Talk:Uncertainty principle/Archive 3

Time and Frequency Uncertainty
Maybe a little bit more detail about the implications of this principle in fourier analysis and signal processing should be added, like a concrete inequality for example. Information from this article: http://cnx.org/content/m10416/2.18/?format=pdf which has been published under creative commons license could be used. 203.167.251.186 (talk) 01:09, 12 December 2008 (UTC)

Fourier analtyc interpretation
Shouldn't the mathematical Fourier transform version of the uncertainty principle get some mention, or link to a seperate page? This is not only connected with the physical principe but has independent interest. —Preceding unsigned comment added by 90.229.231.115 (talk) 18:09, 9 February 2009 (UTC)

h or h-bar?
According to the intro: can never be smaller than a small fixed multiple of Planck's constant:

\Delta X \Delta P \ge {\hbar \over 2} $$

But I thought Planck's constant is h, and h-bar is Dirac's constant? that is what the Wikipedia article on Planck's Constant says.

Either the article on Planck's constant needs to be corrected, or this article needs to be corrected. Either we need to change "Planck's Constant" to "Dirac's Constant" or we need to rewrite the formula so as to use h rather than h-bar (or we could provide two formulas, one describing the principle using h and one using h-bar). Slrubenstein  |  Talk 11:23, 27 May 2008 (UTC)


 * Or since the two are proportional with a small fixed multiple, we can recognize that there is no conflict and leave it as is.Likebox (talk) 15:33, 27 May 2008 (UTC)

I do not understand what you mean that there is no conflict. Either h-bar is Dirac's constant 9as one article says) or it is Planck's constant (as another article says). It cannot be both and both cannot be right. Slrubenstein   |  Talk 20:53, 27 May 2008 (UTC)


 * $$\hbar$$ is always Dirac's constant, and this is exactly the same thing as Planck's constant, except divided by 6.28. If something is a small fixed multiple of Planck's constant, like say 5 times planck's constant, it is also a small fixed multiple of Dirac's constant, it is 5/6.28 times Dirac's constant. If something is a small fixed multipl of Dirac's constant, like hbar/2, it is a small fixed multiple of Planck's constant, namely h/4pi.Likebox (talk) 00:45, 28 May 2008 (UTC)


 * In addition, if this is not immediately obvious to anybody reading this article then god help us all Likebox (talk) 22:49, 11 June 2008 (UTC)

The given equation is correct since h-bar = h/2$$pi$$ —Preceding unsigned comment added by Srinivasvuk (talk • contribs) 11:32, 8 May 2009 (UTC)

Using this talk page to discuss wording changes
I have removed several parenthetical statements that this article is saying things poorly. Comments such as "There may be some way of stating Popper's position precisely; but if this is it, it's ridiculuous " belong here were we can determine a better way to state this information before it goes in the article.

T&#949;x &#964;  ur&#949;  14:14, 8 July 2008 (UTC)

Stupid point
The operator norm used to derive the UP here is:


 * $$ \|A\| = |\langle\psi|A|\psi\rangle|$$

but for some choices of psi the differentiation operator is unbounded even in this norm, because taking a derivative makes a powerlaw falloff slower. But the proof works still, because the infinite norm object has an infinite momentum uncertainty, meaning a divergent standard deviation for the momentum, so the heisenberg principle is automatically satisfied. So maybe the requirement that the operators are bounded is not necessary, because the inequality is just trivial when the operators are unbounded.Likebox (talk) 22:05, 8 July 2008 (UTC)

More to the point, the whole thing doesn't work, at least not in any way I could see. In order to make the argument, the operator norm needs to coincide with the expected value, but then it is not true that:

\| A B \| = \|A\| \|B\| $$ which is assumed implicitly. I removed the argument, perhaps it is correct with some crazy norm, but I couldn't figure out how to define it.Likebox (talk) 21:18, 10 July 2008 (UTC)

I should stop thinking in public: the previous argument was using the norm
 * $$ \|A\|^2 = |\langle\psi|A|\psi\rangle|^2$$

a psi-specific operator norm which obeys:
 * $$ \|AB\| \le \|A\|\|B\|$$

by Cauchy Schwarz, and which also obeys the triangle inequality:
 * $$ \|AB - BA\| \le 2\|AB\|$$

and the argument just needed a less than or equal sign to instead of an equal sign when taking the norm of the matrix product.
 * $$ \|AB-BA\| \le 2\|AB\| \le 2\|A\|\|B\|$$

so I was just being stupid.Likebox (talk) 00:45, 11 July 2008 (UTC)

Deletes
Two deletes undone:


 * 1) Removed Bohr's answer from Einstein's thought experiment using a box of light, which makes it seem that Einstein found a flaw in the uncertainty principle, which he didn't.
 * 2) Removed physicist criticism of Popper's thought experiment, which makes it seem like Popper was actually saying something deep, which he wasn't.Likebox (talk) 18:10, 20 August 2008 (UTC)

Not a Requirement
Physically, the uncertainty principle requires that when the position of an atom is measured with a photon, the reflected photon will change the momentum of the atom by an uncertain amount inversely proportional to the accuracy of the position measurement.

To be clear for the lay reader, this text should be removed since the measurement of the position is not exclusive to an atom or the use of a photon for measurement purposes. The above quote surely leads readers to confuse the observer effect with the uncertainty principle. The Uncertainty Principle must hold regardless of the method of observation. The above quote could be better as:

Physically, the uncertainty principle requires that when the position of a particle is measured, the particle's momentum will change by an uncertain amount inversely proportional to the accuracy of the position measurement.

thanks guys in advance for making the necessary changes! —Preceding unsigned comment added by 71.142.74.187 (talk) 08:53, 21 August 2008 (UTC)

Measurement
I think the words involving measurement should be removed from the first paragraph to avoid confusion with the observer principle. Suggest modifying to "uncertainty principle states that accurately calculating the location of a particle makes its momentum uncertain; and conversely, that calculating its momentum of the particle precisely makes its position uncertain. Note that this is true even in theoretical calculations where the particle's properties are known without physically measuring them." Can someone just confirm that these theoretical calculations I mention do exist? I assume they do but am not certain. 93.97.48.217 (talk) 22:22, 9 October 2008 (UTC)


 * The problem with rewording like that is that the "observer effect" is not that wrong, it's just the way a logical positivist would say the uncertainty principle. While positivism is not popular anymore, it's still a valid point of view, so it's probably not best to overemphasize the observer-effect/uncertainty-principle distinction too early. I mean, if a shy person can't speak when people are looking, that's the observer effect, but its not the uncertainty principle. But if you look at an electron with x-rays and it starts jumping around that's the uncertainty principle, and it can also be thought of as the observer effect.Likebox (talk) 22:30, 9 October 2008 (UTC)

The Physicists Have Really Hijacked This

 * and so they should Kevin aylward (talk) 10:20, 20 September 2009 (UTC)

You have to read pretty deep into the article before you get to the common understanding of the uncertainty principle, and there someone has dismissed that common understanding.
 * The common understanding is misleading, so why continue it? Kevin aylward (talk) 10:20, 20 September 2009 (UTC)

If most people think the uncertainty principle signifies something, then that's (at least among) what it signifies.
 * So, if the majority believes the would is flat, then we should just all go along with that? Kevin aylward (talk) 10:20, 20 September 2009 (UTC)

Also the intro is turgid. The article reads to me like people who know physics refining their own narrow understanding of the word.
 * The uncertainty principle is an aspect of physics, not basket weaving. It is the physicists job to state what principles of physics mean, not basket weavers. The physicists "narrow view" is usually the correct one.Kevin aylward (talk) 10:20, 20 September 2009 (UTC)

But I would guess most visitors here would like to understand how the principles is usually understood. The article should be rewritten as something more expansive and the bias against the common understanding of the principle should be excised.
 * I would guess most visitors would like to know what the mass market popular misconceptions are and contrast those with the actual truth. Kevin aylward (talk) 10:20, 20 September 2009 (UTC)

(Sorry, don't know how to sign this.) —Preceding unsigned comment added by 66.65.60.243 (talk) 03:25, 26 October 2008 (UTC)


 * It used to be even worse. I tried to fix the residual problem--- hope it reads better now.Likebox (talk) 06:07, 26 October 2008 (UTC)
 * It is still really, really bad. I doubt anyone other than a physicist or maybe engineer can understand this. This isn't wikipedia for physicists. I don't think there should be many formulas on any wikipedia physics entry. Wikipedia is meant for non-experts. Only physicists find value in (or can understand) these formulas. I can only understand this type of subject when it is described mostly in words, rather than numbers and formulas.
 * Unfortunately, you don’t understand this, you only think you do. Understanding a wrong verbal explanation of a subject does not mean you understand the subject. Physics can not be understood without equations.  That’s just the way it is. Kevin aylward (talk) 10:20, 20 September 2009 (UTC)
 * I think this makes the article largely worthless for most people. If they can't understand what the entry describes, they won't read it and they won't be able to understand the subject matter. RomanHistorian (talk) 09:24, 26 October 2008 (UTC)
 * I'll try to take a stab at it, if I have the time. The lead section is too long, and I don't think the displayed formulas belong there. -- Army1987 (t — c) 09:29, 26 October 2008 (UTC)


 * Wikipedia has several purposes, and I think it can serve them all well. The primary mission is to inform the general public, as you said, so that the introduction should be as accessible as possible. But Wikipedia has also been of immense importance to specialists, because it allows them to read and understand the literature. Each subfield has a specialized jargon, which mostly just repeats stuff you already know in a new language. Before Wikipedia, you had to spend a year or two familiarizing yourself with the language and basic results of a field before you could start to do active research. This tower of Babel effect is pronounced in mathematics, and even more pronounced in the humanities, but Wikipedia cuts this time down to next to nothing.


 * Unfortunately, with articles like this one, it does nothing but add confusion a “to be” real physicist. It can take years to finally exorcise oneself of all the daft, but poplar, fundamentally incorrect explanations that are handwaved in unvetted media such as Wikipedia. Kevin aylward (talk) 10:20, 20 September 2009 (UTC)


 * So while I agree that it is important to keep things generally accessible at the beginning, I also think that it is possible to make the articles clear enough so that any interested and dedicated person can become as informed on scientific and mathematical issues as the specialists. This second mission requires us to briefly summarize all of human knowledge, and that includes all that technical stuff.Likebox (talk) 15:13, 26 October 2008 (UTC)

Explanation request
Can someone please explain the following statements from the article:
 * It is also misleading in another way, because sometimes it is a failure to measure the particle that produces the disturbance. For example, if a perfect photographic film contains a small hole, and an incident photon is not observed, then its momentum becomes uncertain by a large amount. By not observing the photon, we discover that it went through the hole, revealing the photon's position.

I don't think it's stated clearly. Thurth (talk) 07:00, 7 December 2008 (UTC)


 * It's saying that sometimes a null-result of a measurement, when nothing happens, alters the wavefunction. So nothing happens, but because of the setup, the fact that nothing happens tells you the position of the particle.


 * A classical example is the hemisphere photon detector--- you have a photon emitted and a huge hemisphere of photon detectors. If you don't see anything, you conclude that the photon went to the other hemisphere. But if the detectors are perfect, and they are perfectly arranged in a hemisphere, and each one is smaller than the wavelength of the photon, then you can get interference rings on the other side. If you repeat the experiment many times, you end up with interference fringes on the edge of the hemisphere.Likebox (talk) 08:34, 7 December 2008 (UTC)

Thanks for the explanation. Now, I understand much better. I was really confused by those statements. Thurth (talk) 05:08, 10 December 2008 (UTC)


 * Could you please fix the article so it's clearer? Someone else will probably get confused in the same way.Likebox (talk) 19:27, 10 December 2008 (UTC)

I just made some corrections to a few lines in the article. I think that's about what I can do without getting into troubles. Further editings have to be a team effort, because this article requires a lot of difficult knowledges in QM. It's really easy to get confused in the different concepts involved. So, only an expert in this area can do it. How about you? Are you interested in doing it? Thurth (talk) 00:52, 12 December 2008 (UTC)


 * I'm afraid the mediocre writing you see there is already mostly mine.Likebox (talk) 02:04, 12 December 2008 (UTC)

It's actually very good. I am translating it into Chinese. Currently, the Chinese version is just slightly more than a stub article. So, hopefully, more people will be reading your contributions in the future. Thurth (talk) 06:10, 14 December 2008 (UTC)


 * Content aside, em dashes should never have this style of space padding in prose--- especially in an encyclopedia. Before you react harshly to someone's edits, Likebox, please make sure you understand them. I clearly stated that if you or anyone else insists on reverting or re-editing back to em dashes, they should make sure they at least do it per wp standards. Yes, I do "feel strongly about it," especially in articles with already-difficult subject matter. Sarcastic edit summaries and editing the article right back to a genuinely worse state was exactly what I expected, sadly. Egos aside, em dashes can be used directly these days—no need for ascii ugliness—and furthermore, if an author prefers spacing, it should be one space on each side and an en dash should be used – like this. Oh, and kudos to User:Michael_Hardy, that's a heck of a collection of contribs. &mdash;Joel D. Reid (talk) 04:51, 19 December 2008 (UTC)


 * I'm embarassed to say, I couldn't figure out how to make the em-dashes! I could have searched through other articles, I suppose, but I don't care so much about the issue. Why don't you please fix the dashes &mdash then I can learn how to do it.Likebox (talk) 01:22, 20 December 2008 (UTC)

Paradigm Bias and Unsourced
The following statement has three flaws. 1. It is unsourced. 2. It is paradigm biased. 3. It is ridiculously bolded.

states with both definite position and momentum just do not exist in quantum mechanics, so it is not the measurement equipment that is at fault.

Under which interpretation are we to assume this is to be so? Considering there is no epistemological or scientific foundation for choosing one or the other, assuming the truth of one system demands, at the very least, indication of such a paradigm choice in the text when making blanket statements like "does not exist in quantum mechanics". Similarly, both source and romanize the text.69.22.238.202 (talk) 05:50, 15 December 2008 (UTC)


 * This is true in Copenhagen/Many-worlds/CCC or any other standard interpretation where the wavefunction is a complete description. This is nowadays synonymous with quantum mechanics, since these only differ in philosophy. There is no dispute about this statement in the physics community.


 * It is true that if you take a Bohmian approach, with hidden variables, that there is more information than in regular QM. But the statement is also true in Bohmian mechanics, because the "momentum" of a particle is not exactly a quantity associated to a particle, but to a measurement procedure that entangles a momentum-meter with the particle, and then measures the meter's dial. There does not exist a single interpretation or extension of quantum mechanics which I know of where the particle's position and momentum can both be well defined at the same time.Likebox (talk) 16:00, 15 December 2008 (UTC)


 * Lay user here reading this page to get an answer to the following: why is uncertainty inferred to be a fundamental property of the universe, if it is the result of experimental limitation? If it is not the result of experimental limitation, why can't it explained without recourse to the concept of measurement? eg. without statements like “When the position of a particle *is measured*, the particle’s wavefunction collapses and the momentum does not have a definite value”. The page doesn't satisfactorily explain how we get from there to the fact that uncertainty is inherent to the world. The statement at the beginning of this section and the comments following it (eg. "there is no dispute about this in the physics community") don't help much. Thanks!lightspeedchick (talk) 21:41, 16 February 2009 (UTC)

"Well known" uncited popular culture
Popular culture references already merit some level of stink eye on notability; i suggest that items that get listed here must at least have a reference to a specific instance of work beyond "Com'on - everybody's heard of it...". Reasons for objections? Quaeler (talk) 23:17, 6 January 2009 (UTC)


 * I don't get it. Have you not heard it?Likebox (talk) 05:58, 7 January 2009 (UTC)


 * Nope, hadn't heard it - nor the other, still there, "well known joke". Beyond that, i'm not sure what there is not to 'get'; the proposal is that popular culture items must have a concrete instance to reference, not a general "it's well known". Quaeler (talk) 06:44, 7 January 2009 (UTC)

Ok, let me rephrase this: we presently have one, and were attempting to have two, 'references to popular culture' in which the reference wasn't a specific concrete instantiation, but rather "oh, everyone has heard of that." What makes this particularly egregious, IMO, is that this is an article on a science/math topic; for people who work in science and/or math, they would Never accept "just because" or "it's obvious" as part of a proof or experimental write-up yet we choose to accept an analogue in the article.

Barring fruitful discussion as to why we should allow such a thing in the article prior to 12.00 GMT 9 Jan, 2009, i will remove the remaining reference to a 'well known joke', and insert comments to editors concerning specific examples. Quaeler (talk) 11:57, 8 January 2009 (UTC)


 * Yeah, yeah. You're right, I know. But come on. Use common sense. There's no motivation to lie about things like this.Likebox (talk) 18:10, 8 January 2009 (UTC)
 * Gotta agree with Quaeler here. Most of the stuff in that section seems to be trivia (and most are unsourced, to boot).  I'm going to add  tags and see if anyone can find a citation/source for those.  DP 76764  (Talk) 18:23, 8 January 2009 (UTC)

(deindent) And I am going to remove those tags. When someone says "In such and so, episode such and such", the source is obvious--- it's the thing that is being talked about.Likebox (talk) 17:12, 9 January 2009 (UTC)

Sentence fragment?
The following text in the article sounds like it's missing a few words.
 * Rather, the motion was smeared out in a strange way: the time Fourier transform only involving those frequencies which could be seen in quantum jumps.

By "time fourier transform", does that mean four dimensional fourier tranform of space+time? And what does it mean by "only involving"? Is the fourier tranform only done on those values, or are those values the only ones that end up with non-zero result in the fourier tranform? Or something completely different? boxed (talk) 10:38, 18 January 2009 (UTC)


 * The time fourier transform means the fourier transform of X(t), the motion of the particle, in time. So it's only a time-frequency fourier transform, that's it. For periodic motions, the FT is nonzero only at integer multiples of 2pi/T, these are multiples of the orbital frequency. But in the original formulation of quantum mechanics the fourier coefficients of the motion occur at nonclassical frequencies which are E_i - E_j/h, where E_i and E_j are allowed energy levels. This is explained in detail in matrix mechanics.Likebox (talk) 06:38, 23 January 2009 (UTC)

In popular culture
The usual question: is there any reason to have this section? It's just cruft (with a load of tags), and adds little or nothing to the article. I'm tempted to remove it all in the near future. Oli Filth(talk 17:42, 23 January 2009 (UTC)
 * Agreed. There are some articles that merit such sections, but this one was out of place. I've removed it. - SimonP (talk) 00:39, 22 March 2009 (UTC)
 * I restored it as it has been, I believe, discussed many times before. I am surprised that nobody has come here to support it. Perhaps I should have left it deleted and that would have attracted them. My own view is that it is mostly rubbish but the uncertainty principle does have a certain status in popular culture, so it should be cut back and improved. -- Bduke   (Discussion)  00:53, 22 March 2009 (UTC)
 * It has been discussed a couple of times before. I'm of the opinion (as before) that it should be removed; about the only reference that's worth mentioning to the reader of the article is that of Copenhagen (play), as it's an entire play about Heisenberg.  The rest are just trivial (throw-away one-liners), and mostly about the observer effect.  Oli Filth(talk 01:03, 22 March 2009 (UTC)
 * What is striking is how random the examples provided are. The pop band seems incredibly obscure, as well as the "Aqua Teen Hunger Force". Examples on that level of relevance could be found for absolutely anything. I propose getting rid of the examples altogether. Hornvieh (talk) 23:13, 27 November 2009 (UTC)

Photons in the Uncertainty vs Observer section
I must have been misinformed.

I thought something needed to have mass for it to have momentum.

I must be wrong though, since the section in question has such brilliant sources referenced.

203.9.200.4 (talk) 03:44, 29 January 2009 (UTC)

Woah. Ignore me. I've just reevaluated the way I think about momentum and energy.

My point still stands that the section in question has no citations.

203.9.200.3 (talk) 05:04, 29 January 2009 (UTC)

"Known" vs Is
This is a philosophical dispute--- is the wavefunction about our knowledge, or is it the full description of the system (or both). The best way to stay neutral is to adopt neutral language. "Known" is not neutral.Likebox (talk) 20:12, 4 March 2009 (UTC)

Hey guys, my first entry to wikipedia: I think this sentence needs to be rewritten: "The position of the particle is regarded as being where the wave amplitude is greatest." I think you just can't talk about the position of a particle, all you can do is calculate the probabilities for measurement outcomes. So I reckon it should say something like "One is most likely to detect the particle where the wave amplitude is greatest." cheers :) —Preceding unsigned comment added by Bojan1337 (talk • contribs) 07:17, 9 October 2009 (UTC)

Certainty of Uncertainty Dissolves Itself
It's a ridiculuos principle to assert.

How can you posit "I know that I cannot know" anything? All you can determine is that either You know, or You do not know. At best, Heisenberg pointed out a shortcoming or limitation of quantum mechanics. —Preceding unsigned comment added by 128.219.198.49 (talk) 20:18, 2 April 2009 (UTC)

Heisenberg's Gamma-ray Microscope Image Needs Modification
The image of Heisenberg's gamma-ray microscope should be slightly modified. The reflected gamma-ray, which is in red, should have a longer wavelength in order to clearly show that some of its initial momentum was transferred to the electron. —Preceding unsigned comment added by ContributorX (talk • contribs) 00:53, 8 May 2009 (UTC)

A Briefer History of Time's mistake?
in this article: "The uncertainty principle is often explained as the statement that the measurement of position necessarily disturbs a particle's momentum, and vice versa—i.e., that the uncertainty principle is a manifestation of the observer effect. This common explanation is incorrect,[..]"

I believe that is the explanation given in 'A Briefer History of Time' Of Hawking. We should definitely add this information in the article if correct. However, I'm not an expert so I'd want someone else to confirm it. What is certain is that it starts the explanation of the U.P. with a similar statement. --AaThinker (talk) 16:22, 19 May 2009 (UTC)

Philosophical implications?
e.g. on hitting determinism. --94.71.114.93 (talk) 17:17, 19 May 2009 (UTC)

Observer effect again
The explanation as a type of observer effect is most definitely not wrong. It is just unfasionable, because it is a logical-positivist sort of thing. It is for some reason very popular now to go around saying "this is a popular misconception", when it isn't. In fact, the popular misconception is that this is a popular misconception.

The explanation in terms of observer effect is only slightly misleading, if you don't already understand that the best measurements are the definition of the state of the system in a logical positivist framework. This was used without comment by Heisenberg and Bohr (as both freely admit), but was resisted by the more religious Einstein.Likebox (talk) 20:03, 22 June 2009 (UTC)


 * Is there a difference between an observer observing a system and a system interacting with itself? Well yes the new system is (observer + system) governed by hbar.  If system can be thought of 2 interacting sub systems as (system a + system b) then by recursion the same must hold for the realtionship between system a and system b.  I think the clarification he wanted assert was that quantum mechanics is not the sole manifestation of the conundrum of observation but instead an inherent part of our reality when things interact as all things do.
 * — Preceding unsigned comment added by 67.82.165.126 (talk) 02:03, 9 October 2009 (UTC)

Pop culture
This is one of the most notable aspects of the uncertainty principle. It has entered the popular culture especially as it relates to the observer effect. Some of the bullets are less notable, but most are pretty ok. If they get too long, there is no reason that they can't be spun off into a separate article.Likebox (talk) 18:48, 23 June 2009 (UTC)


 * As has been argued a couple of times before, the section is already article-bulkingly long, and adds little to the article (what is the reader learning by reading every single example we can think of mentions of the UP?). The version you've restored it to simply demonstrates the accumulation of listcruft!  I would strongly suggest culling it down to the most salient, notable examples, at most.


 * For comparison, there is no such section at the Big Bang or black hole article, which are equally likely to appear in "popular culture". Oli Filth(talk 19:04, 23 June 2009 (UTC)


 * I agree that the casual reader learns nothing. But a person who is scratching his head trying to remember which episode of which TV show mentioned the uncertainty principle would be very happy to have this information collected here. It makes it easy to find references to something, which people often search for. I am not sure about all the bullets though. Some of them are only tangential.


 * There is no uniform standard for this, and I am not sure that everything requires a cultural list. For some things, though, like this, I think that the popular references are very notable.Likebox (talk) 19:09, 23 June 2009 (UTC)


 * I would really prefer it if there was some demonstration in the list that these mentions were indeed notable. As I've said in previous discussions on this, IMO this is pretty much limited to things like the Copenhagen play, rather than the majority in the list which could easily be throwaway mentions (or as you put it, "tangential").
 * I'm going to attempt to cut the list down to leave those I believe are the most relevant (but please don't take that as an endorsement of the idea!).
 * Incidentally, I'm pretty sure that the purpose of a serious encyclopaedia article is not to remind someone about an episode of a TV show! Oli Filth(talk 19:20, 23 June 2009 (UTC)


 * I like the approach, but I do think the purpose of Wikipedia is more nebulous. It is a catalog of human knowledge, after all. So if there is a TV show, a quick name/episode format should give enough of a handle to somebody to look up the reference if they really need it. Maybe that's a good solution for other pages with dubious pop-culture sections. If you like this approach, the music one can fit in it too, while the "heisenberg compensators" reference and the Heisenberg joke can be worked into the body of the text, as introductions to sections.Likebox (talk) 20:08, 23 June 2009 (UTC)


 * I think this format can expand indefinitely without undue burden. For the joke, I heard it many times, and I only found crappy web references to it. I wish I knew who the anonymous author was.Likebox (talk) 20:31, 23 June 2009 (UTC)


 * I've just come back to this article, and IMO, whilst the abbreviated format of the "casual reference" list is infinitely preferable to before, it serves zero purpose. Without context each item in the list is meaningless, but in each case the context is so trivial that it's really not worth mentioning.  Therefore I suggest removing the "causal" list again.  Oli Filth(talk 16:15, 27 June 2009 (UTC)


 * I an unfamiliar with the correct way of editing citations but I found the Questionable Content comic that is mentioned: Powers of ObservationLorialei (talk) 19:50, 5 July 2009 (UTC)


 * There appears to be no end to people adding useless junk to the pop culture section. I propose we siphon it off into its own article to avoid cluttering up this scientific one.  If the uncertainty principle really has nabbed a significant place in pop culture, having a separate article would not be too unorthodox.  What do the rest of you think about this idea? Teply (talk) 15:36, 17 August 2009 (UTC)


 * I agree that this approach would reduce the clutter in this article. However, I don't believe there's enough material to warrant a separate article.  My opinion, as always, is just to remove the whole lot!  Oli Filth(talk&#124;contribs) 11:17, 31 August 2009 (UTC)


 * I support removing it, the examples provided are completely random and seem pretty obscure, I've never heard of the pop band or the "Aqua Teen Hunger Force". Hornvieh (talk) 23:15, 27 November 2009 (UTC)

Logical Positivism/ Realism
Please do not use these terms without some familiarity with their history. The idea of logical positivism, as propounded by Mach and emphasized repeatedly by Pauli, Heisenberg, and Bohr, is that the only notion of "reality" is defined by best possible measurements. So that the fact that it is impossible to measure the position and momentum at the same time is exactly the same thing as saying that a particle does not have a position and momentum at the same time. There is no difference between the two statements.

In other words, positivism says that what is "real" is defined by what is measurable. This idea is still used in physics without reservation, although historically it was associated with the labels "logical positivism" and "empiricism".

Realism is the statement that there is an underlying thing underneath it all, a consistent mathematical framework that can be identified with reality. This idea says that it is possible to talk about elements of reality independent of measurements, and that measurements are clues about these elements of reality. In this philosophy, what could be "really" going on is some sort of Bohmian, and the reason we can't measure position and momentum is because our instruments are too crude. This philosophy is not minimalist, and is rejected by Copenhagen style interpretation. Standard quantum mechanics can be made to be "realist" to some extend by adopting many-worlds philosophy.Likebox (talk) 14:34, 2 August 2009 (UTC)

Wikipedia defining what is true due to its particular phylosophy or POV
This line in the first paragraph in the article: "This is not only a statement about the limitations of a researcher's ability to measure particular quantities of a system, following the tenets of logical positivism, it is a statement about the nature of the system itself."

This is totally based on one of the interpretations or philosophical views that exist, Wikipedia should not take sides with any particular POV, philosophy or interpretation, so I'm editing out that part from the first paragraph, the whole Logical Positivism stance is already discussed further down the article in its correct section, or if anything wants to expand on it or re-add that part you can but do it in its right section specifying it is only one of the many interpretations and not as the only universal absolute one. —Preceding unsigned comment added by 189.224.24.181 (talk) 04:02, 27 August 2009 (UTC)

I've boldly just removed the positivism part
Although there are many interesting discussions about whether or not there are hidden variables in QM that we cannot measure, this is not the place to discuss them. As Bohr pointed out the Heisenberg, once you accept the idea that the "position" of a wave packet has a meaning, then this position and the frequencies of the waves in the packet have this relationship. That's true even if quantum mechanics is not involved. It's true of water waves! Quantum mechanics simply asserts that the position of a "particle" is assocated with wave packet given by de Broglie's rules. The rest follows, as is detailed later in the article. S B Harris 04:48, 27 August 2009 (UTC)


 * Thank you. This restores the gist of an edit I made some time ago ("Whereas, following the tenets of logical positivism, this is only a statement about the limitations of a researcher's ability to measure particular quantities of a system, according to scientific realism it is a statement about the nature of the system itself."), which was mutilated by another user. I don't mind not explicitly mentioning the philosophies of logical positivism and scientific realism, although some readers might find this interesting.WMdeMuynck (talk) 12:59, 27 August 2009 (UTC)

One correction and one thought.
The article originally said:
 * The position is uncertain to the degree that the wave is spread out, and the momentum is uncertain to the degree that the wavelength is ill-defined.

I believe that is clearly wrong, and I have changed "ill-defined" to "well-defined." It's possible that some well-intended general reader thought it would make more sense as above and changed it without its getting noticed.


 * The sentence you changed was technically correct, but it needs parallel construction to be clear. I've re-written it thusly (see what you think):


 * The position is uncertain to the degree that the wave is spread out (well-defined wavelength), but the momentum is certain (well-defined) only to the degree that the wavelength is well-defined. Thus, position and momentum for a particle have opposite requirements for a good definition, so that both position and wavelength cannot simultaneously be well-defined. S  B Harris 03:03, 9 October 2009 (UTC)

On another subject, I wonder whether it is worth noting that Bohr immediately objected to Heisenberg's "microscope" paper because it made it seem that the indeterminacy came out of the physical intrusion of the experimenter on the physical interaction being studied. Saying that:
 * Today, logical positivism has become unfashionable in many cases, so the explanation of the uncertainty principle in terms of observer effect can be misleading.

makes it seem that the misleadingness occurred because, the while the statements stayed the same, the social framework in which the statements were read changed and so they began to convey an incorrect meaning. I believe that Bohr saw right away that the explanation of the uncertainty principle in terms of observer effect would have to be misleading.P0M (talk) 23:16, 20 September 2009 (UTC)

Energy Measurement
According to some references, there does appear to be a sense in which the time interval affects the measurement of energy. For example, paraphrasing from Kenneth Krane’s Modern Physics (New York: Wiley, 1983, p. 95), if you measure a 100 Hz signal for 1 second, you have measured 100 periods with an uncertainty on the order of 1/2 period, or 0.5 Hz. Alternatively, you can measure 200 periods over 2 seconds, again with an uncertainty on the order of 1/2 period, but a reduced frequency uncertainty of 0.25 Hz. Krane goes on to argue for a classical uncertainty relationship of ∆ω∆t≈1. The energy-time relation then follows by multiplying both sides by Planck’s constant. Ephesians 2:10 (talk) 11:34, 27 September 2009 (UTC)

Too long intro
I think only the three first paras are really needed in the intro, and that they introduce the article topic good enough [INS:very well] (IMHO). The following paras in the intro actually constitute a background material that could instead constitute the basis for a hypothetical Background section, that needs some "synchronization" with Historical introduction, which instead should be named History since it is too complex for the ordinary reader that hasn't read the background. ... said: Rursus ( m bork³ ) 08:57, 27 November 2009 (UTC)
 * And, another less important improvement: the first para in the intro should need some few more links, so that the reader that understands NIL, can surf there and improve their knowledge to more than NIL. ... said: Rursus ( m bork³ ) 09:06, 27 November 2009 (UTC)

Heisenberg limit
Heisenberg limit redirects here but is not mentioned in the article. This needs to be covered as it is a current topic in news reports. See http://www.physorg.com/news186395462.html Lumos3 (talk) 00:43, 28 February 2010 (UTC)

Certainty principle
Is this external link relevant to the subject matter of the article? To me it looks like original research but I may be wrong.--81.108.131.163 (talk) 17:54, 27 March 2010 (UTC)
 * It's not particularly relevant so I removed it. UBER  ( talk ) 18:17, 27 March 2010 (UTC)

WP:NOR-policy prohibits original reserches in texts of WP-articles. External links to original researches are Ok. This link is relevant and important. So, I put it back. Fintil (talk) 23:12, 8 April 2010 (UTC)

Wave Packets
Wave packets need to be explained a little bit, as a group of sine waves being added together, and that the particle may be in any energy state corresponding to any one of those sine waves.


 * Reply: The second paragraph discusses wave packets, and the first mention has a link to the article wave packet for more information. Dirac66 (talk) 18:40, 29 April 2010 (UTC)

Heisenberg uncertainty relations for angular momentum
I have adapted the recently added formulation of the interpretation of the Heisenberg uncertainty relations for angular momentum to the more careful treatment of the Heisenberg uncertainty relations for position and momentum in the first paragraph of the article.WMdeMuynck (talk) 22:47, 11 April 2010 (UTC)


 * I understand your point that the interpretation in terms of measurement is not accepted by everyone. However the phrase "is often interpreted as implying" could suggest that there is no generally accepted interpretation. Instead I would prefer to follow the first sentence of the article more closely and replace the idea of measurement with that of knowledge, as follows:


 * "This relation implies that only a single component of a system's angular momentum can be known [or perhaps "defined"] with arbitrary precision, normally the component parallel to an external (magnetic or electric) field." What do you think? Dirac66 (talk) 00:01, 12 April 2010 (UTC)


 * The essential point in the reference to Ballentine's 1970 paper is that in that paper the standard interpretation of the Heisenberg uncertainty relations (viz. as a property of a simultaneous measurement of incompatible observables) is demonstrated to be untenable. Unfortunately the standard interpretation remains folk wisdom (even among physicists), and therefore cannot be omitted on this page. According to Ballentine the real meaning of the Heisenberg uncertainty relations is that if two incompatible observables are measured separately, then the standard deviations of the two measurements satisfy the Heisenberg uncertainty relation.


 * Although the question could be asked what the cause of this latter phenomenon is (if it is not mutual disturbance), I do not think it desirable to go into such questions here. However, lacking the insight that the Heisenberg uncertainty relation is as much a property of the wave function (and therefore of the preparation of the system), reference to `knowledge' will direct attention to `measurement', and hence to the standard interpretation. For this reason your proposal "This relation implies that only a single component of a system's angular momentum can be defined [or well-defined?] with arbitrary precision, normally the component parallel to an external (magnetic or electric) field." would have my preference, although this would imply reliance on the Talmudic properties Bohr according to Einstein possessed.WMdeMuynck (talk) 08:03, 13 April 2010 (UTC)


 * I like Dirac66's wording with "defined". It's not a matter of knowledge. If I have an electron which has just come out of a Stern-Gerlach experiment which measured its sz to be +ħ/2, I completely know what its spin state is: namely |↑&rang;. But this doesn't allow me to predict what a measurement of its sx will yield, because it just doesn't have a well-defined value of sx (it's not in an eigenstate of it). It does allow me to know the probability with which it could take either state upon a measurement. (The Italian name of the HUP literally translates to "principle of indeterminacy", one of the extremely rare examples of Italian vocabulary making more sense than English.) ― _ _ _ A._di_M. (formerly Army1987) 14:24, 13 April 2010 (UTC)


 * OK, I'll put the sentence in the article using "defined" instead of known. Dirac66 (talk) 14:56, 13 April 2010 (UTC)

New inequality...
Recently, a new uncertainty relation has been proven (see Found. Phys. 2009 ) but has not yet been introduced in the article. The inequality is as follows:

Whenever a particle is localized in a finite interval $$\Delta x>0$$ (e.g. by preparation, single slit, etc.), then, the standard deviation $$\sigma_p$$ of its momentum satisfies the following inequality
 * $$\sigma_p \cdot\Delta x \geq \pi\hbar $$.

The equal sign is given for wavefunctions $$\psi(x)\propto\cos(\pi x/\Delta x)$$.

The prove is quite different from the ordinary | Cauchy-Schwarz argumentation.

So, the inequality is new, different from the ordinary known inequalites (even with regard to the corresponding measurment process) and finally it is simple and of practical relevance. Therefore, it might be an enrichment.

Zetafun (talk) 06:50, 29 May 2010 (UTC)

missing citation...
There is a hint that citations are needed in the section Uncertainty principle and observer effect at the sentence:


 * "In quantum mechanics, states which have both definite position and definite momentum at the same time just don't exist."

It seems that this statement is too strict to find any rigorous citation for it. The first boldfaced part refers to Dirac-Delta-peaked-like states which are not square integrable and thus cannot be part of the standard Hilbert space. Instead, if this part of the statement is weakened, then we could refer to results which have been proven on the standard Hilbert space.

In this case, we have to consider the second boldfaced part of the phrase, i.e. "...just don't exist". It probably refers to the (original) inequality $$\Delta x\Delta p \gtrsim h$$ of Heisenberg. The latter tries to tell us that physical states do not exist if the position localization $$\Delta x$$ and the momentum localization $$\Delta p$$ of the particles have to satisfy $$\Delta x\Delta p < h$$. If this statement is strictly true, then one should cite Heisenberg's original work at this point.

However, in modern quantum theory the statement "do not exist" is sometimes formalized by the statement that "the probability $$P$$ to registrate any particles with the property $$\Delta x\Delta p < h$$ is identically zero". Unfortunately, there are many states in Hilbert space which have positive probability, even though they satisfy the latter condition; for instance, the case of a simple state-"wall", i.e. $$\quad\psi(x)=1/\sqrt{\Delta x}\quad$$ of compact support $$|x|\leq \Delta x/2$$. There, about 50% of momentum measurements with $$\Delta x\Delta p = h/2 < h$$ are possible and thus do exist. Many other examples could be given.

Thus, the statement "just don't exist" given in the article should be weakened too. Zetafun (talk) 04:46, 1 June 2010 (UTC)


 * Perhaps it is better not to complicate fundamental discussions by the mathematical problems induced by considering toy models like the infinite potential well. Such wells simply do not exist in the real world. Real problems should have wavefunctions that are differentiable on the whole real line. Hence the solution $$\scriptstyle\psi(x)=1/\sqrt{\Delta x}$$ if $$\scriptstyle|x|\leq \Delta x/2$$ (and zero elsewhere) is not allowed because it is not a solution of any realistic Schroedinger equation.WMdeMuynck (talk) 09:43, 10 June 2010 (UTC)


 * The argument I mentioned also applies for ordinary continuous solutions of the Schrödinger equation, supposed they are sufficently localized. That is why this problem is not of minor matter. However, I agree to you that it is better not to complicate the discussion. Therefore, in my opinion, the text should be reduced to those statements that are not misleading. --Zetafun (talk) 16:40, 10 June 2010 (UTC)

Matrix mechanics, wave mechanics
Both of the representations Matrix mechanics and wave mechanics are the old pioneers of the modern Hilbert space representation which is the unifying bridge between both of them. In my opinion, the formal derivation of inequalities in the framework of these old formalisms matrix mechanics and wave mechanics should be carried out (if at all) in their corresponding articles Matrix_mechanics and Schrödinger's_equation.

The present derivations of inequalities in the old fashion style seem somewhat misleading to me and why should we carry out the formal derivation of the dispersion relation as many times? I propose to remove both of the sections Matrix mechanics and wave mechanics from the article. That also reduces the complexity of the article. --Zetafun (talk) 05:13, 10 June 2010 (UTC)


 * I do not agree with this proposal. The derivation of the Heisenberg inequality, if to be explicitly inserted at all, belongs in the article on the uncertainty principle. If advantageous to some purpose it could safely be removed from the articles on Matrix_mechanics and Schrödinger's_equation. What might considerably raise the standard of the present article, is a discussion of the confusion about the interpretation of the Heisenberg inequality as a property of simultaneous measurement of incompatible observables.WMdeMuynck (talk) 09:15, 17 June 2010 (UTC)

Incorrect identification of quantum mechanics to the Copenhagen interpretation
The article says something that seems incorrect to me:


 * ''For one, this explanation makes it seem [...] that the disturbances are [...] a property of the measurement process— the particle secretly does have a definite position and a definite momentum[...] This interpretation is not compatible with standard quantum mechanics. In quantum mechanics, states which have both definite position and definite momentum at the same time just don't exist.

But the last two statements are incorrect, indeed as you can read here the statements are false in the Bohm's interpretation.--Pokipsy76 (talk) 14:54, 22 August 2010 (UTC)


 * Should we modify "This interpretation is not compatible with standard quantum mechanics" to "This interpretation is not compatible with the standard (Copenhagen) interpretation of quantum mechanics."? Dirac66 (talk) 23:11, 22 August 2010 (UTC)

Incorrect, the original statement was true. Bohm, de Broglie, and Einstein all assumed similar theories; hidden variables [or parameters] to satisfy deterministic results. John Bell, who agreed with their objective locality, took the theory as the basis for his experiments; he hypothesized there were hidden variables that pre-determined or influenced the particles paths, but the experiments demonstrated this was not the case. The only alternative explanation to the particles' responses concerning random angles during Bell's experiment is the conception of nonlocality, which demands a peculiar unity between the two particles traveling in opposite directions while abiding by Heisenberg's uncertainty principle in conformance with the observer. Bohm-de Broglie's theories were relevant pre-John Bell experiments, but judging from the evidence, post-John Bell experiments, their interpretations were false. Standard quantum mechanics rests on the foundation of Heisenberg's uncertainty principle and nonlocality. —Preceding unsigned comment added by 209.105.184.93 (talk) 16:13, 26 September 2010 (UTC)


 * As far as I know the Bohm's interpretation what you are sying is not true. The Bohm's interpretation is indeed an interpretation of the formalism and therefore cannot be falsified by any experiment which is consistent with the standard quantum theory. Indeed here you can read:
 * ''The de Broglie–Bohm theory makes the same (empirically correct) predictions for the Bell test experiments as ordinary quantum mechanics. It is able to do this because it is manifestly nonlocal.
 * --Pokipsy76 (talk) 13:14, 30 September 2010 (UTC)

While it is true that Bohm's interpretation predicts correctly, it's merely a reinvention of the Schroedinger equation, with an addition of hidden variables to objectify quantum mechanics in the same manner that classical mechanics can be predicted and measured precisely. But there are two flaws in his interpretation, and this is why the Copenhagen interpretation of quantum mechanics, and not Bohm-Broglie's, is the dominant interpretation; Bohm's initial assumption was that of a 'quantum-field', which he described as the collective effect of all the potential states of a particle. This is Schroedinger's equation re-labeled, which states that before a measurement is taken place, every possible potential state within the system/particle are all equally probable. This is why his theory makes correct predictions, it's a simple re-labeling of an already existing equation.

Bohm's second mistake, where he and De Broglie agreed and lead their initial investigations was to assume that particles are directed and governed by a deeper 'hidden variable' as if matter exists as discrete chunks. De Broglie's hidden variable was waves, while Bohm's assumed a new kind of hidden variable at the sub-atomic level that would result in a similar governing, which would eliminate both the potential states of Schroedinger's equation and the act of measurement collapsing to a single observable state; for his variable to work, there would have to have been a mechanism within each particle or guiding each particle that would determine the outcome of each event, but the problem was, he never suggested what that mechanism is or how it operates.

So, again, while it's true [initially] that Bohm's interpretation concerning his quantum-field theory 'makes the same (empirically correct) predictions for the Bell test experiments as ordinary quantum mechanics', it does not add or clarify anything of benefit to quantum mechanics. It simply repeats what the Schroedinger equation (about probabilities) already says. Repeating; the De Broglie and Bohm theories fail because they both assume hidden variables, which was also what John Bell hypothesized heading into his experiments, but the results eliminated the possibility of hidden variables, thus affirming that the Copenhagen interpretation is the standard interpretation of quantum mechanics post-Alain Aspect (1980 and on).

Another objection to that link, and perhaps to this page, is where it says ". . .it is shown that the nonlocality does not allow for signaling at speeds faster than light". However, this is in contradiction to the nonlocality concept itself. I posted this on the no-communication theorem talk page, but I will reference it here as well, a Nature article where Alain Aspect confirms that signaling at speeds faster than light are a necessity of nonlocality. —Preceding unsigned comment added by 209.105.184.93 (talk) 09:36, 21 October 2010 (UTC)


 * Wow, this section (observer effect) needs some serious work. A lot of statements are just flat out wrong. I'll see if I can wade through and help out with that at some point in the future, but just to clear up some of the issues under discussion here: First of all, there definitely IS an observer effect whenever a measurement is made, because (unless it happens to be in the exact same outcome state beforehand) the state undergoes collapse to whatever state corresponds to the measurement result, which necessarily changes the expectation values of other observables. The article is definitely in error when it says this (observer effect) is not compatible with QM. First of all because this definitely happens, secondly because whether or not quantities definitely exist (realism) is an unanswered question. All we know, due to Bell's theorem, is that QM is manifestly nonlocal. So nonlocal hidden variable theories are allowed, of which Bohmian mechanics is the prime example. So its predictions are fully consistent with quantum mechanics, including any of the situations involving entanglement. But the kind of nonlocality exhibited in measuring entangled systems cannot be used for faster-than-light communication, because this would lead to causal contradictions. Measuring one part of a greatly-separated entangled system effects the statistics of the other part and vice versa, but there is no way to detect this unless you know what is going on on the other end. Like the Nature article says "It is worth emphasizing that non-separability, which is at the roots of quantum teleportation, does not imply the possibility of practical faster-than-light communication. An observer sitting behind a polarizer only sees an apparently random series of - and + results, and single measurements on his side cannot make him aware that the distant operator has suddenly changed the orientation of his polarizer." Basically, if you're confused, whatever you do don't read this section of the wiki article. Isocliff (talk) 07:41, 25 October 2010 (UTC)

Time Energy Uncertainty
The wiki page currently shows: delta(E).delta(t) >= h But the correct thing would be: delta(E).delta(t) >= hcross/2 Perryizgr8 (talk) 05:32, 2 November 2010 (UTC)

Meaning of Heisenberg uncertainty relations
I am unhappy with the recent edit by 207.59.145.201 (talk) because it perpetuates a widespread misunderstanding about the meaning of the Heisenberg uncertainty relations. By itself there is some truth in the editor's remark that "a system cannot be defined to have simultaneously singular values of these pairs of quantities". However, this is not evidenced by the Heisenberg uncertainty relations but by the Kochen-Specker theorem. The Heisenberg uncertainty relations do refer to measurement, although not to simultaneous measurement of incompatible observables, but to standard deviations of probabilities of measurement results obtained in two separate experiments (not influencing each other). This is not inconsistent with the remark made by the editor, but the appropriateness of that remark does not follow from the Heisenberg uncertainty relations.WMdeMuynck (talk) 09:43, 5 December 2010 (UTC)

Popper's Criticism?
Why does the comment note "Karl Popper criticized Heisenberg's form of the uncertainty principle, that a measurement of position disturbs the momentum" Does Popper use the word "disturbs" or does Heisenberg use the word? I would have to see a citation for the either since the certainty is what the principal suggests is "disturbed" and not the actual position/momentum. —Preceding unsigned comment added by 68.143.177.35 (talk) 20:51, 23 January 2011 (UTC)
 * I have added an unreferenced tag to this section. This whole view must come from somewhere. The words "doesn't trouble" look biased and non-NPOV. I am reading Popper on QM now - his objections to Heisenberg mainly seem to be based on the view (in the section) that the principle is statistical and not about individual particles. More later. Myrvin (talk) 06:49, 8 April 2011 (UTC)
 * As I suspected, I found a quote from Popper for the statistical idea, but not for the rare events and the idea that it 'doesn't worry' particular physicists. Myrvin (talk) 12:30, 8 April 2011 (UTC)

This whole section was deleted because: "Popper is great as a philosopher of science, but why should we care (WP:DUE) that someone who was neither physicist nor mathematician misunderstood QM? Lots of people do that.)". The section has been there for a while, and is expunged because someone thinks Popper's views don't matter. I reverted the delete - they matter to me and many others. That he "misunderstood" is an opinion. See my views on Quality of Physics articles and Talk pages, on Wikipedia talk:WikiProject Physics. Myrvin (talk) 06:57, 9 April 2011 (UTC)


 * Popper's views matter quite a bit - I am rather a fan of falsifiability, actually. This particular example, however, does nothing but show how even someone who is intelligent and engaged with the scientific method can make gross missteps when making statements about other fields. The reason why the modern research culture has such an emphasis on cross-disciplinary collaboration is because it is very difficult to make meaningful contributions to disparate fields; embarrassing missteps are the norm, and no source currently under discussion indicates that this example is particularly noteworthy as such. It does a disservice to Popper to quote him outsidöe his field of expertise like that. Of course, if some source may be found discussing how Popper's view contributed to the development of the uncertainty principle (either mathematically or, more likely, philosophically), then I will withdraw my objection. As the sources stand, that section may warrant inclusion at the biography, but there is no indication why it should be here. - 2/0 (cont.) 07:22, 9 April 2011 (UTC)

Well let's see. Popper is a great philosopher of science, and he is known to have views about QM. He knew and conversed with Bohr, Schrödinger and Einstein about these matters. There is a whole book on his views about QM. Calling his ideas a 'misstep' is just to say that QM people think he is wrong - as they would (and that's in the section, although uncited). To say the worked-out views of such a man are not noteworthy because he hasn't 'contributed to the development of the uncertainty principle' is unfair. That would rule out the thoughts of every philosoper of science on most sciences. This principle might be one of the most philosophically worrying concept of the 20th century, so people would expect to see the views of a philosopher of science. In the spirit of compromise, I can find nothing so far about the falsifiability part of the section, and also about the views of QM people about him. So I would be happy for the section just to include his ideas about the statistical nature of the principle. That should be in the article somewhere. Myrvin (talk) 10:47, 9 April 2011 (UTC)

Also, there is an article on Popper's experiment, (a precurser to EPR?) about which: "Popper was inclined to believe that the test would decide against the Copenhagen interpretation, and this, he argued, would undermine Heisenberg's uncertainty principle. If the test decided in favour of the Copenhagen interpretation, Popper argued, it could be interpreted as indicative of action at a distance." Even if it is wrong (as QM people think EPR is wrong) he should not be ignored.

This book [] has a whole chunk on his Physics - mostly QM. Myrvin (talk) 12:24, 9 April 2011 (UTC)

This book [] has a piece on P. Calling his ideas an antecedant to Bohr, Kramers and Slater, it even says: "But, following Popper, the Copenhagen school chose to ascribe statistical distributions ...". Myrvin (talk) 12:40, 9 April 2011 (UTC)

This book [] says "It may be that the final writeup [of EPR] was influenced by a paper of Karl Popper criticizing the uncertainty relations." Einstein had received a note about this from Popper. Myrvin (talk) 12:56, 9 April 2011 (UTC)

This book [] talks about "two often discussed proposals have been made by Heisenberg and Popper". Myrvin (talk) 15:31, 9 April 2011 (UTC)


 * I think it might be better to establish a brief section on challenges to the Uncertainty Principle that just lists them, and then provided interested readers with a sub-article that goes into the challenges. Otherwise I think we risk confusing the general reader regarding a theory or a model that is already very hard to comprehend. P0M (talk) 18:17, 9 April 2011 (UTC)

Perhaps Section 2 should be moved to the end. Myrvin (talk) 18:23, 9 April 2011 (UTC)


 * Perhaps "contributed to the development of the uncertainty principle", even with the clarifying parenthetical, was poorly phrased. My intended meaning is only that just because Popper is quite prominent to his field does not mean that we should necessarily include his views at every article on every topic on which he has commented. It is also necessary to establish why his ideas are relevant to the history of the development of this idea. His book establishes relevance at Karl Popper, but what establishes relevance to this article is other people found it worthwhile to comment on his ideas (conversations with Einstein, physical realization of his proposed experiment, &c.). While we are on the topic of the tenor of talkpage conversations: Myrvin, your first post comes across as quite condescending and uninterested in the contributions of your fellow editors. Please remember that nuance and tone do not communicate very well in a pure text medium.
 * Consider by way of analogy Lord Kelvin: he is best remembered as a fantastic physicist who made invaluable contributions to the field. He is also known for making a number of pronouncements that were not born out by experiment. If we were to add each of those to the relevant articles, it would create the entirely misleading impression that he was a buffoon. The old section was worse than nothing in that regard.
 * Thank you for finding those sources. I have attempted to rewrite the section based on them and others, giving a brief outline of the proposal and its reception (this is what I mean by "contributing to the development"), while leaving the main discussion at Popper's experiment. The 1987 Foundations of Physics paper is not very good, but I guess it is needed to complete the discussion; a secondary source that places it in context would be better. I believe that this version of the section is an improvement in that it neither makes Popper out to be ridiculous nor fails to establish the place of his argument in the ongoing epistemological and empirical development of the quantum theory. I am not sure that I have properly accounted for his propensity theory, though. Please take a look and improve where indicated. No particular opinion on splitting to a sub-article, though I concur that we should avoid over-weighting this article. - 2/0 (cont.) 19:41, 9 April 2011 (UTC)

Didn't mean to appear condescending sorry. Myrvin (talk) 20:10, 11 April 2011 (UTC)

Problem with wording
The article currently says: "For example, in spectroscopy, excited states have a finite lifetime. By the time-energy uncertainty principle, they do not have a definite energy, and each time they decay the energy they release is slightly different. The average energy of the outgoing photon has a peak at the theoretical energy of the state, but the distribution has a finite width called the natural linewidth. Fast-decaying states have a broad linewidth, while slow decaying states have a narrow linewidth."

The imprecision of this passage bothers me. How can an excited state decay more than once? What does "decay" mean? Return to equilibrium state? How can one photon have an "average energy"? I think that the writer probably meant to indicate that many photons are being investigated and that when the experimental apparatus is prepared in identical ways the results of using this apparatus, photon by photon, gives slightly different results. Averaging these runs gives an "average energy of the outgoing photons." P0M (talk) 07:40, 24 March 2011 (UTC)

Incorrect form of angular uncertainty principle
In the example of mathematical derivations, there is a equation said:
 * $$\Delta \Theta_i \Delta J_i \gtrapprox \frac{\hbar}{2} $$

However, the equation is wrong since $$Theta$$ is not hermitian at all (Rev. Mod. Phys., 40, 411, 1968). I suggest remove this equation. —Preceding unsigned comment added by 140.112.55.133 (talk) 12:05, 28 April 2011 (UTC)

Future momentum
The lead may well be correct when it says that it is the FUTURE momentum that can't be determined as well as its position. However, that's not what most commentators seem to say. So we need a good citation for this assertion. I note that the word future does not occur in the body of the article; and it says "Any two variables that do not commute cannot be measured simultaneously — the more precisely one is known, the less precisely the other can be known. ". Myrvin (talk) 16:51, 13 May 2011 (UTC)

Penfold in The road to reality p, 524 or Feynman in QED, p.54 have something like it. But maybe a translated Heisenberg quote would be better. Myrvin (talk) 17:34, 13 May 2011 (UTC)

H seems to deny any sense in "definite properties such as coordinates, momentum and so on" at all. Myrvin (talk) 17:44, 13 May 2011 (UTC)


 * He means that the new wavefunction gives only probabilities for position, direction, and velocity going forward.P0M (talk) 17:50, 15 May 2011 (UTC)

This seems to say what the article doesn't want it to. Myrvin (talk) 17:47, 13 May 2011 (UTC)


 * Heisenberg is saying that if, e.g., we locate a particle in space and time (maybe a proton is bounced off a suitable sensor), then we do not know where it is going from that time on. The next measurement may be on a detection screen a short time-distance away, but we can only state probabilities for which spot on the detection screen it may hit.P0M (talk) 17:50, 15 May 2011 (UTC)

This is better, but it does talk about "simultaneous values". Myrvin (talk) 17:57, 13 May 2011 (UTC)


 * The whole idea of "simultaneous values" is problematical. It does not refer to experiments. It refers to human cognitions about experiments. Both Heisenberg and Schrödinger are very clear about this issue when they are talking about making experiments. You cannot do two things at once. The best you can do is to make two measurements that are very close together in time. But the clearer you get on measurement one, the wider the results will be apart from each other on measurement two. Consider that you could determine the position of a photon shot toward a detection screen by putting up a wall midway with a circular hole in it. If the hole is large you only can infer that the photon was somewhere in that diameter in mid course. So you look at the position of your laser and the position of the dot on the screen and imagine that the photon went on a straight line path from one place to the other. You think, "I'll close in on it." So you reduce the radius by half. Surprisingly, the edge of the dot on the screen blurs a bit. You reduce the radius by half again, trying to get it centered. You put a piece of paper over the hole in the center and use the dot that shows up there to try to center the barrier hole perfectly. The result is more blurring. The more determinate the measurement of position is made by reducing the size of the circular hole, the blurrier the measurement of final position (and the presumed straight line path from center hole to detection screen) will become. Trying to get closer to a simultaneous measurement of things, the distance from circular hole to detection screen can be decreased. Doing so will reduce the time gap, but the angle of maximum deflection (or the line from center of circular hole to perimeter of blurry circle on the screen) will remain constant.


 * In short, Heisenberg is saying (I think) that if I think, "I now know the position of the photon, and I now know where it is headed," I must be wrong. If I take a measurement based on that presumption, my successes will be probabilistic. (The center of the blurred spot on the detection screen does get many more hits than the dimmest region on the blurred spot that I can see.)P0M (talk) 17:50, 15 May 2011 (UTC)

nicely written
Very good article, not too "techie", but not simplistic. Personally, I can't see how anyone could ever know where or "when" a particle in motion is as no measurements in either realm are instantaneous. Hence, we can only measure the past time and space of the object. Anyway, this article could become a featured article...  &#0149;Jim 62 sch&#0149; dissera! 19:56, 13 May 2011 (UTC)


 * We even have trouble with macro-scale objects. One of the peculiarities of cameras with focal plane shutters is that the leading edge of top of the race car is one place in relationship to the film in the camera at the start of the exposure, but a thousandth of a second later the point directly under that point but on the bottom of the car is somewhere else. So the whole car will appear slanted.P0M (talk) 18:03, 15 May 2011 (UTC)

Heisenberg uncertainty principle disproved?
24.214.230.66 (talk) 21:27, 30 March 2011 (UTC)


 * The "New Scientist" article which you reference oversimplified the original Nature article. The Nature article claims to have experimentally achieved a "super-Heisenberg scaling" in a quantum metrology setting; this is subtly and technically distinct from a disproof of the Heisenberg uncertainty principle in general. PoincareHenri (talk) 02:39, 18 June 2011 (UTC)

Unsourced "edfredkin" edit
The second paragraph has what appears to me to be original research. Is there any documentation to support this presentation?P0M (talk) 16:36, 15 May 2011 (UTC)
 * To me the argument given implies more than is actually present. Looking backwards in time, things appear deterministic. That is probably one of the reasons that common sense insists on inferring that looking forward there must be a deterministic path, even if we are unable to know it due to the presence of unknown variables.
 * Consider the behavior of a man who goes on a walk with his nephew. At each corner he waits for the next beep from some one of four remote geiger counters monitoring isolated minute quantities of radium. If device one beeps he and his nephew turn right. If device two beeps they go left, and so forth. Their progress is totally random both in regard to direction and to time. (We could expand the example to make the angle of turn have infinitely more choices.) An observer, e.g. the nephew if he was not in on the plot, would have a complete record of when and where their journey changed directions and make certain assumptions about the determinacy of their progress. Their GPS being connected to a recording device and being timed by an atomic clock, there is hardly any leeway in determining when and where they were when they turned. Looking at the results alone there is no indication of the random nature of their turns. Looking at the results alone it may appear that they moved in straight lines from corner to corner and at a uniform velocity.
 * Were the described experiment actually to be performed with a slight modification, helium ions could be shot into the sphere with approximately uniform velocities, and then trials in which ions moved from bank shot at position x to bank shot at position y in the same length of time could be compared to see whether they all moved to the same succeeding position z, and so forth.P0M (talk) 17:01, 15 May 2011 (UTC)
 * Hi Patrick. This is more uncited stuff - it should be removed. It IS reminiscent of Popper's experiment. Myrvin (talk) 19:34, 15 May 2011 (UTC)
 * Following no objections, I've removed the paragraph to here:


 * The Uncertainty Principle is often misstated so as to imply that simultaneous measurements of both the position and momentum cannot be made. There is a simple Gedanken experiment that illustrates what physics does allow.  Imagine a hollow evacuated sphere where the internal surface is covered by microscopic detectors that measure the position and time of contact of a He atom.  Inside the sphere is one single He atom that bounces randomly from one point to another.  Each time it contacts the wall, its position is measured to arbitrary accuracy, therefore its future momentum is uncertain.  The time of the contact can be measured with arbitrary accuracy, therefore the future energy is uncertain.  However, at the next contact with the inner surface of the sphere another accurate measurement of position and time can be made.  Knowledge of those accurate times and positions allows us to compute a history of arbitrarily accurate simultaneous positions and momentums along with times and energies.


 * Still don't like the rest of the uncited "future" stuff in the lead. Myrvin (talk) 12:04, 3 June 2011 (UTC)

Encyclopedic
All you math and physics junkies have forgotten a very important part of this...Wikipedia is an encyclopedia. That means that people who know nothing about the subject come here to learn about the subject. That means that the various mathematical derivations, etc. are far less important than explaining the meaning and significance in laymen's terms. It also means that you need to address the most important reason a layman would be coming to this article: the widespread popular misconceptions about what the Heisenberg Principle says. Take a step back and ask yourself if this article addresses the questions that a wikipedia reader is seeking. I think this article needs to be split into multiple articles. It is important/complex enough to warrant it and popular enough to need it. 99.203.188.211 (talk) 06:54, 10 March 2011 (UTC)


 * I think you are right. From the first paragraph, there are idea such as "wave packet" that will make no sense whatsoever to the average well-informed reader. It talks in such a way as to suggest that it is possible to make simultaneous measurements of, e.g., position and momentum, when in fact that is not only impossible but the point at which indeterminacy reveals itself.


 * The fact is that physicists are taking physical actions that affect the photons, electrons, or whatever they are interested in at the moment, and getting physical results that they can "see" that give them information. They then take the information and make models that try to describe (in a prediction-useful way) what is going on.


 * Take a most simple experiment -- shooting photons through a big hole in a barrier. If the size of the hole is a meter or a foot in diameter and the laser or other light source is aimed at the center of the hole, you won't know with any great precision where each photon goes. Actually, the idea of a photon "going" is one of the ideas that we import from our macro world. Some people imagine that a photon "goes" the way a bullet fired from a gun goes. Other people imagine that a photon "goes" by all possible paths -- with some very small but finite possibility of showing up far from the "line of fire." But staying with the macroscope picture, the photons that get notice all show up as a dot of small diameter. What accounts for their not arriving at a single mathematical point? Perhaps it is just slop in the system. Perhaps it is not. But with a very high degree of accuracy we can predict where the photon ought to show up. It behaves like a highly crafted bullet shot from a highly crafted gun locked in a vice in the macro world. In other words, the gun and bullet picture is a successful model for predicting how the photon in this situation will behave. But, basically, the experiment consists of setting up the laser, the barrier with a hole in it, and the detection screen and seeing where the photons show up. We get no data on where the photon was at mid path except that it "must have been" somewhere within the circumference of the big hole.


 * A variation of that simple experiment is shooting photons through a tiny hole. If the hole is the size of one of the holes in the window screen of a microwave oven, and the photons are microwave wavelength photons, the photons won't go through. The hole has to be a certain minimum size. When we open the hole to that minimum size, we know that whatever it means for the photon "to go" from laser to detection screen, something was happening within the circumference of the enlarged hole. So we take this fact as a reasonable assurance that the photon was there when it was in mid flight. So in this case the position is measured first, and the momentum (which includes factors of both velocity and direction) remains to be determined. But then the photon does not reliably show up on a straight line course that goes from laser through the center of the hole in the barrier. Instead, it displays diffraction.


 * If the situation is reversed and the photon is caused to show up somewhere (giving direction of travel first), then it will be known for sure where it was at that point because a physical event will have occurred. But then the direction of travel for a successor photon will not be in a predictable straight line from that point. The phenomenon was being investigated by Kramer, with the assistance of Heisenberg, and the math involved in figuring out what could be derived from the experiment (of a predictive nature that is) was one of the things behind Heisenberg's breakthrough with quantum mechanics. The picture that one forms from studying that experiment is that a photon is shot into something, say a quantity of oil, and that another photon emerges, but within only a predictable cone of dispersion.


 * Long story with a short conclusion: All these experiments, despite occasional use of the word "simultaneous," are two-shot procedures. In the same article in which he discussed his lamented cat, Schrödinger gives a very enlightening discussion of what it is like to work with these things in the physics lab, pointing out that one has to do the same experiment time after time after time just to try to correct for contingencies, and that "the same" experiment often means identically prepared versions of an experiment. The apparatus might include different lasers, different barrier screens, etc., but the setup has to be the same. Moreover, each time the experiment is run, the apparatus has to be returned to the same initial conditions.


 * The big argument has always been whether we are uncertain about "what is really there," and must be uncertain about what is there because of limitations in what we can do to the world or get from the world, or whether "what is really there" is indeterminate, and in wringing results out of a physical experiment we make something, e.g. momentum, become determined but at the same time make something else, e.g., position, become very much more unpredictable.


 * The basic argument, possibly to be settled by Bell's inequalities, is whether there are hidden variables that determine how the photon in such an experiment "was always going to behave," or whether there are no hidden variables and everything ultimately comes down to probabilities.


 * What are the "widespread popular misconceptions about what the Heisenberg Principle says?" We ought to know what these misconceptions are because that would help make the article more likely to steer people away from them. To me, the main misconception is the one that Heisenberg set himself up for -- that things are "determinate" until we mess around with them by trying to measure them. Bohr was right to warn Heisenberg away from using his "microscope observing electron" example because it assumes that the electron was "really" going someplace with both a definite position and a definite momentum until observers hit it with one or more gamma photons. Is this the only misconception? Please be specific.P0M (talk) 15:43, 10 March 2011 (UTC)


 * I do not believe a split will help the layman. This not to be confused with a different split for different reasons in the previous section. The lead is already marked as too long. It needs to be shortened and simplified. I will come back and take a cut at that in a few days. I propose once that is done, we'll reassess where we stand. --Kvng (talk) 22:29, 11 March 2011 (UTC)


 * This section is not about a split. It is about another question entirely.P0M (talk) 19:43, 13 March 2011 (UTC)


 * It has certainly veered off. The original comment ends with this though: "I think this article needs to be split into multiple articles." That's what I'm responding to. --Kvng (talk) 23:54, 13 March 2011 (UTC)


 * O.K. Now that I look again I see that the comment at the top of this section sort of went in two directions to begin with. P0M (talk) 02:22, 14 March 2011 (UTC)


 * What I meant was that the derivations and discussions should be split off to other articles. The top level article of a subject this important should not have any calculations, criticisms, revisions, etc. directly explained in it. They can be expounded upon in dedicated articles. This page should simply explain in laymen's terms what it is and what it is not, IMO. Then, the leads of those in depth articles should be included with a link to that article. Math, knowledge of quantum physics, reference to quantum particles, Einstein's criticisms, new formulations, etc. do not belong in a *top* level article. A high school student should be able to read this, and I doubt many college graduates can. 173.129.215.9 (talk) 02:34, 15 March 2011 (UTC)


 * What you say certainly makes sense to me. There are some basic issues involved with indeterminacy that can be discussed in plain English. P0M (talk) 14:16, 15 March 2011 (UTC)


 * Can you add a new piece on indeterminacy to the article then? In general, we can't split off the cruft if doing so leaves us with nothing. First step is adding new accessible content or reworking existing content to improve accessibility. Once we have that, the next step (e.g. proposed splits) should be more clear. --Kvng (talk) 04:59, 16 March 2011 (UTC)


 * Sure. I'll make myself a sandbox in my user space and draft something there. I'll come back here when I have something. Meanwhile, if anybody knows what these supposed "widespread misunderstandings are," please enlighten me. Otherwise I will probably delete that part for lack of a citation.P0M (talk) 14:51, 16 March 2011 (UTC)


 * I just finished re-reading Brian Greene's Elegant Universe, or at least all the parts that talk about indeterminacy, so I should be able to make a kind of introduction that goes into the half dozen or so main things that can be discussed in plain English. I hope I will be able to do so within the next few days.


 * I am still concerned to know what the supposed "widespread misunderstandings" are supposed to be. Unless the article can specify them it will serve no useful purpose to tell readers that "people" have been spreading misinformation, and I will delete that part of the article. P0M (talk) 06:51, 24 March 2011 (UTC)


 * In order to help remedy the need to simplify and split this article up, I've written up an article that contains the key derivations of the uncertainty principle with a little bit of discussion on my user page User:PoincareHenri/Uncertainty Principle Derivations. I propose that we cut out the section in the present article under "Mathematical Derivations", create a new page on that topic using the one I've created and add whatever additions people deem necessary. Any thoughts or comments? PoincareHenri (talk) 04:45, 20 June 2011 (UTC)

I don't understand how this principle isn't considered "weak".
If in the future someone finds a way to measure particles using smaller particles, say small 'strings', wouldn't the uncertainty principle seize to apply? --212.54.199.211 (talk) 13:08, 1 September 2011 (UTC)


 * No, it wouldn't, unless those future developments happened to violate quantum mechanics postulates. That would be a very surprising development which is obviously very speculative. There is no reason for us to believe that would happen. Dauto (talk) 13:22, 1 September 2011 (UTC)
 * In other words, simply speculating that some day in the future we may discover a phenomenon that violates a principle that is currently believed to be correct doesn't make that principle weak since that's just wild speculation, nothing more. Dauto (talk) 13:39, 1 September 2011 (UTC)

Splits
Are Uncertainty principle and Uncertainty principle actually related to the Quantum mechanical topic of this article? If not, they probably need to be split off into their own articles. --Kvng (talk) 17:08, 9 March 2011 (UTC)


 * I second this motion. I don't see why these two sections should be in this article.PoincareHenri (talk) 02:50, 19 June 2011 (UTC)
 * Done the former. The latter apparently didn't survive at all.  4pq1injbok (talk) 20:47, 8 September 2011 (UTC)

Gabor limit
Gabor limit redirects here. Why? There is no mention to Gabor... 124.147.77.153 (talk) 05:49, 15 October 2011 (UTC)
 * Perhaps it should redirect, instead, to Uncertainty theorems in harmonic analysis.P0M (talk) 05:45, 16 October 2011 (UTC)
 * ✅ 121.102.117.177 (talk) 07:58, 16 October 2011 (UTC)

More General Scope, Less Derivations
Alright, I've done lots of editing here. It would be great to discuss any problems anyone has with the edits, but to preface my explanations I will simply explain that I have a degree in physics and did my undergraduate work in the area of quantum mechanics, so I'm not just some dolt who's read too much Stephen Hawking and wants to quibble with the mysteries of quantum mechanics. At any rate, on to the edits... According to the previous discussion on this talk page, I've taken out lots of the later portions of the article that seem to go beyond the scope of a top level article. I've added a new article "Uncertainty Principle Derivations" where I've rewritten and added to much of the more advanced material. I've also combined much of the material that discusses anything other than the position-momentum uncertainty principle, and put it under "Additional Uncertainty Relations." And I've also cut/edited the following:

The section on "Physical Interpretation" is not needed, in my opinion, since the entire first half of the article essentially gives physical interpretations of the uncertainty principle, such as the discussion under "Heisenberg Microscope." Consequently, I've cut the section "Physical Interpretation" out.

I rewrote and moved the section of "Mathematical Derivations" into a new article Uncertainty Principle Derivations. I moved the derivation to make the article more in line with what a top level article should be. I redid the derivation in Uncertainty Principle Derivations because the derivation given isn't really the most clear derivation of the uncertainty principle (there are many ways to derive it). In the new article I've included a version of the derivation of the uncertainty principle in Griffiths' commonly used textbook on quantum mechanics. I think most physicists would agree that Griffiths does an excellent job of presenting quantum mechanics in a straight-forward manner.

I edited out the section discussing the Schrödinger uncertainty relation, and gave it more thorough coverage in the article Uncertainty Principle Derivations.

I deleted the section "Uncertainty principle of game theory" since from what I can tell, this has nothing to do with the uncertainty principle of quantum mechanics other than a vague association with a mathematical commutation relationship. If someone wants to make an argument that this should be included, then I think it should be in another article, such as Quantum game theory.

Like others have written on this talk page before, I've recommend that we possibly split "Uncertainty theorems in harmonic analysis" into it's own article. This section doesn't seem to belong on an introductory page on the uncertainty principle of quantum mechanics. However, I'm not entirely sure if it fully justifies it's own article or if it should be placed in the article Fourier transform, for example. Any comments on this would be helpful. PoincareHenri (talk) 04:17, 7 August 2011 (UTC)


 * Regarding the uncertainty principle in harmonic analysis: This does belong here because it IS the traditional uncertainty principle with physical content removed, for two wave functions that are Fourier transforms of each other, such as the position and momentum wave functions. Its not just a curious fact that the two have the same mathematical structure, but rather it explains and embodies the application of the uncertainty principle to this particular case. Also - there is already a separate section in the Fourier transform article dealing with the uncertainty principle in harmonic analysis, so I think the mathematics could be outlined here, and then the reader could be referred to the Fourier transform article for details. Off on a tangent: I also am glad to see that the "entropic uncertainty principle" remains, because I am beginning to believe that it has more fundamental significance than the traditional uncertainty principle. It is more restrictive than the traditional principle. The traditional uncertainty principle can be derived from the entropic uncertainty principle but not vice versa. As I understand it, it is maximally restrictive - there is no more restrictive uncertainty principle from which the entropic principle can be derived. This means that e.g. the position wave function is more fundamentally viewed as an encoding of experimentally derived information concerning the position of a particle, rather than a collection of various moments and the fundamental uncertainty principle is best expressed in terms of this information content rather than in terms of the moments. The concept applies to the general case as well, not just the specific case of a continuous wave function. PAR (talk) 13:25, 7 August 2011 (UTC)


 * If we are to keep the section on harmonic analysis, I think that the relationship of the Fourier analysis to the traditional uncertainty principle needs to be made more explicit. The lead-in to the section should probably include some more explanation and mathematical tie-ins to quantum mechanics. An additional concern I have about this section is that I think the subsection on Hardy's uncertainty principle may be too dense for a top level article. I'm not sure what should be done with it, however, other than to just delete the derivations and keep the final result along with some explanations. PoincareHenri (talk) 23:08, 7 August 2011 (UTC)


 * I am totally opposed to deleting useful material for cosmetic purposes or because it's "too abstruse". If it is too detailed or abstruse for one article, it should go into another article or into its own article. PAR (talk) 17:49, 8 August 2011 (UTC)
 * I don't really approve of the way the content has been reorganized. The article currently fails even to mention the uncertainty principle in harmonic analysis, and it fails to convey adequately the uncertainty principle for two observables other than the position and momentum.  All such information has now been ghettoized to the no-man's land of Uncertainty principle in harmonic analysis and Uncertainty Principle Derivations (the existence of which violates our MoS to boot).  Basic summary style should be observed in this top-level article: summarize the more advanced content here as well.
 * Moreover, the basic version of the harmonic analysis result is now very difficult to motivate, whereas before it was just the uncertainty principle for the operators x and p=d/dx obeying the canonical commutation relations (although maybe that could have been emphasized more). The section on derivations included this as an example, but that example seems to have been cut from the exposition.  Sławomir Biały  (talk) 11:46, 9 September 2011 (UTC)


 * There is no question that it was a mistake to remove the mentions of the harmonic version. It may be good to let the separate article live on and put a more terse version back it, but this article definitely needs it. Also I just edited to opening section because the existing version was extremely shoddy and/or wrong. Isocliff (talk) 15:09, 9 September 2011 (UTC)


 * Totally agree - The Heisenberg uncertainty principle and the "Harmonic uncertainty principle" are identical when the two complementary quantities are Fourier transforms of each other. Heisenberg was the first to derive the "Harmonic uncertainty principle", wasn't he? This removal was done by someone who thought that the "Harmonic uncertainty principle" was some disconnected concept that happened to have the same name. The principles that followed were variations on a theme. I will restore the section soon unless someone has a better idea. PAR (talk) 03:56, 10 September 2011 (UTC)
 * No, Heisenberg didn't derive it from harmonic analysis because Heisenberg was not happy with wave mechanics in general. He had his microscope example, but it was actually Bohr who pointed out to him quite early that if one accepted de Broglie waves (where particles are just wavelets with a Born interpretation of where they are) then Heisenberg uncertainty follows directly from harmonic uncertainty (long known before quantum mechanics). It's a property of any wave, and as soon as you posit "matter waves" with h as the link between wavelength and momentum, then Heisenberg uncertainty follows immediately for matter waves also. Heisenberg was not pleased by that, but the uncertainty relation has been derived in QM books from harmonic analysis (rather than how Heisenberg did it) for a long time. Fermi does it that way in the Fermi Lectures, for example. It's not a "measurement problem". It's a CONSEQUENCE of wave behavior. To the extent that you believe in wave behavior, you must believe in "HUP". S  B Harris 20:53, 24 November 2011 (UTC)