Talk:Uncertainty principle/Archive 4

Time freeze definiteness
Need a little more clarification for laymen: Why do scientists so insist that uncertainty is an inherent nature rather than human's limits? If the Laplace's demon can actually freeze time (like what briefly happens at an event horizon) and do measurement with its extra-sensory perception rather than its vision, then can't it still measure the definite velocity and momentum of a particle?Mastertek (talk) 14:14, 23 October 2011 (UTC)


 * The "proof" lies in the Bell theorem. Einstein thought that it was a "human limitation" issue, and never gave up on that belief. The trouble is that he had to postulate extra variables that were "there," but that always escape observation by humans. Bell found a way to show that if things were predetermined rather than waiting to be determined, then there would be certain observations that would be found. When those observations are expected but not found, Bell concludes that the "predetermined" idea is wrong.


 * Writing an article such as this one involves problems of "how big a bite can the reader chew at one time." Theoretically, articles are limited to 32k bytes, the idea being that if there is more to say it should be in sub-articles that are foundational to the main article so that if the reader wants to know, e.g., the answer to your question, then the reader can go to something about the Bohr vs. Einstein debates, or to the Bell Theorem discussions, absorb that information, and then come back to read about the Uncertainty Principle.P0M (talk) 19:21, 23 October 2011 (UTC)


 * See the "EPR paradox for entangled particles" section for Einstein's complaints and Bell's way of showing that Einstein's theory could be falsified. (That's all science can really do -- show that some idea is wrong and then look for another way to understand what is really going on.) P0M (talk) 19:27, 23 October 2011 (UTC)


 * Thanks for your instructions, Patrick. I am trying my best to understand Bell theorem, Bohr-Einstein debates and EPR Paradox. But it seems Bell's theorem did not conclude that "the 'predetermined' idea is wrong" as you said. It only states that either locality or realism/counterfactual definiteness (CFD) must be violated which means CFD can still go with nonlocity. So the values in nature at any point of time, though not measured (and affected by measurements of any means), can be definite, predetermined by nonlocal properties. In other words, something can be definite must we never know it, right? Mastertek (talk) 06:18, 25 October 2011 (UTC)


 * Is "either locality or realism/counterfactual definiteness (CFD) must be violated" a quotation from somewhere? O.K., now I see where you got it: "Quantum physics must necessarily violate either the principle of locality or counterfactual definiteness." The article later explains: "This states that if the results of an experiment are always observed to be definite, there is a quantity that determines what the outcome would have been even if you don't do the experiment."  Let's see what consequences follow from the two things that are "violated." If we start with the idea that non-local changes can occur, then it is possible to give a coherent account of why entanglement happens. If we start with the idea of "there is a quantity that determines what the outcomes will be", then we can explain how the results otherwise described as "entanglement" can happen. So we have these two "outs." But they are inconsistent with each other.


 * I guess maybe that is the way that it is supposed to be stated. It is trying to say that there are two ways out of being tangled up with entanglement. The problem is that they can't both be right. Einstein had an idea that was expanded into the idea of "hidden variables" because he couldn't stand the idea of non-locality (or "spooky action at a distance"). The idea of non-locality is consistent with the idea that things are truly indeterminate. The idea of "hidden variables" is consistent with the idea that things are determinate in certain contexts. But Einstein had already made many attempts to find ways to have determinate positions and momentums for the ultra-small particles that quantum mechanics talks about. Each time he thought he had it all sewn up, Bohr proved he was wrong. Entanglement was a sort of last-ditch defense against the idea of indeterminacy. (I think Heisenberg's word is better because it doesn't suggest that these physicists ever thought that people were merely uncertain about what they were experiencing.)


 * Until Bell came along people thought they were stuck not knowing which of these two ways of accounting for what came to be called entanglement was the real explanation for what was going on. But Bell argued that there was an experimental basis for deciding which one of these possibilities was correct. It eventually became possible to do real experiments. Einstein's view has not been supported by experiments done up to now.P0M (talk) 06:13, 26 October 2011 (UTC)


 * You may find more easily assimilated help if you will get Brian Greene's book, Elegant Universe, that gives an example of (or an analogy for understanding) the "inequality" that Bell's work indicates. Einstein looked at the theoretical conclusions that you could draw from quantum mechanics. Those conclusions included one that indicated entanglement. Einstein argued that what quantum mechanics could predict was o.k., but that it was not complete. It was o.k. in that it predicts that if, e.g., you simultaneously produce two photons in a certain operation, then one will measure out as having one kind of spin, and the other will measure out as having the other kind of spin. Before quantum mechanics if somebody had done the experiment they might have assumed that both photons could have the same spin in any run of the experiment. The reasoning would have been that there is no reason (no causal factor) that could determine the spin of either one, and that the spins were analogous to tossing two coins. Over time you would get an equal number of heads and tails, but you would be a bad gambler if you bet that if coin one came up heads, then coin two would have to come up tails. After quantum mechanics you realize that it always works out this way, i.e., one will always be heads (or clockwise spin) and then the other will always be tails (or counter-clockwise spin. But, Einstein asked, how can it be that quantum mechanics tells us that there is no spin until a measurement is made and only then does the photon decide (whatever that means) which way to spin. If the spin of photon one wasn't determined until some time after it was emitted, then by that time it could be very far from where the other photon was. So how can we possibly explain the fact that we always see the opposite spin in the second photon to be measured? Either you say that the photons were both predetermined to spin in whatever way they turned out to spin, or you say that making one decide to spin some way made the other one decide, as a consequence, to spin the other way. But then you would have to believe that some causal sequence went forth through space and told the second photon that it had to spin the opposite way from the one that had just been measured. However, there is nothing in quantum mechanics to even hint of such a weird "decision" to communicate about how the second photon should "decide" to spin. And on top of that there was no time gap between measurements assumed by quantum mechanics, so according to quantum mechanics if the guys measuring the two photons had their atomic clocks synchronized they could easily time their measurements so that a communication through normal space-time from the first to the second photon would not get there in time. So Einstein concluded that rather than try to deal with mumbo-jumbo it was better to believe in everyday reality and say that even if quantum mechanics was correct and that each photon was "spinning both ways" until measured, each was nevertheless predetermined to come out of its both-way spinning in accord with a determination laid down in some other variable (ideally measurable characteristic that in reality escapes measure).


 * If you do not understand things the way Einstein did, then what are you going to say? One way is to say that even though the two photons are not together in three-dimensional space, they are nevertheless "together" in some other sense, and that the measurement that is made by somebody in some position in three-dimensional space acts as though the photons were in the same space (or the physicist was in both places). That is such a nasty idea that everybody has decided to speak of "non-local" action. Or you can say that when it became possible to actually perform the experiments that would test quantum mechanics people always found the predicted spins, and so one thing that could be concluded (if it suit your fancy) was that our ideas of "locality" were violated. We had previously thought that somebody had to be "in touch with" something to do something to it, and this experiment was definitely upsetting to our belief.


 * What does "counterfactual definiteness" mean? How can that mouthful be "violated"? It's even harder to think about when one says that CFD has been violated. Therefore I am not sure that I know what I am going to try to explain. That being said, it looks to me like it ought to mean "a definiteness as to there being one spin or to there being the other spin that is asserted by somebody but turns out not to be the case." How does one "violate" something like that?! (I'm sure that people who write like that will be able to defend themselves, it's just that I don't like the idea of having to jump through hoops to see what they were trying to say.) Option one was that we had the idea that cause and effect were "local" to each other, and that idea got squashed. Then we could explain the matching of spins by saying they occurred because of "non-local" action. So maybe option two is that we could explain the matching of spins by saying that they occurred because our idea of "realism" got squashed, or our idea that "the lack of definiteness as to spin that we would normally (i.e., outside quantum mechanics) expect" got squashed. Are those supposed to be exclusive alternatives? It seems to me that "locality" is squashed and "total randomness (coin flip) of spin" got squashed.
 * I just discovered that there is an article about this topic. "Counterfactual definiteness" means "the ability to speak with meaning of the definiteness of the results of measurements that have not been performed" .  How can you violate the ability to speak of something that doesn't quite exist yet?
 * Violating "locality" is clear enough. We have an idea that there has to be a chain of physical causation for a change in one place to produce a change in another place. I can push you with my hands, with a pole, or with an electromagnet. But I can't perform a magical ceremony in America and have somebody break his nose in Australia.P0M (talk) 03:41, 26 October 2011 (UTC)


 * What Brian Greene says seems to me to agree with what everybody else says, and you can check out:

http://en.wikipedia.org/wiki/Talk:Quantum_entanglement/Archive_5
 * down near the bottom. Basically his argument is that if you have a system in which more than just one measurement of spin can be made, and you calculate the probabilities both on Einstein's assumption that there is something already decided before either photon is measured, and on the assumption that there are 50-50 probabilities and nothing is predetermined, then you get different probabilities. So if you want to know who is right then you do the experiment and find out how the probabilities work out. Einstein's probabilities turn out to be wrong -- unless you really scratch for possible exceptions. I'm told that nobody takes that idea seriously even though nobody has worked out why the exceptions would not do their intended job.. P0M (talk) 03:45, 26 October 2011 (UTC)


 * Thanks, Patrick! I believe I'm gradually understanding most of what you said, including the crossed paragraphs. I also do feel that "definiteness over locality" (definiteness + nonlocality) is more acceptable than the otherwise (indefiniteness + locality). I will check out Brian Greene's argument too. It's interesting since it's to calculate the "probability of assumptions on probabilities" (one is 100-0, and one 50-50).

Why delete this paragraph ?
The following paragraph is deleted by Myrvin on 15 May 2011.


 * 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.

because it is uncited, and is "reminiscent of Popper's experiment".

I don't agree on the second reason, this is actually very different from Popper's experiment. This paragraph is very important for the readers to have a correct understanding of the principle, however it's probably not very well formulated.

If there is no objection, I'm thinking about putting this paragraph back, by taking the cloud chamber as an example. Measurement of both the position and momentum at a given time to arbitrary accuracy IS POSSIBLE, but a simultaneous measurement is not possible. Adrien (talk) 21:21, 23 November 2011 (UTC)


 * "At a [single] given time" and "simultaneous" can mean the same thing. "At 3 a.m. on 2 December 1874, Marshall Dillon was seen leaving Kitty's Saloon." "At 3 a.m. on 2 December 1874, Festus was seen leaving Kitty's Saloon." It might be, however, that one observer is an eyewitness reporter, and the other "observer" is a photographer who managed to set off his camera and flash pan at the same time and pointed from the outside at the back door. The presence of Festus hightailing it out the back door was not known until the film was developed hours later. In court there would be discussion about how to prove that the film was exposed when the photographer said it was exposed, etc. Of course Adrien Chen's statement also covertly assumes that the act of measuring the position of a particle does not change the momentum with which the particle proceeds to the second observation point where that momentum will be measured.


 * Perhaps what Adrian Chen needs to say is that measurement of the position of a particle at one time and formation of an argument to show what the momentum "must have been" at that time based on an observation or observations made and utilized later are both possible. The hidden assumption operative here is that nothing accelerated the particle between measurement at the time it left the first position and measurement at the time it arrives at the second position. Perhaps the particle has collided with something else along the way or has been subjected to field forces. If it's a photon, then perhaps a solar sized mass has lengthened its path beyond what it would be in interstellar space.


 * Heisenberg was rather imprecise sometimes when he was describing quantum scale measurements because he spoke of "simultaneous" measurements of position and momentum. However, when pinned down, he always spoke of the best that one could do in the real world, which is to mesure one of them and then measure the other one as soon as possible thereafter -- before anything else could happen to mess things up. Once in a while a chance encounter with a gamma wave might knock a helium nucleus around, but the quicker momentum were to be measured the less chance that there would be any such errors in a string of measurements. However, try as you might, you could never get rid of quantum indeterminacy. That uncertainty is introduced immediately upon making the first measurement.P0M (talk) 08:45, 25 November 2011 (UTC)


 * If you put it back, include a "citation needed" tag, and I hope you consider it your responsibility to find a citation. It shouldn't be deleted on the basis of being "reminiscent" of anything. Poppers experiment is not about the effect considered here. Also, this whole scenario can be simplified to the case of a 1-dimensional sphere - that is, an infinite square well, with a particle bouncing back and forth off the walls. PAR (talk) 23:01, 23 November 2011 (UTC)


 * Hello everyone. This was a long time ago. The problem seems to have been raised first by PoM on 15th May. I actually removed the piece on the 3rd June "following discussion". After several weeks nobody had objected. Nothing to the article happened on the 15th May. It was reminiscent of the Popper thing to me, but only vaguely (lots of detectors in a circular shape). The real reason is that it is not cited. It's a longish piece about what the principle is NOT (and has more words than what the principle IS), and has nowhere for us to check the details. Much of the physics articles were/are like this. Uncited, didactic stuff, which I think may be from student notes. Nothing should be added to the article, or put back, without having a citation. This experiment could have been dreamt up by anyone. A cited piece could go after the lead - it's very odd in the lead. Myrvin (talk) 09:48, 24 November 2011 (UTC)

-
 * I think this paragraph can only be regarded as original research unless Adrien Chen can come up with a citation leading to some reputable physicist's peer-reviewed work. The same mention of that physicist's reconstruction of what "really happened" would have to be balanced by Richard Feynman's reconstruction according to which the particle "actually" went by all possible paths. And there is actually a discussion of the cloud chamber idea either in George Greenstein's The Quantum Challenge or in one of Brian Greene's works. I'll have to look for it.


 * The sort of extended Wheeler experiment, the one in which a series of photons are emitted by a distant star, travel a path toward Earth, and are lensed by a black hole so that from Earth we see two stars separated by some distance that are actually the same star, asks: "Which route did any particular photon come by?" If we set up an experiment by aiming one telescope at the star on the right, then we conclude that the one we recorded came by the path we have been watching and not the other path. If we aim one telescope at the star on the left, then we make observations of photons that we conclude came by the other path. But if we merge the inputs of the two telescopes on one detection screen we can observe interference of individual photons allowing us to conclude that the photon traveled by both paths. One conclusion is that the photon obviously came by the path that we observed it to come by, and that therefore the astronomer who makes a decision in the present to cap one or the other telescope, or just to look through one or the other telescope, has retrocausally determined which path was taken by the photon thousands or millions of years ago. The other conclusion is that something went both ways, whatever "ghost" that thing is that can take more than one path at the same time.


 * The fact that we observed something that we claim went by a single path does not preclude the possibility that it went by two paths or any plural number of paths. The act of "observation" determines what we will observe, no?


 * Isn't this the same argument that Einstein had with Bohr? Einstein believed that entangled particles must necessarily have been going to be spin-up or spin-down (or pick your favorite parameter, momentum or whatever) all along because it was observed to be spin-up or spin-down when a measurement was taken?


 * If the uncertainty principle is truly "often misstated" it is interesting that so many highly reputable physicists make that "misstatement." P0M (talk) 15:48, 24 November 2011 (UTC)


 * One difficulty with Adrien Chen's picture is that it assumes "accurate measuremen[s] of position and time." It is logically wrong to assume what you are trying to prove as a basis of the proof. You do not find these "accurate measurements," or else quantum mechanics is fundamentally wrong. Quantum mechanics argues that even after removing experimental measurement error there is an irreducible indeterminacy factor of h magnitude. Between one quantum mechanically fuzzy measurement of position and time to another quantum mechanically fuzzy measurement of position and time it is impossible to determine a single list of "arbitrarily accurate simultaneous positions and momentums" that would give a determinate trajectory.


 * See:
 * Mott problem
 * [History of 20th C. Philosophy of Science] which says: "Therefore, when [Heisenberg] thought that he was observing the trajectory of an election in the cloud chamber, the theory that was deciding what was being observed was the Newtonian theory, not his quantum theory. Then secondly after reconsidering the Newtonian observations and recognizing that it is not necessary to think in Newton­ian terms, he viewed the phenomenon as merely a series of ill defined and discrete spots through which the electron had passed, somewhat like the water droplets which of course are much larger than the dimensions of the electron. Then thirdly he reformulated his problem, and asked how quantum theory instead of Newtonian theory can represent the fact that an electron finds itself approximately in a given place and that it moves approximately with a given velocity.  Using Einstein's thesis that the theory decides what can be observed, Heisenberg concluded that the processes involved in any experiment or observation in microphysics must satisfy the laws of quantum theory.  The magnitude of the observed water droplets suggested room for approximation for the minute electron, and Heisenberg asked whether it is possible to make these approximations so close that they do not cause experimental difficulties.  He then derived the mathematics of the uncertainty principle in which the approximations are governed by a limit that is a function of Plank's constant."
 * [The picture viewed by Gunn Quznetsov] ]\


 * [Albert Messiah's view.] See the footnote on that page. It is copyrighted so I can't copy it here.


 * I had a quick look through the indices of books by Greenstein and Greene, but haven't found the reference I was looking for, so I've patched together what I have managed to find in a short Google search.P0M (talk)


 * I found it. See User_talk:46.147.211.114/Event-probability_interpretation_of_quantym_theory.


 * Here is how I interpret your experimental device, and the problems with it:




 * Stepping away from the cloud chamber and back to the evacuated sphere, the problem with determinate trajectories is that the spatial locations of each charge-coupled device on the inner surface of the sphere are not geometrical points, but instead are (actually rather large) finite areas. The time measurements for the activation of any of these CCDs are also not infinitely small. A helium atom is also indeterminate in regard to its center and also in regard to where its electrons are at any moment. So where the helium atom was when it hit CCD1 and where it was when it hit CCD2 are not determinate measurements. The time measurements will be indeterminate both in respect to the limits of the clock speed, and also with respect to the possibility that the clock pulses are not true square waves and so (in line with other experiments) it would be possible for the detection to be associated with pulse n and/or with pulse n+1. You may find it helpful to review the article on the time version of the double-slit experiment. [Gerhard Paulus experiment] P0M (talk) 00:56, 25 November 2011 (UTC)


 * Having chew around the edges of your paragraph (i.e., the one quoted above), I am still not sure that I have comprehended it correctly. Does the following agree with your argument as far as positions and momentums are concerned?

"We assume that measuring a potential at some CCD at some clock time is close enough to pass for a point event. The fact that we observed a potential on CCD1 at t1 means, under these terms, that we know absolutely the place and time of one contact. But we believe QM when it says that whenever position is known with complete precision, all precision regarding its momentum thereafter is lost. Nevertheless, before long the helium nucleus hits CCD233 at t2. We can calculate from that measurement the direction that the helium nucleus traveled, the time it took to get there, and we can measure the distance between the two CCD devices. We know the mass of the helium nucleus. Therefore we can calculate the momentum that it must have had after it left the first CCD."


 * I'm not saying that I agree with the above argument, just that I believe that I am correctly expanding on what you have said.P0M (talk) 04:40, 25 November 2011 (UTC)


 * After thinking about it, yes, you can establish the position and time of a measurement to arbitrary precision. That means that, for two measurements, you can come up with a very precise measurement of mass times delta x over delta t, but what does it mean to say that that was the momentum of the particle after the first measurement, which was arbitrarily precise in position as well? What you are really saying is that if it were a classical particle, you could have put the detector at half the distance and measured the impact in half the time. But its not a classical particle, you cannot make or prove that statement, and so it means nothing. It is a statement that contains no information. You have not, in fact "measured the momentum" of the particle after the first measurement. You have calculated a number that would have corresponded to the momentum the particle would have had if it were classical and you had measured the position and momentum simultaneously at the first measurement.


 * Please sign your postings.
 * It appears that you and I agree with Myrvin on the paragraph that was deleted—that it should not be re-added. If there is somebody of real standing who has argued for the Adrien Chen's position, then we would have to include it as a genuine point of contention. I think that the original anti-QM argument that sparked the idea of entanglement was changed somewhere along the way to the idea that position could be determined for one mass and momentum could be determined for the entangled mass. It strikes me that this derivative argument and the argument provided by Adrien are similar enough that it might give him some cover. On the other hand, it's a minority point of view even in the original form. Maybe Adrien can come up with a good citation. Meanwhile, there is not justification for putting in something that has the problematical features that we have point to above.P0M (talk) 09:00, 26 November 2011 (UTC)
 * Heisenberg himself has something well worth reading in this regard. See the first paragraph on page 20 of his 1930 book The Physical Principles of the Quantum Theory. It is also in vol. II of The World of Mathematics, p. 1051.P0M (talk) 03:49, 27 November 2011 (UTC)

Problem one
One problem may be that this article does not give the average well-informed reader (or the reader that does not already well understand the subject) a fair shot. Consider the following statement: "Mathematically, the uncertainty relation between position and momentum arises because the expressions of the wavefunction in the two corresponding bases are Fourier transforms of one another (i.e., position and momentum are conjugate variables)." This sentence falls short of being an argument. It is merely an assertion, so the reader has to take it on faith that it would make logical sense if only he/she were able to supply the part that should come next.
 * They are Fourier transforms of one another.
 * AND
 * Fourier transforms of one another are characterized by.....

Also it would be possible to inform the reader that:
 * Position and momentum are conjugate variables.
 * Conjugate variables are characterized by the mathematical property that...
 * Therefore:
 * There must be a factor,f, such that.....

It shouldn't be that onerous to fill this argument out and therefore make it something that a bright high school student could follow instead of an item from the arcanum.P0M (talk) 09:17, 26 November 2011 (UTC)

Problem two
What does this stuff mean? "If the box is mounted on a scale, it is naïvely possible to adjust the parameters so that the uncertainty principle is violated." The discussion about Einstein's box can surely be explained more clearly than that. How on earth is something "naïvely possible"? I don't think anybody at the time thought that Einstein was "naïve." If all it takes to break the uncertainty principle is to be credulous and to mount a box on a scale, it would not be a principle. Maybe this solution to the problem of how to break quantum mechanics comes from the Star Trek world where all you have to do is to "reconfigure the sensor array." Kidding aside, we probably all know where to go to get the real puzzle that Einstein unsettled Bohr with, but what is the average well-informed reader supposed to make of the statement above? P0M (talk) 02:47, 27 November 2011 (UTC)

Experimental Evidence for Violation of the Uncertainty Principle
Recently there has been evidence published in a respected peer reviewed journal (Nature Physics) that violates the uncertainty principle as originally formulated but Heisenberg, but confirms the uncertainty principle as formulated by Ozawa in 2003. I'm not saying this evidence is correct or incorrect, but a mention of this belongs in the "Criticism" section of the article because it is pertinent and current. I provided references to both the recent reference regarding the experimental evidence, as well as Ozawa's formulation published in 2003. I take no position on this argument; readers may judge for themselves. Reebopareebop (talk) 20:02, 9 March 2012 (UTC)Reebopareebop (talk) 20:00, 9 March 2012 (UTC) — Preceding unsigned comment added by Reebopareebop (talk • contribs) 19:56, 9 March 2012 (UTC)


 * I believe the statement is not NPOV as purported here, and thoroughly confusing, indeed, misleading, to the inexpert reader. Ozawa's discussion, in which he finesses the experimental interpretation of Robertson's theorem (which, as a theorem, cannot fail!) and the narrow and naive interpretation of Heisenberg's heuristic discussion,  designed to educate the sceptics of the 20s and 30s, may have a place, perhaps in a separate stub, comprehensible to a patient expert. My point is that the inexpert reader first reads that the general principle cannot be violated, and has the power of a theorem, and then gets hit by a misleading statement that it has already been disproved experimentally, which is downright bizarre. If you had the patience, you might explicate Ozawa's subtlety, in a manner comprehensible to a high-school student, and then, mention in passing that there might be experimental support for the interpretational position. However, as it stands, the section contributes to the article's problematic, and amply sadly justified!, C rating. Cuzkatzimhut (talk) 20:16, 9 March 2012 (UTC)

Sorry, I'm not an expert on the subject. I would be more than happy to have an expert further refine the entry. I'm simply reporting on something relevant to the subject, which in my opinion belongs in the article. Reebopareebop (talk) 20:35, 9 March 2012 (UTC)

Matter wave section?
I'm not going to delete the matter wave section because I don't know enough about it, but I think it may be crackpot science along the lines of Standing Wave theory of Matter. Could someone with more knowledge look it over?

http://www.reddit.com/r/askscience/comments/pqlj4/questions_about_the_standing_wave_theory_of_matter/ — Preceding unsigned comment added by Jabo (talk • contribs) 17:47, 16 March 2012 (UTC)


 * It is not crank, it is just clumsily and ineptly written. It is identical to (and should be merged with) Section 5. Cuzkatzimhut (talk) 18:40, 16 March 2012 (UTC)

The intro is contradictory and the article is potentially fundamentally flawed.
Most physicists nowadays believe the principle is not based on machinery that interacts with particles, yet the intro paragraph postulates exactly that. -- f s  01:42, 4 January 2012 (UTC)


 * What "machinery" do you have in mind?
 * Principles are never based on machinery. We can have, and indeed must have, discussions about some kind of macro-scale apparatus that interacts with particles. By using some apparatus we get indirect information about particles. For instance, humans never see photons. We see a black spot on a photographic plate, a spot that is much bigger than the photon that showed up there. We work backwards from the measuring devices (CCD units in electronic cameras, etc.) to models about photons, electrons, etc. We can then talk about how these never to be seen things, electrons for instance, interact with each other. We can predict, e.g., what would happen if we shot two electrons so that they were on a collision course. But then we have to check on our ideas by looking for spots on film, spikes on meters, etc.—things that are big enough for us to see or otherwise perceive.
 * Perhaps what you have in mind is some discussion like Heisenberg's microscope, a kind of reductio ad absurbum that Bohr criticized Heisenberg for even in advance of its being published. The present article does not assume that any particle has a definite position that is messed up by its being measured.P0M (talk) 06:59, 4 January 2012 (UTC)
 * I think my question is related to this thread. The current introductory description of the uncertainty principle from this article doesn't tell me much.  It's just the (hopefully) commonsense idea that if you measure something, your interaction with it will change it in some small way, and if the thing itself is small enough, that will be a significant change, preventing other meaningful measurement.  I came here looking for whether the principle says anything deeper than that, like what is in the last sentence above (but which is not in the intro).  Is Heisenberg's uncertainty something that is merely practical, due to having to physically interact with what is being measured, or something that is theoretical, a mathematical or logical impossibility?  Can we say that quantum particles even possess single positions and velocities at the same time?  Or can we prove they do not, regardless of our inability to perform such a measurement? 24.57.210.141 (talk) 02:00, 4 February 2012 (UTC)


 * The Uncertainty principle very definitely says something "deeper than that." Determinacy or Certainty is mathematically impossible if you accept quantum mechanics. We cannot then say that quantum particles "possess single positions and velocities at the same time."


 * Science does not prove. It can only disprove. But research can add confirming instances upon confirming instances, which will make people pretty sure that the science is reliable. Quantum mechanics is, I think, one of the most thoroughly confirmed-through-experience theories that we have. So I think it is fair to say that Uncertainty as a fundamental characteristic of the universe is a very reliable idea. It has withstood some very high-class opposition. See below.


 * After working through some of the background of this question, the lead of this article finishes up with the words: "The uncertainty principle states a fundamental property of quantum systems, and is not a statement about the observational success of current technology." What it is trying to say would come across more clearly if people had let Heisenberg have his way and call it the "indeterminacy principle." The reason that things like position and momentum are not determinate is that they are just that way, they are just indeterminate. There is not some problem on the technological side. It is not the case that the electron or whatever it is really has both a position and a momentum that are definite, but that we mess the definite stuff up in the act of measurement. It is a fundamental condition of photons, electrons, etc., etc. that they do not have a position and they do not have a momentum that is definite. There is a kind of fundamental "jitteryness" in the very makeup of things that we cannot get around.


 * Let me try to make that idea a little more concrete. Imagine that somehow we create a bottle that is totally empty (just to reduce the chance of accidental collisions) and put an electron into the bottle. Then we want to determine its position. So we use magnets and/or electrical fields (working from outside the bottle) and we steer the electron into a funnel. The small end of the funnel is just barely big enough for the electron to get through. So we get a very clear idea of where the electron is at that one moment when it is sort of halfway out of the small end of the funnel. The problem is that when we constrain the jitteryness of the position of the electron by cornering it in the funnel we increase the jitteryness of the speed and direction of the electron. So which direction it is going to head off in and at what speed is now much more wildly jittery than it was in the beginning.


 * One could argue about whether the Indeterminacy Principle is true or false, but what Heisenberg's math shows is that if you accept the physics theory that for the first time allowed people to say some very useful things about this world of very small things, then you have to accept indeterminacy. The indeterminacy comes right out of the math. Heisenberg noticed this "problem" while he was creating his Matrix mechanics, and he thought he had just made some funny kind of mistake that he could iron out later. But it turned out that his math wasn't wrong. If you didn't accept the math, then you were back to square one, wondering how you could possibly account for certain characteristics of nature, and, therefore, how you could make the predictions that scientists have to do for very much of modern science and technology. If you did accept the math, then you were stuck with indeterminacy.
 * Einstein could not be at peace with the idea of a universe in which an electron was not going somewhere definite, but was only more probably going one way than another. The EPR paradox was his attempt to defeat Heisenberg's nasty math. That paradox led to the idea of Entanglement, and now humans are beginning to use entanglement because it really occurs. (Einstein thought it couldn't possibly occur and, since Heisenberg's work predicted it, Heisenberg must be wrong.) People thought, for a very long time, that Einstein would have his opinion, and Heisenberg et al. would have their opinion, and that was the end of it. Then Bell came along with the "Bell inequalities" and (except for a few diehards) it is widely accepted as having decided matters in favor of Heisenberg and his group.


 * Bottom line, indeterminacy is real, and no matter how we might try to get around it we won't.P0M (talk) 03:46, 4 February 2012 (UTC)

"Outdenting"

I have to agree with both of the above questioners. The lead, as it is currently written, needs to make a more stark division between indeterminacy and inaccuracy. The word "fundamental" in the first sentence evidently is not strong enough to warn readers away from the thought that the quantum indeterminacy is really an artifact of measurement technologies. "The electron really had a position and momentum, but the measurement messed things up." The "in layman's terms" part leads to misunderstanding.

After it says, "Intuitively, the principle can be understood by considering a typical measurement of a particle," the article goes into a paraphrase of the Heisenberg microscope way of trying to make things "accessible" to people. As Bohr must have foreseen, doing things that way leads to trouble.P0M (talk) 04:19, 4 February 2012 (UTC)
 * I don't see any trouble, it's just wrong. Well, one could argue Newtonian physics are wrong but this is not even Newtonian Physics, it's specifically a Quantum Mechanical subject. -- f s  14:35, 13 February 2012 (UTC)


 * Yes, it should be highlighted in the text that this is an analogy, the actual reason is nothing to do with the measurement. IRWolfie- (talk) 11:58, 9 April 2012 (UTC)


 * By "nothing to do with", I refer to the photon hits particle kind of analogy people have. IRWolfie- (talk) 09:50, 18 April 2012 (UTC)

The fourth paragraph (the one that begins with "Intuitively") describes the observer effect, not the uncertainty principle (people often confuse the two). The change in the path of a particle by scattering light or other particles off of it (observing it) has nothing to do with the uncertainty principle. The entire paragraph is wrong and should be deleted. Hatster301 (talk) 07:26, 2 May 2012 (UTC)
 * I agree. Let's delete it.P0M (talk) 00:19, 4 May 2012 (UTC)
 * I have a better idea. Let's move it down to the last part of the lede, cut it a bit, and state that the observer effect is confused with the HUP, and that this is partly due to Heisenberg himself, who (unfortunately) used the observer effect to illustrate his own principle. That helps the reader begin to understand the debate we've had here. I'll make a first pass at this. S  B Harris 01:05, 4 May 2012 (UTC)
 * It would be a huge mistake to thus sideline or marginalize Heisenberg's intuitive and pedagogical argument. In fact, the only interesting part of the observer effect article is its utility in providing reassurance that "no matter how hard you try, you'll never beat the uncertainty principle". An expert appreciates the UP is a self-evident triviality of Fourier analysis inequalities describing the only correct theory of the world---QM. However, the layman has been finding this counter-intuitive for the last 90 years, and the principal function of this article is to make it more palatable. Rooting out all the "what if"s does not help the layman reader who comes to wikipedia for reassurance. I feel the reader should not get a glimpse of this debate, unless they bother to delve into the talk page.Cuzkatzimhut (talk) 01:22, 4 May 2012 (UTC)
 * If the issue is presented with just enough historical context it should not be too confusing for readers. Heisenberg made his fundamental discovery, he thought of a way to argue against the classical view by starting with the classical view and exposing what would have to happen if the classical view were true. Then Bohr warns him not to publish this argument because it assumes what quantum mechanics denies and because it throws the new students of the subject back into the classical worldview that the new physics is trying to get them out of. I think it would be fair to say that Bohr was correct about the counterproductivity of this approach.
 * It's a little difficult to explain the interaction between Heisenberg and Bohr without cluing readers in to the idea of "reductio ad absurdum." Books can enforce a linear approach to problems. Encyclopedia articles, especially on-line articles, tend to put foundational ideas in as links. Maybe this is a situation wherein it would be appropriate to have a sidebar on Heisenberg's "skill in means" argument? P0M (talk) 02:11, 4 May 2012 (UTC)

Possibly. But a large fraction of the entire article would then have to go into that sidebar... I am not sure the "skill in means" discussion is a quaint historical choice of Heisenberg's, and only meaningful in the context of acceptance of QM. It is just about the first question that comes to mind for most people encountering quantum ideas at first, then and now. As the introduction stands now, it is valid, but there is a condescending whiff of "oh, people were so confused back then"... Cuzkatzimhut (talk) 19:50, 4 May 2012 (UTC)


 * I'm unsure of what you mean by "it" in "It is just about the first question..."
 * To say that "it has since become clear that quantum uncertainty is inherent in the properties of all wave-like systems" is problematical, and perhaps whiffy, because it suggests that neither Bohr nor Heisenberg had figured out that the indeterminacy had more to it than just the observer effect.P0M (talk) 03:55, 5 May 2012 (UTC)


 * The "skill in means" question comes to mind immediately as soon as one first hears about the uncertainty principle: "What is going to stop me from measuring incomeasurate observables?". It is OK to contrast to the observer effect, but the observer effect does not prevent specification of commuting observables. So an acceptable refined version of Heisenberg's microscope argument is appropriate to the introduction. (Not to defocus the discussion of introductory presentation, but if one started fussing, in phase-space quantization, to Dirac's major consternation, QM is operating in phase space, with incommeasurable variables, just fine. It is just the uncertainty principle that prevents unphysical questions, like negative probabilities in the Wigner function: the impossibility to do excessively localized measurements on something one describes all the time. So one can talk and think about x and p at the same time: one should simply bear in mind that measuring them at the same time is bound to fail. Ignore if obscure: it is at the heart of Weyl quantization.)  Concerning the condescension, well, Heisenberg directly all but copied the resolution arguments for waves/light in microscope/telescope measurements——thereby exorcising, with brilliant ironic revenge, cf. his PhD thesis defense debacle. So he most certainly knew about the uncertainty principle in generic wave diffraction, "ultimately". But I don't have the time to reform the wording myself. Cuzkatzimhut (talk) 14:28, 7 May 2012 (UTC)
 * Personally, I don't think that the observer effect even helps to reassure the student that there's no way to getting around HUP. All this does is make the student think that if he can beat the observer effect with some indirect measurement that doesn't affect the system, that THEN he might beat the HUP. This is wrong. The HUP would work even if we guaranteed that the observer did not interact with the observed system at all. It's easiest to see with energy/time conjugate problems, where you see that if you're to get the energy exactly right, the system has to "show" you its frequency exactly, and that takes infinite time to do, since its exact frequency is a statistical problem which, for Fourier reasons, you must take time in order to close in on, as a given value (and it must take time, in order to show itself to you). On the momentum-distance side, you can see that you must let the particle occupy an infinite-volume of space in order to perfectly tell its momentum, for basically the same reasons. If you set space limits, now the particle is forbidden to fit into a longer space or larger volume, and now those wave-modes are gone, and so are their contributions, which are all that keeps the momentum pure (we need all fundamentals to keep the "note" of the sine wave pure)-- this is like the Casimir effect. And since we don't have infinite space or infinite time available to measure particles (even if we never touch them), therefore the HUP. That is all. S  B Harris 18:36, 7 May 2012 (UTC)


 * I think you are right. By "skill in means" above, I meant "telling an untruth that is useful in moving the uninitiated toward a more correct point of view." (It's a technical term from Buddhism, and I should not have used it in this context.) The microscope example is dangerous because it applies some pressure to the reader to accept the Newtonian premises on which it is based. It assumes, for the sake of the argument, that an electron has a position along a trajectory before it is "measured" by directing a beam of photons at the general region where it is expected to be and then picking up the photon that bounces off the electron in a microscope--but giving the electron a kick in the process. Once the reader is given to understand that the electron has a trajectory before it is measured, there is a misapprehension formed that will need to be corrected later.
 * What may be "the first question that comes to mind for most people encountering quantum ideas at first, then and now," is unknown to me. My first reaction was that it is one thing for something to be inaccessible to human observation, and another thing for there truly to be nothing definite there. I think that was Einstein's reaction too. The microscope argument paints the picture of something being there. Bohr saw that kind of assertion as wrong. It is a trap for the reader who is not primed to read it as a sort of RAA argument, something that says, "If you start with classical assumptions and ask what would happen then the result is, even then, that you cannot get both position and momentum. If we are going to say anything about the microscope thought experiment then we need to have the reader contextualize it correctly.P0M (talk) 17:09, 8 May 2012 (UTC)
 * I'm not sure I can contribute more to the debate, to the extent that we are all modeling the mind of a proverbial novice. Someone familiar with QM need not be here, but someone unfamiliar with it implicitly already has all types of classical notions, without formalizing them into sharp categories of trajectories and such, and they really need to be rattled.... "QM is weird", and arguably, after interference, this is the most accessible handle. All the novices I have dealt with start sputtering when the model they already have in their mind runs afoul of the principle... Just telling them to jettison that model, because they can't think about position and momentum in the same breath,  without reassurance, is harsh, and a teaching moment is lost... Eventually, through phase-space quantization, they'll revise that prejudice, but they'll need to be motivated, so, ipso facto, fewer. I'm sure they'll end up picking up the WH microscope elsewhere, flawed or not.Cuzkatzimhut (talk) 18:37, 8 May 2012 (UTC)

Outdenting again.

I have to revise my thought about this problem because I cannot find the source that claimed Bohr to be unhappy with the 1927 paper on the grounds that it implicitly assumed a definite position and trajectory for the electron. I did, however, find a comparatively very complete record of the arguments that centered around this paper in Mehra and Rechenberg's The Historical Development of Quantum Theory.

Probably we need a double strategy, one side to fit the reader whose mind has not been prejudiced by reading inaccurate treatments, and another side to fit the reader who may have already drawn and already have sought confirmation for ideas that will interfere with a correct understanding.

Mehra and Rechenberg indicate that Bohr took the thought experiment in a fully serious way, and only objected when Heisenberg's treatment ignored/overlooked significant features that would crop up in a real experiment.

More later.P0M (talk) 19:34, 8 May 2012 (UTC)

I may have had in mind the last paragraph or two of: http://www.aip.org/history/heisenberg/p08b.htm There is still a problem with using the microscope thought experiment, it's just that Bohr was not making that argument.P0M (talk) 21:02, 8 May 2012 (UTC)

multiple suggestions, edits
I agree with Cuzkatzimhut that this article, despite being of top importance, deserves its sorry C rating. After a long time of not getting around I'm about to make several major edits to this article. The main points to be addressed are as follows:


 * State the dang principle in the introduction! It's important enough that it's the main image in the main quantum mechanics template, yet the introduction manages to huff and puff for 6 paragraphs without a single, mathematical relation.  Compare the Chinese version of the article, which does just that.  The Chinese article is considered a "good article" (a status which I could argue is too high, but whatever).


 * Show some examples! I've chosen the QHO, coherent states, and a particle in a box as the three best examples.  More than three examples may just get too long.


 * This is a physics article, so let there be physics! As it is now, I have to scroll halfway down past a bunch of only somewhat relevant historical misinterpretations before I finally get to the meat of the article, which is currently under the header "Additional uncertainty relations" as if the physics is just an "additional" side note.


 * Delete the redundant uncertainty principle derivations page. The main item of interest there is the Heisenberg uncertainty relation derivation, which can easily be incorporated into the section here with a collapsible box.

Fortunately Wikipedia seems to have gotten better in the last year or so in having random edits with unimportant pop culture references or crackpot garbage. I hope these edits are a step in the right direction, and of course everyone is welcome to improve it more. Teply (talk) 23:51, 9 May 2012 (UTC)

Merger proposal
I propose that uncertainty principle derivations be merged into the main uncertainty principle article. The main purpose of this article, as I see it, is the proof of the Schrödinger uncertainty relation. When the Schrödinger uncertainty relation is proven, the Robertson proof becomes overly redundant. Since I've already put the Schrödinger uncertainty relation proof collapsible box into the main uncertainty principle page, there's not much purpose left for this page. Any of the historical remarks or discussions left over may as well be merged into the main article. Teply (talk) 00:17, 10 May 2012 (UTC)


 * Done. Teply (talk) 06:47, 6 June 2012 (UTC)

Sorry C rating
I too would like to see this article improved. It goes wrong from almost the very beginning, at least from the standpoint of the average well-informed reader who would like to know what the uncertainty principle is really about.

The second paragraph starts out with the words: "The reason for the uncertainty principle arises from the differing eigenstates of non-commuting observables." Anybody who already knows what eigenstates and non-commuting observables are will probably already know quite well what the uncertainty principle is. Anybody else will receive a virtual dope-slap and will take it as an invitation to go away.

Then there is a beautiful image with the citation: "The wave function of an initially very localized particle." To which the most common response will be, "So what?" People who already know will understand what the picture is supposed to illustrate. For others, it will mean nothing unless it is linked in.

Next comes a rather violent twist in the presentation for the ordinary reader who would like to know what the uncertainty principle is about, and not (at the very beginning at least), what it is not: "Historically, the uncertainty principle has been confused with a somewhat similar effect in physics, called the observer effect...."

In the body of the article, the first paragraph starts with some plain old bad writing: "According to the de Broglie hypothesis, every object in our Universe is a wave, a situation which gives rise to this phenomenon." The section title is "Matter wave interpretation." What is the reader supposed to do? Guess about what the writer had in mind when s/he wrote "this phenomenon"? Even if the reader gets lucky and had sort of outlined the article in his/her own mind and so concludes (rightly?) that "this phenomenon" is supposed to be indeterminacy, that is not much comfort because the reader is probably still not clear about what "indeterminacy" or "uncertainty" means. People could even read the sentence as an elliptical version of, "Every object is our Universe is a wave, i.e., it is a situation which gives rise to this phenomenon." Naturally the reader who goes down this false path will probably realize that things are not making sense and so will back out of that path and try another one. But why not avoid the possibility of confusing the reader? Quantum mechanic is confusing enough already, no?

Good writing uses topic sentences that give the reader a clear idea of what the paragraphs that follow each of them are going to prove or otherwise demonstrate. So if one reads only the topic sentences in sequence one should get a summary that indicates the flow of argument of the text, and the substantiations of each of these points should come in the bodies of their respective paragraphs. However, the second topic sentence of the main part of the article has no connection with the first topic sentence. So the article goes from "According to the de Broglie hypothesis, every object in our Universe is a wave, a situation which gives rise to this phenomenon." to "The only kind of wave with a definite position is concentrated at one point, and such a wave has an indefinite wavelength (and therefore an indefinite momentum)." So every object with a definite position is a wave that is concentrated at one point and has an indefinite wavelength and indefinite momentum. If readers already know what the sentence I have just cobbled together means, then I guess it (and the two topic sentences) won't hurt them. But if the reader does not have a mind capable of operating at a highly abstract level, capable of keeping in memory recently stated abstract assertions, and/or lacks the good luck to take all these abstract sentences in exactly the way they were intended, then that reader's reaction is likely to be confusion and dejection.

Forgive me, but the beginning of the next paragraph is not even a properly formed sentence. "A mathematical statement of the [uncertainty?] principle is that every quantum state has the property that the root mean square (RMS) deviation of the position from its mean (the standard deviation of the x-distribution):" I think the writer must have intended the $$\sigma_x $$ in the following line to be in apposition to "the root mean square (RMS) deviation of the position from its mean" and for the sentence to be finished by the $$ = \sqrt{\langle(x - \langle x\rangle)^2\rangle} \,$$ and so forth in the several lines below. Do we really need to burden the average well-informed reader with a sentence that is half in English and half in mathematics?

Then the reader hits the next topic sentence, "The uncertainty principle can be restated in terms of other measurement processes, which involves collapse of the wavefunction." So does "restating" the uncertainty principle involve collapse of the wavefunction? Of course not. It would help a tiny bit if "involves" were made to agree in number with "measurement processes," but I don't think that would keep our intended audience from feeling helically rotated at a rapid rate. (Even the word "wavefunction" may trip up the average well-informed reader.)

I could keep going, but instead I invite others to look at:
 * http://www.aip.org/history/heisenberg/
 * http://hyperphysics.phy-astr.gsu.edu/hbase/uncer.html
 * George Greenstein and Arthur G. Zajonc in The Quantum Challenge, a book written specifically for undergraduate physics, math, and engineering students, pp. 45-50.

For the average well-informed reader, both of the web articles do a better job explaining things than our article does—even though they are from groups that might be expected to take a sort of elitist point of departure. The discussions are crisp and clean in the way their arguments are marshaled and the relevant information is presented. They do not assume that the reader already understands the material. The "Challenge" book assumes a readership of university students most of whom would be physics majors, math majors, or engineering majors. But it does not presume that, e.g., a student who has just finished his/her first year as a physics major will need to be confronted with vocabulary and concepts that go much beyond classical physics and ten hours of calculus.P0M (talk) 07:34, 10 May 2012 (UTC)


 * I've already made some changes to the introduction to soften it since you have last seen it by moving easing into the whole non-commuting observables paragraph. It's still not ideal.  The biggest issue is probably the "Historically..." paragraph, which discusses less what the UP is and more what it isn't.  Perhaps some of this content could get moved below to introduce the "History" section?  Some of that paragraph is salvageable.  The sentence in italics probably does belong somewhere in the main intro.
 * I removed the unhelpful image. I don't even know what it was trying to show.  Was this supposed to be a 2D delta allowed to evolve in free space?  Some replacement image could be warranted.  Maybe you have something like http://hyperphysics.phy-astr.gsu.edu/hbase/uncer.html#c2 available?
 * I shuffled around the existing sections so as to try to avoid spending too much time rewriting the material myself. In this shuffle, I felt that the (badly written) "Matter wave interpretation" section was the most accessible progression instead of just throwing linear algebra and "ten hours of calculus" at the novice.  Yes, it needs to be improved.  The two links you sent are better than this article, and you are welcome to try using them as a model.  Contrast this, however, with the old version of the article, which had both the "History" (formerly "Historical introduction") and "Critical reactions" sections before any physics!  Popper's misguided criticism of the uncertainty principle is more important than the uncertainty principle itself?? Really?! Teply (talk) 16:34, 10 May 2012 (UTC)


 * I've asked Madschen if he can make something that would "grow" the first diagram in time as the viewer watches. If that is possible it should really be instructive.
 * I like the approach in Quantum Challenge because it starts with the concrete and lets the novice reader see what the problem is before math is used to quantify the problem.
 * One thing I think would be very helpful: The fundamental "quirk" in the quantum system was clear to Heisenberg at 3 a.m. or even earlier on the night when he first put things together. He saw that multiplication of pairs like momentum and position were going to be different depending on the order (pq or qp). And with a very short time after Born saw the weird equation that Heisenberg left for him to puzzle over, he had seen that (as our local quantum physics guy put it) "this equation is [a recipe for] the multiplication of two matrices." (This local-to-me physicist had apparently never seen the Heisenberg equation before, but his reaction came immediately upon my showing it to him.) Born not only saw that, but he saw that the difference between pq and qp would be a small number involving i and h as factors. So the fundamental discovery, it seems to me, was implicit in the math from the very beginning. In the beginning Heisenberg was annoyed by it and hoped to get rid of it somehow. So in a strange way the abstract came before the concrete in this case. They had, basically, the numbers and then had to figure out, "What is the deepest significance of these numbers?"
 * Maybe we don't need to go into all of that stuff except to say that the indeterminacy betrayed its existence from the very beginning, and then go on to explain how indeterminacy is experienced in the simplest of measurements that go for both of a pair.
 * In explaining "what you would see in the laboratory," I like what Quantum Challenge has done. In very unsensationalistic language is says that you, the student, might imagine that you could reduce experimental error as much as you could afford to pay for, but that you would then find that there is a limit beyond which no amount of technical finesse will give you a better answer. That discussion is concrete. It is then modified and perfected by giving students the math I think that after the math it would be appropriate to add the information I've mentioned above, the idea that Bohr and Heisenberg would not have accepted the idea that a particle has a trajectory before that particle is measured.But maybe doing so would overload the capacity of the reader to accept novelty. It is very difficult, I think, to accept the idea that something that is completely out of contact with the universe does not have a position. Maybe that part needs to be left until later. It is at times like this that it becomes most clear that the hypertext and multipath way of reading about physics on Wikipedia is different from reading a single-pathway book. But maybe rather than moaning about multi-pathway reading and study I should just make sure that the "particle has no position until..." idea gets an appropriate link in case the reader wants to follow the idea up sooner rather than later.P0M (talk) 00:57, 11 May 2012 (UTC)

Copied from User talk:Patrick0Moran

I'm so sorry about the delay!... I already have images like this on wave-particle duality:

and Schrödinger equation:

Are these good? (of course we can change the captions). I'll produce a diagram analagous to the one you mentioned for the spectrum of superimposed waves that form a wavepacket, if thats wha you're after. Word of caution: as you may know I am NOT an expert, just an undergraduate, and only know physics up to the second year... Again apologies and thank you for your polite and kind words, I just don't get on WP anymore... Maschen (talk) 18:49, 18 May 2012 (UTC)


 * Those are on the right track, but they're missing an important subtlety. The first figure from wave-particle duality shows a pure sine wave, but this is actually an equal mixture of forward and backward momenta.  This should be fairly obvious from the identity
 * $$\psi(x) \sim \sin(kx) = \frac{1}{2i} \left( e^{ikx}-e^{-ikx}\right).$$
 * I see you tried to override this blur with a forward-pointing arrow, but that's not really correct. Don't worry.  It's a very common error for physics students around their second or third year!  Just think of the eigenstates of the particle in a box.  In real space, they are slices of sine wave.  The average momentum, however, must be zero, which is the average of the forward and backward momenta.
 * Really the best way to represent this is to show the full time dependence. This may give readers a better sense of where the momentum is going.  I'd stick to wave packets/pulses to avoid the measure issues of pure sine waves.  You could do a broad packet and a narrow packet, similar to the Schrödinger equation figure.  The plots could then show $$|\Psi(x,t)|^2$$ to keep the domain in the real numbers.  We wouldn't need the ħ → 0 limit because that's really only useful in the Schrödinger equation article's discussion of the Hamilton-Jacobi equation.
 * Check out the wave packet article. This gives an explicit solution u(x,t) that solves the Schrödinger equation given the initial condition of Gaussian*exp(ikt), in other words a Gaussian starting out with a direction.  A movie of $$|u(x,t)|^2$$ would be great for both this article and the wave packet article.  — Preceding unsigned comment added by Teply (talk • contribs) 23:15, 18 May 2012 (UTC)


 * I'm in the process of it now.. please be patient... Maschen (talk) 19:59, 18 May 2012 (UTC)


 * A little distracted and had to do something else, but its done now: is this what you guys are looking for?


 * Uncertainty principle.svg (red) increases the localization of the resultant wave packets (purple, shown normalized). A is the least localized (position of is spread over a large region) while p and λ can be known fairly accuratley. B through D are increasingly localized, but p and λ are not easily known, since λ is not constant and can only be averaged.]]
 * Let me know of any problems... Best, Maschen (talk) 23:04, 18 May 2012 (UTC)


 * New figures as I'm editing! These have the same sin vs. exp problem mentioned above.  They also look really busy. Teply (talk) 23:18, 18 May 2012 (UTC)
 * If they are all completley wrong they will have to be deleted from every single article that has them (I don't have time right now to make modifications - exam period)... (why has no-one deleted them from the linked articles if they are wrong?...). As for File:Uncertainty principle, its just like , but I superimposed them all in one place becuase I didn't want to copy the diagram suggested at that link.Maschen (talk) 00:32, 19 May 2012 (UTC)
 * The figures are not completely wrong per se... A sine wave is indeed a correct solution to the Schrödinger equation.  It's just a bit misleading to show unidirectional momentum from something that's visibly smearing its momentum in both directions.  From the wave packet article: "no matter how narrow the initial wavefunction, a Schrödinger wave eventually fills all of space."  It's also a bit special that the Schrödinger equation gives the time evolution of states with the necessarily imaginary exp(iωt).  In the example above, you can think of the sine wave as a mixture of exp(i(kx-ωt)) and exp(i(kx+ωt)), which is to say a wave moving to the right and a wave moving to the left.  Other wave equations have different solutions (most notably the wave equation), which may be real and often given by more generic sine waves like sin(kx-ωt).  If you're wondering why nobody has deleted these figures from the linked articles, it's for the same reason that this top-priority physics article is still C-rated in 2012.  It's better than no article and better than pseudoscience, but there's much room for improvement.  I'd work on this myself, but I'm not very skilled with movies. Teply (talk) 05:37, 19 May 2012 (UTC)


 * I'll try fix it all later today, be warned I'm no good with animations eiher (simple ones like on my user page is the best I can do...), sorry about this... Maschen (talk) 07:42, 19 May 2012 (UTC)

Here is the Guassian wavepacket, according to your suggestions above. I just decided to show |ψ|2.



Everyone else can usualy create images at the speed of light, it takes me time just to do something simple. Feel free to delete the others. Again I'm sorry I can't help with an animation, but hope this helps... Maschen (talk) 19:02, 19 May 2012 (UTC)


 * OK, I'll try adding that image. I understand it although maybe someone who doesn't can offer more suggestions for clarification?  I also added a movie of my own with the constant momentum example, so that everything stays going in one direction. Teply (talk) 22:48, 19 May 2012 (UTC)


 * As I look more closely at that first non-intro section, I see it tries to develop this from the standpoint of adding together lots of plane waves. Maybe someone more skilled at computers than I am can try to make an animated version of Maschen's figure showing wave packets as a superposition of plane waves? The animation would hopefully show one plane wave at a time getting added to the sum.  If the figure shows cosine/sine waves, be sure to clarify that we're looking only at the real part of the wave function, and that the plane waves are generally the complex exp(ikz).  Alternatively, the figure could show exp(ikz) in the complex plane, with different functions on the complex plane adding together. Teply (talk) 22:58, 19 May 2012 (UTC)


 * One way to draw the wavefunction in 1d, showing the real and complex parts, is to draw a coil of varying ampltiude where the phase of the wave is the angle turned through by the coil. If this is ok and I had the time, I'd draw an image of this type. Not sure if it would help understand the uncertainty principle though... just a suggestion on what you said now. =) Maschen (talk) 16:42, 20 May 2012 (UTC)


 * Could we do something like this? (Only much nicer and with more than just a couple sine wave being superimposed, one by one. I used Inkscape, which lets me draw sine functions but not add the results.)

P0M (talk) 19:49, 20 May 2012 (UTC)


 * I've added a time-dependent example that shows trading off position and momentum uncertainties. It's a bit equation-heavy, but it's worth it for the animation, I think. Teply (talk) 20:14, 20 May 2012 (UTC)


 * Hooray! I made a great superposition principle animation that I think achieves P0M's vision.  I had to learn some code on the way.  There's still some overall formatting issue involving the layout of the new animation and Maschen's figure.  Maybe someone can arrange everything to look pretty? Teply (talk) 21:58, 20 May 2012 (UTC)
 * Congratulations. Another very nice diagram to help novices understand indeterminacy. Elegantly simpler than my construction. Having the waveform appear at the top and drop into the waveform that is already there is intuitively clear. Thanks.P0M (talk) 00:56, 21 May 2012 (UTC)


 * I have left wikipedia (see my user page). At any rate well done and thank you, Teply and P0M - the suggestions made and images created by both of you (and others if they come along) will certianly improve this top-prioty article. Keep up the splendid hard work! =) Best, Maschen (talk) 18:09, 25 May 2012 (UTC)

Suggested addition
The lead currently says: "A pure tone is a sharp spike at a single frequency. Its Fourier transform gives the shape of the sound wave in the time domain, which is a completely delocalized sine wave." A single-frequency sound could be represented by a schematic diagram of a standing wave on a violin string. The location of the wave would be judged by most people to be at the center of the string. A more complex vibration, typical of a note plucked on the string of a fine violin, would show a number of harmonics in addition to the fundamental vibration of the same string, and most people would agree that the "location of the wave" becomes ambiguous because of the presence of multiple peaks of displacement of the string.

If one measured the frequency of the sound produced by such a string, when it was plucked so as to yield no harmonics then there would be activity at only one frequency. But when plucked in another way the string might produce activity at several frequencies. So the question would then become, "Which of these frequencies is the true frequency of this vibrating string?"

The part about the shape of the sound wave in the time domain is, however, too abstract for me to follow it. Could somebody make a diagram or improve the description so that it is clear how a wave can be delocalized in time?P0M (talk) 08:41, 6 June 2012 (UTC)


 * That was one of my edits to soften the introduction to make it more accessible to the non-physicist, who is probably more familiar with sound waves. If you can think of a better way of explaining this to the non-expert, by all means make the change! Teply (talk) 07:24, 10 July 2012 (UTC)

WRONG? Quantum harmonic oscillator with Gaussian initial condition
Working thru the math, I get for the position wavefunction


 * $$|\Psi(x,t)|^2 = \mathcal{N}\left( x_0 \cos{(\omega t)}, \frac{\hbar}{2 m \Omega} \left( \cos^2{(\omega t)} + \frac{\Omega^2}{\omega^2} \sin^2{(\omega t)} \right)\right)$$

(sin and cos terms in the variance terms are squared). Can someone check this? PAR (talk) 06:17, 11 July 2012 (UTC)
 * Yes, typos copied wrong from my notebook. Fixed now.  I'm glad to see readers out there interested enough to work through these problems on their own and not just take my word for it. Teply (talk) 17:51, 15 July 2012 (UTC)

Spelling, taking a bath at least once a month, etc.
I found this page riddled with solecisms, including hyphens where en-dashes belong – one of them prominently displayed in a section heading – indiscriminate italicization of non-TeX mathematical notation, as in c=1/2 rather than c = 1/2 (and it lacked proper spacing before and after "=") and p0 instead of p0, and other things. Please note that WP:MOS and WP:MOSMATH both exist. En-dashes are used in ranges of pages, years, etc., and in things like Bose–Einstein, and in parenthetical offsets like the one in my first sentence above. Mostly fixed now, I hope. Michael Hardy (talk) 19:14, 6 September 2012 (UTC)

New experiment weakens observer-effect explanation. Fourier version is the correct one.
Poor Heisenberg's heuristic takes one on the chin, as a new direct experiment suggests again the Bohr interpretation of this principle as indeed a simple Fourier uncertainty limit for de Broglie waves in wave-mechanics (or an oscillating psi function with time in any quantum system), and not the result of an observer effect (at least for photons alone). . S B Harris 23:04, 16 September 2012 (UTC)

Possible typo?
Re: Under the images of the plane wave and wave packet, the paragraph beginning "Propagation of de Broglie waves...," ends with the sentence: "As the amplitude increases above zero the curvature decreases, so the decreases again, and vice versa..." 'so the decreases again' might be missing a noun?

Hpfeil (talk) 17:39, 18 September 2012 (UTC)


 * Fixed, also done at Schrödinger equation (Particles as waves). Maschen (talk) 18:08, 18 September 2012 (UTC)

Section on aesthetics and philosophy
The section on aesthetics and philosophy at the end of the article seems to be very much on the fringes. The publishers of two of the cited sources (C. Winter and AMS Press) do not seem to be reputable and, in any event, seem to be used as primary sources to produce a novel synthesis. The last source seems to be placing undue weight on a viewpoint that is outside of mainstream scholarship on the philosophy of science. (Indeed, he even seems to conflate "relativity" and "indeterminacy".) I would suggest that the section be deleted in its entirety. This can always be spun out afresh from more reliable sources on the philosophy of science, but I don't think anything is worth saving at the moment. Sławomir Biały (talk) 18:12, 4 November 2012 (UTC)

Unhelpful animation ?


This animation seems to me to be helpful because it gives a clear example of the uncertainty principle : when the position is determined with excellent precision, the momentum can't be. Thierry Dugnolle (talk) 09:32, 11 November 2012 (UTC)


 * Nice work! Maschen (talk) 11:12, 11 November 2012 (UTC)

Thank you. When I knew it had been removed a few months ago, I was disappointed. It was designed especially for Wikipedia. Thierry Dugnolle (talk) 12:00, 11 November 2012 (UTC)


 * Indeed, it is very nice. It certainly would be a prized asset to Wave packet. Here, I am not too sure it is useful to the novice, especially without the term "free Gaussian wavepacket" in the caption. The spreading is an illustration of runaway increasing uncertainty, when, really, a fixed uncertainty rates just fine. Frankly, a perverse undergraduate could ask how come this free wavepacket illustrates the uncertainty principle, but a non-spreading gaussian wavepacket does not in a harmonic potential--a harmonic oscillator coherent state ? It certainly comports with the uncertainty principle, and has the feature that its uncertainty in fact is not constant but grows with time! But unless the student consults with the wave packet section, its illustration of the uncertainty principle is not quite direct, so it mystifies more than it illustrates. My sense is that a cogent, sound paragraph in the text would help.  Cuzkatzimhut (talk) 20:32, 11 November 2012 (UTC)

The uncertainty principle is here about the initial time. See new caption. One way to measure momentum is to measure positions at two different times. This is true both in classical and quantum mechanics. Knowing the initial position, the dispersion of the second position, given by the wave packet, is also a dispersion of the initial momentum. Thierry Dugnolle (talk) 21:56, 11 November 2012 (UTC)


 * If you could possibly reduce the file size, this would be highly preferable. The information in this GIF is really pretty low. At nearly 12MB, an unwary reader clicking on the thumbnail may get an unpleasant bandwidth cost (and download delay) surprise. Secondly, is the initial position in fact known with certainty (a Dirac impulse?), or simply highly localized? Is it in 2d or 3d? My (very much untrained) intuition suggests that for a perfectly localized particle, the momentum spread would be infinite, and the expected energy would also be infinite. This kind of insight should be accessible the beginner. If it is merely highly localized, a lesser initial localization with consequent slower spread may be easier to follow. — Quondum 00:46, 12 November 2012 (UTC)

See new caption. Not a Dirac impulse but a very narrow gaussian packet in a two-dimensional space. Thanks for the suggestions. Thierry Dugnolle (talk) 09:57, 12 November 2012 (UTC)


 * I've modified the caption again. I expect the diagram will be qualitatively different according to whether the initial localization makes the wavepacket relativistic (energy spread large compared to the particle rest mass), intermediate (comparable) or cold (much less than particle rest mass). I suspect that this is the comparable case. It might be worth mentioning this parameter, at least in the description associated with the file. — Quondum 12:01, 12 November 2012 (UTC)

The animation makes visible a solution of the Schrödinger equation for a free particle. This is not relativistic quantum mechanics. Thierry Dugnolle (talk) 12:31, 12 November 2012 (UTC)


 * Oops. My bad. (I always did prefer the Klein–Gordon equation...) — Quondum 13:19, 12 November 2012 (UTC)


 * I still think it is useful to emphasize that the uncertainty of this wavepacket, ΔxΔp, asymptotically, is increasing linearly in time, as detailed in the actual more descriptive explicit formulas for it in the article Wave packet, in which this figure also belongs. Of course, there, they cover only 1- or 3d gaussian wavepackets, but the suitable prefactor is self-eident. Cuzkatzimhut (talk) 15:52, 12 November 2012 (UTC)

Proven measurement-disturbance relationship
Does somebody has an idea why the inequality $$\sigma_p\Delta x\geq\pi\hbar$$   (Found. Phys. 2009) has been removed from the article? It is new, sharp (i.e. cannot be further improved), it is different from the inequality of Kennard and Ozawa, and very closely related to the original measurement process considered by Heisenberg and Bohr. --Zetafun (talk) 12:05, 2 December 2012 (UTC)
 * Isn't it the same as the Ozawa inequality, only adapted to a particular single-slit experiment? Let $$\eta_p=0$$ and $$\epsilon_x=\Delta x /2 \pi$$.  I think I might have removed it in favor of the more universal Ozawa one just because the article was getting a little long and the single-slit example seemed a little more specialized.  Maybe it's OK to put somewhere, at least as a reference. Teply (talk) 04:31, 3 December 2012 (UTC)

As far as I can see, all expressions of "uncertainty" in Ozawa's inequality are mean-square-errors, i.e. they are statistical expectation values. In contrast, the symbol Δx defined in [http://link.springer.com/article/10.1007%2Fs10701-009-9310-0 Found. Phys. 2009] is an interval but not a statistical expectation value. Therefore, any algebraic identification of Ozawa's εx and Δx is non-admissible since both are different measures of uncertainty. For that reason, the expression $$\sigma_p\Delta x\geq\pi\hbar$$ cannot be a special case of Ozawa's approach. Moreover, their corresponding measuring processes are different too.

Actually, the inequality in [http://link.springer.com/article/10.1007%2Fs10701-009-9310-0 Found. Phys. 2009] is created for particles "disturbed" by the "von Neumann-Lüders" projection to the support Δx. Applied to the ordinary single-slit setup it encourages the original measurement process of Heisenberg and Bohr, but not the measurement process corresponding to Kennard's inequality. For that reason (imho), the inequality $$\sigma_p\Delta x\geq\pi\hbar$$ should be introduced directly after the Kennard's. I don't think that one could break this bound, because all expressions specified therein are well and unique defined and leave no space for misinterpretation. --Zetafun (talk) 07:16, 3 December 2012 (UTC)


 * Isn't the relation between εx and Δx roughly like how you can express the standard deviation of a uniform distribution in terms of its width? Anyway, I disagree that this should be presented right after the Kennard inequality.  This is a rather long article viewed by many students learning QM for the very first time, many still struggling with the concept of σ all by itself.  Putting this near the top is very likely to cause mass confusion.  It can maybe go somewhere, I suppose, possibly around where the Ozawa is placed.  There's also been some discussion (and inaction) with regard to moving some of the other stuff in that vicinity to unclutter (move most entropic uncertainty stuff into entropic uncertainty and the harmonic analysis stuff possibly into its own new page). Teply (talk) 12:17, 4 December 2012 (UTC)

Let me try to elaborate the difference of both measuring processes in a few words. Therefore, consider the normalized wave function ψ of a particle: 1. The disturbance caused by the Neumann-Lüders projection gives a normalized state φ, which is non-vanishing only in the interval Δx, but zero outside. Then, the root-mean-square error of the momentum is computed with the state φ, but not with ψ. Thus, this measurement process is sequential, corresponding to the original concept of Heisenberg and Bohr, but not to that of Kennard.

2. As far as I understand your argumentation (i.e. ηp=0), the noise-disturbance εx is computed for the state ψ (maybe with a result = Δx/2π), while the root-mean-square of the momentum is also computed for the state ψ. This measuring process is not sequential but corresponds to the situation originally considered by Kennard, except that here we consider the measure εx instead of σx.

For that reason, the case 2. cannot be a formal representation of the original (sequential) measurment process of Heisenberg and Bohr. In my opinion, the argumentation in his original work on page 9 was a (merely) adequate attempt to prove his own fundamental principle with help of the formal framework of non-sequential measurements. Therefore, I do not agree to say that Heisenberg was wrong. -- Zetafun (talk) 06:29, 9 December 2012 (UTC)

These new findings ...
... should be added in this article: http://lanl.arxiv.org/abs/1208.0034 85.179.68.53 (talk) 22:43, 18 November 2012 (UTC)


 * Totes agreement. There's actually more in the news on this topic now; the experiment has been replicated reliably with photons.  March 3rd 2013: http://www.sciencedaily.com/releases/2013/03/130303154958.htm  I think this has been in the news long enough that some mention might be in order, but I'd prefer to defer to experts in the field. TricksterWolf (talk) 23:22, 6 March 2013 (UTC)

Clarification
There is a sentence in the Many-worlds interpretation article stating the following: &ldquo;For example the uncertainty principle specifies that an observer cannot know all properties of a particle, but nevertheless the particle itself does have those properties&rdquo; – is this an invalid (ignorant) statement that is derived from the observer effect and a way that Heisenberg tried to explain the uncertainty, or is it actually true? If it is correct, would it be okay to state such clarification in this article? BeŻet (talk) 12:22, 23 January 2013 (UTC)

Important Pt ?!
Doesn't HUP say that Neither variable such as position and momentum can be absolutely precise since the inequation qx * qp >= h/2 means that neigher qx nor qp can be zero b/c that would violate the inequality since zero is less than h/2 ? So both position and momentum can NOT be absolutely precise at a point in time! Right? — Preceding unsigned comment added by 98.246.218.103 (talk) 06:39, 10 March 2013 (UTC)

Classical Uncertainty
There should be a treatment on wikipedia and a referance here on classical uncertainty and its relationship to quantum uncertainty through the Planck limits. Though I am not familiar enough with the issue enough to supply referances a description of it should be familiar enough to someone with expertiese to do so.

The classical uncertainty with motion can be illustrated by imagining measuring a car's motion through a mile distance, which is assumed to continue constantly beyond the mile, by sampling its location in several places in a one mile distance. If we measure its location as 0 at time 0 and one minute later at location 0+1 mile (two samples) we cannot be certain of its speed beyond the measured mile because it may be accelerating in the measured mile. Since any acceleration can be accelerating it can have an infinite number of accelerations of accelerations still resulting in the samples of 0 at time 0 and one minute later at location 0+1 mile. We therefore would need an infinite number of measurments in the one mile distance to be certain its future position based on its motion in the mile. As Planck limits the number of samples to finite due to the planck length measurment limit we cannot have infinite samples. Therefore, even if there were a mathematical treatment solving for the infinite samples requirement of classical uncertainty, due to Planck limits we can never physicaly satisfy the infinite sample requirement of classical uncertainty.

98.164.120.241 (talk) 21:39, 20 April 2013 (UTC)

Information for the Curious Public
This article has become so elite and obtuse that a casual browser can no longer find simple expressions for momentum and energy uncertainty. I would not dare tamper with all that abstract math even myself. But someone should fix it pronto, or Wikipedia will no longer be the goto source. Rlshuler (talk) 02:27, 24 April 2013 (UTC)


 * Agreed. When an introduction section is not an introduction, what is the general reader supposed to do? P0M (talk) 17:12, 24 April 2013 (UTC)


 * I'm only in partial agreement. I think the preamble and the introduction outline quite well what the principle is about, and the math that follows is actually useful to a physics undergraduate, or a graduate engineer. I think using the σ for the standard deviation is appropriate for a statistical theory, and somebody unfamiliar with quantum mechanics should not expect to bypass it or pick it up with this as the gateway article, and thus the slippery use of Δ is deprecated--soundly. I tried to at least steer Rlshuler to the time-energy relation by boldfacing it, but i agree with him that it is not usable as it stands, except to somebody who understands QM. Note however, there is an entire semi-sound discussion of that principle, as a separate section, which is now commented out in the editing input, presumably by dint of the inability of someone to clean it up with suitably qualifying and explanatory words. The math is just fine and should be left alone. I think the Encyclopedia Britannica should not be dismissive of it! Cuzkatzimhut (talk) 18:55, 24 April 2013 (UTC)


 * I commented it out because it no longer flowed with the structure article though it had some gems possibly worth retaining. For one, the section is a bit more historical/quotational than mathematical.  That doesn't mean the content isn't encyclopedic.  Historical information is fine.  But when a paragraph begins, "One false formulation of the energy-time uncertainty principle says..." or the next, "Another common misconception is..." you might begin to wonder whether you're confusing the reader.  The main point is what the time-energy uncertainty relation most commonly seen in practice is, not what it isn't.  You can maybe try moving some of the commented out part to the history section at bottom.  For that matter, the history section as a whole could use quite a bit of revision, and much of "Critical reactions" doesn't even address the specific topic of UP. Teply (talk) 23:07, 24 April 2013 (UTC)


 * I see your point. Yes, the stuff is tetchy and formulaic. I wonder if, with suitable weasel words to make things inoffensive, chunks of it could be salvaged. I might make an effort, but only as a start for someone else to improve on. I agree the cultish attachment to history is a bit much. Another option is for somebody, not me, to move the remainder to a separate stub on time-energy uncertainty.... Cuzkatzimhut (talk) 23:37, 24 April 2013 (UTC)

Yep, the level is wildly wrong for WP. WP articles are supposed to be written for a general audience. There are plenty of treatments of the uncertainty principle out there that are understandable to a lay reader.--75.83.76.23 (talk) 00:00, 18 May 2013 (UTC)


 * I'm sorry, you lost me on this one. Are you still talking about the time-energy uncertainty relation, which, basically has no business reaching a non-techncal audience, or the entire article? I think the level of the overall article is just fine. It has enough for the nontechnical audience in the preamble and the introduction, and it makes it clear that this is a logical property of quantum mechanics encoding its weirdness; it then goes on to address things at a quantitative undergraduate level; and it hints at extensions a graduate student might be motivated to pursue independently, having gotten an honest impression here. What the article should not do, under any circumstances, is help erect a pagoda of bullshit verbiage for an innumerate layman pining for bogus revelation. Popular books on science, strings, etc... without mathematical honesty are already blithely performing this unwholesome and corrosive function, and one could discern no well-meaning reason to drag WP into that. In fact, if you look at the history of the article, it already has been saved from that ugly morass at least once, last year--a solid "thank you to Teply! I seriously hope you are not adducing WH's refs in the next section as helpful introductions to a lay reader. Cuzkatzimhut (talk) 00:35, 18 May 2013 (UTC)