# All Science Fair Projects

## Science Fair Project Encyclopedia for Schools!

 Search    Browse    Forum  Coach    Links    Editor    Help    Tell-a-Friend    Encyclopedia    Dictionary

# Science Fair Project Encyclopedia

For information on any area of science that interests you,
enter a keyword (eg. scientific method, molecule, cloud, carbohydrate etc.).
Or else, you can start by choosing any of the categories below.

# Talk:Quantum mechanics

archive of recently removed discussion: /Archive1

 Contents

## Where should I add a link to an example of quantum phenomena?

I just turned in a lab report on the Ramsauer-Townsend effect and finished up the article on it I started a week ago. the effect is discussed in quite a few quantum mechanics textbooks and is an example one phenomenon you need quantum mechanics to explain (specifically, the wavelike nature of the electron). i worked on it as part of a course, an introduction to quantum mechanics for junior-year physics undergraduates. is there another page i should edit to add a link to it? --Blick 08:06, Feb 26, 2005 (UTC)

There are hundreds of phenomena that you need quantum mechanics to understand. I don't think making such a list is particularly useful. If you are interested in a topic, just work on it and link to quantum mechanics; there is no need for a return link. -- CYD

Perhaps some mention of the problem that inspired Planck to invent Quantum Mechanics is in order. IIRC, physicists were trying to figure out what electromagnetic waves were in an oven that had a certain amount of heat in it. They knew that an integer multiple of the wavelength of the light in the oven would have to equal one of the dimensions of the oven, but every time they tried to figure it out, they ended up concluding that the oven had infinite energy in it. Planck was able to find the answer by assume that the energy in an electromagnetic wave was quantised such that E ∝ f. This went directly counter to the classical mechanics assumtion that E ∝ Amplitude.

not quite, in classical mechanics it's proportional to both the square of the amplitude and the square of the frequency 63.205.40.243 05:12, 8 Jan 2004 (UTC)

## Opening

The opening paragraphs are terrible. This should be linked to quantum eletrodynamic and quantum chromodynamics

Maybe this happens later in the artical...

April 11, 2005: The general reader, first of all, needs to be assured of the unique status of qm, which by now sets it apart from virtually everything else in the field of (scientific) knowledge (continuing loophole discussions notwithstanding). And that we became confident of this by relentless testing, not merely because it is a "theory" which is dear to us, or by faith. To the uninitiated, despite the entertainment value, puzzles and paradoxes tend to somewhat undermine confidence, no matter how stimulating we find them as professionals. With all due respect. -Guest

## Transactional Interpretation

quoting removed section:

The transactional interpretation, put forward by John Cramer, describes interactions in terms of standing waves in space-time. These standing waves are formed when advanced (forward in time) and retarded (backward in time) waves interfere. Once formed they look identical to a particle. This interpretation avoids the need for an observer to collapse the wave function. It also makes use of previously discarded backward in time solutions to wave equations, and resolves all of the so-called quantum paradoxes (see above). Despite the elegance of this interpretation, it does not seem to have caught on.

This is an interesting idea, but it is not nearly accepted enough to be mentioned alongside standard interpretations. Also, the idea of four-d support of the wave function in Hilbert Space with an external evolution parameter is hardly new. Many others have suggested it, and to attribute it one person is very misleading. -- Decumanus 21:34, 13 Feb 2004 (UTC)

Thanks for correcting. As many others have thought of it, do you not think it is at least worth mentioning? Not up there with the big ones, but as an interesting note? It seems a very elegant way of resolving a number of nasty problems with the CI. I often wonder how classical theories like general relativity would look if you replaced the notion of particles with the notion of a standing wave in spacetime. My degree level physics isn't up to it though! -- Mike Howells 21:50, 13 Feb 2004 (GMT)

I very much sympathize with your wanting to include mention of such things. It is very difficult in an article on Quantum Mechanics to include it in a way that is worthy of its acceptance (or lack of) among the community of physicists. There is perhaps a way to include such material as the transactional interpretation, but putting it beside more accepted interpretations is not the place. I myself have done much research in this area, but I am extremely cautious about including my own work in physicis article. In fact, I simply don't, as a rule, even though it is published.  :) -- Decumanus

In that case, you may wish to do something with the (now orphaned) article on the transactional interpretation. It does get a mention in popular science books like Schrodinger's Kittens, so it perhaps deserves a mention somewhere on Wikipedia? MH

Good point. The article on transactional interpretation itself is certainly worthy, in my opinion, of an article, since it is published research. I don't know the topology of these article pages well enough to know where it should go exactly, as a link, but I'm sure that other people do. If not, perhaps there should be a page on non-standard interpretations of quantum mechanics. The problem is that such a thing opens the door to what we call "crankery". The TI is certainly not in that category, however. There are many such theories that fall into the category of published-yet-still-speculative, especially in regard to quantum systems. -- Decumanus 22:12, 13 Feb 2004 (UTC)

## A few concerns

I'm a relative newcomer to this article (responsible for adding the Willis Lamb quote) and the quantum-physics branch of the Wikipedia, and have a few questions:

• Why do we have separate articles on, say, quantum states?
• Why do we continue to use the obfuscatory and outmoded term "wave function" when we simply mean "state"? ---The field was developed by physicists who were familiar with physical waves and the literal analogy was comforting to them. However the word state has a static connotation which is unsatisfactory, considering the continually fluctuating nature of the wavefunction before a measurement. Ancheta Wis 17:54, 17 Oct 2004 (UTC)
• What is the point of including a section of "gee-whiz" quotations, most of which make it sound as though QM is ridiculous as opposed to merely nonintuitive?

Also, I *strongly* object to the statement that the Heisenberg uncertainty principle (presumably the position-momentum one--the time-energy one is a different and more subtle issue) is a result of "wavefunction collapse". Wavefunction collapse (as has been rehashed time and time again) is not a process, furthermore, the uncertainty principle says nothing about measurements separated in time, so even if there really was such a thing as wavefunction collapse (it's just a \$10 word for "measurement"), the uncertainty principle, which is about simultaneous measurement, would not be a consequence of it. Forgive me for being pedantic about it, but position-momentum uncertainty principle is a generalisation of a truth about noncommuting observables. (Most phenomena that can be ascribed to the uncertanty principle, (which is an excellent heuristic) and some that usually are not (such as vacuum fluctuations in the light field), are actually the result of a noncommutativity. None result from the "collapse".)

There are many people who think that wavefunction collapse is a process. Indeed there are precise and mathematically rigorous equations which aim to describe it without reference to a concept of measurement or observers. It may be less mathematically elegant but it is certainly more conceptually elegant. [1] Of course this kind of material does not belong on this wiki page, but i don't think it's worth burning bridges unnecessarily.

That one cannot simultaneously diagonalize with respect to noncommuting observables is easy to show mathematically in a few lines to anybody familiar with linear algebra; the general uncertainty principle is a little trickier to obtain but still is an elementary relation between the product of the deviations and the commutator of the associated observables. This is all very simple to a mathematically literate reader, but may be too technical for the target audience of this article. However, I do believe that noncommutativity can be succinctly described in plain English. David Finkelstein's treatment in "What is a Photon?" (OPN Trends, Vol 3 No 1, Oct 2003) would be a good start. (For those interested in simple and direct exposition of quantum mechanics, I actually recommend the entire issue, especially the Loudon, Finkelstein, and Muthukrishnan/Scully/Zubairy articles.) I'm willing to take a crack at it, and also to add some material to the Uncertainty Principle article. I find the current state, with the glaring inaccuracy, to be rather embarassing, especially given that this is supposed to be a featured article.

--[User:bkalafut|bkalafut], 31 March 2004

I'm not sure what you mean about "wavefunction" being obfuscatory and outmoded. I use it all the time. So do all the papers I read, so do my colleagues. The PRB paper I'm in the process of writing will use it.
I completely agree with you on wavefunction collapse, I think it's a horrible concept. But I'm too afraid to say that in a public place, generally speaking. I'm laughed at when I say it's rubbish in real life, and Wikipedia is not the place for personal opinions. It's a horrible, ugly concept, but unfortunately it is very widely used by physicists. It guides their thought and the way they speak about a wide variety of topics. I have to admit it may be conceptually useful at times. It's certainly too important to ignore. What you have to understand is although it's an inelegant way of expressing an elegant mathematical concept, the Copenhagen interpretation is successfully used by many physicists who are fully aware of the mathematical and conceptual issues. They hold several philosophical viewpoints in their head at once, and switch between them freely.
Also you have to consider Wikipedia's audience. The fact is that most readers of this article would not understand the statement "one cannot simultaneously diagonalize with respect to noncommuting observables". Perhaps it is better to stick with the conventional way of speaking, and thus build on what readers may have picked up in school, college and popular science. -- Tim Starling 06:20, Apr 25, 2004 (UTC)
Umm, where in the article is it stated that the uncertainty principle is a result of wavefunction collapse? I don't see it. -- CYD
I think I took it out, or somebody else did. Good riddance! Bkalafut 04:36, 13 May 2004 (UTC)

I've stayed out of the "Copenhagen" debate on epistemology and metaphysics, and I'll stay out here. I have no problem with the concept of "collapse"--and I don't see it as not happening in the Everett Many-Worlds interpretation--my objection is to the term. --Bkalafut 04:36, 13 May 2004 (UTC)

## quantum physics, quantum theory

I saw that this was discussed before, but nevertheless I was not happy to see that "quantum physics" and "quantum theory" are listed as simply synonyms of quantum mechanics, when often they are used to make a distinction. I added a couple of sentences to this effect to the introduction, telling that someotime they are meant to mean something slightly different...please check and modify, but, please, dont let them again as simply alternative names.--AstroNomer 09:28, Jun 2, 2004 (UTC)

Are you saying that quantum physics is a superset and quantum theory is a subset? Bensaccount 16:59, 13 Jun 2004 (UTC)

I think what is needed is to have all three articles created (Quantum mechanics, quantum physics, & quantum theory) and then note the difference between them.Bensaccount 17:09, 13 Jun 2004 (UTC)

The following paragraph has been added by various anons over the last few days.

Revaz Dogonadze was a main author of the quantum-mechanical theory of the elementary act of chemical, electrochemical and biochemical reactions in polar liquids (1970s-1980s) and co-author of the quantum-mechanical model of enzyme catalysis (1970s). He was one of the founders of Quantum Electrochemistry.

I think it does not belongs here. There are thousands of scientists who have done research on quantum mechanics and related topics. The ones that we mention in the article are very, very famous ones: Einstein, Dirac, etc. I do not think that Dogonadze has done research of the same magnitude as Dirac. He is real, he has published papers which are getting cited (53 citations in 2003, according to Science Citation Index) but I suspect he is more like one of hundreds of good physicists whom we do not mention, rather than Einstein, Dirac or one of other Nobel laureates whom we mention here.

I removed it yesterday, because I saw some dubious past contributions from one of IPs that added this paragraph. It got restored by another anon. I would like to hear what other people think, before doing anything again.

Any opinions on this? Andris 22:17, Jun 26, 2004 (UTC)

Dear Andris, Professor Revaz Dogonadze (1931-1985) was one of the greatest scientists of the XX century, founder of the well-known scientific school of Quantum Electrochemistry, main author of a well-known Quantum-Mechanical Theory of the Elementary Act of Chemical, Electrochemical and Biochemical Processes in Polar Liquids. He was author of many classical scientific works. With kind regards, Professor Zurab D. Urushadze. July 26, 2004.
Dear Prof. Urushadze, please, substantiate your claim. If you can give references to scientific books/articles/print encyclopedias (either in English or Russia) that recognize Dogonadze as a distinguished scientist and his works as "classical", that will be very helpful. Andris 08:46, Jul 26, 2004 (UTC)
Dear Prof. Zurab Urushadze, thanks for providing links and for very quick reply. I will look at them. I noticed you have created Zurab Urushadze article. Please, be aware that Wikipedia has a "no auto-biography" policy which says that people should not add information about themselves, their papers or other subjects they are closely related to. Read Wikipedia:Auto-biography for more details. With best regards, Andris 15:58, Jul 28, 2004 (UTC)
Dear Andris, I have NOT CREATED Zurab Urushadze article, I am not author of this article! With best regards, Prof. Zurab Urushadze, July 29, 2004
I agree with Andris. Let's keep only the most important textbook quantum mechanics topics in this article. If it's not in standard quantum mechanics textbooks, then it doesn't belong in this article. Please stop adding it, I am getting tired of this revert war! - Lethe | Talk
Yes. The revert war is quite annoying. I'm new here - so don't pay much attention to what I say... - but I came exactly looking for Quantum mechanics (QM). IMO the article should focus on the breakthroughs leading to QM's creation and evolution. At the level of those made by Planck, Einstein, De Broglie, Heisenberg, Schrödinger,etc.. It should also mention QM's major practical applications. Probably Dogonadze's work would fit there nicely, along with solid state physics (trasistor, laser,...) and others, including quantum information wich seams to me still too recent to deserve a place in "History"--Nabla 15:05, 2004 Aug 7 (UTC)
Dear friends! Professor Revaz Dogonadze (1931-1985) was one of the greatest scientists in the field of Quantum Mechanics, founder of the well-known scientific school of Quantum Electrochemistry, author and co-author of many outstanding, classical works. He was a main author of a Quantum-Mechanical Theory of Kinetics of the Elementary Act of Chemical, Electrochemical and Biochemical Processes in Polar Liquids. With best regards, Professor Zurab D. Urushadze, August 8, 2004.
I doubt your claim. I recently searched arxiv.org which contains about 100,000 recent physics papers. It contains 4 papers referencing Dogonadze's work. A person who is cited by only 4 out of 100,000 recent papers is hardly a "one of greatest scientists". Andris 11:56, Aug 8, 2004 (UTC)
Dear friends, please see following important materials: 1) J.O'M. Bockris, Shahed U.M. Khan, "Quantum Electrochemistry", Plenum Press, New York, 1979, 538 pp. (ISBN 0306311437); 2) Encyclopedia of Electrochemistry, Vol. 2, Interfacial Kinetics and Mass Transport, Edited by Allen J. Bard, Martin Stratmann and Ernesto J. Calvo, Wiley Publishers, 2003, 563 pp. (ISBN 3527303944); 3) Journal of Electroanalytical Chemistry and Interfacial Electrochemistry, Vol. 204 (Revaz Dogonadze Memorial Issue), 1986; 4) Russian Journal of Electrochemistry, 39 (2), 2003 (Dedicated to the seventieth anniversary of R.R. Dogonadze); 5) Nobel Lecture of Rudolph A. Marcus, 1992 ( http://www.nobel.se/chemistry/laureates/1992/marcus-lecture.pdf ). With best regards, Prof. Zurab Urushadze, August 9, 2004.
Why do you keep removing Max Born? --Yath 07:18, 9 Aug 2004 (UTC)
Thanks for the links, Professor Urushadze. I will have a look at them. In the mean time, please stop editing the article until a consensus can be reached. If you can't agree to wait for a consensus view in this matter, and to abide by that view, I am going to ask for moderation. - Lethe | Talk 09:28, Aug 9, 2004 (UTC)
While Professor Dogonadze is indubitably a fine fellow, my opinion is that he does not belong in this article. Consider that it does not mention Fermi and Landau, let alone Fock, Heitler, Hund, Jordan, Klein, Lande, London, Onsager, Oppenheimer, Sommerfeld, Wigner, or any of the scores of other physicists who have arguably made far greater contributions to the theory of quantum mechanics. -- CYD

Because it seems to me that the discussion has not been productive, and we are still involved in a revert war, I have added this page to Wikipedia:Requests for comment in a first step towards resolution. - Lethe | Talk

I came here via the Rfc page. I read through this discussion and browsed several of the references given by Prof. Urushadze, which convinced me that Prof. Dogonadze was an influential scientist who made some important discoveries. However I haven't been convinced that they are important enough to the field of quantum mechanics proper to be included here. And more importantly, as CYD indicates many other scientists go unmentioned in the article whose names and discoveries are familiar to every student of quantum mechanics. The latter cannot be said about Prof. Dogonadze. I would suggest reverting the article to its previous version. regards, High on a tree 03:28, 12 Aug 2004 (UTC)

I agree. I'm a Ph.D. student in physics and I had never heard of Dogonadze until I looked at this discussion. Although I'm sure he's made some outstanding contributions, he is not notable enough to quantum mechanics to be included in this article. He seems suitably represented in the quantum electrochemistry article as well as in his own article. –Floorsheim 06:20, 15 Aug 2004 (UTC)

Totally agree. I've also come over from WP:RFC, and have studied physics. Not only would the reference to Dogonadze be a distortion in this article, the reference in Quantum chemistry should be improved to be a more relevant link to Quantum electrochemistry and the Quantum electrochemistry should be put on Cleanup — it reads more like a biography article on Dogonadze, tells us very little about Quantum electrochemistry and has the wrong title capitalisation. The Revaz Dogonadze article looks alright though. -- Solipsist 19:45, 18 Aug 2004 (UTC)

Dear friends, Quantum Electrochemistry is a new scientific direction of Theoretical Physical Chemistry on Quantum Mechanical aspects of Electrochemistry. Quantum Electrochemistry was developed by Revaz Dogonadze and his pupils in the 1960s-1970s. In 1971 Professor Dogonadze, Professor P. Kirkov (Jugoslavia), Professor J. Ulstrup (Denmark) and others founded the International Summer School on Quantum Mechanical aspects of Electrochemistry (Ohrid, Jugoslavia). The first quantative quantum-mechanical electron transfer theory was created by Dogonadze in 1959-1961. The first quantum mechanical model of proton transfer in polar solvents taking into account the dynamic role of the polar solvent was suggested also by Dogonadze and his pupils in 1967. In 1973-1979 the quantum-mechanical theory of kinetics of atomic-molecular transformation in condensed media was also developed by Dogonadze and his pupils. Professor Dogonadze was co-author of the first quantum-mechanical (physical) model of Enzyme Catalysis (1972-1975). The lowest energy vibration of anthrance serves as an extremely efficient accepting mode for the energy supplied for charge transfer by the external voltage. Such excitation of a vibrational quantum mode is described in the famous treatment of non-radiative transitions of trapped electrons in non-polar semiconductors by R. Kubo and Y. Toyazawa (1955) and has been introduced into the quantum-mechanical theory of electron-transfer reactions of redox ions by Dogonadze and his pupils in 1972. In 1984 Professor Dogonadze was organizer of the International Conference "Electrodynamics and Quantum Phenomena at Interfaces" (Telavi, Republic of Georgia, October 1-6, 1984). With best regards, Prof. Zurab D. Urushadze, August 20, 2004.
That is an impressive summary of the school of quantum electrochemisty, Professor Urushadze, but it does not convince. Has any of this work effected the understanding of quantum mechanics? Why should an important (but not Nobel winning) chemist be along side a series of Nobel winning physicists? I would ask you to please stop adding your text to the article until a consensus has been reached on this talk page that you have made a convincing case. At present, the majority opinion seems to be against you.-Lethe | Talk 17:53, Aug 22, 2004 (UTC)

### Is it time for mediation?

At this point, I don't feel like an agreement has been reached, nor like one is near, nor even that productive dialogue is happening, so I would like to go to a next step in dispute resolution, possibly mediation. To summarize the consensus so far, it seems to me that we have a consensus that while the work of Dogonadze is important and noteworthy, it does not belong alongside the the names of the Nobel-winning founding fathers of Quantum Mechanics. (Note that the Nobel prize acceptance speech for quantum electrochemistry that Urushadze links above is not received by Dogonadze, but rather by Rudolph Marcus, and it was not a Nobel for physics, but rather for chemistry. This something which I would consider pretty definitive evidence that the creators of the field of Quantum Electrochemistry may have been among the most influential chemists of all time, their impact on physics in general and quantum mechanics in particular was minimal. Their work was an application, rather than a development in theoretical foundations, of Quantum Mechanics. (Obviously, this last is my own opinion, not necessarily the consensus view))

The following 7 users have reverted the Dogonadze text:

additionally, some others have explicitly voiced support for the noninclusion of the Dogonadze text, including

edits from anonymous users at IP addresses in the 213.157.193.x range, including 4,15,43,45,49,54,65,82,128,171,179,188,196,199,209,219, which are all presumably the single person, Zurab Urushadze, support the view that Dogonadze is "one of the greatest scientists in the field of quantum mechanics", both by reversions of the article, and by comments made on the talk page.

I think steps need to be taken by an outside party for any agreement to be reached by the two parties. The revert war makes up virtually all of the last 50 edits in the history of this article, and shows every sign of continuing in perpetuam. -Lethe | Talk 17:04, Aug 15, 2004 (UTC)

## proposed structure for the article

My last edits reflects my view that this is the best way to present a scientific theory:

• start with the limitations of previous theories (here: electromagnetism): no quantization and no wave-particle duality
• describe the theory, and how it overcomes the limitations of the previous theory (this is the bit that I saw missing, and corrected)
• describe predictions of the new theory (here: entanglement)
• describe limitations of the new theory

Pcarbonn 12:12, 11 Jul 2004 (UTC)

I have now restructured the article along those lines. See Wikipedia:WikiProject Science to further discuss this. Probably needs some more work though. Pcarbonn 19:46, 16 Jul 2004 (UTC)

This is fine, only you have now, perhaps accidentally, deleted the insertions I had made a few weeks ago to soften any implication that Bell test experiments had conclusively confirmed quantum mechanics. They have not. There are still serious loopholes in all the experiments -- they are still trying to design a loophole-free one. Caroline Thompson 21:49, 16 Jul 2004 (UTC)

Sorry, this was accidental. I had to move quite a few things around, so this may have happened. I would suggest your insert it again in the "Quantum effect" sub-section. (you know this subject better than me) Pcarbonn 19:04, 18 Jul 2004 (UTC)

## quantum entanglement, Bell's inequality

I have a question about these two sentences:

"This phenomenon is called entanglement and its difference from ordinary correlation is described by Bell's inequality. Experimental violation of Bell's inequality are, despite the presence of loopholes, currently accepted as one of the major verifications of the quantum theory."

If the difference of the quantum phenomenon (entanglement) and the normal correlation is described by the Bell's inequality, then its verification would be the verification of the quantum theory, wouldn't it? Or better the "ordinary correlation described by Bell's inequality" should be written.

Pál 23:51, 14 Jul 2004 (UTC)

## Wave-particle duality vs uncertainty principle

I think the subsection "Quantum mechanical effects" has a false suggestion. Say thinking of the momentum-spatial coordinate uncertainty principle it suggests, that of of them is particle like variable, and the other is wave like. There are two basic representations, the Schrodinger (spatial coordinate) and the Heisenberg (momentum) representation of QM, and both have the wave-particle duality. The relativistic theory prefers the momentum representation, but it does not mean, that either the wave or the particle behaviour is lost. The propagation is wave like and the creation and annihilation is particle like. User:Hidaspal 20:30, 15 Jul 2004 (UTC)

Fine. In the section 'Quantum mechanical effects', I would really like to have an explanation on how those effects are explained by the theory, e.g. by referring how the wave function behaves when those effects are observed. Otherwise, the section just explains what wave-particle duality is, but we can find that in the corresponding article. I'm sure many people would find this interesting. Unfortunately, I don't know enough myself to explain it correctly. Could you help ? Pcarbonn 19:26, 16 Jul 2004 (UTC)

## Caption

I just tried to follow the guidelines at Wikipedia:Captions to revise the caption on this page - please check it for correctness and make improvements as needed. (The caption that was there didn't mean much of anything to me, and I studied orbitals in chemistry class a decade ago, so I thought it worthwhile to translate to make the picture more meaningful to the masses.) -- ke4roh 18:39, Jul 30, 2004 (UTC)

I have a problem with the word orbit which implies the electron is a satellite of the nucleus, moving in an orbit - if that were so, this charge would be accelerating, hence radiating energy, which is not observed; in a sense, the electron is everywhere the probability density shows it to be, simultaneously, but it takes an observation to place it. I am replacing the word orbit with orbital Ancheta Wis 07:58, 31 Jul 2004 (UTC)

## Funny that there is no slit here

Has the double-slit experiment been superseded by another explanation which actually does not appear here? I fancied it was one of the clearest introductions to the subject, but as of 1 Aug 2004 the word "slit" does not appear in the article... ?? Pfortuny 09:43, 1 Aug 2004 (UTC)

## Unraveling some jargon and Historical development

Having just read the article, I think the words operator and wavefunction both deserve some unraveling. These concepts may be intuitive to a physicist, but they are not intuitive to the general public. I don't mean that their explanations need to be mathematically rigorous, but they should describe what these terms mean.

Also, I would love to have the image of hydrogen probability density functions described further. When I was in high school, I saw pictures of these in my physics and chemistry textbooks, and now they make a lot more sense to me. The wavefunctions associated with these pdf's form an orthogonal set, and that is a thing of beauty.

The History section looks and reads like it was tacked on. The history of quantum mechanics is an amazing topic, one that probably deserves its own article. The connection between these early experiments and their role in developing quantum mechanics is de-emphasized in this article. Some important experiments to add:

• Discovery of the electron
• Franck-Hertz experiment
• Young's double-slit experiment, and as applied to electrons (agree with above comment)

Another thing I don't like is the statement about quantum mechanics being incompatible with general relativity in the Interactions... section. While this is true, could someone please explain why it is true? This is a claim that is made in lots of popular accounts of physics, but it is hardly ever backed up. What are the fundamental assumptions of quantum mechanics that are violated by general relativity? This has never been explained well to me. --Hfs 01:23, 2 Aug 2004 (UTC)

Notice that the Young diffraction experiment has been tested with up to buckyballs, which are quite large... Pfortuny 21:19, 7 Aug 2004 (UTC)

Andris is right. It is the absolute square of the inner product. Floorsheim 11:37, 17 Aug 2004 (UTC)

## Question of Interpretation

I have not seen this stated anywhere outside this article and would appreciate learning its source:

Immediately after a measurement is performed, the wavefunction becomes one of the wavefunctions compatible with the measurement, i.e. a wavefunction that gives 100% probability for the result obtained. This process is known as wavefunction collapse, and the wavefunctions compatible with the measurement are known as eigenstates of the observable. The probability of collapsing into a given wave function depends on the type of measurement, ...

My question is about the wavefunctions compatible with the measurement are known as eigenstates of the observable. I am thinking back to my teacher, analyzing a spherically symmetric situation, and expanding the solution in spherical harmonics. The shapes of the wavefunctions are eigenfunctions and the constants which satisfy the eigenfunctions are observable via experiment. Thus the experiment and the computation of the constants yield identical results. What does not follow for me is the statement The probability of collapsing into a given wave function depends on the type of measurement, .... The fact that the situation involved spherical harmonics was due to the symmetry of the situation and not due to the type of measurement. The statement as it stands seems to be putting the cart before the horse. Ancheta Wis 03:10, 11 Sep 2004 (UTC)

You can't just have eigenfunctions, they have to be eigenfunctions of an operator. The shapes you're thinking of are eigenfunctions of the Hamiltonian. A measurement causes a collapse to an eigenfunction of the measurement operator, not to an eigenfunction of the Hamiltonian. The eigenfunctions of the measurement operator are called the measurement basis, and a measurement could be seen as a projection onto this basis. This is dealt with in most undergraduate-level quantum physics textbooks, for example Sakurai Modern section 1.4 (ISBN 0-201-53929-2). -- Tim Starling 03:03, Sep 13, 2004 (UTC)
In other words, the characteristics of the measurement apparatus are explicitly included in the results of the measurement or computation. Ancheta Wis 18:27, 17 Oct 2004 (UTC)

## Suspect text

This text was recently added by an anonymous user. There are several things that are suspect. The style is not quite encyclopedic and googling for names mentioned in it returns very few google hits. (None for "Nikola Kalitzin", 8 hits for "Josiph Rangelov").I removed it for the time being, comments from experts in this area are welcome. Andris 20:45, Sep 21, 2004 (UTC)

What is the physical cause for quantum behaviour of micro particles? Why we use a wave equation of Schrodinger for description of quantum behaviour of micro particles instead to use a corpuscular equation of Hamilton-Jacoby, descripteng the classical behaviour of macro particles? What is a diference between these two equations? What is a difference between classical trajectory and quantum wave function?

It 1952 year Nikola Kalitzin supplements the electromagnetic interaction between the electron electric charge and the electric field of the zero-point electromagnetical fields to classical motion equation of same electron, taking in consideration the Lorentz' friction force of its charge. In this wаy Kalitzin first have obtained why coordinate and impulse of such electron don't comutate. In 1954 year A.A. Sokolov supplements the oscillation force to the electromagnetic interaction whitout to ezplain the cause for this and have obtained more correctly commutation equation.In 1980 year Josiph Rangelov explains what means Kalitzin's takinkg in consideration of the electromagnetic interaction between the electric charge of an electron and the electric field of the zero-poind electromagnetic fields of the fluctuating vacuum and Sokolov's oscillation force. In this way Rangelov explains that the quantum motion of the quantized electron is a sum of two motions : in first the classical motion and in second the stohasstic motion as a result of the electromagnetic interaction of its electric charge and the electric field of the vacuum fluctuations. In results of this the narrow path of the classical corposcule turns in wide highway of the quantum micro particle and classical determinism turns in quantum probability. Therefore if we add the kinetical energy of the micro particle stohastic motion to classical Hamiltonian-Jacoby motion than we would obtain the quantum Schrodinger equation. Therefore quantized micro particles parameters of motion have dispersion instead definite values.

In second Rangelov explain that the electric charge of the reletivistic electron participates in some inner motion, called by Shcrodinger as Zitterbewegung. This inner motion creates the own electromagnetic filds, the own magnetic dipole moment and its inner mechanical angular moment, called spin.

Interesting that all the google hits for Josiph Rangelov seem to be posts from him to a blog or forum. Could this be a case of self-promotion? -- Tim Starling 02:48, Sep 22, 2004 (UTC)

The text in question definitely isn't standard quantum mechanics. --Matt McIrvin 01:19, 25 Sep 2004 (UTC)

## Introduction

While the article itself is incredible in content and breadth, the introduction needs some work.

Its not inaccurate in any way but it does need restating. That Quantum mechanics does something better than something else is not really a good introduction to what it is.

"Quantum mechanics is the study of how the universe functions at very small scales, where classical theories break down" might be a good start (I'm not editing it myself yet as my education is in other areas and I read about the subject material purely as a recreational mental exercise). "The study of quantum mechanics revolves around the interactions and behaviors of the particles that make up the universe. When doing experiments and measurements in the atomic and subatomic scales, scientists have found classical physics lacking in an ability to explain their results. Quantum mechanics is a set of theories that attempts to explain these results and interactions."

If you think those would work, feel free to use them, or I can do it myself -- in this case, I'd rather comment and wait for discussion (if any).

## Runsguy2003@yahoo.com

moved this page to Runsguy2003@yahoo.com . I moved it back to Quantum mechanics, and am listing Runsguy2003@yahoo.com on WP:RFD -Lethe | Talk

## "Totalitarian principle"

Could someone versed in quantum physics verify the new article Totalitarian principle and look if it is correct, a fringe interpretation or just patent nonsense? Thanks - Marcika 01:23, 16 Nov 2004 (UTC)

I didn't know this principle had a name, but it is definitely something that is really talked about in particle physics. I think it's a good article. -Lethe | Talk
It's fine, see [2] -- Tim Starling 13:50, Nov 16, 2004 (UTC)

## Sum of Histories

I have heard that concept long time ago. It is intereseting that "history" becomes an object in physics. Could somebody write an article on it? --wshun 10:04, 5 Dec 2004 (UTC)

See path integral formulation. -- CYD

## Phrase "quantum physics"

The phrase "quantum physics" was first used in Johnston's Planck's Universe in Light of Modern Physics.

Do we have a reference for this claim? I can find only three pages in Google that make this claim, and they are all different versions of this Wikipedia article!--Susurrus 05:02, 17 Dec 2004 (UTC)

## Quantum darwinism

I just created the quantum darwinism article. Could someone more knowledgable than I please mention it in quantum mechanics and any other relevant articles. Much thanks. --RoyBoy 22:20, 27 Dec 2004 (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?

## 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

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

## 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) 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

Last updated: 06-01-2005 02:56:02
03-10-2013 05:06:04