Talk:Uncertainty principle

New stuff goes to the bottom, not up here

_____

More General Scope, Less Derivations

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

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

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

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

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

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

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

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

I am totally opposed to deleting useful material for cosmetic purposes or because it's "too abstruse". If it is too detailed or abstruse for one article, it should go into another article or into its own article. PAR (talk) 17:49, 8 August 2011 (UTC)

I don't really approve of the way the content has been reorganized. The article currently fails even to mention the uncertainty principle in harmonic analysis, and it fails to convey adequately the uncertainty principle for two observables other than the position and momentum. All such information has now been ghettoized to the no-man's land of Uncertainty principle in harmonic analysis and Uncertainty Principle Derivations (the existence of which violates our MoS to boot). Basic summary style should be observed in this top-level article: summarize the more advanced content here as well.

Moreover, the basic version of the harmonic analysis result is now very difficult to motivate, whereas before it was just the uncertainty principle for the operators x and p=d/dx obeying the canonical commutation relations (although maybe that could have been emphasized more). The section on derivations included this as an example, but that example seems to have been cut from the exposition. Sławomir Biały (talk) 11:46, 9 September 2011 (UTC)

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

Totally agree - The Heisenberg uncertainty principle and the "Harmonic uncertainty principle" are identical when the two complementary quantities are Fourier transforms of each other. Heisenberg was the first to derive the "Harmonic uncertainty principle", wasn't he? This removal was done by someone who thought that the "Harmonic uncertainty principle" was some disconnected concept that happened to have the same name. The principles that followed were variations on a theme. I will restore the section soon unless someone has a better idea. PAR (talk) 03:56, 10 September 2011 (UTC)

No, Heisenberg didn't derive it from harmonic analysis because Heisenberg was not happy with wave mechanics in general. He had his microscope example, but it was actually Bohr who pointed out to him quite early that if one accepted de Broglie waves (where particles are just wavelets with a Born interpretation of where they are) then Heisenberg uncertainty follows directly from harmonic uncertainty (long known before quantum mechanics). It's a property of any wave, and as soon as you posit "matter waves" with h as the link between wavelength and momentum, then Heisenberg uncertainty follows immediately for matter waves also. Heisenberg was not pleased by that, but the uncertainty relation has been derived in QM books from harmonic analysis (rather than how Heisenberg did it) for a long time. Fermi does it that way in the Fermi Lectures, for example. It's not a "measurement problem". It's a CONSEQUENCE of wave behavior. To the extent that you believe in wave behavior, you must believe in "HUP". SBHarris 20:53, 24 November 2011 (UTC)

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:

Sorry that the green wires from CCDs to clock are too thin to show up well.

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)

Why is this article still graded "C"?

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)

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. --fs 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. --fs 14:35, 13 February 2012 (UTC)