Talk:Quantum mechanics

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Image Excellence

Just wanted to mention that the image (the red and black one on top) is excellent! However, is there a source for it? I highly doubt that that picture was taken by a home camera. :D

If you click on the image you can see the image description page. This particular image was uploaded by User:FlorianMarquardt, who I'm sure used some software to create the image rather than a camera. His user page says he mostly uses Yorick (I would've guessed Matlab), but if you want to know for sure how they're done, you can always ask him on his talk page. — Laura Scudder | Talk 15:58, 18 October 2005 (UTC)

Experimental confirmation of predictions

As it stands, experimental confirmation of the theory seems to be mentioned only within the "philosophical consequences" section, where it crops up in relation to the Bell tests and entanglement. Perhaps "Experimental confirmation" should be a section of its own? Caroline Thompson 17:14, 14 Jan 2005 (UTC)

I suggest a separate article; otherwise , too much in one article.

wording quibble

"Quantum mechanics is a physical theory which, for very small objects such as atoms, produces results that are very different and much more accurate than those of classical mechanic" First, it's not just small things, there are macroscopic q. phenomena, eg superconductivity/fluidity/lasers blackbody radiation spectra, heat content of solids, etc ; and it's not that for atoms it provides a more accurate theroy than classical mech, it's that classical mech. doesn't provide ANY theory that's EVEN CLOSE to the facts, for atoms, and those other things I just mentioned. Needs rewriting.67.118.116.145 04:38, 21 Jan 2005 (UTC)

I agree with your points. I made an attempt to address them. Tell me what you think. -Lethe | Talk 05:14, Jan 21, 2005 (UTC)

Gnome!?

In a recent edit, someone added a picture of a garden gnome and nothing else. I could just be missing some obvious connection between gnomes and quantum mechanics, but I doubt it. I'm removing it for the moment.

Feynman

Richard Feynman was not among the founding fathers of QM. I added Pauli's name there instead.--Ashujo Feb 11, 2005

More founding experiments?

Doesn't the line spectra of atomic hydrogen hold its place among the ones mentioned? I am from Sweden so I might be biase to Rydberg, but I guess Bohr migh side with me on this...

Maybe also the photo-ekectric effect - connecting Plank's constant with something else than the black-bodies?

I tried to add the citation to Rydberg, but it would take the addition of Fraunhofer lines etc. etc. So perhaps the citation should go into History of Physics with a link to QM? Ancheta Wis 14:49, 28 August 2005 (UTC)

more fundamental theory

CYD, I noticed that you removed my remark about quantum mechanics being suitable a more fundamental theory. Didn't you like it? Basically, I have in mind that any theory with the larger domain of applicability should be said to be more fundamental. -Lethe | Talk 08:00, Mar 3, 2005 (UTC)

Okay, now I see what you are getting at. I put it back in a slightly different form. -- CYD

new intro

"It is believed to be a more fundamental theory than Newtonian mechanics, because it provides accurate and precise descriptions for many phenomena where Newtonian mechanics drastically fails. Such phenomena include the behavior of systems at atomic length scales and below (in fact, Newtonian mechanics is unable to account for the existence of stable atoms), as well as special macroscopic systems such as superconductors and superfluids."

Many of these failures are more accurately attributed to the failure of Maxwellian electromagnetism.

Also, there needs to be mention of the discovery of the photoelectric effect by Hertz.

I disagree with the above. ""Believed" is superfuous—This fact is more certain than almost anything else in this encyclopedea. Whether something is mechanical or electromagnetic is not a matter of accuracy. Einstein explained the photoelectric effect. I have not seen it mentiond who observed it first. Heinrich Hertz varified Maxwell's equations by inventing radio. I do find a refference to the Frank/Gustav Hertz experiment http://hyperphysics.phy-astr.gsu.edu/hbase/FrHz.html#FH, but that is not exactly the photoelectric effect. --David R. Ingham 15:42, 27 July 2005 (UTC)

I have some comments about the new intro:

1. I like the idea of the new intro. It would be useful to put quantum mechanics into the larger context of other kinds of mechanics.
2. but don't just insert a new intro in front of the existing intro
3. respect the conventions of the article. For example, this article uses the phrase "quantum mechanics" to mean any theory that is quantized. Therefore, to distinguish quantum mechanics from relativistic quantum mechanics is confusing.
4. furthermore, I would not seperate relativistic quantum mechanics from nonrelativistic quantum mechanics. The only difference between the two is basically a choice of Hamiltonian.
5. quantum field theory, on the other hand, is the true marriage of quantum mechanics and relativity. And it is a qualitatively different theory from quantum mechanics (single particle).
6. what you consider to be a significant fraction of the speed of light depends of course on your needs. GPS satellites probably don't even go 0.1% the speed of light, but still the engineers use relativistic mechanics with them. Because they require great accuracy.
7. we changed in the old intro some wording to make clear that it's not the smallness that makes quantum mechanics apply. Some atoms are classical, and some macroscopic systems are quantum. So it's inaccurate to just say "small things like atoms" are quantum systems. and again, it depends on the level of accuracy.
8. Classical mechanics includes many things besides Newtonian mechanics. I would distinguish Hamiltonian and Lagrangian mechanics from Newtonian mechanics. I might also distinguish fluid mechanics, statistical mechanics.
9. what about general relativity? Shouldn't it fit in some where?

-Lethe | Talk 23:40, Apr 13, 2005 (UTC)

To make the article less tedious, how about moving the first five paragraphs elsewhere to other articles in the physics category? This preliminary non-quantum prose might even be a welcome addition to a section of the major physics article. The state of the article when it had just become featured was pretty good. Right now, a re-run of other topics makes for tedious reading. There isn't an equation in sight, for some reason. Ancheta Wis 00:38, 14 Apr 2005 (UTC) My thanks to LauraScudder for the improvements as I was typing this.

As of 08:36, 14 Apr 2005 (UTC), the first paragraph belongs to a parent article. My vote is to move it to physics or mechanics. Ancheta Wis 08:36, 14 Apr 2005 (UTC)

The new intro has got us arguing over whether Newtonian mechanics is all there is to classical mechanics and I've been editing such things too until I realized that the subfields of classical mechanics have nothing to do with quantum mechanics and just distract and confuse the unintiated while boring the others. I shortened that segment to:

Most physicists would divide mechanics into four major areas: classical mechanics, relativistic mechanics, and quantum mechanics.

But in physics, quantum mechanics can be regarded as the fundamental theory.

I think it simplifies the intro significantly and takes it back to the spirit of the first featured version while still putting the field into context for those who want to clicky clicky like mad. The distinction between nonrelativistic quantum mechanics and relativistic quantum field theory is made on the appropriate quantum field theory pages.--Laura Scudder 18:28, 14 Apr 2005 (UTC)

Introduction

You are losing our reader with this introduction, although the worst was taken care of during the last few days. Please consider the frame-of-mind of someone seeking info on "quantum mechanics" as a fairly unfamiliar topic. This reader does not want to hear about Newtonian mechanics, or relativity, or any number of other fancy classifications, at least not until later. Give the reader a break, at plainly start by telling what it is about. And why anyone should take an interest, besides the specialists. April 15, 2005 - Guest

I agree, in making the introduction more "accessible", we have severely bogged it down. Also doesn't really match the Wikiproject science guidelines now either. I'll be bold and if people disagree, edit away and/or discuss here. --Laura Scudder 18:13, 14 Apr 2005 (UTC)

Yes, much nicer. However, I have to say that "relativistic" should not be extracted from either classical or quantum mechanics. Both include relativity (special, of course), and one takes a non-relativistic limit as the need arises. I know that most university course plans start out non-relativistically, and this should of course be mentioned, and is quite reasonable, but it is not really fundamental. We don't hit students with relativity on day one, of course (we wait a couple of months:-). Also, something must be done for the general readers, there has got to be many at this place, and they should be able to come away with something too. -Guest April 15, 2005

It appears you are advocating the position of a reader who has not yet considered the microcosm. This suggests that the article might start off with the atomic hypothesis, then radioactive decay, or perhaps cosmic rays (leakage from a Leyden jar, etc.). ... This approach might then culminate with the statement about general applicability of QM as a fundamental theory, and the current non-relationship to GR. A complete rewrite or new article history of quantum mechanics. Ancheta Wis 10:32, 15 Apr 2005 (UTC) ( By the way, you can date-time-stamp your posts with the 5-tilde notation: ~~~~~ )

Well, yes and no, advocating "the position of a reader that has not yet considered the microcosm". Of course, the large scale history as you describe it belongs elsewhere. However, as anyone who teaches (science not least) will confirm, it is very easy to assume too much pre-knowledge, and not advisable. In a *pedia one really should be forthcoming towards uninitiated readers, at least when dealing with a difficult topic (if ever there was one) which receives much public attention. For instance, consider the general use of the term "theory" as some sort of idle speculation, while quantum theory is often presented in the media as a collection of "puzzles and paradoxes". It ought to be clearly stated up front how most serious an enterprise it really is.

Here is what I had in mind - hope I managed to incorporate your latest contributions. It would perhaps be fair of me to let you know a little of my background, but on the other hand, it's the words that count, so maybe better to do without. -Guest April 15, 2005

Umm, no. An introduction has to introduce the topic clearly and concisely. Quantum mechanics is regarded by virtually all physicists as the most fundamental framework currently available for understanding physical nature (but it is not the only one in use) is a terrible way to start an article. -- CYD

I can assure it is true, and what people want to be sure of when paying tuition - but suit yourself. -Guest April 15, 2005

Let me elaborate on that sentiment. I think, Guest, that you're trying to do an admirable thing by making this article more accessible to the unititiated, especially since it has become featured, but are going about it the wrong way. For someone who doesn't understand the distinctions between fields of physics well, the most important thing to know right off the bat is that quantum mechanics means quantization and that it's the best theory we've got right now (argue that one with the string theorists).

According to Wikiproject science guidelines, we do need to put it into context, but too much context is just making distinctions the newcomer doesn't understand (quantum physics versus quantum mechanics versus quantum field theory - not to mention that I disagree that studying fields is outside of mechanics) while boring the experienced. I think saying its the best theory we've got and has some mindbending consequences (wave-particle duality) is a pretty good motivation take an interest in it. --Laura Scudder | Talk 16:42, 15 Apr 2005 (UTC)

It's the centuries-old question: my kid would do well to become a lawyer or a doctor, but he/she wants to be a physicist (it used to be astronomer) - but that's all up-in-the-air, or isn't it? When coming to an article like this, the reader is entitled to a clear and unambigous statement, of what this subject means in the world, and not to go directly into some jargon for the initiated. As a professional physicst, who has taught quantum mechanics to those kids for a long time, I know very well that the point is quantization, but that makes no sense at all outside of physics. First question to answer: is it any good?

And by the way, from your quotes it seems like you're not looking at my version - which was the "soft learning curve" one. -Guest April 15, 2005

Thank you for your thoughts on the intro. Here is my take on your 4-paragraph precis of QM:

1. QM is a fundamental framework for understanding Nature. It has withstood a century of experimentation, and therefore is worth your intellectual investment required to learn it (as the student).
2. QM applications and successes.
3. QM has some surprises for anyone wishing to invest time learning it.
4. as for QM vs GR, the story is not complete yet; there is hope that you (the student) can add to the physics, should you care to accept the challenge.

I do not disagree that the 4-part story is intriguing. The English is immaterial and can be word-smithed if everyone is agreeable that the 4-part structure (+the 5th para. of names) makes a good intro. I like what I see. Ancheta Wis 02:25, 16 Apr 2005 (UTC)

Now if I may, Prof. G., ask you some questions: The Schrödinger picture is really how I think of the topic, based on my brainwashed view of the flow of time, but I am told that Dirac espoused the Heisenberg picture; it takes an odd frame of mind to view the system using time as an independent variable upon which we can travel at will. I have to admit difficulty visualizing such a system. But if we take a GR POV, and view the cosmos as evolving in time and space, much like a tree growing, I can visualize that. Might it be possible that the Heisenberg picture is more like GR (or statistical mechanics) that way? That would give me more of a feel for the evolution operator. So right away, the framework aspect of QM comes up for explication and evaluation. (Your paragraph 1 of the intro) It's difficult, in another way. Unless the student can take that on faith, somehow. It's like the student has to start all over again, on another kind of kinematics. I would imagine that the dropout rate would be high, to get through the framework part. That implies that the successes (paragraph 2) are what sustains the student. Ancheta Wis 02:25, 16 Apr 2005 (UTC) Yet upon reflection, to state that the framework is the general entry point for learning QM, has to be a conclusion based on the century of development and experimentation; QM certainly didn't start out with that status at all. So the 4 part intro can't be the TOC for an article or course, it would have to start with experiment, perhaps a failed hypothesis or two, and then the string of successes.

Another line of questioning: QM is the basis for computational chemistry, which takes up a ton of computing power. Yet we do not hear much about the codes currently in use by Peter Coveney et. al. I would think that your students could gain some significant experience if they got some background for that area. I still am unclear on how much the QM computer codes compare in processing load, compared say to Earth Simulator.

I recognize that the questions are unfair, but it doesn't hurt to ask. Maybe we can find some answers. Ancheta Wis 02:25, 16 Apr 2005 (UTC)

Umm, most of this is dealt with in the rest of the article, if one bothers to read anything apart from the introduction. See, in particular, the section Interactions with other scientific theories. See also Wikipedia:Manual of Style#Introduction. -- CYD

Reply to Ancheta Wis: Thanks for taking time with my suggested intro (which is at "intro with softer learning curve" here>; it was immediately thrown out by CYD).

Just passing by as a guest, I got somewhat disturbed at the impression an uninitiated reader of this featured article would get. Science is not faring too well among young people, and I find that it is partly due to the way it gets represented in the media: too much nerdy whizzkid, too little serious business. Choosing a line of study, we all need to see the long professional aspect, not just the instant gratification entertainment value. Therefore I find it important to provide a readable and understandable intro, where the reader can hang on as long as possible. I'm pleased to see that you recognize this.

My contribution is/was an attempt to simplify the flow of ideas, which seemed to me to have gotten rather entangled (with all due respect, probably an artefact of the editing procedure). As we all know, of course, to start a fresh version can often help.

Here are my answers to your (welcome) questions (and some thoughts while we're at it):

> QM is a fundamental framework for understanding Nature. It has withstood a century of experimentation, and therefore is worth your intellectual investment required to learn it (as the student).

Indeed, and your financial investment too (as a parent). As a community, physicists can assert this in absolute honesty, and with complete confidence. The scientific test procedures involved in that so many physicists have worked on this, everywhere, every day, for a hundred years, is so tremendous that it needs to be asserted explicitly. No one outside science or technology can possibly have any realistic idea of the degree of certainty that has been achieved here. Now, I am well aware, of course, that as an academic one tends to shy away from making such blunt statements - and that's why it's not well understood outside of science. Now, since practically every professional physicist (and chemist as well, I suppose) agrees, I believe it should be said here, in this article, in an unambigous statement, that, this is what most of us find, and that many of us use quantum mechanics day in and day out (except, of course, ... you know). It does not have to be presented as an absolute and final truth (which no physicist of course would subscribe to), but the strong confidence must come through. It is justified.

> QM applications and successes.

Yes, most readers will appreciate this when listed in general terms. And I linked to the quantum specific pages.

> QM has some surprises for anyone wishing to invest time learning it.

Now that we have said that quantum mechanics is serious, and works, it's motivating to know this.

> as for QM vs GR, the story is not complete yet; there is hope that you (the student) can add to the physics, should you care to accept the challenge.

Yes, we really hope that one of you (students) will be the one to make a discovery, like what Planck did, to find the more fundamental framework of the future.

> I do not disagree that the 4-part story is intriguing. The English is immaterial and can be word-smithed if everyone is agreeable that the 4-part structure (+the 5th para. of names) makes a good intro. I like what I see. Ancheta Wis 02:25, 16 Apr 2005 (UTC)

Thanks.

> Now if I may, Prof. G., ask you some questions: The Schrödinger picture is really how I think of the topic, based on my brainwashed view of the flow of time, but I am told that Dirac espoused the Heisenberg picture; it takes an odd frame of mind to view the system using time as an independent variable upon which we can travel at will. I have to admit difficulty visualizing such a system. But if we take a GR POV, and view the cosmos as evolving in time and space, much like a tree growing, I can visualize that. Might it be possible that the Heisenberg picture is more like GR (or statistical mechanics) that way? That would give me more of a feel for the evolution operator. So right away, the framework aspect of QM comes up for explication and evaluation. (Your paragraph 1 of the intro)

As you know, the Heisenberg picture is mathematically and physically equivalent to the Schrödinger picture, by unitary transformation. It is good for theoretical work, and is quite widely used. For visualization, I recommend using the H picture with the Ehrenfest procedure, to recover the Newton equations of motion, where the time dependence nicely associates with the observables, as we are used to. Indeed, in this way I derive classical relativistic electrodynamics, for the (graduate) students in relativistic quantum mechanics, so it is basically all there.

> It's difficult, in another way. Unless the student can take that on faith, somehow. It's like the student has to start all over again, on another kind of kinematics. I would imagine that the dropout rate would be high, to get through the framework part. That implies that the successes (paragraph 2) are what sustains the student. Ancheta Wis 02:25, 16 Apr 2005 (UTC)

Yes, we wait until the second year to do q.m., but in principle one could start with it, in principle. If systematically presented it is not hard to understand, but the mathematical framework must be taught in mathematics beforehand. Many students, of course, are more interested in other things, and just need to see a bit of it, at some stage, to be convinced that it works, and understand how material properties get deduced in q.m. Some day we may even be able to compute masses, some day...

> Yet upon reflection, to state that the framework is the general entry point for learning QM, has to be a conclusion based on the century of development and experimentation; QM certainly didn't start out with that status at all. So the 4 part intro can't be the TOC for an article or course, it would have to start with experiment, perhaps a failed hypothesis or two, and then the string of successes.

Indeed, so we should imply these empirical foundations via the Part 2. Anyhow, It still helps to know that there is a reliable mathematical framework, even if you do not intend to become a specialist in it. So the general framework part is important for building confidence, although the learning is done via more specialized calculus formulations. Hope I understood your question here.

> Another line of questioning: QM is the basis for computational chemistry, which takes up a ton of computing power. Yet we do not hear much about the codes currently in use by Peter Coveney et. al. I would think that your students could gain some significant experience if they got some background for that area. I still am unclear on how much the QM computer codes compare in processing load, compared say to Earth Simulator.

This topic is beyond my scope, so I have to pass on that.

> I recognize that the questions are unfair, but it doesn't hurt to ask. Maybe we can find some answers. Ancheta Wis 02:25, 16 Apr 2005 (UTC)

Not at all. Let's hope it becomes possible to have an introduction that part of the way, at least, makes sense to all readers. -Guest April 16, 2005

Dear writers. Quantum Mechanics is a difficult and confusing subject. What is the essence ? How can it be explained shortly and understandably ? To me it is the following. "Quantum Mechanics identifies energy and frequency. The unit of frequency, the hertz, is also a unit of energy. The number of joules per hertz is Planck's constant. As energy is a property of particles and frequency is a property of waves, quantum mechanics identifies particles and waves. When the frequency is low, the particle aspect fades away and it looks like 'classical' waves like those on the sea. When the energy is high, the wave aspect fades away and it looks like 'classical' particles like grains of sand. So Quantum Mechanics merges two distinct classical theories into one. It is actually a conceptual simplification". Bo Jacoby 09:49, 13 September 2005 (UTC)

Yes, that's why I added electromagnetism in the first paragraph, but I am not sure "unifies" is the best word. I think "Quantum mechanics is a theory of mechanics, a branch of physics that deals with the motion of bodies" is wrong. It is not a theory, it is the theory, and as above it is not just about mechanics, or at least that implies lack of generality. I'll see if I can find an improvement. --David R. Ingham 16:30, 13 September 2005 (UTC)

Needs a more simplified definition for the lay person

"Quantum mechanics is a fundamental physical theory that extends, corrects and unifies Newtonian mechanics and Maxwellian electromagnetism, at the atomic and subatomic levels." is going to tell a person SQUAT unless they already know what newtonian mechanics and maxwellian electromagnetism is. A more simplified basic definition is needed before expounding in the excellent detail this article gives.

well i am a layman (high school student infact) and i dont find the introduction difficult

-protecter

I wouldn't have had any problem understanding that when I was in high school either, because I had already read a lot of physics and astronomy, but not everyone is so interested in science.

How about adding, at the very top, something like "Quantum mechanics is based on the observation that, on a very small scale, waves and particles are not different sorts of object but complementary properties of all objects." --David R. Ingham 20:29, 19 September 2005 (UTC)

Or how about, at the very top, "Quantum mechanics accounts for the fact that motion, as well as matter, does not have unlimited detail, but is built up of tiny elements. The tiney elements of matter are called atoms. The tiney elements of motion are called quanta." This is the way I started to introduce the idea to a smart ten year old (and her mother). (This omits optics, but, at this level, that is appropriate.) David R. Ingham 17:57, 28 September 2005 (UTC)

I have to agree with David. Having a good basic layman's knowledge of the subject, I found the intro overwelming. There is no mention of what makes Quantum mechanics so exciting, a simple explaination of wave/partical duality. Maybe an early reference to the "double slit" experiment to give the newer readers an idea what it's all about. Everything in the intro is needed, but maybe not all of it in the intro. Intro should be shorter, more attention grabbing. Just a thought. 12.218.132.240 13:17, 7 December 2005 (UTC) S. O'Reilly 12/7/2005

generality

People took out my generalization of the introduction. Please read The Feynman Lectures on Physics, vol. 3 first. He words it much differently, but he does explain the generality when he introcuces the subject. So what I said is not only true, but it is the best known way to teach quantum mechanics. If this makes it too hard to read, then re-word it or add something more basic, as my suggestions in the previous sub-heading, above it. David R. Ingham 17:57, 28 September 2005 (UTC)

Navbox

In order to make the quantum-theory Navbox more accessible in the other articles, I propose that it move up just under a heading, such as Quantum mechanics#Quantum mechanical effects. Thus by inserting a parenthetical link ([other articles on QM]) in the child articles, the Navbox becomes more accessible other places. Is that alright with everyone? Alternatively, smaller versions of the quantum-theory Navbox might be placed in the child articles; as its transclusion would overwhelm many of them, currently. Ancheta Wis 08:25, 19 Apr 2005 (UTC) Template:TopicInQuantum-theory As it turns out, the first article I had chosen , on the commutation relation, did not have a link back to QM, so I inserted a small version of the Navbox there. The other articles appear to at least mention this page, so the need for a link to the Navbox is partially answered already. The little navbox is titled {{TopicInQuantum-theory}}

Minor edit

I removed this paragraph, which can't be understood (to put it nicely):

Another difficulty with quantum mechanics is that the nature of an object isn't known, in the sense that an object's position, or the shape of the spatial distribution of the probability of presence, is only known by the properties (charge for example) and the environment (presence of an electric potential).

-Guest April 19, 2005

I am reading a book "Quantum Generations: The History of Physics in the Twentieth Century" by Helge Kraugh that details all the inaccuracies and crises in quantum theory as it developed over the past century. The statement: "The predictions of quantum mechanics have never been disproved after a century of experiments." (introduction, 7th paragraph) is completely false and I removed the sentence. It had repeatedly been contradicted and the science has very clumsily evolved due to all these contradictions.

-Brian, February 5th, 2006

You know, how do you reconcile the predictions of Quantum Electrodynamics with your categorical statement? Are you in fact talking about the shift from the Classical to a QM viewpoint? Are you disagreeing with the QM framework? The QM framework is very broad. Curious to hear more critique by Helge Kraugh . --Ancheta Wis 22:21, 5 February 2006 (UTC)

I am not talking about Quantum Electrodynamics specifically but about QM as a whole. Each major experimental or theoretical development (discovery of new particles, uncertainty/complimentary theory, properties of high energy cosmic particles, etc) was argued and often rejected or ignored among the leading physicians at the time it was concieved. While many of these were wrong, the ones that were right often conflicted directly with the current theories and provoked serious modifications. Some of these (that are currently accepted) weren't taken seriously until decades after they were formulated.

I am not rejecting quantum mechanics. What I am rejecting is a theory of quantum mechanics that was developed in the early 1900's and remained unchanged and accounted for everything. Quantum mechanics evolved as scientists gathered more experimental evidence and dispelled groundless theories. Even the basics of quantum theory (such as the existance of the nucleus, the proton and the neutron) wasn't even accepted or confirmed by experiment until less than 100 years ago. The neutron wasn't confirmed until 1932.

The statement "The predictions of quantum mechanics have never been disproved after a century of experiments." is false not because quantum mechanics is entirely wrong (it is not) but because quantum mechanics has historically been a very unstable field. Disproofs and contradictions have been a major force driving its development throughout its history.

-Brian, February 5th

The 6th Solvay Conference (1930) is the one where Einstein decisively lost his debate with Bohr; thereafter Einstein refrained from direct attacks and instead used philosophical arguments against QM. Using the QM machinery, he formulated the EPR paradox, leading to Schrödinger's cat etc. I am curious what Helge Kraugh has to say about this; we, as a civilization, have not yet come to terms with what QM has to say about this. The QM framework includes definite predictions, some of which have subsequently been observed. Those observations have to be counted as successes for the framework (i.e., Schrödinger equation etc.). --Ancheta Wis 03:23, 6 February 2006 (UTC)

BTW we need an article on Théophile De Donder (he wrote on relativistic QM and was a supporter of Einstein). De Donder was a major influence on Ilya Prigogine. Does Kraugh mention De Donder? Ancheta Wis

Hmmm, we might be arguing along different lines. Kraugh repeats exactly what you said above.

I just read the history section and I see where a problem could arise: between old quantum theory and new quantum theory. Since the wording was "a century" I intepreted the meaning to be "since 1900". But it is probably since the mid to late 30's, which I have little knowledge of. The 1920's and early 30's were full of the crises, dead ends, the freak discoveries and ignorance to correct theories that I was talking about. Specifically, Helge Kraugh mentions that high energy particles, available at that time only from cosmic rays, did not fit the mathematical model used for lower energy particles. The problems with the 1929 Heisenberg-Pauli theory of QED was emphasized. She states: "In spite of promising features, it was infected with paradoxes and divergent quantities. In particular, the self-energy of the electron (the energy of an electron in its own electromagnetic field) turned out to be infinate, which was, of course, an unacceptable result." She also includes a 1933 letter from Robert Oppenheimer to his brother: "As you undoubtedly know, theoretical physics- what with the haunting ghosts of neutrinos, the Copenhagen conviction, against all evidence, that cosmic rays are protons, Born's absolutely unquantizable field theory, the divergent difficulties with the positron, and the utter impossibility of making a rigorous calculation at all- is in a hell of a way" The Einstein-Bohr arguments, as well as other examples (the faulty early atomic models; the electromagnetic view of the early 1900's; the often rejected theories of relativity; and the problems that erupted when antiparticles and other non-fundamental particles were discovered) are some examples of how the physics community was not all on the same page. Helge Kraugh continually depicts the early years of quantum physics (atleast till the mid 30's) as a period where quantum physics confused the most brilliant minds and divided the whole community over a number of issues. She details many theories of quantum physics which couldn't be agreed upon unless proven or disproven through experiments. Are you referring to the QEM models from the late 30's?

I have been looking for references to De Donder but have not been able to find any yet. Sorry about that. I'll let you know if I do.

-Brian, February 6

QM arose historically from spectroscopy, cosmic rays, and radioactivity (called 'modern physics' -- the physics after Newton and Maxwell's pictures of the world). At the beginning of the twentieth century, there was still the concept that the atom was the ultimate Platonic object, indivisible and immortal (or 'hard spheres', in physics-talk). Statistical mechanics can be formulated from this mental picture, which can be used to derive thermodynamics. But in 'reality' the hard spheres are in flux - the neutron decays into its constituent parts in 15 minutes. Our very bodies are in flux. QM takes this as a given. It has taken a century (loosely speaking) to renounce the little spheres and replace them with jello -- a world of approximate objects with finite lifetimes. (Now I admit that protons have very long lifetimes.) Even in the realm of very low temperatures, the objects are still jello-like; they jiggle. Eric Cornell has illustrated this very well in his public lectures. The pictures of Newton and Maxwell are still valuable, of course; the engineered objects we use today were built from this worldview, but there are more POV's out there, resting on QM, like lasers. --Ancheta Wis 11:14, 8 February 2006 (UTC)

From up top of this section, "difficulty with quantum mechanics" is entirely wrong. The "difficulty" is with ordinary language, which is not intended to deal with the microscopic world. David R. Ingham 09:45, 12 February 2006 (UTC)

From the bottom paragraph, "Statistical mechanics can be formulated from this mental picture" is not correct. First, one cannot directly formulate equations from mental pictures, in the sense of pictures that can be expressed easily in words. Historically, part of the origin of qm was that the statistical mechanics that was formulated from the classical view of nature, that it had unlimited detail like the Mandelrot set, was inconsistent or gave unrealistic results.

David R. Ingham, I appreciate your comment; the hard sphere approach is the program of Kerson Huang's Statistical Mechanics. Huang was a collaborator with Max Born, as well. Michael Faraday formulated the picture which Maxwell proceeded to express in his equations. --Ancheta Wis 11:54, 12 February 2006 (UTC)

"engineered objects we use today were built from this worldview" is not exactly correct. Did you mean the simpler objects like floor mops and earth dams? Qm has been used to understand semiconductors since at least the time Bell Labs invented the transistor. Chemistry has depended heavily on qm, at least since Linus Pauling explained the chemical bond. Lasers, though in principle a classical phenomenon, have always been understood using quantum mechanics. As an engineer as well as a physicist, I feel slighted by that remark.

David R. Ingham 10:30, 12 February 2006 (UTC)

David R. Ingham, I do not disagree, and actually believe that lasers are squarely in the QM world because lasers use QM phenomena for the laser action. My personal belief is that QM's most useful contribution is the solid explanation of the periodic table. But even a transistor can be understood, from an engineering POV, without QM. 'Guest' is the one who removed the sentence in the 'minor edit'; Guest mentioned that the Ehrenfest procedure can be used to map a QM description (in the Heisenberg picture) to a time-averaged description which seems somehow less abstract to me. So I admit that the Schrödinger picture feels more real to me. But I am trying to formulation a question for you. Something seems entangled here (pun intended). If a macroscopic-scale observer, who seems to get time from his scale , were to shrink down to electron-sized scale, would time flow equally for him? I am not trying to trip you up. I am honestly trying to get an insight here. If the Ehrenfest procedure is an important-enough process to give us time, then it ought to be possible to come up with a phenomenon which transcends time, just as q. entanglement transcends space. From a macroscopic perspective, that seems to contradict my prejudices. If we somehow could define simultaneity using some natural feature like polarization or spin, we could define some pretty good clocks, etc. --Ancheta Wis 11:54, 12 February 2006 (UTC)

I can sharpen my question -- QM applies even at regions of low temperature, where the celebrated BEC phenomena occur, and which show QM up at macroscopic scale. Obviously QM applies to the very small, with apparent applications at macroscopic scale (lasers, transistors, etc.). There are other continuous parameters out there; mass is one example. If we could shrink the quantity of mass for an object, what would happen? Would time flow equally for two synchronized objects, one of which was subject to decay in mass? Conversely, what would remain invariant? --Ancheta Wis 12:16, 12 February 2006 (UTC)

Ancheta Wis, I think I finally understand your intepretation of that sentence. You meant "Quantum mechanics as a worldview has never been discredited by experimentation during its century long development. Experiments support this jello-like existance of the atom." I completely agree with that intepretation. As you have probably guessed, I derived a very literal meaning of the sentence: "The sole Quantum mechanical theory, proposed around 1900, has predicted a whole bunch of stuff that can't be disproven by experiments." You can see why this bothered me.

"The predictions of quantum mechanics have never been disproved after a century of experiments." may need to be reworded before it is reinserted.

-Brian, February 13

Entanglement, 1905

Looking back on a certain historic event, it is possible to characterize the following as an type of quantum entanglement -- just view the clocks referred to below as Cesium clocks : Einstein's 1905 special relativity challenged the notion of an absolute definition for times, and could only formulate a definition of synchronization for clocks that mark a linear flow of timeTemplate:Fn:

If at the point A of space there is a clock ... If there is at the point B of space there is another clock in all respects resembling the one at A ... it is not possible without further assumption to compare, in respect of time, an event at A with an event at B. ... We assume that ...

1. If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B.

2. If the clock at A synchronizes with the clock at B, and also with the clock at C, the clocks at B and C also synchronize with each other.

• Template:Fnb Einstein 1905, Zur Elektrodynamik bewegter Körper [On the electrodynamics of moving bodies] reprinted 1922 in Das Relativitätsprinzip, B.G. Teubner, Leipzig. The Principles of Relativity: A Collection of Original Papers on the Special Theory of Relativity, by H.A. Lorentz, A. Einstein, H. Minkowski, and W. H. Weyl, is part of Fortschritte der mathematischen Wissenschaften in Monographien, Heft 2. The English translation is by W. Perrett and G.B. Jeffrey, reprinted on page 1169 of On the Shoulders of Giants:The Great Works of Physics and Astronomy (works by Copernicus, Kepler, Galileo, Newton, and Einstein). Stephen Hawking, ed. 2002 ISBN 0-7624-1348-4

Quantum Physicists are just catching up with Relativity!

I understand quantum mechanics just enough, not to make any great discoveries in the field, but enough to understand the basics. Special Relativity is the same way. I found something interesting though, relativity implies both wave-particle duality and supersymmetry! A wave is a carrier of eneergy from place to place. A paritcle can be viewed as a carrier of mass from place to place. Relativity says energy is the fourth-dimensional extendsion of momentum (which is mass times velosity). This implies that waves are fourth-dimensional extendsion of particles! This also implies that the carriers of energy (Bosons) are extendsions of the carriers of mass (Fermions)! Wave-particle duality and supersymmetry. It seems so simple I'm surprized that this was overlooked for so many years.--SurrealWarrior 18:35, 20 Jun 2005 (UTC)

Reverted contribution.

If we are going to retain the "Bohm interpretation" which is "not popular among physicists", surely we also need the main stream interpretation that I was taught in graduate school by famous physicists. I propose including the following:

"According to a lecture by Herbert P. Broida to his students at UCSB, the probabilities and other difficulties always come from the relation between quantum and classical physics, not from quantum mechanics in isolation. To explain the meaning of this, since Classical Mechanics is now only an approximation to quantum mechanics (the same approximation as Geometric Optics) and not an independent theory, this makes the probabilities belong to classical physics, not to quantum mechanics. The difficulty is that one cannot do any experiment without using Classical Mechanics to describe the apparatus."

There is also a problem that the "interpretations" listed here don't confine themselves to philosophical interpretation. The "Bohm interpretation", as described, is physically verifiable and therefore physics rather than philosophy. The "Everett many-worlds interpretation" on the other hand is so unverifiable that it is not even philosophy.

Quantum mechanics has become established, over a full century and is in no way in question. If it were in question, that would be a matter of physics, not philosophy. The philosophical issue is how to speak about it. The way that research physicists do speak about it is to call the quantum wave function "reality" and Classical Mechanics an "approximation".

David R. Ingham 4 July 2005 17:48 (UTC)

I think the paragraph is vague, except for the last sentence: "The difficulty is that one cannot do any experiment without using Classical Mechanics to describe the apparatus." With a little more clarity, this is more of a measurement in quantum mechanics type of contribution. Also, skip the Broida reference unless you want to explain who he is. PAR 4 July 2005 19:59 (UTC)

I'll think about it some more. I strongly feel that it is wrong, to ascribe probability to quantum mechanics, when it really belongs to the Classical Mechanics (= Geometric Optics) ray approximation to the quantum mechanics of massive particles, and to the zero energy per particle approximation to the quantum mechanics of light and sound. The Copenhagen Interpretation did not go far enough in this direction. The statement that "all of the mathematical consequences of quantum mechanics can be trusted" is enough to get right answers, but it is not philosophically tidy— One might be led away from using wave packets to account for details of the interaction between microscopic and macroscopic systems, when they are needed. David R. Ingham 5 July 2005 23:23 (UTC)

I sympathize. I have my own personal points of view on quantum mechanics, which are at odds with or not addressed in this article, but I don't think this article is the place to air them. This article should contain only those aspects of quantum mechanics where there is rather broad agreement, and a list of contentious areas with enough information so that someone who is interested can follow up. PAR 5 July 2005 23:45 (UTC)

I agree. Karol July 6, 2005 07:31 (UTC)

The Ultimate Unified Theory?

It seems that in the 20th century, Quantum Mechanics and Relativity are the only leading theories, because General Relativity is not capable of describing the beginning of the universe etc., another "ingredient" is required to make the "recipe" perfect, and it seems that Quantum Mechanics is the best candidate. If unified, the new theory shall be named as Quantum Theory of Gravity, which Wikipedia has an excellent on it, we should start working! For information on the grand unified theory, superstring theory is the best candidate that can unify everything, I am not very sure about that, and superstring theory also seems to be the most popular theory. When you try to apply to work as a researcher in a physics working office, it seems that you will be instantly selected to work in their office if you study superstring theory, and if you study other theory, they will consider considering you as their researcher colleage, which is quite a pain. Anyway, I think that a unified theory, or the Grand Unified Theory (which is quite of an exaggeration) is definately needed to describe our own cosmic habitat. Feel free to email me to discuss about issues on quantum mechanics and physics etc.: timothyphtse@gmail.com

uncertainty principle

i have a question about degenerated matter. when a star shrinks, the maxium uncertainty in the position of a particle for example electron decreases, so it minimum uncertainty in momentum increase. what i dont understand is what is uncertainty in momentum? does it mean that the particle is traveling with multiple momentum at the same time? because i read from somewhere as the minimum uncertain momentum increase the particle's minimum velocity increase, and i just dont get it (is it like the particle's velocity can be 0-something?)

Yes, a particle does have multiple momenta and multiple velocities at the same time, just like a particle of light goes through both holes in a diffraction experiment or through both sides of the lens of a camera or telescope. To really understand this you have to accept that the description of a particle's motion with a single momentum and single position is an approximation that breaks down on a very small scale. It is the same approximation as Geometric Optics. To really understand quantum mechanics you need to give up thinking that a particle really is in a single place. The only reality (though not the only mathematical description of reality†) is the wave function. If you want to get closer to what you see directly, take up art or literature. --David R. Ingham 17:59, 18 July 2005 (UTC)

†The Heisenberg formulation does not take the form of a function.

• Robert Martin Eisberg, Fundamentals of Modern Physics, John Wiley and Sons, 1961, p. 177

--David R. Ingham 04:41, 26 August 2005 (UTC)

Bohm interpretation

There seem to be other problems with this paragraph, besides not being elegant physics. The Schrödinger equation is not a function but a unique and explicit formula for the time development of the wave equation. Non-locality is a property of equations, not of functions. If distant particles interact instantaneously, that is not described by the Schrödinger equation, which is local. Non-locality is physics and not philosophy. --David R. Ingham 21:19, 24 July 2005 (UTC)

Improvement Drive

A related topic, Astrophysics is currently nominated on Wikipedia:This week's improvement drive. Come and support the nomination or comment on it.--Fenice 07:31, 6 August 2005 (UTC)

spin

can someone please tell me what is spin? i heard it can be oriented in up and down and its parallel/antiparallel to the local magnetic field, but whats all that "spin 1/2, 2,1, 0"? like everywhere i read about spin it never says what it is, only it is an intrinsic angular momentum. what does that mean? maybe i just dont know when it is telling what it is, can someone just tell me in ordinary language? (not like everyday language, just dont use a technical term in every sentence)

thanks

-protecter

To begin with, it is the angular momentum of a particle, in units of ℏ (h bar is Planck's constant deviede by 2 π). Angular momentum can change only by integer multiples of ℏ, that is, it is quantized. --David R. Ingham 23:45, 8 August 2005 (UTC) Revised in format--David R. Ingham 16:34, 9 August 2005 (UTC)

---

angular momentum tells you stuff like how much how long you'll have to apply a torque to something to get it to stop moving, and how fast other things will will start spinning if they collide with that something. Angular momentum usually comes from things that are rotating, but elementary particles also have a built-in angular momentum, just like they have a built in charge. The total angular momentum of something is the sum of all the intrinsic angular momenta as well as the orbital angular momenta (which are the angular momenta that come from rotating).

you can't take away intrinsic angular momentum from a particle, it's always there, so the analogy with torques and collisions doesn't apply. But you can still tell that the intrinsic angular momentum is there from things like the dipole moment (electric or magnetic) of a particle.

The number you hear associated to spin (0, 1/2, 1, 2) tells you how the thing behaves under rotation. Like, a dipole behaves like a pointing finger, when you rotate it 30 degrees, the finger points 30 degrees further. Other things behave slightly differently. Like if you rotate your coordinate system 30 degrees, and consider the moment of inertia of an object, you have to apply two 30 degree rotations to two coordinate axes to get the new moment of inertia. That's because moment of inertia is a second rank tensor.

So that spin number really tells you how things behave under rotation. Electric fields behave like vectors, and anything that behaves like a vector is called spin 1. anything that behaves like a second rank tensor is called spin 2. things that behave like invariants (look the same no matter how you rotate) are called spin 0.

And when you add quantum mechanics into the mix, you gain the possibility of things that have half integer spin. These guys pick up a minus sign when you rotate all the way around.

according to the spin statistics theorem, spin also determines whether things act like fermions (with the Pauli exclusion principle) or like bosons (which have no Pauli exclusion principle.

After you plug through some math, you find that the spin number, which tells you how things behave under rotation, is proportional to the angular momentum, which tells you how torques apply and how collisions happen. so spin tells you both how things behave when you rotate your coordinates, as well as how much angular momentum something has. the fact that some angular momentum is intrinsic just means that it doesn't come from rotating objects, but is just there. -Lethe | Talk 01:37, August 9, 2005 (UTC)

thankyou for your explanation, i have now a faint idea of what it means. however i am finding it a bit advanced for me. (never heard of second rank tensor). so are you basically saying spin describes the direction of the field (like dipole) around a particle under rotations? also, this may sound silly, when do they teach the full concept of spin?

-protecter

the easiest way to think of a second rank tensor is just to think of it as a 3x3 matrix (although that misses a lot of the meaning). when you do a change of basis to a matrix A, you have to multiply it something like D^TAD, where D is the change of basis matrix. The point is to notice that you have to multiply by the change of basis matrix twice, once on the left (which a transpose or inverse) and once on the right. A third rank tensor would get multiplied three times. This is one way to understand tensors, though eventually you'll want a more intrinsic understanding.

a vector is a first rank tensor, because when you change basis, the vector v goes to Dv. a vector can be represented by 3 components while a second rank tensor uses 9 components. So it's not 100% accurate to think of a second rank tensor as a pointing arrow. On the other hand, it is sometimes possible. (technical stuff: if the tensor is symmetric and traceless, for example. then it lives in a faithful irrep of the rotation group, and we can assign a unique rotation to it.)

so yes, to answer your question, the spin describes the direction of thhe field (like a dipole). that's the general idea. to understand it better of course, you'll have to learn the math.

so, where do they teach spin? of course, everyone's first introduction is in their Quantum Mechanics class, but I find that the lessons learned there are unsatisfactory. You'll get some more mathematical machinery in quantum field theory, although some of the more experimental particle physics text (Peskin and Schroder?) still leave you confused. The best way to learn it is to take a course in representation theory (of Lie groups, especially), and then just sit and think about how physical systems have to live in irreps of the rotation group (or its central extension, in the case of a quantum system). you will have learned what the irreps of the rotation group are in your representation theory course. there are 1, 2, 3, 4... etc dimensional representations. then you write down a field theory and discover that a system that lives in the n-dimensional rep has intrinsic angular momentum (n-1)/2. When you learn how to construct these representations, you'll see that the 1 dimensional rep is just a scalar (scalars have 1 component), the 2 dimensional rep is a spinor (spinors have 2 components), like you learn in QM, the 3 dimensional rep is a vector (3 components), the 4 dimensional rep is a spin-3/2 space like a vector times a spinor, the 5 dimensional irrep is a rank-2 symmetric traceless tensor, so that's what describes a spin-2 system. (2 = (5-1)/2)

To sum up, representation theory tells you what possible multicomponent guys there are that behave simply under rotations. how they behave under rotations tells you what their angular momentum is, and the rep tells you what kinds of objects can have that angular momentum. Quantum field theory books have the most relevant coverage, but they're notoriously hard to read if you don't already know what they're talking about. -Lethe | Talk 08:05, August 16, 2005 (UTC)

To sum up,

Spin of light

In quantum mechanics, the polarization of light and other wave length ranges of electromagnetic radiation is called the spin or helicity of the photons (particles). Linearly polarized light consists of photons that have a linear combination of positive and negative helicity.--David R. Ingham 17:33, 9 August 2005 (UTC)

quantum mechanics and general relativity, in the introduction

I am not sure about the statement that this combination is a problem, but I don't know enough to change it, at this time. The theory of the decay of black holes seems to indicate that the two can work together. As I remember, propagating gravitons (gravity particles) present no problem.

There is a very real problem in describing gravity quantum mechanically; Google for it. The Hawking black hole radiation theory is not really relevant, because it's only a "semiclassical" theory. You could say that it describes the effect of gravity on quantum mechanics, while ignoring the effects of quantum mechanics on gravity. -- CYD

What does this sentence in the introduction mean: "Often, it is the answer to questions when general relativity fails." ?
I find it a weak sentence and am going to change it but before I do that would someone like to pipe up if there is a deep signifigance to it that should keep it as is? -- Sajendra

Category

Why is it in the category "Unsolved problems in physics"?

the article quantum teleportation

i have posted here because i think no one will respond at the discussion there

it says: Indistinguishability Let's say that Alice has a rubidium atom (the element physicists in this field like to use for their experiments), which is in its ground state, and Bob also has such an atom, as well in its ground state. It is important to see that these two atoms are indistinguishable; that means that there really is no difference between them.

If Alice and Bob had, say, two glass balls, which exactly look alike, and they exchanged them, then something would change. If you had a powerful microscope, you could certainly find some difference between the two balls. For atoms of the same kind and in the same quantum state, however, there really is no difference at all. The physical situation with Alice having the first atom and Bob the second is exactly the same as vice versa.1 In a certain sense, it is even wrong to say that the two atoms have any individuality or identity. It would be more appropriate to say that the two locations in space both have the property that the fundamental quantum fields have those values which define the ground state of the rubidium atom.

how can rubidium atoms be in the same quantum state? are they like helium 4 or something? or does the exclusion principle apply only through a maximum distance? sorry for the stupid question but im the person who asked the spin so you would know i dunno much

-protecter

plain English section needed!

I am an (ex-)physicist, but also a writer, and frankly the article on Quantum Mechanics causes me pain to read, or at least the introduction. There should be a plain English paragraph at the start for the non-technical reader who has stumbled here or just wants a quick idea what's going on. This article reads like it was written by physicists for physicists. This is an encyclopaedia, not the Feyman lectures!

In fact, I propose that every technical article of any length should have a plain English paragraph. Feynman said (I'm paraphrasing) that if you can't explain something to a 1st year college student then you don't understand it fully. We need a paragraph for an even lower level than this, in essence making the absolute minimum assumptions of the reader's prior knowledge.

Alternatively, I propose that long technical articles could have a separate "explanatory" article written in the simplest language possible.

Here is a quick shot:

"Quantum Mechanics is a theory in physics which primarily tries to explain how extremely small bodies, such as atoms, behave. Scientists generally agree that it is a very accurate and successful theory and it has very important applications in today's world as all electronic devices, such as computer chips, depend on Quantum Mechanics is some way. It is also important in understanding how large objects such as stars and the Universe as a whole are the way they are.

Despite how successful Quantum Mechanics is at explaining what we see, it does it does have some controversial elements. For example, the behaviour of microscopic objects is very different from the behaviour of everyday objects, and some of its results appear to contradict the Theory of Relativity." Paulc1001 13:03, 1 October 2005 (UTC)

To paraphrase Eric Cornell, we might add to "extremely small bodies" the phrase "wavelike entities". Their wavelike character becomes become more and more apparent as we explore the regimes of extremely low temperatures. In other words, their edges cease to become distinct but merge into each other, even at macroscopic scale. For example, in his public lectures he displays a picture of rubidium Bose Einstein condensate at millimeter scale for a collection of about a million Rb atoms in a magnetic trap, at a millionth of a Kelvin, with a common wave function. A wave function 1 millimeter across! (He actually characterized it as a picture of a wave function squared.) I am trying to ascertain the license conditions for his images, as he works for NIST. They would be a dramatic addition to the QM article as examples of wave functions. Ancheta Wis 15:12, 15 October 2005 (UTC)

Meh. The fact that you can see quantum mechanics on a macroscopic scale in BEC's is nice but hardly new. BEC's are basically another type of superfluid. We've had experimental evidence of those for around sixty or ninety years, depending on how you count. -- CYD

The distribution of the superfluid vortices in Cornell's image is highly regular, beautiful even. I am trying to find a good public image for others to see. The image is nontrivial. Ancheta Wis 10:16, 24 October 2005 (UTC)

Again, the vortices that you see in BEC are exactly the same as vortices in superfluid helium and superconductors (in fact, the ability to form vortices is "built-in" to the idea of a superfluid). Here's an image of vortices in a superconductor from 1967: [1] -- CYD

I tried to read this to learn more on the topic and gave up. I strongly suggest a very simplified page in the simple english wiki.

One thing that is wrong in the proposed Plain English description is the characterization of atoms as "extremely small bodies": common experience would make those bodies 'little hard ball bearings' but that is exactly the point of the BEC discussion above -- they are not little -- they can be 1 millimeter across, acting 'together' in an extremely coordinated way -- millions of atoms (but not little balls, more like waves, all behaving identically) together. The Plain English discussion needs to integrate the Heisenberg principle, so that the little ball picture can be left behind. Ancheta Wis 10:06, 29 October 2005 (UTC)

The discussion above exemplifies bullets ii) and iii) in the 3rd paragraph in the introduction to the article. 10:35, 29 October 2005 (UTC)

Spatial quantization

I wonder if someone can explain how we know that energy states, momentum and various other quantities are quantized, yet space is not. It has often seemed to me that if we are unable to unify gravity fully with quantum mechanics, then one or other of them must be wrong in some fundamental manner. What would the consequences be on physical theory if in fact the universe was fully quantized? And would there be an easy test to prove that the universe is not in such a state? Has anyone done any work in this area?

Yeah. Plain English Please

I'm a general studies student and I'm writing an anthropology paper about technology in post-modern society. I'm pretty sure quantum physics is a big part of this but I couldn't understand a thing in this article. Some plain 'explain it to a novice' language would be really nice. Also that this article has recieved so much attention is great but it doesn't help the lay person and in fact it makes one feel kind of intellectually inadequate.

No slight is intended. In a nutshell, our common-sense ideas about place (ie position in space) would have to change if we truly were to integrate the knowledge of QM into our current civilization; you can model the world at many levels; look at History of science for an overview in the broadest terms. In fact Newtonian physics (1700) (approximating the world with hard spheres and rigid bodies) is adequate for understanding a huge part of our civilization. We are just now reaping the benefits of Maxwell's equations (1865) with the electronic circuits of today ( not derived from QM). Look at solid state physics (which uses some QM) if you want to see the physical basis of our understanding of microelectronic technology. The precision and repeatability of our integrated circuits are applications of optics, especially photography and cameras, and the ideas behind the printing press (1041) and lithography (1798). But laser physics (1960) and physics of condensed matter (1900-present) is just starting to reap the benefits of the QM viewpoint. In other words, you don't need to understand the QM viewpoint until you start studying physics, engineering and especially chemistry. And you don't meet too many people who worry about the nature of spacetime or matter on an everyday basis. It truly is a subject for specialized study, in our current civilization. --Ancheta Wis 23:25, 26 November 2005 (UTC)

QM, the uncertainty principle in all of its quantum weirdness

I wrote this illustration on the "uncertainty principle" talk and wanted to share. Also, I haven't looked at this article on QM in awhile and it has improved, but still may be too complicated in the intro. I'm going to "think on it".

To explain QM, especially the uncertainty principle, I will use a simplified anthropomorphic illustration of electrons in orbits around the atom applying the principles of uncertainty and QM to show how "strange" strange really is. First, let's start with the retained QM features of the Bohr atom model. Imagine an electron as a person, in fact, say you are the electron and you are running around a circular track about 10 feet wide. There is another inside track in further from your track by another few yards. This inside track is also 10 feet wide. There is a refreshment stand at the center of the track which is the nucleus and although you are attracted to it, the probability of you ever being able to get to the refreshment stand is zero. No can do. You are using up more energy to do laps running on the outside track, so you want to move to the inside track. However, the probability of you being able to cross those few yards to the inside track is zero. Therefore, you pull out your handy triquarter and say, "Beam me up Scotty," and you are instantaneously transported to the inside track. (quantum leaping) Another weird thing is that if someone is looking at you (but not measuring where you are), they think they have very blurred vision because you seem to be blurred across the whole ten feet of the track. Most of your body is concentrated at your position, but the rest of you is stretched out across the track. (uncertainty) Now there is another guy who comes along and wants to run on the inside track with you. You look at him and you see that he is identical to you in every way. In fact, no one looking at either of you can ever tell you apart. (indistinguishable particles) Now he starts running on the inside track with you but in the opposite direction. (spin) He is also spread out over the 10 foot width of the track and is fuzzier and less distinct toward the edges of the track. All of a sudden, you decide to turn around and run in the same direction he is running. But as you turn around, he turns around too as if reading your mind. This happens every time. (quantum entanglement) --- I could go on, but this should be weird enough. The true facts are that the track would describe a sphere and you would be stretched out all over the sphere at once which is even harder to imagine. Not only that, but you would be standing still (standing wave) and moving at the same time (angular momentum). That is why Bohr said "if you don't think QM is strange, you haven't understood a single word."

I love what Einstein had to say about all this:

• (after Heisenberg's 1927 lecture) "Marvelous, what ideas the young people have these days. But I don't believe a word of it."
• "The Heisenberg-Bohr tranquilizing philosophy - or religion? - is so delicately contrived that, for the time being, it provides a gentle pillow for the true believer from which he cannot very easily be aroused. So let him lie there.

Further, the fact that Einstein didn't like uncertainty didn't mean he wasn't still a brilliant genius. In fact, the challenges that Einstein brought to QM have transformed it and tweaked it and refined it.

My personal favorite anachronistic quote about QM is the ironic fact that it came out of Copenhagen in Denmark and Shakespeare said in Hamlet as if speaking of QM itself:

• "There is something rotten in the state of Denmark...There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy."

--Voyajer 16:51, 23 December 2005 (UTC)

It is much easier and much more physical to imagine the electron in the atom to be not some tiny point jumping from place to place or orbiting around (there are no orbits, there are orbitals), but to imagine the electron being an occupation of an extended orbital and an orbital being a vibrating wave confined to the neighbourhood of the nucleus by its attracting force. That's why Chladni's figures of acoustics and the normal modes of electromagnetic waves in a resonator are such a good analogy for the orbital pictures in quantum physics. Quantum mechanics is a lot less weird if you see this analogy. The step from electromagnetic theory (or acoustics) to quantum theory is much easier than the step from point mechanics to quantum theory, because in electromagnetics you already deal with waves and modes of oscillation and solve eigenvalue equations in order to find the modes. You just have to treat a single electron like a wave, just in the same way as light is treated in classical electromagnetics.

In this picture, the only difference between classical physics and quantum physics is that in classical physics you can excite the modes of oscillation to a continuous degree, called the classical amplitude, while in quantum physics, the modes are "occupied" discretely. -- Fermionic modes can be occupied only once at a given time, while Bosonic modes can be occupied several times at once. Particles are just occupations of modes, no more, no less. As there are superpositions of modes in classical physics, you get in quantum mechanics quantum superpositions of occupations of modes and the scaling and phase-shifting factors are called (quantum) amplitudes. In a Carbon atom, for example, you have a combination of occupations of 6 electronic modes of low energy (i.e. frequency). Entangled states are just superpositions of combinations of occupations of modes. Even the states of quantum fields can be completely described in this way (except for hypothetical topological defects).

As you can choose different kinds of modes in acoustics and electromagnetics, for example plane waves, spherical harmonics or small wave packets, you can do so in quantum mechanics. The modes chosen will not always be decoupled, for example if you choose plane waves as the system of acoustic modes in the resonance corpus of a guitar, you will get reflexions on the walls of modes into different modes, i.e. you have coupled oscillators and you have to solve a coupled system of linear equations in order to describe the system. The same is done in quantum mechanics: different systems of eigenfunctions are just a new name for the same concept. Energy eigenfunctions are decoupled modes, while eigenfunctions of the position operator (delta-like wavepackets) or eigenfunctions of the angular momentum operator in a non-spherically symmetric system are usually strongly coupled.

What happens in a measurement depends on the interpretation: In the Copenhagen interpretation you need to postulate a collapse of the wavefunction to some eigenmode of the measurement operator, while in Everett's Many-worlds theory an entangled state, i.e. a superposition of occupations of modes of the observed system and the observing measurement apparatus, is formed.

--DenisDiderot 21:07, 23 December 2005 (UTC)

• • Thanks for your unnecessary explanation. I am well versed in physics. My analogy was meant to be humorous and over-simplified.--Voyajer 21:12, 23 December 2005 (UTC)

Please don't feel insulted by my clarification which adresses many other readers as well. Most beginners are confused and demoralized when the weirdness of quantum mechanics is overemphasized and they are confronted with lots of contradicting statements. --DenisDiderot 21:29, 23 December 2005 (UTC)

Au contraire, I am not insulted. I just think you don't have a sense of humor. My colleagues found my analogy highly amusing.

What does bother me though is that you think your explanation above is for beginners in physics or beginners in anything for that matter. I would think you would have to have a pretty heavy knowledge of waves, acoustics, and optics to understand your analogy at all. You would need to understand the concept of standing waves as normal modes of bounded systems such as harmonics and the quality of sound. You would need to understand the significance of Chladni's figures. You would need to understand ultrasonic and infrasonic waves. You would need to understand the concept of waves in media like transverse waves in a uniform string, gravity waves and ripples, superposition of waves such as in linear homogeneous equations and nonlinear superposition. Also, you wouldn't be using the terms fermionic and bosonic to beginners and using the terms eigenvalues and eigenfunctions to a neophyte in physics is ludicrous. In other words, your so-called explanation for "beginners" appears simply absurd and conveys the idea that you are simply trying to make a display of your erudition. If you really want to help the beginner, then you should describe in detail the idea of a standing wave, why we view the electron as a standing wave, what an orbital actually is, why an electron is said to be an occupation of an orbital, and the basics of wave-particle duality. Of course, that is just my opinion. It appears to me that much of the "talk" here is by people complaining that everyone is answering questions and explaining things in a pseudo-intellectual fashion not for the edification of the beginner but simply to show off. Of course, all of this is just my opinion, so take it for what it's worth.--Voyajer 00:36, 24 December 2005 (UTC)

Your way to discuss things is obviously highly aggressive, and I wonder what it is that makes you so furious and arrogant. I'll just ignore any further aggressive remarks on your part. Maybe it is you who needs some sense of tolerance and humour (humour does not mean forcing other people to laugh about your jokes).

I have a long experience in explaining quantum mechanics to students the way described above (of course, the text given above is just a sketch), and I found it to be highly successful. Even children can easily grasp the concept of waves and of superpositions of waves, and it is a lot of fun for them to see Chladni's figures. You can do many experiments with standing and propagating waves without any complicated instrumentation, and acoustics is interesting in itself. Much of this is already common knowledge at the age of 12, and in Wikipedia, you can read about all this if you follow the links I provided. The concepts of fermionic and bosonic occupations are defined by the sentence given above, and they are easily grasped by students after delving a little further into some examples and explaining the Pauli exclusion principle and stimulated emission in this context. As soon as the students have grasped the picture and have overcome the prejudice that the electron had to be some pointlike object as they see the orbital to be quite extended, all the weirdness disappears. Of course, many questions arise -- as is always the case when people are bursting with curiosity -- and I'm happy to answer them, because if people are demoralized and think quantum mechanics is just some incomprehensible mess, they cease asking questions.

--DenisDiderot 11:07, 24 December 2005 (UTC)

Not to be annoying; but I'm not a neophyte in quantum mechanics (although I'm not a physicist either), and I had to read your statement twice over, and with the care of reading a college textbook to understand what you were trying to say. And Voyajer is right; using the word eigenvalue for anyone without knowledge of linear algebra, let alone for a total novice in a field, is an improper approach. Nor can you expect someone without a mathematical, engineering, or scientific background to understand 'phase-shifts'. Words like 'Bosonic'--even if explained--will probably throw most people off, and force them to re-read the sentence to understand your prose. Jargon like 'system of linear equations', 'spherical harmonics', and the like don't help out either; nor does the fact that one would have to click on numerous links just to understand some of the ideas you use. My Two Cents. 69.84.100.123 02:25, 28 December 2005 (UTC)Don

It was just a sketch of the main ideas of how such an explanation for beginners (including quantum field theory) avoiding all the weirdness could look like. See Quantum mechanics explained for more details. Feel free to ask questions on the talk page.

--DenisDiderot 02:30, 28 December 2005 (UTC)

Prose

Can we please call a break here? I think I need to draw the line at Line 44 in the diff. This is a Featured Article. It took work to get it to this state. Line 44 is attempting to state in words what can be said in only a few math symbols. If we want some Simple English we might be able to work this out on the Talk Page. Another alternative is to create a link to some tutorial material on another page, much like a '{{main}}' template to main article. It is also possible to lose Featured status on an article due to overworking the prose. --Ancheta Wis 08:10, 24 December 2005 (UTC)

One tactic we might use is something like the 'Ants and Martians' device that Feynman used with his son Carl. It ought to be possible to devise a transforming mechanism which allows the sympathetic editor some freedom in explanation for an absolute beginner. But again, the Line 44 diff highlights the need for a stylistic "zoom lens". Or perhaps a stylistic "instant replay" for explanations for the absolute beginner. One possibility that comes to mind is a Portal treatment for the prose of the Line 44 diff. --Ancheta Wis 08:22, 24 December 2005 (UTC)

Oops. I just re-read the Line 27 diff. We need to walk carefully here. One possible interpretation of the diff is to call into question the 'eigenstate' formulation, which is very basic to the QM picture and which does not contravene the Uncertainty principle. --Ancheta Wis 08:33, 24 December 2005 (UTC)

I have just re-read DenisDiderot's formulation above and believe it might be possible to use an optical cavity as a device for some explication of QM ideas. That is pretty concrete, is intimately tied to the ideas of QM and allows us to tie into some laser physics, which rests on QM ideas. --Ancheta Wis 08:56, 24 December 2005 (UTC)

OK - here is a possibility for some Line 44 rework: we use the [Black-body EM radiator], which is the experimental root of QM anyway, and then use optical cavity to explain some basics about waves. Just like the pictures of electron orbitals in the article. That frees us from the need to have a wave travel from position A to position B - a mechanical picture which we don't need (its Newtonian physics, well established and not the problem being addressed). What we do need is some explanation of the radiators -- that is what Planck was worrying about anyway. That is intimately tied to the laser physics I was referring to above -- which is matter-dependent, and where QM shines. --Ancheta Wis 09:19, 24 December 2005 (UTC)

Let's see if we can work through a revision which is sympathetic to beginners without destroying QM's Featured status. --Ancheta Wis 11:08, 24 December 2005 (UTC)

A contrary argument

• Line 44 reverted back and as is now in the article: "The first type of quantum effect is the quantization of certain physical quantities. In the example we have given, of a free particle in empty space, both the position and the momentum are continuous observables. However, if we restrict the particle to a region of space (the so-called "particle in a box" problem), the momentum observable will become discrete; it will only take on the values $n{\frac {h}{2L}}$, where $L$ is the length of the box, $h$ is Planck's constant, and $n$ is an arbitrary nonnegative integer number. Such observables are said to be quantized, and they play an important role in many physical systems. Examples of quantized observables include angular momentum, the total energy of a bound system, and the energy contained in an electromagnetic wave of a given frequency."

• Ancheta Wis reverts from prose explanation because he says: "Line 44 is attempting to state in words what can be said in only a few math symbols."

Reasons this approach is flawed:

• 1. There are many complaints in the "talk" regarding: "plain English please".
• 2. Mathematical formulae in the form of notation and symbols that can only be known and accessible to people who are already acquainted with the language of science is an inappropriate shortcut in encyclopedia article.
• 3. It's true, perhaps the prose was too wordy, not concise enough, but necessary. In other words, it should be re-worked but not eliminated.
• 4. The QM featured status will not be destroyed by a more accessible explanation if it is worded expertly in the manner of the major encyclopedia. In other words, all the major encyclopedia do not simply state a formula to explain a concept. It isn't done. Especially without an accessible explanation of the scientific notation in the formula.
• 5. Also, this article on QM underemphasizes the importance of Planck's constant by not explaining it. In the Encyclopedia Brittanica, the second paragraph on QM says: "In the equations of quantum mechanics, Max Planck's constant of action h = 6.626 ´ 10-34 joule-second plays a central role. This constant, one of the most important in all of physics, has the dimensions energy ´ time. The term “small-scale” used to delineate the domain of quantum mechanics should not be literally interpreted as necessarily relating to extent in space. A more precise criterion as to whether quantum modifications of Newtonian laws are important is whether or not the phenomenon in question is characterized by an “action” (i.e., time integral of kinetic energy) that is large compared to Planck's constant. Accordingly, if a great many quanta are involved, the notion that there is a discrete, indivisible quantum unit loses significance."
• 6. It is important to delineate what Planck's constant is, its importance in QM, its pervasiveness throughout QM, BEFORE any mathematical formula are introduced that include the constant h and just say it is Planck's constant in some off-hand manner.
• 7. Wikipedia is becoming an inaccessible encyclopedia due to the fact that many articles on physics are simply reduced to mathematical formulae. This is very uncommon in the major encyclopedia like Encyclopedia Britannica and MSN Encarta where formulae are kept to a strict minimum and prose dominates.
• 8. MSN Encarta before introducing any formulae states in its introductory article on QM: "Momentum is a quantity that can be defined for all particles. For light particles, or photons, momentum depends on the frequency, or color, of the photon, which in turn depends on the photon’s energy. The energy of a photon is equal to a constant number, called Planck’s constant, times the frequency of the photon. Planck’s constant is named for German physicist Max Planck, who first proposed the relationship between energy and frequency. The accepted value of Planck’s constant is 6.626 × 10-34 joule-second. This number is very small—written out, it is a decimal point followed by 33 zeroes, followed by the digits 6626. The energy of a single photon is therefore very small." Again another example of properly explaining and emphasizing Planck's constant and its place in QM.
• 9. So finally, the simple mathematical formula used alone as a definition for quantization is actually a faux pas in the world of major encyclopedia.

• IN CONCLUSION, it is therefore a necessity, a priority, and a duty to find a way to include a prose explanation of Planck's constant before introducing mathematics. So instead of simply erasing my prose explanation, either edit it yourself or come up with a better prose explanation. I agree it needs honing down and was unnecessarily wordy. --Voyajer 13:32, 24 December 2005 (UTC)

I much appreciate your responsive edit. There is yet another custom in this community of encyclopedists, which is that we work together by consensus. But it actually harms us to see the prose of Encarta, which is a tertiary source (doubly filtered). Back when the encyclopedia started, we had nothing. So the prose you see is the result of the community. We agree not to publish original thoughts, but that does not prevent us from having thoughts which we think through on our own, and then find citations for the original sources, for which we can cite our (and their) thoughts. That means, on a practical level, that the other editors on this article have a say, and that we do not attempt to browbeat others. After all, they have something to contribute as well. (But we also do not slavishly copy Encarta, etc.) There is actually a template which exists to flag the existence of copied text.

Back to Planck's constant, h. Deutschland's greatest physicist, for which Max Planck Institute is aptly named, solved a problem which caused a crisis in the philosophical foundations of his science. We are privileged to have witnessed a century of development of a framework for that science which has not yet been integrated into our civilization, other than for a tiny fraction of the billions on our planet. In one of his popular lectures Richard Feynman wrote out a decimal point, followed by 33 zeros wandering around the board, with the significant figures for h. Perhaps that is why Encarta took the trouble to write out the value. And Planck actually came up with that number before (1899) the blackbody radiation calculations (1900).

So there is something going on here which we can write about, or simply link to. I personally hope that you and DenisDiderot can work out a conversation here, or perhaps on the article page itself, one thought leading to another, one editor talking to another, using the prose of the article, but doing justice to the subject, with a conscious effort to use the skills and viewpoints of each other as well as our own.

As an aside, I hope that someday Helgoland will somehow get a mention under the QM rubric, which is, after all, where QM was born. --Ancheta Wis 17:05, 24 December 2005 (UTC)

• I thought the Encyclopedia Britannica quote was infinitely more important than the MSN Encarta quote because I agree whole-heartedly with you on that particular point.
• I am not quite clear on what equation exactly that Heisenberg first formulated in Helgoland.
• I am not sure exactly how to go about expanding the article on QM to include the information that DenisDiderot presented since it would look more like the length of a textbook than an article. You appear to be proposing a link to something else with more clarification on QM. But I'm not quite sure what that would be either. Do you have any ideas? Personally, I think many readers would appreciate more clarification, more background on Planck, more history of development, and more illustrations relating to waves and acoustics, that is, if they were given enough background to understand the connection to QM. I just did a search and found an article that made me cringe when reading it called Quantum Mechanics - simplified. I suppose this could used as a page for the type of further clarification we were discussing. --Voyajer 18:09, 24 December 2005 (UTC)

Well, what immediately comes to mind is the picture that DenisDiderot is filling in below this text: There is a medium (called the field -- but the name is immaterial, it is something that fills a manifold ) which is shaped/affected by the boundaries upon which the system (The Operator) works. For the picture below, it is air, but what the heck. For example, if we have a thing (and wave is not too far from my intuition) which is affected by the energy we/Nature are pouring into it, then the medium takes on shapes. Like the electron orbitals in the article. Now the geometrical part (the manifold) is the mathematical side, and the System (the Energy,etc Operators) is the physics side. Like in GR, where the math side (the pretty side)= the physics side (the messy part with Stress-Energy). So for an optical cavity we have light filling it, and that light is augmenting the energy states of the material in the cavity. But since we have artificially shaped the boundaries of the cavity, and since we are pumping in energy, we are getting back specific transitions of electron energy levels in the material, which is specific frequencies of light. The specific equations of QM, depending on the picture (Schrödinger picture or Heisenberg picture) describe the System under consideration. I have to admit more comfort with the wave (Schrödinger) description than the more rigorous state description (Heisenberg). But - and this is the non-intuitive part - the Heisenberg picture, which does not operate in space/time can be translated to a wave-like (more intuitive) view by the 'Ehrenfest procedure' (discussed by Guest in the talk page above) which allows the computations of time averages, occupying space. That's the crazy part which as a macroscopic being brought up on large time and space scales, I personally do not have a feeling for. The best description I have seen is Feynman's characterization of the Uncertainty principle as something like silly putty, where if you squeeze it, it (the medium/air/field) fights back. But that is where you have a nice description, given above. --Ancheta Wis 19:04, 24 December 2005 (UTC)

Some of the ramifications of "...which does not operate in space..." can be seen in Bell's theorem and quantum entanglement.

• Although you gave a nice explanation, that isn't what I was asking. I meant where does Helgoland come into the picture? What was Heisenberg working on in Helgoland? Heisenberg born 1901 Wuerzbrug, Bavaria was Sommerfeld's student and in 1922 he co-authored two papers on the atomic theory of X-ray spectra and the so-called anomalous Zeeman effect. In 1921 Heisenberg published his own paper on the anomalous Zeeman effect introducing half-interger quantum numbers. In 1923 Heisenberg collaborated with Born on perturbation methods to describe the helium atom after which Heisenberg went to Goettingen. In 1924 Heisenberg went to Copenhagen to develop quantum theory with Bohr. In 1925 Heisenberg wrote "On a quantum theoretical re-interpretation of kinematical and mechanical relationships" based on anharmonic oscillators which became known as matrix mechanics. In 1927 Heisenberg developed the uncertainty principle. QUESTION: Therefore, which of the above theories was developed in Helgoland?--Voyajer 21:21, 24 December 2005 (UTC)

Google tells me it was Matrix Mechanics. --Ancheta Wis 21:44, 24 December 2005 (UTC)

• "In June 1925, while recuperating from an attack of hay fever on Helgoland, he solved the problem of the stationary (discrete) energy states of an anharmonic oscillator:
• Heisenberg (1925), "Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen" ("About the Quantum-Theoretical Reinterpretation of Kinetic and Mechanical Relationships"), Zeitschrift für Physik.

Time-out.

OK folks, those of you who are watching the show, please go to the refrigerator or switch to another channel while we take a game-break. Otherwise, stay tuned while we work thru some details about this article's construction. What I am seeing is several sincere editors who have clearly stated programs for making this Featured article more accessible to beginners. Some of the differences I see are stylistic, others are philosophical.

I will be taking the phrases that pop-out at me and will attempt to place them in outline form, for starters. Please feel free to interrupt, re-arrange, etc. --Ancheta Wis 11:21, 24 December 2005 (UTC)

Planck

• a standing wave,

A standing wave is considered a one-dimensional concept by many students, because of the examples (waves on a spring or on a string) usually provided. In reality, a standing wave is a synchronous oscillation of all parts of an extended object in which the oscillation profile (in particular the nodes and the points of maximal oscillation amplitude) doesn't change. This is also called a normal (= uncoupled) mode of oscillation. You can make the profile visible in Chladni's figures and in vibrational holography. In unconfined systems, i.e. systems without reflecting walls or attractive potentials, traveling waves may also be chosen as normal modes of oscillation (see boundary conditions).

• why we view the electron as a standing wave,

An electron beam (accelerated in a cathode ray tube similar to TV) is diffracted in a crystal and diffraction patterns analogous to the diffraction of monochromatic light by a diffraction grating or of X-rays on crystals are observed on the screen. This observation proved de Broglie's idea that not only light, but also electrons propagate and get diffracted like waves. In the attracting potential of the nucleus, this wave is confined like the acoustic wave in a guitar corpus. That's why in both cases a standing wave (= a normal mode of oscillation) forms. An electron is an occupation of such a mode.

• what an orbital actually is,

An orbital is a normal mode of oscillation of the electronic quantum field, very similar to a light mode in an optical cavity being a normal mode of oscillation of the electromagnetic field.

• why an electron is said to be an occupation of an orbital, and

In my view, this is the main new idea in quantum mechanics, and it is forced upon us by observations of the states of electrons in multielectron atoms. Certain fields like the electronic quantum field are observed to allow its normal modes of oscillation to be excited only once at a given time, they are called fermionic. If you have more occupations to place in this quantum field, you must choose other modes (the spin degree of freedom is included in the modes), as is the case in a carbon atom, for example. Usually, the lower-energy (= lower-frequency) modes are favoured. If they are already occupied, higher-energy modes must be chosen. In the case of light the idea that a photon is an occupation of an electromagnetic mode was found much earlier by Planck and Einstein, see below.

• the basics of wave-particle duality.

If you do a position measurement, the result is the occupation of a very sharp wavepacket being an eigenmode of the position operator. These sharp wavepackets look like pointlike objects, they are strongly coupled to each other, which means that they spread soon.

---

File:DiderotVanLoo.jpg

Diderot

• waves
• superpositions of waves

Waves can go through each other without disturbing each other. It just looks like there were two superimposed realities each carrying only one wave and not knowing of each other. That's what is assumed if you use the superposition principle mathematically in the equations.

• Chladni's figures.

On page Chladni's figures you find some very enlightening pictures in the links provided.

• What about emission, absorption, particle processes?

All processes in nature can be reduced to the time evolution of modes and to (superpositions of) reshufflings of occupations, as described in the Feynman diagrams. For example in an emission of a photon by an electron changing its state, the occupation of one electronic mode is moved to another electronic mode of lower frequency and an occupation of an electromagnetic mode (whose frequency is the difference between the frequencies of the mentioned electronic modes) is created. --DenisDiderot 11:44, 25 December 2005 (UTC)

• experiments with standing and propagating waves
• fermionic and bosonic occupations

Electrons and photons become very similar in quantum theory, but one main difference remains: Electronic modes cannot be excited/occupied more than once (= Pauli exclusion principle) while photonic/electromagnetic modes can and even prefer to do so (= stimulated emission). --DenisDiderot 12:17, 24 December 2005 (UTC)

This property of electonic modes and photonic modes is called fermionic and bosonic, respectively. Two photons are indistinguishable and two electrons are also indistinguishable, because in both cases, they are only occupations of modes: all that matters is which modes are occupied. The order of the occupations is irrelevant except for the fact that in odd permutations of fermionic occupations, a negative sign is introduced in the amplitude.

Of course, there are other differences between electrons and photons:

• The electron carries an electric charge and a rest mass while the photon doesn't.
• In physical processes (see the Feynman diagrams), a single photon may be created while an electron may not be created without at the same time removing some other fermionic particle or creating some fermionic antiparticle. This is due to the conservation of charge. --DenisDiderot 11:44, 25 December 2005 (UTC)

• Pauli exclusion principle and
• stimulated emission

---

optical cavity

• Now let's look at Planck's problem. From his article, we see that he was trying to solve a practical problem, which was to derive an expression for the energy radiating from a light bulb and the rest is history, (well-known, etc., etc.) ...

Planck was the first to suggest that the electromagnetic modes are not excited continuously but discretely by energy quanta $h\nu$ proportional to the frequency. By this assumption, he could explain why the high-frequency modes remain unexcited in a thermal light source: The thermal exchange energy $k_{B}T$ is just too small to provide an energy quantum $h\nu$ if $\nu$ is too large. Classical physics predicts that all modes of oscillation -- regardless of their frequency -- carry the average energy $1/2k_{B}T$, which amounts to an infinite total energy (called ultraviolet catastrophe). This idea of energy quanta was the historical basis for the concept of occupations of modes, designated as photons by Einstein. --DenisDiderot 12:59, 24 December 2005 (UTC)

--- What about operators, eigenstates, measurements and all that?

The system of modes to describe the waves can be chosen at will. Any arbitrary wave can be decomposed into contributions from each mode in the chosen system. For the mathematically inclined: The situation is analogous to a vector being decomposed into components in a chosen coordinate system. Decoupled modes or, as an approximation, weakly coupled modes are particlularly convenient if you want to describe the evolution of the system in time, because each mode evolves independently of the others and you can just add up the time evolutions. In many situations, it is sufficient to consider less complicated weakly coupled modes and describe the weak coupling as a perturbation.

In every system of modes, you must choose some (continuous or discrete) numbering (called "quantum numbers") for the modes in the system. In Chladni's figures, you can just count the number of nodes of the standing waves in the different space directions in order to get a numbering, as long as it is unique. For decoupled modes, the energy or, equivalently, the frequency might be a good idea, but usually you need further numbers to distinguish different modes having the same energy/frequency (this is the situation referred to as degenerate energy levels). Usually these additional numbers refer to the symmetry of the modes. Plane waves, for example -- they are decoupled in spatially homogeneous situations -- can be characterized by the fact that the only result of shifting (translating) them spatially is a phase shift in their oscillation. Obviously, the phase shifts corresponding to unit translations in the three space directions provide a good numbering for these modes. They are called the wavevector or, equivalently, the momentum of the mode. Spherical waves with an angular dependence according to the spherical harmonics functions (see the pictures) -- they are decoupled in spherically symmetric situations -- are similarly characterized by the fact that the only result of rotating them around the z-axis is a phase shift in their oscillation. Obviously, the phase shift corresponding to a rotation by a unit angle is part of a good numbering for these modes; it is called the magnetic quantum number m (it must be an integer, because a rotation by 360° mustn't have any effect) or, equivalently, the z-component of the orbital angular momentum. If you consider sharp wavepackets as a system of modes, the position of the wavepacket is a good numbering for the system. In crystallography, the modes are usually numbered by their transformation behaviour (called group representation) in symmetry operations of the crystal, see also symmetry group, crystal system.

The mode numbers thus often refer to physical quantities, called observables characterizing the modes. For each mode number, you can introduce a mathematical operation, called operator, that just multiplies a given mode by the mode number value of this mode. This is possible as long as you have chosen a mode system that actually uses and is characterized by the mode number of the operator. Such a system is called a system of eigenmodes, or eigenstates: Sharp wavepackets are no eigenmodes of the momentum operator, they are eigenmodes of the position operator. Spherical harmonics are eigenmodes of the magnetic quantum number, decoupled modes are eigenvalues of the energy operator etc. If you have a superposition of several modes, you just operate the operator on each contribution and add up the results. If you chose a different modes system that doesn't use the mode number corresponding to the operator, you just decompose the given modes into eigenmodes and again add up the results of the operator operating on the contributions. So if you have a superposition of several eigenmodes, say, a superposition of modes with different frequencies, then you have contributions of different values of the observable, in this case the energy. The superposition is then said to have an indefinite value for the observable, for example in the tone of a piano note, there is a superposition of the fundamental frequency and the higher harmonics being multiples of the fundamental frequency. The contributions in the superposition are usually not equally large, e.g. in the piano note the very high harmonics don't contribute much. Quantitatively, this is characterized by the amplitudes of the individual contributions. If there are only contributions of a single mode number value, the superposition is said to have a definite or sharp value.

In measurements of such a mode number in a given situation, the result is an eigenmode of the mode number, the eigenmode being chosen at random from the contributions in the given superposition. All the other contributions are supposedly eradicated in the measurement -- this is called the wave function collapse and some features of this process are questionable and disputed. The probability of a certain eigenmode to be chosen is equal to the absolute square of the amplitude, this is called Born's probability law. This is the reason why the amplitudes of modes in a superposition are called "probability amplitudes" in quantum mechanics. The mode number value of the resulting eigenmode is the result of the measurement of the observable. Of course, if you have a sharp value for the observable before the measurement, nothing is changed by the measurement and the result is certain. This picture is called the Copenhagen interpretation. A different explanation of the measurement process is given by Everett's many-worlds theory; it doesn't involve any wave function collapse. Instead, a superposition of combinations of a mode of the measured system and a mode of the measuring apparatus (an entangled state) is formed, and the further time evolutions of these superposition components are independent of each other (this is called "many worlds").

--DenisDiderot 21:12, 24 December 2005 (UTC)

As an example: a sharp wavepacket is an eigenmode of the position observable. Thus the result of measurements of the position of such a wavepacket is certain. On the other hand, if you decompose such a wavepacket into contributions of plane waves, i.e. eigenmodes of the wavevector or momentum observable, you get all kinds of contributions of modes with many different momenta, and the result of momentum measurements will be accordingly. Intuitively, this can be understood by taking a closer look at a sharp or very narrow wavepacket: Since there are only a few spatial oscillations in the wavepacket, only a very imprecise value for the wavevector can be read off (for the mathematically inclined reader: this is a common behaviour of Fourier transforms, the amplitudes of the superposition in the momentum mode system being the Fourier transform of the amplitudes of the superposition in the position mode system). So in such a state of definite position, the momentum is very indefinite. The same is true the other way round: The more definite the momentum is in your chosen superposition, the less sharp the position will be, and it is called Heisenberg's uncertainty relation.

Two different mode numbers (and the corresponding operators and observables) that both occur as characteristic features in the same mode system, e.g. the number of nodes of one of Chladni's figures in x direction and the number of nodes in y-direction or the different position components in a position eigenmode system, are said to commute or be compatible with each other (mathematically, this means that the order of the product of the two corresponding operators doesn't matter, they may be commuted). The position and the momentum are non-commuting mode numbers, because you cannot attribute a definite momentum to a position eigenmode, as stated above. So there is no mode system where both the position and the momentum (referring to the same space direction) are used as mode numbers.

--DenisDiderot 12:32, 25 December 2005 (UTC)

• What about the Schrödinger equation, the Dirac equation etc?

As in the case of acoustics, where the direction of vibration, called polarization, the speed of sound and the wave impedance of the media, in which the sound propagates, are important for calculating the appearance and the frequency of modes as seen in Chladni's figures, the same is true for electronic or photonic/electromagnetic modes: In order to calculate the modes (and their frequencies or time evolution) exposed to potentials that attract or repulse the waves or, equivalently, exposed to a change in refractive index and wave impedance, or exposed to magnetic fields, there are several equations depending on the polarization features of the modes:

• Electronic modes (their polarization features are described by Spin 1/2) are calculated by the Dirac equation, or, to a very good approximation in cases where the theory of relativity is irrelevant, by the Schrödinger equation and the Pauli equation.
• Photonic/electromagnetic modes (polarization: Spin 1) are calculated by Maxwell's equations (You see, 19th century already found the first quantum-mechanical equation! That's why it's so much easier to step from electromagnetic theory to quantum mechanics than from point mechanics).
• Modes of Spin 0 would be calculated by the Klein-Gordon equation.

--DenisDiderot 13:08, 25 December 2005 (UTC)

---

• But let's also look at Helmholtz. He ran an experiment which clearly showed the physical reality of resonances in a box. (He predicted and detected the eigenfrequencies.)

---

• • • DenisDiederot and Ancheta Wis have put together some wonderful fundamental information on QM here. It seems a shame that it will eventually get lost in the "talk" discussion section. Does anyone have any idea of how to include this information in Wikipedia? Will it bog down the current article? If so, under what article title could this information be included, as a whole, as a further explanation of QM? --Voyajer 18:26, 24 December 2005 (UTC)

Thank you very much. I'm sure we'll find a solution, maybe on a page like Quantum mechanics explained. Merry Christmas to everybody! --DenisDiderot 21:12, 24 December 2005 (UTC)

And Merry Christmas to you both! --Ancheta Wis 21:52, 24 December 2005 (UTC)

Merry Christmas ,From TW.--HydrogenSu 07:20, 25 December 2005 (UTC)

I moved the texts to the new page Quantum mechanics explained, because this talk page might otherwise get too large. Let's see if we can create a text providing an exact (non-simplified) explanation for beginners. --DenisDiderot 13:35, 25 December 2005 (UTC)

25 Dec 05 is over

24.91.73.141 plopped http://www.nytimes.com/2005/12/27/science/27eins.html in external links. I suppose the travel of enlightenment seekers is apt to be in the other direction: from the there to here. How can something actually be two contradictory things may be the question. Honest-liar, clod-swoosh, correct-incorrect. Here's a quote from that article: "This fall two Nobel laureates, Anthony Leggett of the University of Illinois and Norman Ramsay of Harvard argued in front of several hundred scientists at a conference in Berkeley about whether, in effect, physicists were justified in trying to change quantum theory, the most successful theory in the history of science. Dr. Leggett said yes; Dr. Ramsay said no." Wouldn't it exact if both were right? The Times links the article to some quotes, for instance: " 'I don't like it, and I'm sorry I ever had anything to do with it.' -- Erwin Schrödinger about the probability interpretation of quantum mechanics". If you can bring yourselves to call the eigenwhosis "discrete value" it might help the jargon averse. Is not precision proven to be unobtainable in a reality sure to be uncertain? Unless it both is and isn't, of course. 207.172.134.175 07:05, 28 December 2005 (UTC)

See cat state. --Ancheta Wis 11:13, 28 December 2005 (UTC) Note: |0> |1> are kets, or states. i.e. It is possible to be precise and abstract at the same time. A cat state might be |00...0> + |11...1>. In this notation 0 and 1 are labels like True and False. Or spin Up and Down. etc. Upon re-reading I see that one issue is the existence or nonexistence of precise states without human action. The current experiment which generated a cat state was artificially induced. It will take work to observe a natural 6-atom cat state.

Yes, quantum mechanics wouldn't state that a person was honest and a liar or an object was clod or swoosh at the same time. It would rather state that there's a superposition of the person being honest and of him being a liar or that there's a superposition of the object being clod and being swoosh -- or, for that matter, a superposition of the cat being alive and being dead. Quantum mechanics routinely deals with superpositions of situations, and it is forced to do so by results as seen in the double-slit experiment. Many-worlds theory takes this idea at face value. Ancheta gave the mathematical notation for superpositions. --DenisDiderot 13:18, 28 December 2005 (UTC)

F. Lindner, M. G. Schätzel, H. Walther, A. Baltuska, E. Goulielmakis, F. Krausz, D. B. Milosevic, D. Bauer, W. Becker, G. G. Paulus in Attosecond double-slit experiment Physical Review Letters 95, 040401 (2005) conclude "The observation of interference and its absence at the same time for the same electron (emphasis added) is a beautiful demonstration of the principles of quantum mechanics," and (oh, by the way) attosecond interferometry will have practical applications. The website of Gerhard Paulus explains the experiment. "Superposition" is certainly more firmly established than Jung's Pleroma; note there, "time as relative concept; all historical processes complemented by 'simultaneous' existence in the Bardo or pleroma". Reality is pretty weird. 207.172.134.175 22:38, 28 December 2005 (UTC)

Roger Penrose's omnium appears to be the Bardo or Pleroma, as well. By the way, Penrose, a mathematician who happens to be vitally interested in physics, as evidenced by his new book Road to Reality (I recommend it; it has a very nice discussion of the mathematical concept called a connection as well as a graphic representation for tensor notation; -- his wife illustrated the book) has found a viewpoint that more firmly supports GR than QM. So you might discover that this thread is currently leading to Penrose and GR, as far as I can tell, rather than to QM. --Ancheta Wis 18:02, 29 December 2005 (UTC)

But hold on, this image

Penrose tiling

which resembles the vortex distribution of a bose-einstein condensate shows there is some application of Penrose's ideas to QM. It closely resembles the symmetries in a BEC bose-einstein condensate picture that Eric Cornell recently displayed at a public lecture of his - his picture was blue with each superfluid vortex a dark spot corresponding to a polyhedron in the Penrose tiling, except that the spots followed a hexagonal distribution rather than the pentagonal distribution you see. --Ancheta Wis 20:44, 29 December 2005 (UTC)

Amazon said they'll ship The Road to Reality to me next year. Congrats on your sysopship - don't let them overwork you. GR & QM facets of the same thing? If so, the connection is opaque to the duality mired (i.e. all of us). Happy New Year! Anon user 207.172.134.175 generally also me, Metarhyme 17:52, 30 December 2005 (UTC)

Thank you! Like the old Texas Rangers, who made their star-shaped badges from 5-peso silver coins, I formed an 8-pointed badge out of an Aztec calendar. And a happy J2000+6 to you! --Ancheta Wis 19:46, 30 December 2005 (UTC)

OPERATION to Schrödinger equation

• By the way show given as :

$-{\frac {\hbar ^{2}}{2m}}[({\frac {d^{2}}{dx^{2}}}+{\frac {d^{2}}{dy^{2}}}+{\frac {d^{2}}{dz^{2}}}+{\frac {d^{2}}{dt^{2}}})\Psi (x,y,z,t)]+V\Psi (x,y,z,t)=E\Psi (x,y,z,t)$

Schrödinger equation's coefficient of the extreamly left can be〝operated〞to 2 parts.

One is for Uncertainty Principle exactly well.$\Longrightarrow {\frac {\hbar }{2}}$ which is good for the limited value of the product by $\Delta P$ and $\Delta X$.

The other is for ${\frac {\hbar }{m}}$,recently without any sense in physics well. --HydrogenSu 09:58, 30 January 2006 (UTC)

The left side is just Kinetic + Potential energy. The left half of the left side is Kinetic energy, the V half of the is Potential energy, for a single particle. If you use the heuristic that 'Observables (Kinetic + Potential energies) are Operators', you get the right side of the Schrödinger equation. --Ancheta Wis 10:55, 30 January 2006 (UTC)

Can we take apart by seprated operation on $\hbar \over 2m$ without any reasons of "Observables or not"? (Just in Math to seperate them away?)Thank you,this is my question after reading your reply.--HydrogenSu 18:10, 30 January 2006 (UTC)

This equation confuses me. Why are time and space treated the same way, on the left side in a non-relativistic equation? Why are there time derivatives but a constant energy. David R. Ingham 07:56, 12 February 2006 (UTC)

A Question of Linear Operators

I have a question on [2]. Why does

${\mathcal {<}}p^{2}>={\Delta }p^{2}+<p>^{2}$?

--HydrogenSu 09:48, 26 January 2006 (UTC)

I switched it to momentum because thats what the picture said. --Ancheta Wis 11:37, 26 January 2006 (UTC)

My question of that belongs to Quantum mechanics. I hope it be kept.:)

By the way thank you.

To answer your question

$\Delta p^{2}\equiv <(p-<p>)^{2}>$

${\mathcal {=}}<p^{2}-2p<p>+<p>^{2}>$

${\mathcal {=}}<p^{2}>-2<p><p>+<p>^{2}=<p^{2}>-<p>^{2}$

Thanks a lot. By the way I edited some of your Math view for good-browsing. It was too long for looking. Sorry:)--HydrogenSu 18:23, 30 January 2006 (UTC)

Quantum darwinism

I started the article a while back and placed a link here; I'm sure it was removed for a good reason... but couldn't it be linked to somewhere in this article? And or going in the Quantum topic template? - RoyBoy ⁸⁰⁰ 08:15, 30 January 2006 (UTC)

My changes: http://en.wikipedia.org/w/index.php?title=Quantum_mechanics&diff=39241812&oldid=39099331

There is so much discussion here that my edit comments may not be considered sufficient explanation for my changes.

"Quantum mechanics uses complex number" The probabilities are not part of the mathematical formulation. The formulation is in terms of complex wave functions, and so forth.

"These are related to classical physics and ordinary language largely with the use of probability." This is essential to interpretation of classical physics and ordinary language in terms of quantum mechanics. Encyclopedia readers will be looking at it from the other direction, but this wording can be read from the classical point of view also.

"Newton's laws of motion" Gravity has little to do with atoms.

"obeys" qm "arises from" all observations of nature.

"the classical position" in qm, things have wave functions. "position", in the sense of an exact position of a particle is a uniquely classical concept. (Position doesn't seem to have a good link so maybe I will remove the link.)

"instead of describing" This change may not be necessary, but is based on the same argument as above.

"Therefore, quantum mechanics, translated to Newton's equally deterministic description, leads to a probabilistic description of nature." I expect a lot of argument about "equally deterministic", but the time dependent Schrödinger equation is first order in time, which makes it explicitly deterministic. The probabilities do not arise until the classical approximation is first used. The (new) probabilities belong only to the relation between qm on one hand and classical physics and ordinary language on the other.

Perhaps "Newton's equally deterministic description" may be inadequate here, because it is not really his view, it is the view of everyone before Schrödinger and Heisenberg.

David R. Ingham 08:59, 12 February 2006 (UTC)

"probabilistic description of nature" I don't like this phrase, but it is explained now. David R. Ingham 09:09, 12 February 2006 (UTC)

Thank you for the careful writing. As Feynman would have said, good! --Ancheta Wis 12:32, 12 February 2006 (UTC)

Thank your Ancheta Wis, but I hope that a favorable comment by an administrator has not inhibited others from expressing their views. Some of these ideas have been controversial in Wikipedia, and I hope to have a chance to continue to support my points of view. I have found already that mention of Richard Feynman or Julian Schwinger often discourages further argument, like "kings X" in children's games. This is especially useful to me, because I have heard them speak and don't have to cite anything that can be checked. David R. Ingham 08:50, 21 February 2006 (UTC)

High School Student here

Dear Scientists,

I am a 10th grader. I am supposed to do a project on Quantum Mechanics for my school and I really do not have the slightest clue about what any of you are talking about. :( If you really want to make a good page you are going to have to simplify it down. Like that guy above said, if you really understand this stuff, then you should be able to explain it to an idiot. So this is a challenge for you guys, please tone the level of scientific facts and words down on here and I think that people will like you more.

I am a big fan of Quantum Mechanics. I think that they are great. However I would really like to learn more about them because I am supposed to write a children's book about them. :(

Well I hope some of you people can take my request to heart and maybe you could try to make

Dear Student. You might want to start with spectroscopy or radioactivity, or even a blackbody (a light bulb). QM doesn't impinge too much in our daily lives, unless you want to count the operation of a transistor or laser. It takes years to understand Quantum physics, although classical mechanics appears on every kid's playground with slides and swings and merry-go-rounds. If you look at the stars you might even wonder why do the stars shine. If you are trying to understand how an atom could exist, you will have just asked a QM question. You should start with the first link at the top of the article. --Ancheta Wis 18:32, 19 February 2006 (UTC)

Thinking about it, your book assignment should be answering what, when, where. How and why are more difficult questions. The physics of the playground answers the first 3 w's only. If you start with why then your level of understanding and and search for answers will take years. 19:03, 19 February 2006 (UTC)

Here is a start at what:

QM can explain the periodic table of the chemical elements.

Now you can start filling in when, where in your book. The illustration for the article shows the first few electron orbitals for chemical element number 1: hydrogen. 19:36, 19 February 2006 (UTC)

But how will you know when you are done with your study for the book? -- When you don't have to click on any link in the Wikipedia article you are studying because you already know what it is going to say. When that is true then you are ready to write. 19:52, 19 February 2006 (UTC)

And what if the words in the articles are foreign to you? Well, you are fortunate enough to still be in school. Ask your teacher about the meanings of those foreign words. I recommend grouping your unknown words or ideas in fewer than seven unknowns at a time. Write each question/ word on a separate index card. When you don't know something, write the unknown down on the card. When you get the answer, write that down on the card as well. Eventually you will have a bunch of cards which you can start sorting into related groups. Use Wikipedia to help you sort the cards. If the words are related, they will be on the same Wikipedia page. Then take the cards with the words on them and construct sentences from the formerly unknown words. If you still can't write a sentence about the words, wait. It takes time to understand anything that is important. That does not mean memorizing everything on the card. If you care about the word, it will remain with you (sometimes for the rest of your life). I hope that you understand that your questions are the most important part of all this research. You can always find answers on the Internet or in a book or article or person you have found. But answers will come to you in their own time, when you are finally ready to understand them. Just wait; I hope you are ready when the answers come.

When the periodic table was invented, it was discovered by a man who also wrote down the elements on index cards. He laid his index cards on the table and grouped like-elements together. When he found a missing element he wrote down a card which predicted the properties of that element.

When Ward Cunningham was inventing the wiki he also used index cards. (Where did the signature go?)

• The signiture "23:14, 19 February 2006 Ancheta Wis" seems to have been omitted here.

I am answering a point at a time, without reading everything first.

There is an attempt to simplify called Basics of quantum mechanics, but I disagree with its claim to avoid advanced topics: most of quantum mechanics can be understood without worrying about probabilities.

Writing a children's book about qm is an even more ambitious project than trying to explain it to high-school students. I think it would be of great value if someone could succeed in writing one that would really be read and understood, because I believe that qm, like foreign languages, is best understood if started early.

I told my 11 year old niece "If you keep on looking through more and more powerful microscopes, you don't keep on seeing more detail forever. Eventually matter is composed of units called atoms and motion is composed of units called quanta." I am not sure that helped her more than it confused her, but I can't think of anything better I could have said. Atoms are traditionally taught before quantum mechanics, but are not more fundamental. There would be no explanation of why they form molecules and crystals. David R. Ingham 04:39, 20 February 2006 (UTC)

Classical mechanics does not have a greater effect on in our everyday lives than qm does. It is just more intuitive and closer to direct observation. When you throw a baseball, where it goes is mostly explained by classical mechanics and your thoughts as you catch it are related to Newton's laws. Why it stays together and occupies space and how you can see it are only fully explained with quantum mechanics. But the qm takes too much mathematics to use on the baseball field. It is used to support technology, mostly in chemistry and engineering, to make things that can be used without understanding their design principles. David R. Ingham 05:44, 20 February 2006 (UTC)

Children's book

How about:

Once upon a time there was a particle of yellow light. We call her Goldielocks, though light particles can't really have names. She wandered until she came to an atom that had three bare electrons. One electron was stuck too hard in the atom. One was too loose. The third was just right, so he and Goldielocks became a photoelectron.  ? David R. Ingham 06:20, 20 February 2006 (UTC)

Explanation:

Quantum mechanics explains the fact that light is composed of particles.

If elementary particles like light and electrons could be labeled with names, much of modern physics would not work. Exchanging two identical particles does not change anything.

The term "bare electron" is used a lot, but it doesn't have any justification here beyond resembling the original version of the tale.

A light particle can excite a "loose" electron but that may be less likely than one that is "just right".

One of Einstein's important early discoveries was an explanation of individual light particles knocking individual electrons out of their atoms. The light particle becomes a part of the electron's motion. David R. Ingham 05:59, 21 February 2006 (UTC)

Quantum Computing

Could we have an addition related to quantum computing to this article? maybe a small introduction linking to another article...