Talk:Introduction to quantum mechanics/Archive 2

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Archive 1 Archive 2 Archive 3

Minor suggestion

I love the fact that there's an "Introduction to" page as well ... very cool --RawEgg 09:16, 26 September 2007 (UTC)

Three things -

  1. This discussion page is indeed quite long as noted by the banner on this edit page. Shouldn't much of this be archived?
Done. P0M
  1. The sentence in the first paragraph I believe is awkward
"This difference between the success of classical and quantum mechanics is most often observed in systems at the atomic scale or smaller, or at very low or very high energies, or at extremely low temperatures."
Am I right in thinking it should be explaining that
"Differing from classical mechanics, quantum mechnics is successful in observing systems at the atomic scale or smaller, or at very low or very high energies, or at extremely low temperatures."
The current sentence is akin to "The difference between Sheila and Frieda is her blonde hair."
The sentence may have been written by someone with experience in Washington. The writer was trying to say that quantum mechanics has had its big successes in explaining things that classical physics could not explain, primarily at the extremes mentioned. Using the word "observing" in a colloquial sense was highly problematical. P0M
3. In the third paragraph:
"While most areas of fundamental physics are understood as quantum theories, some areas remain difficult, such as developing quantum gravity which requires Einstein's general relativity to be quantised."
I feel this is a little beyond the "Introduction" whereas I suggest:
"While most areas of fundamental physics can be described with quantum theories, some areas remain diffcult, such as developing a quantum gravity theory."
and putting the "why" in a footnote. Possibly adding a basic description of the difficulty of quantum gravity, which I understand as the weakness of gravity in comparison to the forces as successfully described by quantum mechanics.

Edreher 18:28, 8 January 2007 (UTC)

The writing is poor. Taking a cavalier attitude toward writing often makes something that sounds impressive but means nothing. What is "understood as" supposed to mean? Can you say something like, e.g., "A mule is understood as a hybrid"? To me, the sentence should be, "A mule is understood to be a hybrid," in order to make syntactically correct English. Even with this change it indicates to the reader that there is something tentative about this "mule = hybrid" idea. It sounds like the weasel words of a true politician. So what should the sentence be saying? Classical physics theories are now recognized to be special cases of quantum physics and/or relativity theory. Dirac brought relativity theory to bear on quantum physics so that it could properly deal with events that occur at a substantial fraction of the speed of light. Classical physics, however, also deals with mass attraction (gravity), and nobody has been able to figure out how to bring gravity into a unified theory with the relativized quantum theory.
The weakness of gravity in comparison to the other forces we know about is an intriguing feature, and one that draws people's attention because it is not easy to guess a plausible reason why it differs so greatly from other. But, as far as I know, if gravity were stronger that would not make it any easier to explain. P0M 23:49, 8 January 2007 (UTC)

Can someone make this page a bit more newbie-friendly? I'm having trouble using it to study due to it's complicated set-up. For an INTRODUCTION, it's not as easily accessible to those unexperienced in the subject as it should be. Remember, you're not just posting facts, you're actually trying to help someone understand those facts. AnimeNikkaJamal 22:53, 5 February 2007 (UTC) AnimeNikkaJamal

I'd say incorrect

Under 3.1 Full quantum mechanical theory, 5th paragraph, it is said:

"The idea that an electron might now be in one place and an instant later be in some other place without having traveled between the two points was one of the earliest indications of the "spookiness" of quantum phenomena."

Knowing what I know about time-dependent perturbations theory, I'd say this sentence is not correct. AFAIK, the electron "travels" between the two orbitals: After receiving the perturbation (photon), its state becomes no more an orbital, but a superposition of many orbitals (and if the photon happens to have the correct energy, one orbital particularly, which you can call destiny, excited, final, etc.). Only when you measure its energy does the electron state collapse to a pure orbital. If you don't, and instead measure its position, you could find it in any position allowed by its state. So it's no way like it is jumping from one orbital to another. Am not I right? --euyyn 19:03, 3 February 2007 (UTC)

Two things. The original intent of the passage was probably meant to reflect the historical changes in ways of imagining the behavior of electrons in orbit. The idea of a trajectory between orbits was the kicker, i.e., thinking about electrons moving between orbits the way that you think about planets getting kicked out of one orbit and moving to another orbit turned out to be inappropriate to things on the atomic scale.
When you say, "It's no way like it is jumping from one orbital to another," that seems to be the same idea that the original sentence was getting at. "Instant" is probably the wrong word for that sentence, since it might suggest 0 time.
Maybe "traveled" should be replaced by "followed a trajectory". And do you have any way of computing the length of time of travel?
I pulled one source that was at arm's length, by George Gamow, that had a nice description of the problems involved in thinking about trajectories and of the new way that one had to think about things, but he was not "spooked" by the idea at all. I think I can come up with a physicist a generation or so earlier who would be saying something like, "Yikes, we don't have any real data on what's going on between orbital occupancies. Now you see it, now you don't, oh, there it is. Weird." P0M 08:52, 5 February 2007 (UTC)
I'm still working on a good citation. Philipp Frank, Philosophy of Science, p 215, gets to the center of the problem:

Some authors have said that according to the contemporary laws of motion for atomic particles the position and velocity of a particle cannot be measured at the same instant. If we measure the coordinate (position), we "destroy" the possibility of measuring the momentum, and vice versa. This formulation is misleading because it gives the impression that before the measurement there was a "particle" that possessed both "position" and "velocity," and that the "measurement of its position" destroyed the possibility of measuring its momentum." As a matter of fact, the atomic object itself cannot be described by the terms "position" or "velocity." Obviously, what does not "exist" cannot be "destroyed." Only if certain experimental arrangements surround the atomic object can the terms "position" or "momentum" be defined, but there is no arrangement in which both can be defined and mesured.

It would be difficult to know that an electron was in a specific orbit around a specific atom. It would also be difficult to determine that the electron had changed orbits. Both of those requirements would have to be met before someone could actually talk about the "movement" of the electron from one orbit to another. The operational definition for determining movement involves two determinations of x,y,z,t for the same object, but we cannot perform those measurements for an electron, and if we try we get in the way of the phenomenon that we are trying to observe. While we might have sufficient grounds for saying that an electron must have been in one orbit and must have fallen to another orbit because we have measured the frequency of the resulting photon, that is about as far as we can get, no?
A hypothetical question: How long does it take for a photon to be emitted? And, is the transition from orbit to orbit not identical (exactly the same thing as) the absorbtion or emission of a photon? Or does an electron start to fall out of orbit, emit a photon, and continue to fall to its second orbit? We might compute the minimum length of time for the orbital transition. But if "you could find it in any position allowed by its state" then the time could be much greater than that minimum, bringing into question (as you suggest) what the electron is doing in that long interim.
I suspect that there can be no answers to these questions because there can be no observations to gain the needed data. So for this reason, as well as for the reason that position and momentum cannot both be determined, there is no movement between orbits in the strict interpretation of the word "movement." In the original passage I think the word "jump" did not mean "to travel a trajectory from point a to point b," but "to disappear from one place and appear in another place," i.e., we can (at least theoretically) determine that an electron is in one orbital at one time and in another orbital at another time, and we can infer that it had to "get there" in some sense, but that is it. That being said, to me it seems equally possible that a wave travels in one orbit at time 1 and a wave travels in another orbit at time 2, and that there need be no disturbance passing through the intervening space. By our ordinary macro-world experiences we would expect something to pass between them, but I think that is just our imagining an interphenomenon to make ourselves feel on familiar ground. P0M 05:35, 6 February 2007 (UTC)

Do we have a new "decider"?

User Special:Contributions/ has twice placed at the head of the article the demand that material s/he considers inappropriate by reason of falling into several categories be removed from this article and placed elsewhere. Such comments or requests (actually it is written as though it were a rule established by the administration of Wikipedia) are addressed to contributors and not to the general public who come in search of information, so it should be placed on the discussion page. I wonder what person knows enough about Wikipedia to consider himself/herself a decider for other people, yet is not a registered contributor. I would prefer not to get into an edit war or to have to appeal for official intervention. P0M 02:47, 6 February 2007 (UTC)

It wasn't me, I don't even know enough about WP to create a new section on the talk page (that's why I keep using other people's). I don't care about range of content, I just want someone to simplify the article so I can understand it, especially in the parts that deal with formulas. AnimeNikkaJamal 23:15, 6 February 2007 (UTC)

I believe you. And, besides, I know which user it is. He has an account but comes in unregistered to do things. I put a message to the numbered account (see above), and I got a reply from a slightly different number.
Please get a user name and please discuss prominent changes before making them. P0M 02:36, 6 February 2007 (UTC)
Get bent.
I think people would make more progress without trying to run things, and without snarling. But some people will probably never come around to that point of view.
Anyway, with regard to your issue, I can't support all of the article. If you read back on this discussion page you will see that I have complained from time to time about things that other people wrote that I can't understand well enough to fix because I can't even figure out what they were trying to say. I may have missed some of the places that unintentionally lead people astray. If you wlll be specific about the problem spots, perhaps bringing them up one at a time, I will try to reduce the rough spots.
I agree about the formulas, in a way. The university where I studied physics had a regular approach to formulas. They did not require students to memorize and regurgitate them. They required students to be able to derive the formulas -- frequently on the final exam. The way they did things, you understood what was going on and then you put it down in mathematical shorthand so you could calculate the results easily.
I have been stuck for quite some time on the subject of the matrix math used by Heisenberg. It isn't just abstruse to you and I. Most people who have commented on the paper that Heisenberg wrote have complained that they could do the math that he had come up with, but they couldn't follow his explanation for how he got there. As if that weren't enough of a barrier, the math that is used was familiar to the physicists that Heisenberg was writing for, and familiar to the chosen audiences of most of the other stuff that was not watered down for the general public. You have to be familiar with a great deal of math symbology if you want to read and understand a few of those formulas. That's one of the reasons that even this Introductory article is difficult. Sometimes if you leave formulas out it seems simpler. But then people might want to be able to at least look at them. Sometimes people have simplified the formulas, and that can be disasterous. For instance they may say that a times b is not equal to b times a in quantum mechanics, and they give the impression that they are talking about an integer a and an integer b when in fact they are talking about multiplying together two matrices called a and b.
Maybe I should just skip over that part of the article and look for other things that need to be improved. You can help by giving your feedback here.
The other thing that is difficult, a source of trouble for beginning readers on this subject, is that our macro world is made up of components on the micro level. We expect the micro world to closely resemble the macro world that is made up out of it, but the micro world just doesn't behave that way. So we are forever getting interference between what we expect to be found on that level and what we expect those things to act like, and what we actually find. If the article just stated the picture of the quantum world as scientists have discovered it to be, then people would get a sort of shortlist of the oddities of the quantum world. But my guess is that they would not be satisfied with just a description of the results without any information on how this shocking re-write of natural history was made.
P0M 08:05, 7 February 2007 (UTC)

A lot from the end of the Collapse of Wavefuction to the Pauli exclusion principle is difficult, even following links and backtracking. I've made a small amount of progress on the formulas (enough to associate them to the rest of the article) and gave up where it goes into detail about matrices (the actual article on matrices is more complicated than the explanation on this page, and that's saying something). AnimeNikkaJamal 02:32, 8 February 2007 (UTC)

If it's after the matrix stuff I probably haven't done much with rewriting it. I'll go over it soon.
There is a rather nice book called Introducing Quantum Theory, by J.P. McEvoy and Oscar Zarate. It has lots of cartoon-type illustrations and little text, but what it does have is, generally, very accurate. About the matrices, however, it just has a cartoon picture of Heisenberg and a "bubble" that says: "I guessed that the difference ... pq-qp was not zero but equal to h/2πim, where i = the square root of negative one, an imaginary number." The only hint that the reader might get that p and q are not ordinary variables (d=rt type that is) is that there is a cartoon picture of two matrix grids below Heisenberg's head.
The trouble with the numbers that fill in the matrix is that they are not simple variables that one might measure with meter stick and gram balance, etc., but variables that represent complex functions. It's bloody confusing because people who are in a field often know what the conventional use of a symbol like σ is, and they don't bother to clue-in the newcomer.
I once had a gif image that illustrated what a matrix does and how multiplying them actually works, in a context where you could tell why Matrix a * Matrix b would give you something sensible like the number of boys per boys dorm room, whereas Matrix b * Matrix a would perhaps give you something like the number of number of girls per boys dorm room... doubtless an interesting number but not one likely to be discovered by mixing up your math. ;-) Anyway, somebody said it was ugly and deleted it.
One of the things that helps most in understanding this stuff is to go back and find the stuff that people like Heisenberg, Einstein, et al. wrote. They are incredibly good writers, and of course you don't have to fear that you are reading something by somebody who doesn't know what s/he is talking about. If you are interested in the exclusion principle, read the beginning part of The Nature of the Chemical Bond by Linus Pauling.
Francis Weston Sears wrote a series of physics books for a university press, MIT I think it was. His writing is beautifully clear. My first-year physics textbook was a fat old cow by people called "Sears and Zemansky," and it was terribly unclear. About midway into that year of physics I discovered that Sears what Francis Sears and that Zemansky had packed three books into one fat book by dint of taking out all the clear prose by Sears. Sometimes less ink is lots more work for the reader/student. Unfortunately, although Sears wrote a book on relativity he didn't write one on quantum theory. P0M 03:59, 8 February 2007 (UTC)

Fixes for some fuzzy points?

Here is an example of the kind of writing that I rather hate: "Amplitudes of position and momentum that have a period of 2 π like a cycle in a wave are called Fourier series variables. Heisenberg described the particle-like properties of the electron in a wave as having position and momentum in his matrix mechanics."

The writer presumably knew what s/he intended to convey. I can guess that there has to be some connection between Fourier series variables that are chosen to represent positions and momentums and the matrices that are alluded to in the next sentence. Of course the claim is uncited, so I'll have to go rooting through my old books until I find something that I can cite. I think maybe the author was trying to say that Heisenberg believed the electrons in their orbits are in an oscillation that could be graphed as angular position set against time, and that it was convenient for him to describe the position and momentum of the electron as Fourier variables and then put those expressions into his matrices. (What the heck is an "amplitude of position" anyway?) P0M 04:29, 8 February 2007 (UTC)

I fixed some of the formulae so that they will be easier to read. Somebody had italicized some of the variables and constants, which only made things harder to read.

The formulae that are now in the article seem to me to involve pretty simple algebra. They may look rather formidible just because of the occasional Greek letter. In one place there is a step by step working out of an important conclusion which derives from some simple equations at the top. I think I probably put that stuff in myself. The reason it should be there is that we can understand where the premises came from, but we couldn't understand where the strange-looking formula at the bottom comes from unless you've actually done the math.

There are other really startling results that come from things everybody knows, and it can be a revelation to the new student with an inquiring mind when they learn how to do the math. There is a way of calculating the time dilation that occurs when something is moving. It depends only on knowing the Pythagorean theorem and knowing that the speed of light is constant. Once you've done the calculation for yourself it demystifies time dilation for you. And once you understand the basic thought experiment involved you can derive the formula for yourself any time that you need it.

We could just tell people:


but then a reasonable question would be, "Where did that dogmatic statement come from?"

If you know that E = h v (i.e., that energy is related to frequency times Planck's constant), and that E/c = p (i.e., that energy divided by the speed of light is related to momentum), and you know the general relationship between wavelength, speed of the wavefront, and frequency, then you can get the interesting results given above. Planck's constant is at the heart of quantum theory, so that is something to learn about. The idea of the relationship between energy and momentum has something to do with the speed of light is a little unexpected, but that the momentum of something is related to a speed is a little closer to home. So with a little algebra we can demystify. With no math at all we could just say, "Wavelength is equal to Planck's constant divided by momentum." How is that related to the fact that the energy photons carry is a function of their wavelength? We wouldn't explain because explaining would amount to writing out all of the equations in plain English and that would be tedious to do and actually harder for the reader to follow.

The one "formulaic" part of the article that I have a little question about is the long discussion of why physicists like to use "h-bar" rather than just using "h/2π". It doesn't do anything to the real math, so in a sense it's an unneeded complication. On the other hand "h-bar" is a mysterious new symbol meaning who knows what when you first stumble upon it, so perhaps it is worth demystifying it up front.P0M 06:04, 8 February 2007 (UTC)

I completely agree with you, "amplitute of position" makes no sense, especially without an explanation beforehand or link to an article that could explain it. I understand amplitude to be the maximum distance of a wave from bottom to top. The position is where something "is" (I sorta sound like Bill Clinton putting emphasis on the definition of the word "is"). Amplitude of position would be the same as saying "position in the amplitude" (much simpler) or "position's amplitude" (how far up AND down the actual position streches, which seemingly goes against the definition of "position" itself). As for the formulas, it would be nice if they included everything possible in the simplest form possible. If someone were to write (I'm not completely sure I'm stating this correctly) ... "E = MC2 put a completely different view on the relation between energy E and matter M , of the constant C (the speed of light) being the barrier at which excess energy is converted into matter. (I forgot where exactly the square goes)."

Or it could go

"E = MC2" E = Energy, the amount present or produced M = Matter, the amount present or produced C = Cerelis, the speed of light

(at this point begins the exact explantion of the formula, how it's applied to the rest of the and why it's important)

That's a pretty reliable and understandable format, leaving nothing to guess. H-bar was annoying for me too since the article neglected to explain it until you were too deep in the application to want to go back and figure out a bunch of formulas that confused you to begin with. Btw, what's the 3 - pointed symbol in the equation you posted above? AnimeNikkaJamal 22:02, 8 February 2007 (UTC)

Do you mean the one that looks a little like 入 ? That's a lower-case (Greek letter) lambda, and is used for wavelength. P0M 01:07, 9 February 2007 (UTC)

Use in Wikibooks?

Perhaps articles like this would have a better place as part of a Wikibook rather than an encyclopedia entry. Fyorl (talk) 09:19, 14 February 2008 (UTC)

Shimony and "passion at a distance"?

This is in response to a recent edit by Cmeyer1969. You say you "Removed confusing joke and added informative reference." I appreciate the reference to the Westmoreland and Schumacher paper; I will read it. Shimony's idea of "passion at a distance," however poorly it may be named, is not a joke. See Abner Shimony and the reference to Sandu Popescu's essay in this article. If you are under the impression that someone added the sentence you removed as a joke or as vandalism, you are mistaken. By the way, I have no personal stake and I did not write that sentence; someone called for a citation to back up the sentence and I found one. — SWWrightTalk 03:20, 8 March 2007 (UTC)

Hi, thanks for the citation. I did see the paper before I removed the sentences. The sentence before it "though it is possible to use it to increase the probability of success in a conflict situation where a number of allies must collaborate against a joint attack without information on what their common enemy is doing at each of their allies' separate locations (except their own)" is clearly garbage. However, I felt that the comment by Abner Shimony was confusing at best. I think it might be best to refer that entire section to the actual Quantum entanglement page and add the "passion at a distance" information there. What do you think? Feel free to edit the sentence back in if you disagree, with perhaps a bit more explanation as to what it is. Cmeyer1969

Cmeyer1969, thank you for responding. I may do so, but first I have to study his writings some more. While I was able to find a citation, I do not yet understand the idea. I do know that Shimony is a highly-regarded physicist; a friend remarked to me that Shimony is the 'S' in "CHSH." This same friend also told me that Shimony is one of the few real physicists who are willing to tackle the hard questions (such as whether quantum nonlocality is real or just a mathematical construct) -- though there are many pseudoscientists willing to muddy those waters. His idea of "passion at a distance" appears to be such an attempt, and the awkward name shows the difficulty of putting it into words at all. — SWWrightTalk 20:46, 8 March 2007 (UTC)


The text currently says: "In May 1926 Schrödinger published a proof that Heisenberg's matrix mechanics and his own wave mechanics gave equivalent results: mathematically they were the same theory. Both men claimed to have the superior theory." Somebody has put a "fact" tag on this claim. It is true that Schrödinger published such a proof. If one theory can be derived from another theory, i.e., if they are "mathematically the same theory," then one cannot be superior to the other. About the only thing one of them might claim would be that his way for formulating the mathicatical relationships is easier to compute under certain conditions. I would be in favor of deleting the claim. It does not help the reader to understand quantum physics. P0M 21:13, 30 April 2007 (UTC)

  • I put that tag there, not doubting that Schroedinger gave the proof (Eckart did too), but doubting that both men claimed their own theory to be superior. I have never before read that. As far as I am aware Heisenberg understood immediately the equivalence proved by Sch. Equivalent theories rank equally as you, H., and Sch. know, but not the author of the sentence. So, I am in favor of deleting the sentence + tag, too. --P.wormer 15:26, 16 May 2007 (UTC)

Upon reading it again I think that the original author intended to refer to the interpretation dispute. Schroedinger felt uneasy about the probabilistic character of QM, while Heisenberg had no problems with it. I adapted the text a little to clarify this.--P.wormer 11:12, 20 May 2007 (UTC)


Spin was discovered by Uhlenbeck and Goudsmit in 1925 as stated in most textbooks of QM. Not by Kronig as myth has it. See --P.wormer 15:10, 16 May 2007 (UTC)

This problem seems to have been fixed. P0M (talk) 17:05, 20 December 2007 (UTC)


"These ideas [waves and particles] seem mutually contradictory, because neither idea by itself can explain electromagnetic radiation".

This doesn't make sense. It's like saying wheels and engines are contradictory because neither alone can explain vehicle motion.

Should the two parts of this sentence instead be separated by but? -- 14:30, 29 May 2007 (UTC)

  • I agree, but couldn't find the sentence--P.wormer 14:41, 29 May 2007 (UTC)
  • Right next to the constructive and destructive interference image. Note that when quoting the sentence, I added the portion in square brackets to make it easier for people to follow the point I was making.-- 15:07, 29 May 2007 (UTC)
  • OK I found it. I would write something like: In classical physics these ideas are mutually contradictory. Ever since the early days of quantum mechanics we know that neither idea by itself can explain electromagnetic radiation. --P.wormer 15:26, 29 May 2007 (UTC)


I see that this has already been reverted 3 times in few days - so, before it becomes an edit war, let's spell it out clearly: Planck constant is 6.6260693 × 10E-34 joule seconds; light's frequency is hertz = 1/seconds; the resulting unit for h * \nu is joule seconds / seconds = joules, so the result is in joules, a unit of energy like the electronvolt, ok ? :-) -- Sergio Ballestrero 17:55, 30 June 2007 (UTC)

Sergio, if the eV is an energy unit then Hz is it too (as is kelvin, cm-1, etc.). The only SI energy unit is joule. All the other "energy units" have a natural constant hidden in it. For the eV it is the elementary charge, for Hz it is Planck's constant, for kelvin it is Boltzmannn's constant, etc. It very much depends on the subfield of physics what "energy unit" is preferred. --P.wormer 07:18, 1 July 2007 (UTC)

Paul, you're right that the only SI energy unit is the Joule, and that you can use other units; but unlike the others you mentioned, eV is a proper energy unit, with no "hidden constant", because the "e" in eV stands for "electron charge with unit": 1 Coulomb * 1 Volt = 1 Joule -> 1e * 1V= 1.602 ×10E−19 C * 1 V = 1.602 ×10E−19 J , so there is only a (quite explicit) numeric factor, the electron charge in Coulombs, not a constant with units. If you use eV for momentum, mass etc then yes, you have implicit, hidden factors and, more important, hidden units, but that's not the case for energy. Aside from this, my main point was that the corrections were replacing Joules with Hertz without adjusting the numerical value, which is incorrect no matter what! -- Sergio Ballestrero 10:32, 1 July 2007 (UTC)
Sergio, I agree with your main point, but only partially with with your first point. If one goes from joule to any other "energy unit", one has to multiply with one or more natural constants. This is also true for the eV, as you say yourself: you multiplied with the charge e of the electron. I call e a natural constant with SI unit coulomb. However, I grant you that the eV is special among the "energy units" in the sense that it has the dimension of energy (as does the hartree), while most of the other "energy units" do not even have the dimension energy (for instance Hz has the the dimension 1/second). --P.wormer 13:24, 1 July 2007 (UTC)

accessible discussion?

I saw the following sentences in this article:

Therefore, an electron in a certain n-sphere had to be within a certain range from the nucleus depending upon its energy. This restricts its location. Also, the number of places an electron can be is also called "the number of cells in its phase space". The Uncertainty Principle set a lower limit to how finely one can chop up classical phase space, so the number of places that an electron can be in its orbital becomes finite. An electron's location in an atom is defined to be in its orbital, but stops at the nucleus and before the next n-sphere orbital begins.

Is this understandable for the proverbial "average reader"? I, for one, don't know what an n-sphere is, and why the phase space [for one particle a 6-dimensional space of points (q,p)] enters here.--P.wormer 14:53, 24 July 2007 (UTC)

Valid criticism to be sure. Can somebody put in explanations and links to make this stuff more accessible? Otherwise it can only be read by the people who already know about it. P0M (talk) 18:07, 19 December 2007 (UTC)
While fixing something else I noticed that n-sphere is defined at its first occurrence in the article. I'm not sure but what its use (or its reuse) serves a valid function. Maybe some diagrams would help? P0M (talk) 07:39, 20 December 2007 (UTC)


I'm new on here, but I found a source to the Heisenberg qoute in 3.3 Uncertainty Principle in the Intro. to QM but am not sure how to go about adding it, if someone else will or give me more specific instructions that would help.

The html is, and they have it cited as "From "The Development of the Uncertainty Principle", an audiotape produced by Spring Green Multimedia in the UniConcept Scientist Tapes series, © 1974."

Thanks RangerA 04:55, 31 October 2007 (UTC)

Done. The original also cleared up some misreading in the quotation. Thanks. P0M (talk) 07:40, 20 December 2007 (UTC)


Where would I find an explanation of the quantum-mechanical understanding of absorption, for example, the absorption of a photon by an atom? Thinking of a photon as a particle, I can imagine it "hitting" an atom and transferring energy, but as a big wave, I don't see it. —Ben FrantzDale 04:07, 6 November 2007 (UTC)

See Absorption cross section? (talk) 13:45, 19 November 2007 (UTC)

I'll have to look around for some of my old notes to find a good book to direct you to, but I think I can explain the basics.

First, nobody ever actually sees either a photon or an electron, so what is said depends on observing what can be observed and then building a "model" that one hopes will not soon suffer the fate of all analogies.

The history of quantum mechanics is closely tied to the efforts to explain black lines in the spectrums of various sources of radiation. Research into that question led to the idea of electrons being able to be in orbitals only at specific distances from the nucleus of an atom. The emission of a photon was attributed to the dropping of an electron from a higher orbital to a lower orbital. Since the orbits were restricted to certain distances, the energies put into various photons were limited by the energy differences between orbitals. Available orbitals to move electrons into favored the blacking out (absorption) of certain characteristic parts of the spectrum when light passed through a gas or a plasma. So the picture that one forms mentally is of an electron dropping down a notch and, coincident with its assuming a lower energy position, the emission of a packet that carries that energy away. Or, an encounter between an electron and a matching photon can result in the electron jumping to a higher orbit. Think of an inflatable dome building. When the ceiling lowers, air is blown out a doorway. When air is blown in from outside the ceiling goes back up again. But to made a better analogy, air would have to move in and out of the building in "chunks" of a certain size. When a photon encounters an atom it can do either of two things. It can be reflected in a perfectly elastic collision, or, it can cease to exist coincident with an electron of that atom rising to a higher orbit. The probability wave that is involved with the propagation of light across space is theoretically infinite in extent. Where on the surface of that probability wave the photon will be manifest by blackening a photographic emulsion is a matter of probability, but the blackening of the photographic emulsion by that one photon occurs in a very small volume of that emulsion, the volume of the new molecule formed through the agency of the energy donated by the "sacrifice" of the photon. I guess that's one reason that one speaks of the "collapse" of the probability wave. One might make the analogy of a large soap bubble that encounters the tip of a leaf. When the bubble is punctured maybe it will shrink toward the sharp tip of the leaf and the soapy water will all end up on the tip of the leaf.

Our ideas of absorption come from things like paper towels picking up water. The absorption of a photon by an atom is more of a phase change kind of thing. Where does the work I do carrying bricks up a scaffolding? Besides moderately contributing to global warming I also make a brick building. If I am later under the building when it collapses I will be certain that the energy did not disappear. I will personally get part of it back -- at a much higher speed than I put the energy out. That's not a perfect analogy, of course. P0M (talk) 08:50, 20 December 2007 (UTC)

Missing book title

Midway through the article there is an author and a page number, but no book name. "Aitchison" is probably I.J.R. Aitchison. That author has two books currently available:

Gauge Theories in Particle Physics and Relativistic Quantum Mechanics

Can anybody help track down the book and revise the in-line citation? Thanks. P0M (talk) 18:04, 19 December 2007 (UTC)

When I went to patch the hole in explanation of the reason for the matrix math I found the citation -- to an article, not to a book.
I hope I've made the new part (starting with "In approaching the problem that Bohr gave him") clear enough. Without doing an actual lab experiment and doing everything in the real world the rationale for the math is very abstract.
Parts of the explication farther down may need to be tweaked a little due to what I've added. P0M (talk) 18:45, 20 December 2007 (UTC)

Writing needs to be improved

I'm moving on through the article now that I've finally figured out something to say about the matrix math rationale.

The first paragraph of the section called "Uncertainty principle" is terribly muddy. Does anyone understand what the original writer of this part was trying to say well enough to make to both clear and correct? P0M (talk) 18:55, 20 December 2007 (UTC)

A questionable assertion

The text currently claims that:

  • A wave is also a moving stream of particles.

It is not clear whether the writer was confusing light "waves" with water waves, talking about light "waves", or talking about water molecules.

A "photon" is a shorthand way to refer to something that is not a classical particle and is not a classical wave. It is an individually created disturbance that has wave characteristics and particle characteristics. The wave that is named in the definition of a photon is not "a moving stream of particles."

If the writer was talking about water waves, the statement is misleading because the water involved in a wave doesn't move across the surface of the body of water that is disturbed by waves. The molecules in a wave are moved up and down. The particles do not "stream" anywhere.

If one were forced to make a physical analogy, the "particle part" of a light wave could be imagined to be a surfer riding a wave in toward the beach. But there isn't any reason to claim that this surfer is different in kind from the wave that it rides. Analogies are risky, but the passage of a photon would be more like a water wave that moves smoothly across the water surface but, upon hitting the beach, delivers all of its force at a very small volume of space.

Does anyone follow what the original writer was trying to say well enough to clarify this point? P0M (talk) 19:28, 24 December 2007 (UTC)

Someone else marked the above-mentioned section for clarification, and, seeing no way to clarify it I have removed it. The idea of reinterpreting a particle-like description in wave terms and thereby rationalizing the uncertainty factor is interesting but highly technical. If it is going to be in the article it needs to be put in a very cogent way. Otherwise it is a hindrance to the reader who is not already very familiar with the subject. P0M (talk) 23:05, 31 December 2007 (UTC)

added tables

The actual development of matrix mechanics has been made the subject of mystery and even mystification (or maybe it's obfuscation). I've at least found outline information on what went into Heisenberg's original calculations and have added two charts that show the kind of information he was working with and, also, give an indication of how suggestive of matrix math this information becomes when so organized.

Does anyone have access to the actual charts or data sets? P0M (talk) 23:10, 31 December 2007 (UTC)

Dogmatic assertion

Someone has tagged a statement for lack of a citation:

It is not possible to use quantum entanglement for information transfer since it would violate Special Relativity. (citation needed)

The statement is problematical for another reason: it uses theory to attempt to predetermine an empirical observation. At most, one could argue that information transfer using quantum entanglement would be inconsistent with Special Relativity. That's why Einstein et al. thought that quantum mechanics could not be a valid theory, which brings the argument full circle.

There is at least one serious proposal that would have to be given "equal time" if a cleaned up version of the quoted assertion is to be retained.P0M (talk) 17:20, 12 January 2008 (UTC)

See, e.g., P0M (talk) 16:57, 13 January 2008 (UTC)


I think that this article should be moved to Wikibooks... any suggestions? CJ Miller. (That's my name.Don't wear it out.) 01:33, 9 February 2008 (UTC)

Why? P0M (talk) 02:36, 9 February 2008 (UTC)

Is this sentence right?

In the following passage (Section "The Pauli exclusion principle", 3rd paragraph):

According to Schrödinger's equation, there are three quantum states of the electron, but if two electrons can be in the same orbital, there has to be another quantum number

I was trying to follow the text up to here and found this sentence dubious (note that I am a complete layman on QM). Shouldn't it be:

According to Schrödinger's equation, there are three quantum numbers of the electron, but if two electrons can be in the same orbital, there has to be another quantum number (talk) 19:30, 25 March 2008 (UTC)

It is badly written, unfortunately. Besides that, that section is lacking in citations. I think it is one of those statements that can be defended if you can figure out for sure what the writer was trying to say in the first place.
Anyway, thanks for pointing this problem out. I'll have a look at what Pauli had to say on the subject and see whether or not I can make it clearer and peg it to Pauling's The Nature of the Chemical Bond. One good thing is that Pauling is an extremely careful and clear writer. (Why is it that the really great physicists are generally clearer writers than the people who are not such great physicists but try to "popularize" their work?) P0M (talk) 02:31, 27 March 2008 (UTC) (talk) 19:36, 28 March 2008 (UTC) Thanks for addressing my question!


I've read the entire article, and I was wondering if someone could prepare a test for me. I'm home schooled. (talk) 16:22, 16 May 2008 (UTC)

Supposing that I were even willing to to do so, before I could make a test I would have to know what level you are operating at and what your goals are. Right now, I'm more interested in the whole issue of testing since we have a national program that is allegedly forcing primary and secondary schools to "teach to the test."
Testing serves at least two legitimate purposes. The purposes are different, so the tests may be different too. One purpose is to guide learning. Weekly quizzes in a language class are very important because they keep students aware of whether they are actually learning things. Quizzes or exams at longer intervals give a pretty good indication of whether the material is really sticking with the student. Another purposes is to certify competence to other people. If somebody has taken French in college for four years and has gotten all A's, the bank that is thinking of hiring this individual to work in a branch office somewhere in France depends on the college to give a good representation of that student's actual level of competence. The bank will probably make further evaluations after the have chosen the individual as a candidate for the job, but an individual who had C's and D's all the way through his or her education in French would not be a candidate to begin with.
Then there is the question of "inside" and "outside" knowledge. I entered the physics department of a major university with a poor math background. Partly that was due to coming from a small town that did not offer courses in spherical geometry or trigonometry, and partly that was due to my own limitations. Our school divided the year into trimesters. During the first trimester we did mechanics (f=ma, etc., but using calculus to derive formulas rather than memorizing formulas), and I did not do very well. During the second trimester I got an A -- not because my math had improved but because the subject was electricity and I had already spent years doing things like making crystal radios, wiring the light dimmers for the spot lights on the stage of my high school, and trying to understand how things like resistors really work so that I could understand why voltage drops more and more as resistances are added in series, but voltage rises as resistors are added in parallel to whatever resistors were already there. So if the book said the formula for resistors in series is R = Ra + Rb +..., I didn't have to memorize the formula because it was just a representation of what I knew as a fact of life. Our grad student lab instructor knew all the math, but he had never really worked with things like voltmeters, and sometimes he made some funny mistakes. ;-) The third trimester we did thermodynamics, and I was lost again.
Being able to report on what some physicist says about some experiment is far different from having done the experiment yourself. Reporting on what Young said about the double slit experiment is far different from having reproduced the same experiment yourself. And just looking at the fringe pattern is different from working out the relationship between the frequency of the light coming into the apparatus, the width of the slits, the distance between the slits, and the pattern that emerges on the screen.
If you are trying to do the physics major kind of physics, then there is not very much in the Introduction to Quantum Mechanics that can really help you. On top of that, much of the math is beyond the level of a student who has taken college calculus five days a week for an entire year.
The math involved in relativity theory where things like time dilation are calculated is not difficult. The hard thing to do was to ask what would happen if the speed of light was taken as a constant. Imagine that you have a device on board a space ship that can measure the speed of light Light comes in at the nose of the ship and exits at the tail. You note the time a pulse comes in and the time when that pulse goes out, so you can compute the speed. What would it mean for things like the measure of time if you discovered that no matter how fast you flew toward a distant star, and no matter how fast you flew away from it, it took the same amount of time for a pulse of light to pass from one end of your ship to the other? In other words, what would it mean if the speed of light turns out to be a constant? That simple question fueled Einstein's thought.
Another thing that happened around the turn of the 20th century was that scientists realized that you have to be very careful about how you define things, and then you have to be consistent, i.e., it will get you into trouble if you change definitions in the middle of things without realizing what you have just done. When some physicist asked, "How do we measure time?" s/he came up with a simple kind of clock. Instead of using a pendulum and the regularity of its swings to make a "tick," the new kind of clock made a pulse of light travel a long distance, hit a mirror, hit a detector adjacent to the place it left from, and then that incremented a counter and also sent off another pulse. Each trip was a "tick" in the new clock. One of the standard texts of relativity theory starts with this simple experiment and then asks what would happen if two spaceships passed each other in interstellar space.
Now, going back to the Introduction to Quantum Mechanics, what are the insights involved that changed people from talking in terms of classical physics to realizing that they had to use the new physics? What did we learn about the fuzzy parts of our thinking? P0M (talk) 18:58, 16 May 2008 (UTC)