Talk:Uncertainty principle/Archive 6

Requested move 19 March 2018

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review. No further edits should be made to this section. 

The result of the move request was: No consensus either way, defaulting back to the stable title, Uncertainty principle. Numerically more participants favored "Heisenberg's uncertainty principle" but not all arguments were sound. In particular, I gave less consideration to arguments that "Uncertainty principle" is too ambiguous - no evidence was presented that other topics of that name challenge this one, and uncertainty principle was left as a redirect, meaning anyone who types in or clicks on that name comes to this article anyway. As such, I find no consensus one way or the other, so the status quo prevails. In this case, Uncertainty principle has been the name for years until it was WP:BOLDly moved a few days ago with no discussion. Cúchullain t/ c 18:53, 27 March 2018 (UTC)

Heisenberg's uncertainty principle → Uncertainty principle – A quick look at the first few pages of hits on Google Scholar reveals that this name seems to be the most common. This title is even less common than "Heisenberg uncertainty principle". The mover of this page moved it without discussion. LaundryPizza03 (talk) 18:34, 19 March 2018 (UTC)
 * To clarify, an editor stated he renamed the page on March 4 from Uncertainty principle to Heisenberg's uncertainty principle. Rolf H Nelson (talk) 06:06, 21 March 2018 (UTC)


 * I could also go with Quantum mechanics uncertainty principle or Uncertainty principle (quantum mechanics), but otherwise I suppose I support the change back. Gah4 (talk) 19:04, 19 March 2018 (UTC)
 * I don't see the need to specify that it's about Quantum mechanics when there's no other uncertainty principle to disambiguate from. --uKER (talk) 19:22, 19 March 2018 (UTC)


 * Support Same reason why the article isn't called Einstein's theory of relativity. --uKER (talk) 19:20, 19 March 2018 (UTC)
 * False equivalence. The theory of relativity is known as special relativity, and there is therefore no ambiguity, and no need for Einstein's name (note that the general relativity equations are known as the Einstein field equations, presumably because just "field equations" is too ambiguous). "Uncertainty principle", on the other hand, could refer to many things unrelated to QM. Also, "Einstein's theory of relativity" isn't more common than "special relativity", whereas the HUP is almost always referred to as such. 1.144.109.18 (talk) 11:53, 26 March 2018 (UTC)
 * Support Move was made without discussion.ZXCVBNM (TALK) 20:12, 19 March 2018 (UTC)
 * Support Agree that his name is unnecessary in the page title. There are various types of uncertainty but only one "uncertainty principle". Tayste (edits) 21:14, 19 March 2018 (UTC)
 * [Edit] I'm now neutral after reading arguments from both sides below. Tayste (edits) 02:38, 22 March 2018 (UTC)


 * Oppose. To the extent there are adequate redirect pages, it should not matter: the issue is one of pure, and unrepentant, symbolism and editorializing. The article is being ritually and regularly abused by fussers. I see little support of the community in patrolling it and fixing the math. Instead, endless philosophical fatuous discussions and insertions by non-physicists--I have watched students of physics shaking their fist at the silliness permeating these issues. Heisenberg discovered the damned thing and he owns it. Chipping away at this central fact through rebranding won't change much. Changed my vote from neutral in response to @Netoholic 's central and valid remark concerning the Disambiguation page entries: anything more restrictive is salutary.  Cuzkatzimhut (talk) 21:56, 19 March 2018 (UTC)
 * Oppose. Very famously known as Heisenberg's uncertainty principle.  Required for recognisability.  Only dropped when already in context.  No advantage to abbreviating.    --SmokeyJoe (talk) 04:13, 20 March 2018 (UTC)
 * Oppose – there are many analogous uncertainty principles, but this is about Heisenberg's, in QM. Dicklyon (talk) 04:15, 20 March 2018 (UTC)


 * Support A quick google search of Uncertainty Principle seems to show about as many with Heisenberg as without, pretty much all seem to be the QM version. Maybe slightly more without than with. In either case, there will be a redirect from the other one. Gah4 (talk) 04:53, 20 March 2018 (UTC)
 * Oppose Even if its not the most common way this topic is described, its acceptable per WP:NATURALDIS to avoid confusion with Küpfmüller's uncertainty principle and anything else listed on Uncertainty principle (disambiguation). I don't mind keeping Uncertainty principle as a WP:PRIMARYREDIRECT though, but we should really encourage editors to move away from it and it might not be a bad thing if it didn't redirect. -- Netoholic @  12:40, 20 March 2018 (UTC)
 * FWIW searching for "Küpfmüller" and "uncertainty principle" on Google Scholar gives only 34 results; most of these results mention Küpfmüller's principle in the context of Heisenberg's uncertainty principle. Rolf H Nelson (talk) 06:10, 21 March 2018 (UTC)


 * Oppose. For this particular UP (uncertainty principle), the discoverer's name, "Heisenberg's", is necessary natural disambiguation. Also, the is an ambiguous term, so shouldn't it be reset to target the UP disambiguation page?   Paine Ellsworth   put'r there  03:08, 21 March 2018 (UTC)


 * Support for procedural reasons (WP:RMUM — to undo an undiscussed controversial move). No comment on the merits.  —  AjaxSmack  03:28, 21 March 2018 (UTC)
 * Support Clear example of WP:PRIMARYTOPIC. Britannica and SEP both title their pages "Uncertainty principle". "Uncertainty principle" is already recognizable by anyone familiar with QM. Nobody techie enough that they want to read about a different, obscure, uncertainty relation will be confused to find the main page is about quantum mechanics. Rolf H Nelson (talk) 06:13, 21 March 2018 (UTC)
 * Oppose – Heisenberg's uncertainty principle precisely specifies the referent with zero ambiguity. There is no dispute as to whose uncertainty principle it is (the one in quantum mechanics, I mean), and therefore there is no reason to deprive its creator of the primary credit for his achievement. In fact, the tradition of naming laws and principles after their discoverers/creators is one of the aspects of science that differentiates it from less constructive, less useful, and less civilized human endeavors. There are far more examples than I need to cite here. The removal of Heisenberg's name from his discovery suggests some kind of agenda that is wholly inconsistent with the history and biography of science. User:Freevito 2018-03-22-0906 (UTC, ISO 8601) —Preceding undated comment added 00:06, 22 March 2018 (UTC)
 * Pauli's exclusion principle rarely sheds its eponymity.Cuzkatzimhut (talk) 00:19, 22 March 2018 (UTC)
 * It's a fair point that we have Pauli's exclusion principle, but we also also have Bohr's Correspondence principle. Rolf H Nelson (talk) 05:03, 27 March 2018 (UTC)
 * If you take a look through Category:Scientific laws and Category:Equations you will observe that named laws/equations vastly outnumber those few counterexamples. 58.166.86.203 (talk) 10:31, 27 March 2018 (UTC)


 * Oppose because those arguing the article should be renamed because of more google search hits should read Google searches and numbers. Also, naming the Heisenberg uncertainty principle after it's inventor is a logical continuation of other theorems and theories naming convention, such as Green's theorem and Stokes' theorem. Furthermore, adding Heisenberg to the name removes ambiguity from other uncertainty theories. Brian Everlasting (talk) 01:11, 26 March 2018 (UTC)
 * Those aren't very good examples, nobody is proposing that we rename Green's theorem to just theorem. Rolf H Nelson (talk) 03:39, 26 March 2018 (UTC)
 * If Green's theorem and Stokes' theorem are the examples, then this should be named Heisenberg's Principle, especially if he doesn't have another one. Gah4 (talk) 04:57, 26 March 2018 (UTC)
 * Unfortunately, while there are probably occasions during discussion among scientists to refer to the HUP as "Heisenberg's principle", that phrase does not satisfy Wikipedia's policy for article titles, and the present title does meet that policy as shown by its usage in reliable sources.  Paine Ellsworth   put'r there  12:10, 27 March 2018 (UTC)


 * Oppose We ought to name this important principle properly so as to give credit to and commemorate it's brilliant inventor.--老陳 (talk) 05:27, 26 March 2018 (UTC)
 * Is there some kind of subtext I'm missing here? This is the third comment stating the article should add Heisenberg in its title in order to honor him or to resist "chipping away" at his legacy or some such. Rolf H Nelson (talk) 05:03, 27 March 2018 (UTC)


 * Oppose per WP:COMMONNAME (almost always referred to as "the HUP" or similar), WP:NATURALDIS ("Uncertainty principle" could refer to almost anything) and WP:CONSISTENCY (see Schrodinger equation, another QM equation; Pauli exclusion principle, also QM; Einstein field equations; Newton's Laws; the list goes on...). I do however belive the article should be moved to Heisenberg uncertainty principle, dropping the possessive, as is the case with, say, the Schrodinger equation.1.144.109.18 (talk) 11:53, 26 March 2018 (UTC)
 * OK, there are theory of relativity, general relativity, and special relativity all not named after Einstein. Gah4 (talk) 05:17, 27 March 2018 (UTC)
 * Yes, theories. Not equations. A group of equations of general relativity are known as the Einstein field equations. This equation from quantum mechanics is known as the Heisenberg uncertainty principle. 58.166.86.203 (talk) 10:05, 27 March 2018 (UTC)

Move to "Heisenberg uncertainty principle"
In the case that the move to the ambiguous name proposed above fails, the possessive should be removed from the title. It is the Schrodinger equation, not Schrodinger's; the Pauli exclusion principle, not Pauli's; Penrose–Hawking singularity theorems, not "Hawking and Penrose's singularity theorems". 1.144.109.18 (talk) 12:02, 26 March 2018 (UTC)
 * Oppose. I agree that the title sans possessive is also a COMMONNAME way to express this principle; however, both:
 * Heisenberg uncertainty principle, and
 * Heisenberg's uncertainty principle
 * seem about equally acceptable in reliable sources, so no page move is needed.  Paine Ellsworth   put'r there  15:12, 26 March 2018 (UTC)
 * I would add that in the lead, the title sans possessive would require definite article "the", as in "The Heisenberg uncertainty principle", where the possessive styling does not need the definite article.  Paine Ellsworth   put'r there  22:38, 26 March 2018 (UTC)
 * As it should! Does Heisenberg own the principle, as in "Heisenberg's house" or "Heisenberg's car"? 58.166.86.203 (talk) 10:02, 27 March 2018 (UTC)
 * Due respect, that doesn't matter to Wikipedia. What matters to Wikipedia here would be adherence to WP:COMMONNAME, and the present title satisfies that policy well enough.  Paine Ellsworth   put'r there  12:02, 27 March 2018 (UTC)


 * Support . —SmokeyJoe (talk) 00:17, 27 March 2018 (UTC)
 * Oppose - Both forms are dead-even in usage, but the possessive is better as page title because it doesn't require "The". I think its fine if both forms are used interchangeably in the article (especially to match whatever source is addressing a particular detail. -- Netoholic @  07:36, 27 March 2018 (UTC)


 * The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.

Post-move
I have reverted a move of this page by away from the title decided by the RM. I closed the RM as no consensus, and so restored it to its long standing stable title Uncertainty principle as it was was WP:BOLDly moved to Heisenberg's uncertainty principle just a few days before. As it just went through a community discussion, the article should not be moved again without a new consensus that the longer title is better. Netoholic participated in the RM just yesterday, so couldn't have missed it.--Cúchullain t/ c 16:34, 28 March 2018 (UTC)
 * I'm a little confused about why you would move this article back to a title that received so much opposition in the above RM? To me it appears that the support args were far inferior to the oppose args, so why not a consensus not to move?  Paine Ellsworth   put'r there  17:17, 28 March 2018 (UTC)
 * I judged it to be no consensus. Numerically more people supported "Heisenberg's uncertainty principal" but not all arguments were sound (chiefly the argument that "Uncertainty principle" is too ambiguous, despite the fact that it remained a redirect). Given that there wasn't a clear consensus one way or another, the status quo prevails, and the article has been at "Uncertainty principal" for years until it was moved a few days ago.--Cúchullain t/ c 17:29, 28 March 2018 (UTC)
 * No consensus is a good call; however, the reason it was changed from the status quo was due to its obvious ambiguity and the fact that this article's title, "Uncertainty principle", is not in accordance with Wikipedia policy.   Paine Ellsworth   put'r there  19:31, 28 March 2018 (UTC)


 * I hate discussions on WP:COMMONNAME, as they are so subjective. It is not easy to do reliable statistics on usage to see what is really common. I got into a big discussion on Ethernet, as the early UTP hubs were repeaters, but that hub isn't technically the same as repeater. Also, it depends if you use technical literature or marketing literature, or something else. Gah4 (talk) 19:44, 28 March 2018 (UTC)


 * In any case, there is statistical uncertainty (haha) such that even if slightly more people voted one way, it would not be a clear consensus, as noted. Gah4 (talk) 19:44, 28 March 2018 (UTC)
 * I can see why it was moved, but the intention to decrease ambiguity was mooted by the fact that "uncertainty principle" still redirected to the article. Meaning, anyone who clicked on or typed in the phrase would end up here anyway. At any rate, I did not see a clear consensus that the bold move was for the best. This may be worth revisiting in the future, when it'll be clearer that "uncertainty principle" is the stable title and the move proposal would move it away from that. In such a discussion, it'll be easier to look at issues like WP:COMMONNAME and the potential need for disambiguation.--Cúchullain t/ c 21:09, 28 March 2018 (UTC)
 * And you seem to have hit on the real controversy here, Cúchullain. That controversy is what to do with the UP title after renaming this article to Heisenberg's uncertainty principle? Should it title the disambiguation page, or should it be a primary redirect and target this article? I think choice one is best. So an ensuing RM should include the request to move
 * Uncertainty principle → Heisenberg's uncertainty principle
 * Uncertainty principle (disambiguation) → Uncertainty principle
 * Since in my opinion this article's present title confuses general readers, the next question is "when"? Since the outcome was no consensus, what in your opinion and in this case would be an appropriate wait to start another RM?  Paine Ellsworth   put'r there  07:09, 29 March 2018 (UTC)
 * It is not the page's title, but the page's contents, that are there to remove confusion in the minds of readers. Interested readers will have no problem locating the page and informing themselves on its topic. Tayste (edits) 07:43, 29 March 2018 (UTC)
 * We can't all agree on everything, Tayste. One look at Uncertainty principle (disambiguation) shows what an ambiguous title there is presently at the top of this article. The larger question is whether or not this article, even if titled "Heisenberg's uncertainty principle", can be considered the primary topic for the dab page I linked, or should the title "Uncertainty principle" be thought of as having no primary topic?  Paine Ellsworth   put'r there  07:53, 29 March 2018 (UTC)
 * I'd say give it a month or so so that it doesn't just turn into an extension of the last RM, but otherwise, no prejudice to reopen.--Cúchullain t/ c 13:40, 29 March 2018 (UTC)
 * Thank you, a month or even two will give supporters time to "load up".   Paine Ellsworth   put'r there  14:01, 29 March 2018 (UTC)
 * - Discounting the "support" votes that only objected to the recent move on principle due to the March 4 undiscussed move (one of which explicitly said he had no opinion on the merits), there is clear consensus for this page to not be at "uncertainty principle". -- Netoholic @ 00:40, 29 March 2018 (UTC)


 * The current title is bad. —SmokeyJoe (talk) 00:56, 29 March 2018 (UTC)
 * I agree. So I guess we have to try again, in the other direction this time, to try to show a consensus. Dicklyon (talk) 01:42, 29 March 2018 (UTC)
 * I disagree. "Uncertainty principle" is a reasonable page title and the name "Heisenberg" is not necessary there. Tayste (edits) 02:28, 29 March 2018 (UTC)
 * I'm sure there are different ways one could parse the results to see whatever outcome they prefer. What they can't say is that there's a clear consensus for any title. They also can't unilaterally move an article that's just been through a community discussion.--Cúchullain t/ c 13:40, 29 March 2018 (UTC)
 * If you are limited in what outcomes you were able to render in that discussion, ie that "no consensus" after an RM held in reaction to an undicussed move defaults to the status quo ante, yet there are so few actual supporters of the title "Uncertainty principle", then I chose to ignore the process and instead worry about improving wikipedia. The correct result should have been to discount the votes which were on procedural grounds only (not on merits either way) and decide a course of action. That course of action would be to agree there is consensus for the article to not be named "Uncertainty principle" but also no consensus between other options, and to leave the article in place and encourage a 2nd RM to decide among those other options. Also, see Netoholic's Law.
 * Also as a general comment, I can see the "status quo ante" result from RMs for this kind of RM being weaponized. Someone who wants the prior name might hold this kind of vote knowing that it can cause confusion and also because of the default result being to move back. Such RMs should instead be held only after the page is moved back to its original and worded as proposals so that it can be a fully discussed move. This eliminates both voter misunderstanding about what change is proposed (Is someone opposed to the current, undiscussed title or are they opposed to the title proposed in the RM?), but also eliminates the procedural votes that are just opposed to the undiscussed move rather than voting on merits of one title over another. -- Netoholic @  14:04, 29 March 2018 (UTC)
 * In addition to circumventing a community discussion where you were heavily involved, you made your moves in such a way that it made a mess of the talk archives, which is certainly not "improving Wikipedia". I did not discount !votes on procedural grounds, because they're perfectly valid: the burden of evidence in a controverted decision is on those supporting a change from the status quo. I did give less consideration to arguments on either side that were weak in terms of policy, as I said. We appear to be in agreement that the best and clearest way forward will be an RM from the status quo title.--Cúchullain t/ c 14:44, 29 March 2018 (UTC)
 * Your words were prophetic: "If a (recent) move was undiscussed and someone has cause to challenge it, the move should be reverted before an RM is started". -- Netoholic @ 15:52, 29 March 2018 (UTC)
 * Yes, this kind of thing isn't uncommon, especially with technical moves and it gets very confusing very quickly. This one could easily have been a technical move, if not just a straight revert of the undiscussed, BOLDly-moved title.--Cúchullain t/ c 15:56, 29 March 2018 (UTC)

Subatomic particle
A recent edit suggests that Uncertainty only applies to Subatomic particles. I could just revert, but decided to discuss here first. It is much easier to observe with smaller particles, but is still true for larger particles, including whole atoms. Gah4 (talk) 03:59, 3 June 2018 (UTC)


 * I'm not sure. Dicklyon (talk) 04:13, 3 June 2018 (UTC)


 * OK, for one, helium is liquid at absolute zero because zero point motion, the result of the uncertainty principle, doesn't allow it to freeze. Well, until you apply enough pressure. With enough pressure, it is frozen up to room temperature or higher. Gah4 (talk) 07:20, 3 June 2018 (UTC)

can be known
The description asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, such as position x and momentum p, can be known. suggests that objects have position and momentum more accurate than the uncertainty principle, but that we (humans) can't measure it. As far as I know, the uncertainty is there, whether we measure it or not. Gah4 (talk) 22:20, 7 July 2018 (UTC)
 * Can. Something that cannot be measured is there? What is your improvement?Cuzkatzimhut (talk) 02:53, 8 July 2018 (UTC)


 * A recent edit changed can exist in nature to can be known. The latter seems to me to imply a person in the system. Gah4 (talk) 07:33, 8 July 2018 (UTC)


 * Sigh... As you might have ascertained by going down the edit history of the article, "can be known" has been around for at least a dozen years. and hashed out again and again and again. This article is about physics, not ontology. The whole innovation and significance of the principle is to avoid discussions of things that are there but cannot be known. Cuzkatzimhut (talk) 13:03, 8 July 2018 (UTC)

Why we call it uncertanity principle?
Is it good to call it UNCERTAINITY principle, i dont think so. It is not an Uncertainity principle.The term is very much misleading and mis guiding to my opinion. After going through this principle i can strongly suggest and prefer myself not to call it UNCERTAINITY PRINCIPLE rather better is to call it "PRINCIPLE OF INDETERMINISM". It may seem to u of no worth but to me it really matters ,because what has been said to us is not true. What we have been taught is not true to my opinion.

The principle says "THE ABSOLUTE VALUE OF TWO COMPLEMENTARY PAIR OF PHYSICAL OBSERVABLES OR TWO CONJUGATE PROPERTIES OF QUANTUM SYSTEM CAN'T BE DETERMINED SIMULTANEOUSLY"

In simple terms IT IS NOT POSSIBLE TO DETERMINE THE MOMENTUM AND POSITION OF QUANTUM SYSTEM SIMULTANEOUSLY ABSOLUTELY.

If one observable is determined completely there will be uncertainity in absolute value of other physical variable and vice-versa.

In Mathemtical way we can say operators for two conjugate pairs of quantum sysytem cant commute.

The principle doesnt limit the precision in the values of single physical variable, rather it limits the precision in values of pair of physical variables.

THE PRINCIPLE DOESNT SAY WE CANT SIMULTANEOUSLY DETERMINE THE CONJUGATE PROPERTIES BUT SAYS MEASUREMENT UNDER IDENTICAL CONDITIONS WITH FIXED VALUES OF ONE VARIABLE, SPREAD THE VALUES OF OTHER VARIABLE OVER A RANGE WITH NOTABLE STANDARD DEVIATION , HAPPENING TO BE INVERSELY PROPORTIONAL TO THE SELECTED ACCURACY RANGE IN OTHER VARIABLE.

The more we open range of accuracy for one variable will tend to converge the values of other property towards standard value or optimum value.

The principle presents a philosophical challenge to one of our basic assumptions about nature of reality, i .e physical objects have precise and definite existence.

It is wrong to call it as uncertainity principle because the name suggests that there is always uncertainity in measurement imparted by observation. Due to this it provides a scope for the resolution of instrument i.e resolution of instrument influences the nature of reality and bring uncertainity. Thus it should be called as {Principle of Indeterminism} which brings a notion that uncertainity in values is intrinsic to such systems no matter what so ever our precision of experiment is.

THE HEISENBERG HIMSELF WRONGLY INTERPRETED THIS STRANGE AND BEAUTIFUL RESULT WITH ROUGHLY TRUE, MISLEADING THOUGHT EXPERIMENT called as HEISENBERG'S MICROSCOPE that is what teachers still teach us that shining a beam of photons over quantum systems disturb their behavior by virtue of which uncertainty in values arises...bla bla bla and this interpretation of Heisenberg to my opinion is wrong as it imparts a notion that in-determinism is due to observation rather than inherent to such systems.

I have tried to explain the principle in abit different way using De-Broglie equation....

The equation is of dualism where "p" is characteriatic of particle and "lambda" as characteristic of wave.

1.When we try to measure the position of electron we r forcing it to behave as particle and to know its momentum we should know its lambda but being forced in particle state we lost information about lambda and hence momentum...

p = h/ lambda

2.But when we try to measure its momentum we should know its lambda and we force the sysytem to behave as wave ...Since wave being continuous we loose information about position.

This interpretation also brings notion of observer effect but not in the way as Heisenbergs interpretation is giving.

My explaination doesnt provide any scope for better resolution of instruments but strongly says that indeterminism is due to wave-particle duality rather observation or measurement effect.

May be people may not connect this interpretation on true grounds but i think this is better than what Heisenberg came up with.

SO WE SHOULD NEVER CALL IT UNCERTAINITY PRINCIPLE BUT PRINCIPLE OF INDETERMINISM. Aejaz Ul Bashir (talk) 03:49, 15 June 2020 (UTC)


 * Article talk sections are only meant to discuss improvement of the article. Your discussion about whether the principle's name is appropriate doesn't have a place in Wikipedia. --uKER (talk) 05:37, 15 June 2020 (UTC)

Proposed merge with Heisenberg limit
Feel like the Heisenberg limit is a specific application of the uncertainty principle that would be better discussed in the context of the latter. Although the target is large, I think merging this wouldn't be a problem since this would only amount to a sentance or two. --Trialpears (talk) 21:36, 28 September 2019 (UTC)
 * Merging from Heisenberg limit makes sense to me, as the uncertainty principle is well-known. -- Beland (talk) 22:48, 18 October 2019 (UTC)
 * I support this as well. Daviddwd (talk) 01:54, 19 October 2019 (UTC)


 * I suppose yes, for the current content of Heisenberg limit, but maybe it should be

improved and extended. It seems to me that Heisenberg limit is more experimental, and less theoretical, and likely has some details not applicable here. But that only makes sense if we actually get those details. Gah4 (talk) 03:07, 19 October 2019 (UTC)
 * Given that the page in question is only a few sentences, smaller than most subsections within the main page, this merger seems perfectly logical, especially considering the similar nature of the two. I would be more than willing to make the edit myself 23:35, 5 December 2019 (UTC) — Preceding unsigned comment added by 2A02:C7F:7EC1:EB00:92:CFA3:7F34:BA19 (talk)

Supporting this argument. The Heisenberg limit article is after all a stub in itself and there is not enough content which proves otherwise, but considering its size and the fact that it can take its place as an example section (more suited for the latter) in the Uncertainty principle page, a merge is highly recommended. - pivotman319 (📫) 17:55, 16 January 2020 (UTC)

Yes these two pages should be merged because either of them is rendered a little incomplete without each other. This a merge will be good. KRONOS2508 (talk) 14:28, 7 February 2020 (UTC)

I support this too. They are incomplete without each other (User_talk:Info12d) — Preceding unsigned comment added by 2409:4063:4E05:B6D3:ACD8:A93C:CD14:9021 (talk) 03:15, 10 August 2020 (UTC)
 * ✅ Klbrain (talk) 21:22, 23 August 2020 (UTC)

Introductory paragraph needs work
I think the initial paragraph should be rewritten, with the sentences broken up for readability (I'm certainly not qualified). The first two sentences are 52 and 54 words long with 10 commas.

That's hard enough to parse if you're dealing with fairly simple subject matter. Almost impossible to parse and digest when you're talking physics.

The main point of a wiki article is to educate everyone from those with a passing familiarity, to those who know nothing about the subject whatsoever. That requires direct plain writing.

I'm an intelligent man, with an interested layman's grasp of the subject. Reading about anything and everything is very much my thing. Those sentences still made my eyes water. Sajiky (talk) 19:54, 16 November 2020 (UTC)


 * You are, of course right, as the constant rewriting of the lede indicates, and the truckloads of archived discussions of this Talkpage attests. But just about anything undermining the complexity of the issue and oversimplifying it would be a betrayal of the message, all too easy to commit on this particular subject. Chopping up issues connected at the hip will then necessitate longer Hemingayesque arrays of sentences with an effort to connect them, and lead to complaints of unclear exposition.  A quick improvement is to split the first paragraph in half, and perhaps substitute a semicolon for a comma or two. The concept is complex and elusive, however, routinely misunderstood by about half the public interested in it, and damage control starts at avoiding brutal oversimplification... Cuzkatzimhut (talk) 23:15, 16 November 2020 (UTC)

Shouldn't the momentum p be qualified as being p_x?
Shouldn't the momentum be qualified as being the x-component of momentum?

The first formula on the page refers only to momentum, in unqualified form. Johanley (talk) 04:45, 8 February 2021 (UTC)

The Uncertainty Principle on the Planck Scale
The article should mention the uncertainty relation $$\Delta r_s\Delta r\ge\ell^2_{P}$$, where $$r_s$$ is the gravitational radius, $$r$$ is the radial coordinate, $$\ell_{P}$$ is the Planck length, which is another form of the Heisenberg uncertainty relation between momentum and coordinate applied to the Planck scale. Indeed, this ratio can be written as follows: $$\Delta (2Gm/c^2)\Delta r\ge G\hbar /c^3$$, where $$G$$ is the gravitational constant, $$m$$ is the mass of the body, $$c$$ is the speed of light, $$\hbar$$ is the Dirac constant. Reducing identical constants from two sides, we arrive at the Heisenberg uncertainty relation $$\Delta (m c) \Delta r\ge\hbar/2$$. The established uncertainty relation predicts the appearance of virtual black holes and wormholes (quantum foam) on the Planck scale.178.120.11.65 (talk) 16:16, 29 November 2020 (UTC).


 * In relativistic physics, in a reference frame at rest relative to a micro-object, there is a minimum error in measuring its coordinates $$\Delta r\sim \hbar/mc$$. This error corresponds to the uncertainty of the momentum $$\Delta P\sim mc$$, which corresponds to the minimum threshold energy for the formation of a particle-antiparticle pair, as a result of which the measurement process itself becomes meaningless.178.120.8.173 (talk) 04:56, 23 August 2021 (UTC)


 * That does not look like a wp:reliable source. - DVdm (talk) 19:07, 29 November 2020 (UTC)
 * I should also feel strongly the article should not spread/flake-off into conjectural extensions in speculative contexts; these might merit their own stub, but it is unconscionable to deliver well-meaning, mainstream eyeballs to them. Cuzkatzimhut (talk) 20:03, 29 November 2020 (UTC)

There are also the Bohr-Rosenfeld uncertainty relations $$\Delta g(\Delta L)^2\ge\ell^2_{P}$$, where $$\Delta g$$ is the uncertainty of the gravitational potential, $$\Delta L$$ is the uncertainty of position, and $$\ell_{P}$$ is the Planck length. Resembles an equation for an invariant interval $$g_{ik}x^ix^k=S^2$$. All these equations are related.178.120.65.155 (talk) 07:37, 1 December 2020 (UTC)

Notes 1 and 2
In the introduction, there are notes which display when you hover over them. Note 2 starts with "Note 1 is in clear contradiction with the Section Systematic and statistical errors...". I feel like the notes in an encyclopaedia shouldn't argue with each other! I have no idea which one is correct, but someone should look into this and rectify it. Extremely confusing for anyone trying to understand this subject. 86.130.89.214 (talk) 15:07, 28 January 2022 (UTC)

Cleanup needed
The introduction contains:

Generally considering the wave nature of matter, to observe a particle a light wave of shorter wavelength compared to the size of the particle must interact with the particle and the reflected wave should observed. Shorter the wavelength higher the frequency when speed is constant 'c' as they are inversely proportional. Higher the frequency higher the energy according to the Planck relation.

The first sentence errs with “should observed”. The next two “sentences” could use some definite articles and a verb each. 96.237.251.50 (talk) 15:54, 19 October 2022 (UTC)
 * I've removed the entire bit, which was introduced in this edit. User:Favonian had reverted the editor once, but the second time it was left standing. --Wrongfilter (talk) 17:23, 19 October 2022 (UTC)
 * Comment: Hi, I just wondered, for an article like this, whether Wiki endorses such a thing as a 'layman's language' section. The lead might start with some simplified summary - in the way that an explainer might introduce a talk. I know a bit about the subject but was actually immediately confused by the lead, because of the terms. Just a thought. Excellent article. Cheers Thelisteninghand (talk) 20:20, 9 December 2022 (UTC)

Very interesting connection to the Cramer-Rao bound
https://link.springer.com/article/10.1007/s11760-019-01571-9 Generalized Cramér–Rao inequality and uncertainty relation for fisher information on Fractional Fourier Transform (2019) Biggerj1 (talk) 21:25, 25 May 2023 (UTC)

Wave mechanics interpretation?
I guess this section is attempting to show the reciprocal relationship of widths in space vs momentum via Fourier transform. I can't make heads or tails of the argument.

I also don't understand the section title. "Interpretation"?

I think the section ought to be called "As a property of waves" and it should demonstrate that matter waves have uncertainty built in. Johnjbarton (talk) 14:23, 9 August 2023 (UTC)

Is the Uncertainty Principle a basic part of quantum mechanics?
The article states, "Introduced first in 1927 by the German physicist Werner Heisenberg." While that is technically true of HUP, the principle of complementary variables was discovered by Lagrange, Fourier, and others at the end of the 1700s or beginning of the 1800s, depending on whom you read. In the 1700s the heat equation and sound waves were the inspirations for discovering, among many other things, the inverse precision in the measurement of complementary variables, such as amplitude and frequency with respect to time.

I'm not sure why so many physicists have stated that Heisenberg's Uncertainty Principle (HUP) is a basic and unique part of QM. It is not any such thing. It is a red herring. It is a distraction. It is just plain wrong.

I would ask them, is the equivalent inverse precision principle due to Joseph Fourier (and others) between the amplitude and the frequency of an audio or electromagnetic signal also part of QM? Or can you physicists out there finally admit that the inverse precision of measurement of complementary variables is entirely due to the interdependence of the two variables, one of which is the derivative or the Fourier transform of the other?

The HUP is usually expressed as $$ \sigma_{x}\sigma_{p} \geq \frac{\hbar}{2} $$. But this scales up without difficulty to the classical regime, in which complementary pairs of variables are not treated as a mystery, merely as the natural result of measurement: it takes one measurement in time to fix the position of a particle, but averaging many such measurements in time reduces the accuracy. Inversely, it requires averaging many measurements in time to measure velocity accurately, but measuring only once reduces the accuracy. It is impossible to measure position and velocity both accurately and no matter whether one or many measurements are made. The same is true of amplitude and frequency. The same is true for elementary particles as for whole planets. David Spector (talk) 16:47, 13 July 2023 (UTC)


 * The Uncertainty principle is certainly a basic part of QM and HUP is both basic and part of QM. There is a vast literature to support that point of view. Historically this results from the sudden and unexpected discovery that matter dynamics are governed by wave equations.
 * The understanding of the wave equation and the Fourier relations of course predate Heisenberg. That is why the HUP was so quickly part of QM discussions: this background was part of the education of all physicists at that time. The position-momentum relationship of course was not part of the older understanding as those wave equations did not have a position-momentum issue to be concerned with. And the specific HUP derivation could not have predated Heisenberg because the operator concepts (commutator) he used where only introduced by Schrodinger (as far as I know). Classical mechanics has Poisson brackets which Dirac eventually connected to the commutator relations.
 * Adding a section to this article on the Fourier relations would be great. I have not found a good reference for the connection between the earlier work and Heisenberg's work. Johnjbarton (talk) 14:38, 9 August 2023 (UTC)

History section contains original research.
The History section has two paragraphs that mention Fourier three times. The citation is to a work of Heisenberg:

Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik The English translation in 1983 (by Heisenberg?) is here: https://ntrs.nasa.gov/citations/19840008978

As far as I can tell, at no point in this article does the word "Fourier" appear. Johnjbarton (talk) 17:23, 9 August 2023 (UTC)


 * The excellent review by D. Sen points to Hardy's 1933 paper as the Fourier analysis.
 * Hardy, G. H., A theorem concerning Fourier transforms. J. London Math. Soc., 1933, 8, 227–231. Johnjbarton (talk) 18:56, 9 August 2023 (UTC)

Dubious
Hello, Johnjbarton. I do not object to your perceived COI of my edits. However, you cannot erase everything en masse. I have marked clearly wrong text in Wikipedia as Dubious. I have the right to do so exactly as you can. The insertion of reference to my work is not necessary for re-writing and revisiting the dubious text. There are other published peer-reviewed works that point out the error and basically say the same thing, see for example: Urbanowski K. Remarks on the uncertainty relations. Modern Physics Letters A 2020; 35 (26): 2050219. http://arxiv.org/abs/1810.11462 http://doi.org/10.1142/s0217732320502193 In summary, I would request to leave the Dubious tag of marked Wikipedia text until someone competent is able to revisit the text in such a way that it is not blatantly false. By the way, I was thinking of possibly uploading my Fig.3 in Wikimedia, however, the resistance by people like you changed my mind. If you are knowledgeable, you could use the quantum mechanical calculations to plot your own images. Best regards, Danko Georgiev (talk) 08:44, 19 January 2024 (UTC)


 * Please note that you have released the figures in https://www.mdpi.com/2073-8994/16/1/100 under CC BY 4.0 and that they can now be used freely (with attribution). Jähmefyysikko (talk) 09:46, 19 January 2024 (UTC)
 * Dear Jähmefyysikko, thank you for pointing out the Attribution part. However, Johnjbarton objected to inclusion of Reference to my article in the first place, that is why he reverted my edits. Consequently, the only way for inclusion of my Fig.3 without Attribution to my published work would be if I agree to release the same figure in the Public Domain. Danko Georgiev (talk) 10:07, 19 January 2024 (UTC)
 * Thank you for your understanding on the COI process.
 * As for the "dubious", you added them with no explanation and no comment in the Talk page. From my perspective you are putting nasty notes on the page. They are unreferenced and unexplained comments; I felt free to delete them. In future please leave edit summaries and preferably comments with references in this Talk page. Then the dubious tags will look like thoughtful suggestions.
 * Johnjbarton (talk) 18:08, 19 January 2024 (UTC)
 * Dear Johnjbarton, What explanation do you want?? The "explanation with references" was the one that you deleted. If you want, you can copy the deleted text from the Wikipedia article revision written by me, paste it on the talk page, and then discuss it all you want. Everything follows from your unprofessional reverting. You complaint is unfounded - you should read something first before you delete it. Danko Georgiev (talk) 19:08, 19 January 2024 (UTC)
 * An edit summary for the dubious tags could have 1) explained your reasoning, or 2) cited Urbanowski, or 3) said "Please see Talk page" where you could have given your reasoning. Any of these explanations would help.
 * You may not be aware that wikipedia pages are routinely vandalized, sometimes in childish or drunken ways, but sometimes in bizarre ways. Edit summaries or talk pages are the only practical way we have to distinguish reasonable edits from silly obnoxious ones. Johnjbarton (talk) 19:18, 19 January 2024 (UTC)


 * Here is the code of the deleted text:

Although the second factor in the left-hand side, i.e. $$\frac{\sigma_{B}}{\left|\frac{d\langle\hat{B}\rangle}{dt}\right|}$$, has dimension of time, it is different from the time parameter $$t$$ that enters the Schrödinger equation. It is a lifetime of the state $ψ$ with respect to the observable B: In other words, this is the time interval (Δt) after which the expectation value $\langle\hat B\rangle$ changes by one standard deviation and it is expressed as:$$ \Delta E \Delta t \ge \frac{\hbar}{2}$$ The Mandelstam-Tamm quantity $\Delta t\equiv\frac{\sigma_{B}}{\left|\frac{d\langle\hat{B}\rangle}{dt}\right|}$ cannot be interpreted as a lifetime because it is a dynamic function of time $\Delta t (t)$ and becomes infinite at the local maxima or minima of the expectation value $\langle\hat{B}\rangle$ of the quantum observable $\hat{B}$, due to vanishing instantaneous rate of change $\left|\frac{d\langle\hat{B}\rangle}{dt}\right| = 0$|undefined. Furthermore, in a single-qubit toy model it can be shown that the angular frequency $$\omega$$ of oscillation of $$\langle\hat{B}\rangle$$ is constant $$\omega=\frac{E_{\max}-E_{\min}}{\hbar}$$, hence independent of Mandelstam-Tamm $$\Delta t$$, which undermines the physical interpretation of $$\Delta t$$ as an alleged "time uncertainty".


 * Comment on lifetime and why Mandelstam-Tamm quantity $$\Delta t\equiv\frac{\sigma_{B}}{\left|\frac{d\langle\hat{B}\rangle}{dt}\right|}$$ is not lifetime.

Danko Georgiev (talk) 19:30, 19 January 2024 (UTC)
 * Definition 1: Lifetime means that the state decays for some amount of time.
 * Definition 2: Infinite lifetime means that the state never decays.
 * Fact 1: Mandelstam-Tamm quantity $$\Delta t$$ becomes infinite.
 * Fact 2: The quantum state clearly decays contradicting the infinite Mandelstam-Tamm quantity $$\Delta t$$.
 * Conclusion: Therefore, Mandelstam-Tamm quantity $$\Delta t$$ is NOT lifetime. Period. Q.E.D.


 * I encourage you to read some of the policy docs for wikipedia, eg not a journal. The goals and thus the criteria for including content in wikipedia is not at all like a journal. For physics, wikipedia is mostly a summary of reviews and textbooks. This is true even when the review is "incorrect" according to some recent work, because recent work quite often turns out to have its own issues. Johnjbarton (talk) 01:40, 20 January 2024 (UTC)

Section "A counterexample" has no references.
The section "A counterexample" appears to have references but none pertain to the counter example. They are simply references to support steps in the argument. Thus the section reads as WP:Original research. Johnjbarton (talk) 19:10, 19 January 2024 (UTC)


 * I can't even figure out what this section is a "counter example" of. Johnjbarton (talk) 00:45, 20 January 2024 (UTC)
 * The counterexample is to the Robertson–Schrödinger Uncertainty Relation, when derived unconditionally for any two Hermitian operators.
 * The reference that you think is missing is:
 * Davidson, E.R. On derivations of the uncertainty principle. J. Chem. Phys. 1965, 42, 1461–1462.
 * What means "unconditional derivation"? Answer: Many authors just write: "For any two quantum observables given by Hermitian operators $$\hat{A}$$ and $$\hat{B}$$, the Robertson–Schrödinger Uncertainty Relation holds." The latter claim is false. The correct formulation, which adds a "condition" is given in my Appendix, namely, "For any two quantum observables given by Hermitian operators $$\hat{A}$$ and $$\hat{B}$$, for which $$\hat{A}|\Psi\rangle$$ is in the domain of $$\hat{B}$$ and $$\hat{B}|\Psi\rangle$$ is in the domain of $$\hat{A}$$, the Robertson–Schrödinger Uncertainty Relation holds." The reference to Davidson 1965 is also given in my Ref.[38]. Danko Georgiev (talk) 11:59, 20 January 2024 (UTC)
 * Thank you, I revised the section and included the Davidson ref. Please review. Johnjbarton (talk) 17:13, 20 January 2024 (UTC)

New section for the time-energy uncertainty relationship
I propose to move the time-energy uncertainty to a new section: Johnjbarton (talk) 00:42, 20 January 2024 (UTC)
 * None of the current refs in the part of the article discussing the time-uncertainty mention Robertson.
 * The refs support the idea that it is not like other relations.
 * The Sen review says: "The time– energy uncertainty relation (TEUR), therefore, does not follow directly from the Robertson–Schrödinger inequality."
 * Dear Johnjbarton, mathematical and physical research is heavily based on definitions. This means that the published text is no longer plain English, hence requires understanding by the expert reader and translation into plain English. The above quotation from Sen makes no sense until you explain what it means in plain English:
 * Does it mean that Mandelstam-Tamm relation is NOT time–energy uncertainty relation?? If yes, then why Mandelstam-Tamm relation is discussed in the section time-energy uncertainty? The logical steps in such interpretation of the Sen quote is: (1) Mandelstam-Tamm relation follows DIRECTLY from the Robertson–Schrödinger inequality. (2) TEUR does not follow directly from the Robertson–Schrödinger inequality. (3) Therefore, Mandelstam-Tamm relation is NOT TEUR!
 * Does it mean that Mandelstam-Tamm relation does not follow directly from the Robertson–Schrödinger inequality?? The logical steps in such interpretation of the Sen quote is: (1) Mandelstam-Tamm relation is TEUR. (2) TEUR does not follow directly from the Robertson–Schrödinger inequality. (3) Therefore, Mandelstam-Tamm relation does not follow directly from the Robertson–Schrödinger inequality. Of course, the latter is mathematically wrong, since the derivation of Mandelstam-Tamm relation can be seen to use the Robertson–Schrödinger inequality in one of the mathematical steps.
 * The purpose of the above example, is first to show you that you should not confuse "original research" with genuine effort by a Wikipedia editor to translate mathematical/physical jargon into plain English that is understandable to ordinary readers. Second, that there is no easy way out of the dilemma --- in order to explain in plain English what Sen's quote probably means you need to put words in Sen's mouth by clarifying that he should be stating that "Mandelstam-Tamm relation is an ALLEGED TEUR, not true/valid/real TEUR" because the opposite would imply that Sen is plain wrong mathematically with regard to the derivation of Mandelstam-Tamm relation.
 * In summary, I wish you good luck in rewriting the section of time–energy uncertainty relation by simultaneously avoiding doing "original research" or cherry picking of text quotes outside of the author's intended context. Danko Georgiev (talk) 09:13, 20 January 2024 (UTC)
 * I only mentioned the Sen quote as one reason to remove the Energy-Time uncertainty from the Robertson-Schrodinder section. Johnjbarton (talk) 16:13, 20 January 2024 (UTC)
 * Well, what you did is simply wrong because you continue to talk about "Energy-Time uncertainty" when you apply action to text on "Mandelstam-Tamm relation". First, "Mandelstam-Tamm relation" is a special case of Robertson-Schrodinder relation so it should stay where it was. Second, Sen states that "Energy-Time uncertainty" does NOT follow from Robertson-Schrodinder relation, thereby implying that "Mandelstam-Tamm relation" which is a special case of Robertson-Schrodinder relation, should NOT be classified as "Energy-Time uncertainty" and should NOT be moved to that section at all. Finally, when you are asked yes/no questions could you please answer the questions so that I understand what you are doing and why you are doing it: 1. Does Mandelstam-Tamm relation follow directly from the Robertson–Schrödinger inequality? Yes or No? 2. Is Mandelstam-Tamm relation expressing the time–energy uncertainty relation? Yes or No? Danko Georgiev (talk) 22:39, 21 January 2024 (UTC)
 * In my opinion relationship between Mandelstam-Tamm and Robertson-Schrodinger is not very important. In the whole picture of Energy-time uncertainty, Mandelstam-Tamm is just one item. In terms of notability, the energy-time uncertainty topic should not be set under the Robertson-Schrodinger section.
 * 1) I have found no reliable reference that " Mandelstam-Tamm relation follow directly from the Robertson–Schrödinger inequality".
 * 2) "Is Mandelstam-Tamm relation expressing the time–energy uncertainty relation?" No, the way the question is asked. The reliable references clearly show that no one ("the") time–energy uncertainty relation exists. On the other hand references clearly support a notable Mandelstam-Tamm relation related to time-energy uncertainty. Johnjbarton (talk) 00:33, 22 January 2024 (UTC)
 * Oh, you did not find a "reliable" reference? What about the original Mandelstam and Tamm 1945 paper?? You do not recognize their Eq.(3) as the Robertson uncertainty relation, do you? Danko Georgiev (talk) 01:16, 22 January 2024 (UTC)
 * The original paper for Mandelstam-Tamm did not mention Robertson. No review that includes Mandelstam-Tamm mentions Robertson. Therefore I don't consider the connection significant. This is not a math exercise.
 * Please also take a look at WP:SYNTH. Synthesis is what you do in publications, not in wikipedia. Johnjbarton (talk) 02:30, 22 January 2024 (UTC)
 * I combined the two sections on energy-time and partly reorganized them.
 * The section has some non-encyclopedic commentary (eg "one false") and its a hodge-podge. I think following Sen more closely would be the better result. Johnjbarton (talk) 01:29, 20 January 2024 (UTC)
 * The original section on "Energy-Time uncertainty" was NOT a hodge-podge, and its original author has made it clear that "special relativity" is important for the derivation. In simple words, this means that you need to use "relativistic QM" and not "nonrelativistic QM". The section became a hodge-podge, after you moved the Mandelstam-Tamm relation which is NONRELATIVISTIC into a section that starts with talk on "special relativity". I would recommend that you move back the text on Mandelstam-Tamm relation into the section on Robertson-Schrodinder relation. Danko Georgiev (talk) 22:53, 21 January 2024 (UTC)
 * The first paragraph mentions special relativity in a discussion about why we even want a energy-time relationship. The Mandelstam-Tamm section starts with "In non-relativistic mechanics, " so I don't see any confusion. Johnjbarton (talk) 00:20, 22 January 2024 (UTC)

Proof of the Schrödinger uncertainty relation?
Do we need to have this section in the article? At the top of the section we learn that this proof is readily available. Surely the one in a hundred reader keen in the proof will find it. I don't believe the proof itself is notable. Johnjbarton (talk) 03:50, 23 January 2024 (UTC)
 * As well as I know, there is no proof, but it just is. Planck found the relation needed for black body radiation, but there is no "proof" of it. Gah4 (talk) 12:01, 23 January 2024 (UTC)
 * The section in question has nothing to do with black body radition. Johnjbarton (talk) 17:01, 23 January 2024 (UTC)
 * The section in question has nothing to do with black body radition. Johnjbarton (talk) 17:01, 23 January 2024 (UTC)

any interaction between classical and quantum objects
The article says: any interaction between classical and quantum objects, but not where we find these classical objects. Gah4 (talk) 12:02, 23 January 2024 (UTC)


 * Thanks, I deleted that sentence, not about uncertainty principle. Johnjbarton (talk) 18:36, 23 January 2024 (UTC)

Proposal to merge Stronger uncertainty relations into this article.
The section of "The Maccone–Pati uncertainty relations" in this article contains almost all of the content of Stronger uncertainty relations; we don't need the latter other than a redirect. Johnjbarton (talk) 19:32, 25 January 2024 (UTC)

Outline for time-energy uncertainty section.
There are lots of refs for time-energy uncertainty. I'm planning an outline like: Johnjbarton (talk) 16:58, 22 January 2024 (UTC)
 * Spectral line-width - lifetime.
 * motivate with primary application.
 * Time in quantum mechanics.
 * Hilgevoord: "Time in quantum mechanics: a story of confusion"; Busch: three kinds of time.
 * Derived relationships
 * Mandelstam-Tamm (based on Sen); Hilgevoord
 * Hilgevoord/Busch "Quantum Clock"
 * Visually interesting example illustrating some more depth in the problem.
 * Quantum field theory
 * virtual particles


 * I did not get to the quantum clock. I think the line-width/lifetime section needs more work: this is the biggest application of uncertainty principle. But I need to work on another project for a while. Johnjbarton (talk) 16:55, 28 January 2024 (UTC)