Talk:Introduction to quantum mechanics/Archive 2

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[edit] 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

[edit] 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)

[edit] Do we have a new "decider"?

User Special:Contributions/136.142.20.181 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)

[edit] 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:

\lambda=\frac{h}{p} or p=\frac{h}{\lambda}

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)