberg can bring characteristics of the hydrogen bright line spectrum that were already well handled in theory with the remaining feature that had not previously been included.

Thank you for your help. Believe it or not you have confirmed some of the conclusions I drew for myself. Clearing up what the letters mean has also been very helpful.

P0M (talk) 19:42, 22 May 2009 (UTC)

Back again. I'm still trying to get a look at the matrices that Heisenberg's original paper would have been expressed in had he known about matrix math. I have tried to puzzle out the math, but I don't have the background needed to figure out how to get values to compare to the empirical amplitudes (i.e. the square roots of the empirical values for intensity). I assume that this must be possible. I've asked a couple of colleagues on my campus without getting very far.

Is it possible that Heisenberg merely jumped to his equation (7) and then simplified it?

Thank you. P0M (talk) 20:31, 30 May 2009 (UTC)

What Heisenberg probably had in mind, is calculating the classical Poynting vector from the expressions for the electric and magnetic fields on p. 880 of the article. However, he restricted himself in the article to one-dimensional examples, so these expressions are not applicable as they stand. The only thing he took from it, is that the fields will depend on the position $\scriptstyle x(t)$ of the electron, this variable being considered as a classical quantity, restricted by quantum conditions of the Old quantum theory. He used for the harmonic oscillator the Fourier expansion

$x(t)=\sum _{n}c_{n}e^{in\omega t},$

in which the quantum condition $\scriptstyle E_{n}=n\omega$ is taken into account. The crucial difference between classical and quantum is that classically the frequency of the field is equal to the rotation frequency of the electron, whereas in quantum theory the Bohr rule is satisfied, equating the frequency of the field with the difference of the rotation frequencies.

Now in the classical theory the amplitude of the field would be proportional to $\scriptstyle x(t)$ and its intensity proportional to $\scriptstyle x(t)^{2}$. Then

$x(t)^{2}=\sum _{nm}c_{n}c_{m}e^{i(n+m)\omega t}.$

For some fixed N in this expression the contribution at frequency $\scriptstyle N\omega$ is

$\sum _{n}c_{n}c_{N-n}e^{iN\omega t}.$

According to Heisenberg this does not work properly, as it does not take into account the Bohr rule (the quantumtheoretical expressions on p. 881) given here as

$\omega (n,m)+\omega (m,n')=\omega (n,n').$

For the harmonic oscillator we have $\scriptstyle \omega (n,m)=(n-m)\omega .$ Heisenberg replaced in the Fourier series the frequencies $\scriptstyle n\omega$ by the Bohr frequencies $\scriptstyle \omega (n,m)$ corresponding to a transition between orbits n and m. Then eq. (7) is directly obtained as the component of $\scriptstyle x(t)^{2}$ at the difference frequency $\scriptstyle \omega (n,m)$:

$\sum _{m'}c_{nm'}c_{m'm}e^{i[(n-m')+(m'-m)]\omega t}=\sum _{m'}c_{nm'}c_{m'm}e^{i(n-m)\omega t}.$

Here matrix multiplication is evident since the component of $\scriptstyle x(t)^{2}$ at frequency $\scriptstyle (n-m)\omega$ (in this one-dimensional example proportional to the intensity of the field at frequency $\scriptstyle (n-m)\omega$) is proportional to $\scriptstyle \sum _{m'}c_{nm'}c_{m'm}.$

Note that this is not quantum mechanics but Old quantum theory. Here no quantum mechanical transition probabilities are calculated, but just field intensities. Note also that eq. (7) is not derived, but guessed by varying the classical theory so as to comply with the Bohr rule.

I hope this will helpWMdeMuynck (talk) 23:29, 30 May 2009 (UTC)

Thank you very much. It may turn out to be only for my own edification since the article I have been working on has been radically altered by another editor. P0M (talk) 07:29, 31 May 2009 (UTC)

Back again. I finally had some time to go over your message and compare it to what Aitchison, MacManus, and Snyder have written, as well as the translation of Heisenberg's 1925 article.

First, you mention "the quantum condition $\scriptstyle E_{n}=n\omega$." I have to guess at the meanings of the symbols. Is $\scriptstyle E_{n}$ the energy of photons pertaining to some harmonic labeled "n"? And $\scriptstyle n\omega$ would then be the (angular) frequency associated with that harmonic? Or was there a typographical error for "$\scriptstyle E_{n}=h\omega$"?

I always take $\scriptstyle \hbar =1$. Here $\scriptstyle \omega$ is the (angular) frequency of the classical electromagnetic field emitted by a classical harmonic oscillator. In general such a classical field is not harmonic but just periodic, and can be represented by a Fourier series with terms corresponding to frequencies $\scriptstyle n\omega$. According to the classical theory these "higher harmonics" are generated by states of the oscillator having these rotation frequencies (and corresponding energies). Unfortunately, this did not agree with Bohr's atomic model in which the frequencies of the field correspond to energy differences rather than atomic energies. Note that in the classical theory of the electromagnetic field there are no photons (I am not sure whether Bohr has ever abandoned his resistence against the idea of photons).

All of these sources assume what you call "c" in:

$x(t)=\sum _{n}c_{n}e^{in\omega t},$

but I do not see how it is calculated.

I guess that in his cooperation with Kramers they have tried to calculate the electromagnetic field classically, just assuming a quantized motion of the emitting particle. This can be done by means of the inhomogeneous Maxwell equations in which the particle motion (mathematically represented by $\scriptstyle x(t)=\sum _{n}c_{n}e^{in\omega t}),$ provides a source term generating the field. In dispersion theory periodic solutions are studied in order to determine the dispersion relation (which describes the possible frequencies of the field).

Heisenberg's (2a) appears to be the same thing. He writes:

$x(n,t)=\sum _{a}A_{a}(n)e^{i\omega (n)at},$

I'm assuming that is a German "A," for which I have no font.

Having calculated the dispersion relation it is in principle possible to calculate the amplitudes $\scriptstyle A_{a}(n)$ of the field from the amplitudes $\scriptstyle c_{n}$ of the particle motion. However, as far as I understand from a perusal of Heisenberg's paper, he does not explicitly calculate the field, but contents himself with calculating $\scriptstyle x(t)^{2}$, which is assumed to be proportional to field intensity (he actually seems to identify the two quantities). The funny thing is that by in this way ignoring the field the idea of matrix multiplication was more readily discovered as a property of the position of the particle (rather than as a property of the field).

Note that here $\scriptstyle c_{n}$ should not be confused with the coefficients in a Fourier series development of a wave function: wave functions do not play any role in Heisenberg's approach.

Aitchison, et al. write:

$x(n,t)=\sum _{a}X_{a}(n)e^{i\omega (n)at},$

Aitchison, et al., seem to identify the term X(n, n-a) as the amplitude.

Heisenberg's contribution has to do with finding a way to change the classical approach I referred to above by an approach in which the terms of the Fourier series refer to the Bohr frequencies rather than to the classical rotation frequencies. This is expressed by the notation $\scriptstyle X(n,n-a)$ referring to the transition from Bohr state of frequency $\scriptstyle n\omega$ to the state of frequency $\scriptstyle (n-a)\omega$.

I am guessing that when you write, "What Heisenberg probably had in mind, is calculating the classical Poynting vector from the expressions for the electric and magnetic fields on p. 880 of the article," that Heisenberg was deriving these amplitudes from the very first two equations given in his paper. (My English translation has different pagination.)

Probably he should have done so, but he didn't. In any case he restricted himself to a one-dimensional example for which the expressions for the electric and magnetic fields do not apply.

That would mean that all the information needed for a quantum theoretical computation of the amplitudes is present, and the comments by some authors regarding the elaborate experimental conditions needed for measuring empirical amplitudes (frequencies, etc.) are important only insofar as those measurements would be necessary to verify the quantum mechanical predictions.

I have been having an argument with other editors regarding the Introduction to Quantum Mechanics. I have seen their position before, from a slightly different Wikipedia angle, and a third time from a more balanced point of view given by a textbook writer. Is the correct approach to never teach classical physics but to start with the Schrödinger equations and teach students the way the world really works from their very first day in a physics class? I think maybe one could do that if a very good laboratory were made available to students so that everything could be something more than book learning, but for the average well-informed reader who already knows his/her physical world well enough to expect a thrown baseball to go through either the left window or the right window, I don't think that will be very helpful. Maybe the end result will be a very short article that says that quantum physics is too difficult for readers to understand, so they should take a few years of math and physics, and meanwhile they may be assured that it is wonderful stuff with many good contributions to modern life. If so I will have to let it go, but I will have learned a bit to expand my own horizons.

This, once again, is a difficult question. You probably should distinguish between "making the microscopic world understandable" and "making quantum mechanics understandable". Experimental physicists actually talk about the microscopic world in remarkably "classical" terms. Although their electrons do not behave like your baseball, might de Broglie's idea that it is accompanied by a wave stearing the particle easily be understood by the analogy of a ship accompanied by its bow wave, the ship going through one opening wheras the bow wave goes through both, influencing the behaviour of the ship in a particular way so as to cause interference phenomena. Problems of understanding are often a result of taking the theory too literally. In particular, the idea that a microscopic particle is a wave packet rather than a point-like object is an important source of confusion, and, moreover, incorrect as now has been experimentally demonstrated (compare Tonomura's experiment on the Double-slit experiment page). Unfortunately, quantum mechanics text books are generally formulated in this individual-particle terminology, thus perpetuating an unnecessarily confused view of quantum mechanics.

I hope you will be able to confirm my guesses, or tell me where I have gone wrong without having to spend too much of your time on it. Thank you very much.P0M (talk) 17:00, 11 June 2009 (UTC)

I hope you don't mind that I try to answer your questions immediately following these in the above.WMdeMuynck (talk) 21:48, 12 June 2009 (UTC)

It is actually clearer the way you have interspersed your comments with my questions. Thank you very much. I gather that $\scriptstyle c_{n}$ represents the amplitudes of the particle motion, so your expression is not the equivalent of Heisenberg's (2a), and also that $\scriptstyle c_{n}$ can be calculated somehow.

It seems that before the 1925 article the frequency of the lines of the hydrogen spectrum could be calculated, but the intensities could not be calculated, and that after the 1925 work neither the amplitudes nor the intensities could be calculated. If Heisenberg could calculate them, it seems to be unknown how he did it. Perhaps he could only calculate them "in principle" and was satisfied to go to publication on the promise that he could do something.

I found a brief article on the WWW in which someone claims to have calculated the first 40 intensities for hydrogen radiation (at the bright-line frequencies), and tried to work backwards from these values to see what a Heisenberg transition amplitude matrix would look like, after which I tried to calculate the intensities by what I judge to be his method. Either I made a systematic math mistake or something more serious is wrong. The answers were not even close. However much earlier I took empirical measures for the visible part of the hydrogen spectrum and tried the same thing. Although there were not enough values to get a very accurate picture, at least the results did not seem ridiculous. Maybe if I got everything right I would still not be able to understand what Heisenberg actually accomplished, and how his way of formulating things gave answers that were consistent with Schrödinger's.

Thank you very much for your generous help.

P0M (talk) 02:25, 13 June 2009 (UTC)

Aitchison's article

Sorry to bother you once more. I have continued to study Aitchison's article (given in the footnotes to the matrix mechanics article). I am interested in a couple of the formulas, which I believe are relevant to the answers he got for amplitudes. But there are a couple more odd notations that are not explained clearly in that article. Could you please have a look at the bottom section of:

User:Patrick0Moran/Aitchison_article

and see whether any of these items are the daily fare of physicists and therefore obvious?

(I have a link to the article at the top of that page.)

Thanks again.

P0M (talk) 21:03, 22 July 2009 (UTC)

Thank you for drawing my attention to the Aitchison_article. I think it is a useful attempt to reconstruct Heisenberg's way of thinking. However, could you please be more specific about which section you refer to as the `bottom section', and to which items?

See below.

As a general remark I could mention a point I missed in the article, viz. that only classical perturbation theory is involved, which may not be daily fare of most physics students acquainted with quantum mechanical perturbation theory.

Another remark might be that Heisenberg's point of departure is dispersion theory, starting from periodic motion of the emitting electron and ignoring any back action of the radiation on the emittor. This allows him in the first part of his 1925 paper to directly relate the amplitude of the emitted field to the position of the emitting particle. In the second part, once again this assumption is being made, assuming the kinematics of the emittor to be independent of any interaction with the electromagnetic field. Actually, conservation of emittor energy is assumed, hence here he is restricting himself to a non-radiating situation. This seems pretty confusing to me, probably even more so to students to whom it would be presented as illuminating the way Heisenberg derived quantum mechanics. Without wanting to diminish Heisenberg's important contribution, I think papers like the Aitchison_article are more useful in a historic perspective (to illustrate how important theories may originate from guesses and half truths) than as a didactic tool.WMdeMuynck (talk) 12:57, 26 July 2009 (UTC)

I think from all indications Heisenberg knew himself to be very confused as he groped with recalcitrant data that refused to shape up. There is one remark in his article where he seems to record a moment when he surprised himself by deriving something familiar from his new approach and he says, "Aha, that is the way it works," or something like that.

I don't know the best way to teach students. It would be interesting to see whether Aitchison ever tried his own idea. All I care about right now is seeing the problem in enough depth not to write any nonsense on the subject.

I have summarized my questions below.

Aitchison 2

General question unrelated to the following two equations:

capping a constant with an umlaut: Does that indicate that the constant represents a matrix?

In eq. (12) $\scriptstyle {\ddot {x}}=d^{2}x/dt^{2}$

(second order time derivative).

λ: undefined variable used frequently, but not obviously any particular wavelength.

λ is a small parameter used in perturbation theory in the following way: let

$\scriptstyle a^{(0)}$

be the zero-order solution, that is the solution of the problem if there is no perturbation. The exact solution of

the problem including the perturbation is written as the series

$\scriptstyle a^{(0)}+\lambda a^{(1)}+\lambda ^{2}a^{(2)}+\lambda ^{3}a^{(3)}+\ldots$

(compare eq. (25)). Hence the unperturbed solution corresponds to

$\scriptstyle \lambda =0.$

Inserting the series solution into the equation of motion yields a power series in

$\scriptstyle \lambda$.

Requiring the solution to be satisfied for arbirary value of

$\scriptstyle \lambda$ yields the recurrence relations (compare eq. (32), etc.) from which the unknown quantities

$\scriptstyle a^{(n)}$

can be calculated.

What is ε₀ -- The same equation (3) has e in the numerator. ε is base of the natural logarithm in Sears Optics, but this article wwrites e. Is ε₀ Vacuum permittivity here???

If you refer to eq. (3) then ε₀ is indeed the vacuum permittivity.

Equations 60 and 82:
(I rewrote (60) to include Aitchison's "β" equation (given under (60)) directly since I am getting ready to work these equations out in a spreadsheet.)

(I've used • to indicate ordinary multiplication.)

(60) a⁽⁰⁾(n,n-1)= ((h/πmω₀)^1/2•(n^1/2)

What does m represent? Mass of the electron? Or something else?

m represents the mass of the unperturbed harmonic oscillator, having eigenfrequency ω₀ (compare eq. (19) in which m = 1 has been taken).

What is a⁽⁰⁾? 0th harmonic? Something else?

Zero order solution (see above).

What is ω₀? Another kind of reference to the harmonic structure?

See above.

(82) a⁽²⁾(n,n-1)= ((11 β³)/(72(ω₀)⁶) • (n·n^½)

What is a⁽²⁾? It is not a², so it has to have something to do with the second harmonic or something like that, no?

a⁽²⁾ is the second order contribution to the perturbed solution (see above).

Thank you very much for helping resolve my confusions.P0M (talk) 21:34, 26 July 2009 (UTC)

Please feel free to ask. However, it may take some time to answer if I am enjoying my retirement at some other place than behind my laptop.WMdeMuynck (talk) 13:25, 27 July 2009 (UTC)

Please enjoy your retirement. Perhaps you will be able to travel or find new fields of activity. It's been interesting to me to see how my cohorts have found so many different creative ways to use their retirements. Already you have helped me grow new brain cells. Thank you.P0M (talk) 14:16, 27 July 2009 (UTC)

Did you mean to write it this way?

On the causality talk page you wrote:

What I was referring to is the Deductive-nomological model, in which deduction is often interpreted as `deduction from initial conditions, using an accepted natural law'.

Did you really mean to write this? Or did you mean "causation is often interpreted as..." P0M (talk) 20:37, 22 December 2009 (UTC)

Sorry, not to have been able to answer sooner.

I think logical positivism shuns terms like `causation' because this term has an ontological connotation, probably being metaphysical. Instead, `causality' is used in the Deductive-nomological model in an epistemological sense (viz. as a way to order phenomena in a theory). This is also referred to as `subsuming under a physical theory'. In the particular instance under discussion this is implemented as the so-called `Cauchy problem' or `initial-value problem'.

The problem with this way of dealing with `causality' is that it cannot be distinguished from `determinism', thus giving rise to the well-known allegation of Einstein's being deterministic when challenging the Copenhagen interpretation in the EPR incompleteness challenge.

Note, however, that Einstein was not a logical positivist, and probably meant the initial condition in an ontological sense (viz. in the sense of an initial-value problem of a measurement process, in which `the particle being there' is seen as a cause of `finding the particle there'). Anyway, nowadays we have less fear of metaphysics, and, as far as we apply `determinism' as a way to express `causality', we think about it in this latter ontological sense. Whether you see this as `causation' is a matter of definition, I think.WMdeMuynck (talk) 16:19, 27 December 2009 (UTC)

I do not want to get too far away from the original statement that I asked you about. It seems that you maintain that the sentence I quoted above is as you intended it to be and does not contain a typographical error. But to me it is almost a tautological statement, "deduction is deduction," that has been saved from meaninglessness by giving it a slightly qualified form. If deduction is "often interpreted" as you say it is, according to some of the deductive-nomological people, then what are the alternative interpretations of deduction that some of them accept?

To me it would seem highly problematical if some physicists were to redefine the meaning of "deduction." Deduction is a process clarified in formal logic, and the only way to change the meaning of "deduction" would be to detach it from that formal system of argumentation. That approach has been taken, of course, starting at least as early as Zhuang Zi (fl. 350 BC), the Buddhists in several schools, et al. Modern scholars such as Hans Reichenbach have explicitly called for a new logic that can handle the world discovered by quantum mechanics. Are you claiming that the logical positivists have accepted an alternative logic? Have they also created an alternative set theory?P0M (talk) 17:41, 27 December 2009 (UTC)

I understand why the logical positivists do not like the term "causation." It seems to me that they should not accept "causality" for the same reason. That is not an issue for me. Nor is it an issue to me that to avoid use of the term they choose to create a more global form of generalization from experience from which some predictive conclusions can be drawn.

Hans Reichenbach was one of the first to contemplate for quantum mechanics a special kind of logic, viz. a three-valued logic. Physicists like Jauch and Piron, and philosophers like Mittelstaedt have done much work to develop other kinds of quantum logic, encompassing different kinds of `deduction'. However, I do not think that many physicists are enthousiastic about these proposals; at least they are seldom if ever applied in papers on theoretical physics. In particular the initial-value problem just employs the classical (Boolean) logic customary in mathematical derivations. As far as I know this holds true for set theory as well.

When I referred to a certain change of attitude with respect to `causality' I alluded to the changed attitude within philosophy of science during the 1980s, in which logical positivism has been replaced by scientific realism, the latter being closer to the ontological way physicists use to discuss their subjects. I think that Hempel and Oppenheim have developed the deductive-nomological model of explanation precisely in order to have a notion of `causality' acceptable to logical positivists. Within physics this model has given rise to the confusion of `causality' and `determinism', however.WMdeMuynck (talk) 23:42, 27 December 2009 (UTC)

response but not an answer

I put something on my talk page. We are going to have 3 faculty guests in the next three weeks, interviewing for a new Japanese language position, so I should be minding my shop... Nevertheless some of these ideas are very close to my interests in Chinese philosophy, and I now realize that if I can find the book on Buddhist causality I bought decades ago I may be better able to understand it. Maybe all "cause" is distributed, and maybe "trigger" is not a bad term. P0M (talk) 18:56, 30 January 2010 (UTC)

I know of two books which you might refer to above i) G. Zukav, The dancing Wu Li masters, William Morrow and Company, Inc., New York, 1979, ii) F. Capra, The Tao of physics, Shambala, Berkeley, 1975. I find the latter far inferior to the former. Contrary to Capra's book, Zukav's presents the physics in an excellent way. This means that from a physicist's point of view 90 percent of the book has a high standard. The remaining 10 percent is about the relation between physics and Zen philosophy. In my view this is the weakest part of the book.

As far as I remember, the title of Zukav's book is referring to the causality problem involved in the strict correlations of measurement results in the EPR-Bohm experiment performed on two spins in a singlet state while the spins are far apart. The dancing Wu Li masters should be compared with the spins: notwithstanding being far apart their dancing synchronously is thought to have no causal explanation, comparable to the absence of explanation of the strict correlations of measurement results in the EPR-Bohm experiment: at least, according to the Copenhagen interpretation (CI) the spins were not instructed beforehand to behave in this way.

In my view Einstein was right in reproaching the CI its negative attitude with respect to causality. He considered causal reasoning to be a methodological imperative for physics, neglected by the CI. As far as this Copenhagen attitude is in agreement with Zen philosophy I think that philosophy to be not suitable to be applied within physics.WMdeMuynck (talk) 16:47, 4 February 2010 (UTC)

I believe I was actually thinking of a book on Buddhist logic. It may or may not be relevant. I remember getting nowhere with it when I bought it years ago. P0M (talk) 20:18, 4 February 2010 (UTC)

answer to Robinson weijman:

Let me first refer to my web site, in particular: http://www.phys.tue.nl/ktn/Wim/qm2.htm#part-wave

As to the points you raised:

1. Electrons behave like particles with one slide but like waves through two.

Individual electrons do not behave observationally differently in single-slit and double-slit experiments. In both they are observed as particle-like impacts e.g. on a screen. Only another pattern is built up by the totality of the electrons. Individual electrons are not described by the wave function, the latter only describing the totality of the electrons (called an ensemble).

2. When one electron at a time is sent, the electrons still show an interference pattern, even though there is nothing with which to interfere.

How does one know that "there is nothing with which to interfere"? According to de Broglie each individual electron is accompanied by a wave (different from the wave function!). De Broglie's wave may be responsible for the interference of individual electrons. In popular expositions the wave function and de Broglie's wave are often not distinguished, thus causing confusion.

3. When the slits are observed (to see which slit the electron passes through), the interference pattern collapses - the electrons behave again like particles.

Here `observation' should be replaced by `measurement'. Electrons are not influenced by any "observation" that not at the same time exerts a physical influence on it. You might, for instance, place detectors near one or both of the slits. This change of the measurement arrangement would influence the interference pattern; however, in general not by way of collapse. The way the pattern is changed can in principle be calculated. It depends on the precise way the detectors are positioned and on the kind of detectors used. See also http://www.phys.tue.nl/ktn/Wim/qm12.htm#double

WMdeMuynck (talk) 23:50, 16 May 2010 (UTC)

Thank you for your apology. For clarification, I don't see anything wrong with popularising science (or anything - that is what Wikipedia does) and calling something nonsense without explaining why comes across to me as patronising. But I accept your apology - enough said.

Thank you also for your detailed reply. To take your points one at a time:

1. It seems that your point is that an individual electron does not behave differently - the only difference is the pattern. Well, OK, but that is still an apparent paradox, right?
2. What I mean is, if you consider a single electron as a particle, there is no other particle for it to interfere with. Is that the key here - that you must consider the electron as a wave here?
3. Here your implication is that the video I presented is wrong to imply that just by watching the electron it behaves differently. However, quickly Googling this shows lots of sites confirming these "paradoxes". So, either way, it is disappointing that the Wikipedia article has such an impenetrable explanation / summary of these paradoxes. --Robinson weijman (talk) 09:05, 17 May 2010 (UTC)

There is nothing wrong with popularising, at least if it is not done in a deceiving way. The problem is that many of the popular ideas stem from around the years 1920-30 when quantum mechanics was a strange new theory even arousing forms of mysticism among both scientists and laymen. In the eighty years we are now dealing with the quantum mechanical world we have discovered quite a few things, in particular that certain ideas stemming from that time are incorrect, or at least far less certain than was thought in the beginning. I think that, having dealt with this issue during half a lifetime, I may be excused to have some ideas not squaring with popular accounts that are still based on worn-out ideas like e.g. the idea of `collapse on observation'. I have experienced that within Wikipedia expertise is not much valued. For this reason I gave up serious editing already some time ago, restricting myself to giving some advice every now and then. As you may have seen, I gave my web site the motto: "In the quantum mechanical forest few paths do not lead into nowhere land." It may either be interpreted as patronizing, or as a reference to the many times I have gone astray. Everyone is allowed to make his own choice.

It is difficult to express things in a few lines in a completely unambiguous way. I do not recognize my intention in what you write above. Of course, an individual electron behaves differently depending on whether there is one slit or there are two. How could, otherwise, the patterns be different in the two different experiments?

De Broglie's idea is that an electron is a `particle accompanied by a wave', the particle going through one slit, the wave passing both. On my web site I compared this with a `boat accompanied by its bow wave' [[1]], the bow wave influencing the path of the boat.

It certainly is disappointing that Wikipedia is not always reliable. In the past I have tried to do something about it. However, some experts-hating administrator did not like it, and deleted it. That's why I restrict myself now to editing uncontroversial issues.WMdeMuynck (talk) 15:02, 17 May 2010 (UTC)

Thank you again. I can certainly identify with your last part about over zealous deleters. I appreciate your boat analogy but, as you imply, I don't think we're going to get clarity in a few lines. I wish the Wikipedia article did justice to these questions (at least stated, assuming you are correct, what the "popular misconceptions" are). Thanks again en de groetjes from a fellow Brabanter. --Robinson weijman (talk) 21:59, 17 May 2010 (UTC)

EPR paradox - thought experiment

Hi. A couple of days ago I made an edit to EPR paradox that was reverted,[2] and it is a subject of discussion in the talk page section Reason for undo of two edits where you are curently making helpful comments. Could you comment over there on my edit? Thanks.

P.S. Please note that my edit was motivated by not seeing any description of the thought experiment of the EPR paper anywhere in the lead or in rest of the article. There are references to it but the article never states what it is.

P.P.S Here's a link to a response I made to Phancy Physics, FYI. [3] Regards, --Bob K31416 (talk) 01:13, 26 August 2010 (UTC)

Bob K31416, I have decided to restrict my contributions to Wikipedia to occasionally indicating flaws in existing text (like this one) and giving advice, leaving more elaborate edits to other users. Previous experiences with expert hating administrators have led me to this decision. As to my expertise you might consult my web site which can be found via my User page.WMdeMuynck (talk) 04:26, 27 August 2010 (UTC)

Thank you for making available the useful material on your website. On my user page is just a video poem about Wikipedia that I had fun making. If you go there, note the little links to videos. Regards, --Bob K31416 (talk) 09:39, 27 August 2010 (UTC)

Wave packet

I noticed you have made substantial contributions to Wave packet. There is an edit war erupting, and I have asked for page protection. You might, or might not, be interested in the disruptive shenanigans involved. If not, pardon the gratuitous bother.Cuzkatzimhut (talk) 22:35, 24 October 2014 (UTC)

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