# Talk:Heisenberg's uncertainty principle

## Comment

The "Heisenberg's uncertainty principle" article in Simple Wikipedia is, in my opinion, a little bit flawed. One statement is: "The minimum range of error in position (x) times the minimum range of error in momentum (p) is, at a minimum, about equal to the Planck constant." What is the need for writing "about"? Can't we write the correct form of the equation((delta)x*(delta)p>=(h/4pi))? Also, the image shown (which is a mathematical statement of the above) doesn't have /4pi either. Shouldn't somebody correct it?

Thanks. 116.68.121.59 (talk) 07:16, 30 March 2013 (UTC)

The (h/4pi) you give is the same, mathematically, as the (h-bar/2) quoted later in this article. The "h-bar" equals h/2pi.Patrick0Moran (talk) 17:21, 31 March 2013 (UTC)

## References

References should be sufficiently complete so that an interested reader could find a book or journal in a library, or purchase a book on-line, or read the journal article on-line. I have shown on the article how a simple in-line reference may carry page numbers without repeating the whole reference. If all the pages are in a single chapter, another way is just to reference the chapter as well as the book title. That way is more economical of the editor's time. Generally speaking, a person is either going to get the book and read the chapter or not. So precise page references are not needed except in certain cases. These include:

1. direct quotes from the source
2. proposale for DYK, PGA etc, where other editors may require absolute precision.
3. Any point which where a reader might reasonably dispute a statement.

Other than that, I think directing to a chapter is fine. Macdonald-ross (talk) 09:25, 30 March 2013 (UTC)

## Merge discussion March 2013

Before we start worrying about 116.68.121.59's comments, I need to point out that we have two complete articles on the topic: this one and Uncertainty principle. So they need to merge. On a very quick look:

1. The other article looks more complete and correct.
2. This one is written in better Simple English.
3. The final location must be the other one, because that is the name in other languages already.

I'd be willing to work through this one, but I cannot possibly get to it until near the end of April. StevenJ81 (talk) 01:47, 31 March 2013 (UTC)

Of course we must merge, but there are some issues to discuss first:

1. We also have a duplication between matter wave and wave-particle duality. That must also be fixed, because I believe they are about the same concept, and it is relevant to the "uncertainty" pages.
2. Our problems indirectly come from our lack of an expert in physics willing to spend time fixing these pages on difficult concepts. Ideally, someone who has had experience teaching these concepts... A first degree in physics would be the next best bet. The problem we have is editors putting in "simple" explanations of concepts like relativity without really understanding whether their explanations are correct physics. I think it would be unwise for anyone to offer to do the work unless their physics was of an appropriate standard. I notice editors user:Patrick0Moran and user:StevenJ81 have interests in this article.
3. About these two articles, I think the present one ("Heisenberg") has the more accurate physics, and the other one ("Uncertainty") is simpler.
4. Working on them will be a nightmare unless the editor makes use of semi-popular works by professional physicists. I would look first to Richard Feynman. The Feynman Lectures on Physics is justly famous. Six easy pieces includes one on quantum behavior, and Six not-so easy pieces has relativity, space-time, symmetry...

Macdonald-ross (talk) 07:39, 31 March 2013 (UTC)

Look, my first degree is in Chemical Engineering. I can just about manage if I need to, but if Patrick0Moran wants to tackle it he's more than welcome. StevenJ81 (talk) 14:42, 31 March 2013 (UTC)
I just had a look at the other article. There are many more assertions in that article than in this one, but I hesitate to try to improve that article because it is so badly written just from the standpoint of an essay in ordinary English. It makes me acutely uncomfortable to try to read it. Maybe it would help that article if it could be outlined, and then the main topics in that outline could be turned into section headings, and the secondary topics could be turned into coherent topic sentences, sentences that state what the paragraph intends to prove or demonstrate.
I could be more specific, but then I would tear into just about every sentence. Contrast that article with Introducing Quantum Theory by McEvoy and Zarate. There is only one place, p. 127, where they throw the reader a curve ball, and they have done their research quite well.Patrick0Moran (talk) 17:42, 31 March 2013 (UTC)

## Point by point

I've been busy with some of my own writing, so I've missed the lead-up to this discussion, sorry. I have responded to the reader who did not like the first few lines of the article. Here is why the article did not start with mathematically more complicated ways of expressing "undertainty":

One of the main issues we should consider is our target population. My understanding is that we are writing for readers coming to problems from other language backgrounds. We do not assume less intelligence or initiative, but more. Even so, quantum physics is not something to jump into without even a sketch map of the territory.

The reason that the article begins with an approximation is that the equation quoted is Heisenberg's formulation. Here is a segment from the English Wikipedia:

In his celebrated 1927 paper, "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik" ("On the Perceptual Content of Quantum Theoretical Kinematics and Mechanics"), Heisenberg established this expression as the minimum amount of unavoidable momentum disturbance caused by any position measurement,[1] but he did not give a precise definition for the uncertainties Δx and Δp. Instead, he gave some plausible estimates in each case separately. In his Chicago lecture[2] he refined his principle:

${\displaystyle \Delta x\,\Delta p\gtrsim h\qquad \qquad \qquad (1)}$

Kennard[3] in 1927 first proved the modern inequality:

${\displaystyle \sigma _{x}\sigma _{p}\geq {\frac {\hbar }{2}}\quad \qquad \qquad \qquad (2)}$

where ħ = h/2π, and σx, σp are the standard deviations of position and momentum. Heisenberg only proved relation (2) for the special case of Gaussian states.[2]

Imagine that you are a bright high school freshman in Afghanistan who has been unable to find anything in languages local to Afghanistan that you can read. You've heard something about the Heisenberg Uncertainty Principle, and you are intrigued. However, ideas from statistics like standard deviation have not come up in your math classes, and Gaussian states sound like they might be deviations too. ;-)

Even if readers are provided with links to other relevant articles, our freshman reader would have to detour through a process of some length to learn about subjects that really were not involved in Heisenberg's kernel of insight, the annoying little math problem that he hoped to make disappear from his already rather hairy equations, the recasting of those equations into matrix forumulation by Born, and Born's almost instantaneous realization that reversing the order of matrices in a multiplication (PX × XP or XP × PX) would always involve a factor of h/2πi.

Physicists have had nearly an entire century to make the expression of the initial kernel of insight much more sophisticated. A bright reader can understand, e.g., a math treatment of the acceleration due to gravity that ignores air resistance and other factors that will make the results in freshman physics lab different from predictions based on the equation in the book.

More later.Patrick0Moran (talk) 16:54, 31 March 2013 (UTC)

I just had another look at the Uncertainty principle article. Without intending to become so, articles in the English Wikipedia can become something of a hodgepodge because different people add things at different times without thinking about the structure of the entire article. Transferring and simplifying is likely to make these problems worse rather than better.

I propose that we begin by making a scratch page somewhere and first create an outline so that we can see what we want in the article, what needs to be given support in other articles (and may involve creating new articles if we don't already have on on the subject), and give adequate thought to what the beginning reader who wants to "crack" either just the English language as used to discuss something for which s/he has adequate preparation in college-level physics and math, or both the English and also the fundamental concepts that were not covered in his/her high school education.

A good outline would give us a clear basis for good topic sentences. If writers control these basic organizational points it is much easier to keep from confusing the reader.

I'll have a look at what Brian Greene and others have done in their books on modern physics. Greene has evidently had lots of experience in keeping people from getting lost in the woods.Patrick0Moran (talk) 17:23, 1 April 2013 (UTC)

## Sandbox

I just started a sandbox here: /Uncertainty sandbox Patrick0Moran (talk) 14:53, 2 April 2013 (UTC) flose them Feynmann's The Character of Physical Law provides a demonstration via the double-slit experiment, and not much else. Greene provides a similar amount of information. Both are appropriate sources for people trying to get into the discussion. Patrick0Moran (talk) 17:42, 2 April 2013 (UTC)

Hi Patrick. I've had to move your sandbox to the Talk namespace, if that's okay. Citations and everything will still work fine, it just needs not to be in the mainspace because it pops up in maintenance reports. Osiris (talk) 01:53, 3 April 2013 (UTC)
Great. Thanks. I didn't want to put it in my own space for fear that nobody else would be willing to put their oar in there. Patrick0Moran (talk) 05:46, 3 April 2013 (UTC)

Checking over the Uncertainty principle article I see that they have two sections that the Heisenberg UP does not have: "History and interpretations" and "popular culture."

Are we going to get into the "Copenhagen interpretation" interpretation business? I have read that there is no one "Copenhagen interpretation," and that different people have chosen to highlight different things that Bohr was keen on keeping stable and at the center of the work of him and his colleagues. Patrick0Moran (talk) 17:46, 3 April 2013 (UTC)

Patrick, here's my view, FWIW. Simple will never be Encyclopædia Britannica in scope or breadth, and I don't think it needs to aspire to that in depth, either. I see it more as the equivalent of the US en:World Book Encyclopedia. In that light, I see the approach to this article as being one that would satisfy a secondary school student or a university undergraduate so that s/he could have a general understanding of the concept. If someone needs more than a lay overview, will they really come to simple?
For that reason, I doubt that the nuances of the "Copenhagen interpretation" are so important here. I think that could be tackled at a high level—including the reasons that Einstein, et al., objected—and would satisfy a reader coming here. I don't think you need to open the whole can of worms. StevenJ81 (talk) 18:11, 3 April 2013 (UTC)
I agree. I wasted time and got long-lasting misconceptions with "A boy's book on EVERYTHING" books as a teenager. Finding George Gamow's book was the first sign of clarity and the beginning of getting untangled. It's not only a general understanding. More importantly, it, and books like it, are entryways into a new world. I love the way Einstein can talk about the trickiest things in his popularizations and never say anything that he would have to take back at a later stage of explication. He never leads people astray. Other writers of much less stature can get readers started wrong from the first sentence, and it is usually not because they don't understand but because they don't know how to write clearly. Anyway, I'm just trying to get a clear shot at all of the things that people would like to have in our article. So far the best model for an article that I've found is in Quantum Challenge. "Rather than relying on jargon... [it] will squarely confront crucial problems facing scientists today."
I think the part about "observer effect" needs to be handled carefully. Quantum effects can produce some observer effects, but so can elbowing the lab apparatus. Not all observer effects are due to quantum-level interactions, but not all observer effects are other than quantum phenomena.
How about the impacts on culture of the uncertainty principle? It's important, but it also often involves misconceptions.
If I don't get any negative comments or corrections on the sandbox stuff I'll start outlining and doing topic sentences. It would be better to get guidance before I go far down the wrong road.
Please check out the animation I just added to the sandbox. I am not sure I have the right "physical intuition" to describe it, but it should be the best way to get to the matter-wave indeterminacy "math" reasons for uncertainty mentioned in the Uncertainty principle article. Please fix it so that we have a good explanation for what is going on with conjugate variables when the location of the wave is made more definite. Thanks.Patrick0Moran (talk) 19:22, 3 April 2013 (UTC)
OK, my major was engineering, not physics, and I'm over 30 years out from my degree. So I really do not know how these things are handled in today's classroom. (Let's stipulate general introductory freshman physics, not "Physics for Poets," but also not the top-level pre-physics major course.) Mostly I think you're in great shape, but I'd make the following three comments:
1. In my experience, people are taught about particle-like (or corpuscle-type) behavior and wave-like behavior as existing simultaneously. I would be a little careful going in the direction of "that's wrong"; I would probably approach it more in the direction of "that can be a useful way to look at things sometimes, though it is only an approximation." If nothing else, if you suggest to people that their physics professors were wrong, you may lose them.
I would not say what you seem to imply I would be saying. What Bohr et al. emphasize is shown in the way they would describe the double-slit experiment. At the double-slit part of the apparatus you can account for what is going on only by looking at the wave aspect of the wavicle. At the detection screen part of the apparatus you can only account for the single scintillation observed there by looking at the particle aspect of the wavicle. The trouble people have in getting clear on what is going on is that they say, "First it's a wave, and then it's a particle." That's not right. That statement is made by taking macro-scale ideas into the domain of the ultra-small where they do not belong. So the same experiment involves both wave and particle aspects of one thing, but you only "see" them one at a time. Patrick0Moran (talk) 20:52, 3 April 2013 (UTC)
I fully appreciate (and agree with) your desire to steer away from the possibility of leading people astray. But we engineers are fond of thinking about initial conditions, and the initial conditions here (concerning people's current education) are what they are. So you probably have to assume you are "un-astraying" them a little.
Right.
2. Concerning your animation: It's cool. And I can work with you on some of this to make sure the language ends up simple, as far as it goes. But my physics is not strong enough (or is at least too rusty) for me to draft an explanation of it myself.
We had a long discussion leading up to several diagrams on the English Wikipedia that may be useful.
3. I think in a general survey like this, the history, personalities, and impact on culture are important. And even if some of this is based on misunderstandings or misinterpretations, it is what people know [or think they know], and it has to be addressed. (Consider: I'm an Orthodox Jew. There's a lot in the King James Version translation I think is simply wrong. But I'd better be at least a little familiar with it, because so much has come into the English language from it.) StevenJ81 (talk) 20:04, 3 April 2013 (UTC)
Right. It irritates me that people tend to ignore Heisenberg's contributions because Schrödinger came along and put the math in another form that was in most cases easier to calculate. There are a couple of dozen pages of heavy math in Heisenberg's 1927 article, and people slightingly speak of his "heuristic" contribution. Fortunately there are people like Mehta who have done the historical research. The Uncertainty people was implicit in the first set of equations that Heisenberg produced. He was irritated with a complication he imagined he could finagle out of his equation when he had more time. He gave his work to Born, who figured out in a week or so that it needed a matrix formulation, and apparently within minutes or a few hours he realized that there would always be a factor involving h that would pop right out of the math. In fairness to the developers of quantum mechanics I think responsible writers will keep the true history. It's wrong to start an article on quantum mechanics with Schrödinger and his equations and then add, as an afterthought, that Heisenberg did a similar thing with matrix math.
The history of the Uncertainty principle involves a thought experiment proposed by Einstein. Heisenberg and Bohr argued that in the quantum world things did not have position and momentum until they were measured. Einstein proposed a thought experiment in which two rocks (or whatever) were in contact at three points or more (so they were not moving in relationship to each other). They were then given an impulse to get them moving in the local frame of reference. At some later time a tiny push operated between them to disengage them. Now they had positions and momenta that were intimately linked. Einstein argued that you could indeed know the momentum of rock A without disturbing its position (trajectory) because you could measure the momentum of rock B (messing with its trajectory in the process) and use that value (and the original momentum and position given to the two rocks together) to compute the momentum of rock A. He believed that measuring the momentum of rock B could not possibly alter the trajectory of rock A. So you could then measure the trajectory of rock A (its position in other words) and you would then know at that instant what its momentum and trajectory were. Asserting that measuring rock B would in any way affect the by now far distant rock A brought us to entanglement, but that is something for another article.
I like the early example of complementarity, but the English Wikipedia article removed reference to it, preferring the wave-nature (what is the location of a wave) example now also used in the Simple English article.
One of the reason that I used the several simulations in the Heisenberg uncertainty principle article is that they makes the connections between momentum and trajectory (or final position on the detection screen) much clearer. Once people can see what is going on, adding a mathematical treatment of the phenomena that puts numbers on the pictures will be fine both for the people who will ignore the math and for the people who will want to work through the math and make it their own.Patrick0Moran (talk) 20:57, 3 April 2013 (UTC)

## Topic sentences

A first draft of topic sentences is now available. It would be better for me to know sooner rather than later what others may find necessary to add to this plan. Thanks. Patrick0Moran (talk) 07:50, 4 April 2013 (UTC)

I've added the topic sentences to the Uncertainty principle argument, and to those topic sentences I have added critiques when the information is wrong or confusing.

Please let me know what in the second outline/topic sentences is not covered but needs to be covered in the new outline/topic sentences.Patrick0Moran (talk) 14:17, 4 April 2013 (UTC)

## Comment

I read Patrick's notes with interest. Is it possible, I wonder, to have both definitions and explanations in two stages, one for readers who are not skilled in maths or physics, and then for readers with basic physics & maths? Perhaps the answer is "no"... Macdonald-ross (talk) 16:42, 4 April 2013 (UTC)

I started to be a little leery about even speaking of "trajectory" and momentum, just because the usual terms are "position" and momentum. How best to approach new readers so as not to spook them off and yet not to get them lost in the brambles is a big question. However, the necessary math is just the one basic Δx × Δp ≥ ħ/2.
It's already been pointed out that the readers are likely to be helped by things that are concrete, including the history of how this principle was discovered. So if the article starts (after the lead, anyway) with what Heisenberg was trying to do when he discovered it, then the article can say that whenever experimenters try to measure position (or determine a point or points on a trajectory) there is going to be a certain amount of what Click and Clack would probably call "slop" in the measurement, and the same applies when the experimenters try to measure momentum. I believe that trajectory and momentum are both close enough to everybody's experience that those two ideas won't cause problems. (Do we have articles on those two concepts?) The numerical value of ħ is not crucial for anything as long as you aren't going to do the real calculations, so what the reader has to understand is that if you want to measure both the trajectory and the momentum of some particle at the same time rather than on two different occasions, then you are in trouble because the more slop you get out of one of them the more slop you are likely to put into the other one, and no matter how light your touch or how fine your instruments are, you will never get rid of that tiny number.
Would it help to explain it up to this point just qualitatively and then state the numerical formulation?
The one place in the "Heisenberg's" article where the math looks pretty hairy is just there for illustrative purposes. The reader doesn't have to do anything with it. Maybe that section should be moved to the very end? Patrick0Moran (talk) 01:19, 5 April 2013 (UTC)
I've put an outline at the bottom of the sandbox and in it I've indicated the places that would use math. A moving picture may be worth 10,000 words. Right now I would like to have a simulation that shows momentum getting jittery as position gets more and more pinned-down.Patrick0Moran (talk) 03:41, 5 April 2013 (UTC)

## Have a look

I have now finished writing a draft. I have tried to keep the math simple but also to write out anything that people writing for upperclassmen physics majors would leave unsaid.

I think I have finished with all that I can do on this article. Any comments?Patrick0Moran (talk) 22:46, 12 April 2013 (UTC)

## Putting indeterminacy into mathematical form

In this section we seem to be saying exactly what the previous section denies, namely that the act of measurement is the cause of uncertainty. I believe the previous section was accurate, but here I just note that we cannot live with this uncertainty!

Now another thing. Spelling. The articles moves between US and Brit spelling. I suggest you choose, but do choose. Remember that 'math' is US; 'maths' is Brit...

I have paid a lot of attention to the intro of each version. My editing changes are just suggestions, of course. I am really making an obvious point, that the intros to science topics are important because many readers just want to 'get an idea', and may read no further. Macdonald-ross (talk) 16:02, 13 April 2013 (UTC)

I'll look at your changes. I have not been working with this document at all recently. I have been working on the sandbox article, which is probably what should be the main focus now.
Talk:Heisenberg's uncertainty principle/Uncertainty sandbox

On the very small scale when we are measuring something like an electron, however, each measurement does something to it. If we measure position first, then we change its momemtum in the process. If we measure the electron's momentum first, then we change its position in the process. Our hope would be to measure one of them and then measure the other before anything changed, but our measuring itself makes a change, and the best we can hope to do is to reduce to a minimum the energy we contribute to the electron by measuring it. That minimum amount of energy has the Planck constant as one of its factors.

I see what you are talking about. I just finished going over the same minefield in the sandbox article. To make the whole thing comprehensible you have to start with the idea of aiming an electron cannon of some kind at a screen. After firing a few million electrons at the screen (the way your old TV set did as it was first warming up or just after you turned the switch off) you will be convinced that you have a very good idea of the path that the electrons are going to take. Maybe you will be aware that quantum mechanics says that there is some probability that an electron might end up at the edge of the screen, but we never notice single electron arrivals. Anyway, we have a pretty good certainty that we know how this cathode ray tube works. We know what to expect, even though theory reminds us that these electrons have neither position nor momentum until we measure them, so they have no position and no momentum between the cathode and the screen. Next, we try to determine either position or momentum at the midpoint between the cathode and the screen. So we squeeze the electrons between progressively smaller holes. Doing so tells us that the electrons that make it to the screen did not go by any path other than the hole, so makes the hole smaller reduces the uncertainty in position, and, guess what, we no longer can depend on the vast majority of electrons ending up in a tiny spot on the screen. Instead we start seeing a diffraction pattern. So the momentum (or we could say the trajectory or the velocity) has gotten less certain than it was before.
What I have done in the "new" article is to put all of the above into concrete terms with simulations that show readers what they would see in the lab, and especially how changing the strictures on momentum necessarily changes the strictures on position. Then I show that there is a mathematical way of saying that same thing.
Thanks for your help.Patrick0Moran (talk) 17:52, 13 April 2013 (UTC)

## simplifying vocab

I've begun to go through the modified/new article using http://www.online-utility.org/english/simple_basic_helper.jsp While their app can turn out files with wictionary links, they will not easily tranfer to Wikipedia.Patrick0Moran (talk) 17:41, 17 April 2013 (UTC)

3. The named reference Kennard was used but no text was provided for refs named (see the help page).