Talk:Uncertainty principle

Old discussions have been archived at Talk:Uncertainty principle/Archive1

A quick question

What would happen if there were two observers measuring an partical,lets say one observes it's momentum and one is measuring it location? 69.4.149.231 02:23, 17 October 2007 (UTC)Regards 69.4.149.231 02:23, 17 October 2007 (UTC)Peter

Big rewrite

I just rewrote the whole article. An annotated version can be found on my user page, explaining all the changes. (I'm worried I may have messed up the cross-references to the article in other languages at the very bottom...someone with the appropriate fonts installed should revert that bit.)

I had to delete a paragraph about the history, since it wasn't in the history section and I don't know enough about the history to fit it smoothly and correctly into that section. Someone more knowledgeable in that regard should see if there's anything worth salvaging in that paragraph, again as indicated on my user page. I also think there should be various notes or a section about which statements in the article are only true nonrelativistically, and maybe what happens in the relativistic regime. I know QFT, but not with enough confidence to do that myself. Steve 14:59, 16 June 2007 (UTC)

Misplaced jokes in humor section?

I'm no physicist, but don't these two jokes relate to the observer effect and not to the uncertainty principle?

An episode of the popular Matt Groening cartoon "Futurama" features the crew of the Planet Express at the horse races. Professor Farnsworth exclaims angrily after his favored horse loses in a "quantum finish" "No fair! You changed the outcome by measuring it!".

Another example is "How many Physicists does it take to change a light bulb?" "Only one, and all the Physicist has to do is observe the light bulb and he changes it."

If You can verify that they are misplaced then please fix this.

Regards, Lars

The uncertainty principle is often explained incorrectly as the observer effect, so I'd vote keeping those in. Can I please put the futurama quote back? Genious. Fresheneesz 08:30, 20 April 2006 (UTC)

Rewrite

I Skimmed the rewrite. The additions and corrections made to the later sections look good. However, I found the intro a bit muddled. In the very first example of making measurements, one should state very early on that it is impossible to measure the system without disturbing the state of the system. Concretely, quote the Heisenberg microscope (what redlink??): to measure the electrons position, one uses a photon. Bouncing the photon off the electron changes the electrons momentum. Alternately, one might measure the electron's position by using a pinhole, but in this case, the electron will diffract off he edges of the pinhole (so even if one envisions the electron as being a finite-sized billiard, rather than a wave, there is a real chance that the billiard will bounce off the edges of the pinhole, and change direction. If these things are not stated, the reader is left thinking "screw the theory, tell me why not". (Which is how crank science starts: not only do the cranks reject the theory, they are also blissfully unaware of simple experiments that disprove their claims.) So I propose anchoring the intro discussion in experimental details. linas 15:53, 22 December 2005 (UTC)

• First of all I'm not exactly thrilled that you archived the "talk" since I just added some new information.

Sorry, it all looked like old discussions. Your diffs looked like spelling corrections. Please pull out anything that is still relevant. linas 17:37, 23 December 2005 (UTC)

Secondly, the introduction of this article on the uncertainty principle specifically states that your idea above is not a proper definition and in fact is a fallacy.

Lets not be so inflamatory. I was trying to make a constructive comment.

The website [1] describes your Heisenberg microscope and says, "Looking closer at this picture, modern physicists warn that it only hides an imaginary classical mechanical interaction one step deeper, in the collision between the photon and the electron. In fact Heisenberg's microscope, although it was a big help in developing and teaching the quantum theory, is not itself part of current understanding. The true quantum interaction, and the true uncertainty associated with it, cannot be demonstrated with any kind of picture that looks like everyday colliding objects." Therefore, in this article we should stick to the exact facts of the Heisenberg Uncertainty Principle and we should not use any invented analogy that is contrary to current understanding.

While I agree with this quotation, this is not how the article is currently written. It spends several paragraph talking about "experiments" and not theory. Insofar as its focused on experiments and measurement, you objections are obviated. If instead the article was re-written to focus on the theory, then this would be a legit complaint.

Heisenberg's theory is not about the collision of a photon with a particle. That may be an easier thing to understand, but that is not what Heisenberg was saying. What he was saying is so completely counter-intuitive that it cannot be illustrated with a thought experiment of any kind. The closest one can come to any kind of approximation to "macro" reality is to use the analogy of a wave that is already included in the article. It is important to be accurate in an encyclopedia. --Voyajer 21:28, 22 December 2005 (UTC)

FWIW, I have a PhD in quantum mechanics, and more precisely in quantum field theory, and have spent a bit of time on the history of quantum mechanics, including Einstein and EPR, and the measurement problem, and so feel very comfortable with these things. From that perspective, I felt that the the chit-chat in the introduction about "experimental errors" and "experimentally measuring" things is mis-leading. It can be fixed by removing these paragraphs entirely, and replacing them by a theoretical discussion of Pontryagin duality, which is the "modern" understanding of the uncertainty principle. The other tack is to add discussions of actual experiments. Larmor precession is a great example of the uncertainty principle at work; however, it is far too complicated an example for this introduction; that's why the Heisenberg microscope, despite the protestions above, is a good example. linas 17:37, 23 December 2005 (UTC)

• • In truth Einstein did say "screw the theory, tell me why not", but it didn't get him anywhere. This is because Heisenberg's Uncertainty principle is not normal. It is not logical. It doesn't follow any previously known physical laws. It seems almost arbitrary. It even feels wrong. If it were so simple to explain and understand as the illustration of Heisenberg's microscope, then Einstein would not have had a problem with it. Einstein had a problem with it because it really isn't explainable nor understandable. Heisenberg was making an unprovable assumption to get around the difficulties he was having in his observations of the atom especially using spectral line patterns, spectroscopy. Because Einstein knew that the theory was in many ways arbitrary, just a way of fudging the values so that some approximate number could be achieved when an exact number could not be known, then for this very reason Einstein rejected the idea. However, when you take an observation of nature and fudge a formula to fit it, then experiments made on nature are going to represent your formula and even appear to prove your formula. This happened with Planck's constant. He fudged the math to match the observed data. The thing is that Heisenberg's principle works because he only used observations of the atom that humans could detect in order to create it. Therefore, of course it's going to work. This doesn't make it a bad theory. It makes it a useful theory. Einstein objected because in all probability there is another way to explain things. But as far as we know so far there is no other theory as useful in making measurements of quantum particles. Werner Heisenberg himself said, "`I myself . . . only came to believe in the uncertainty relations after many pangs of conscience. . . ." He knew what he was saying didn't make sense, but it helped measurements at quantum levels so much, he did it anyway. Richard Feynman, another major contributor to quantum theory said, "We have always had a great deal of difficulty understanding the world view that quantum mechanics represents. At least I do, because I'm an old enough man that I haven't got to the point that this stuff is obvious to me. Okay, I still get nervous with it.... You know how it always is, every new idea, it takes a generation or two until it becomes obvious that there's no real problem. I cannot define the real problem, therefore I suspect there's no real problem, but I'm not sure there's no real problem." He meant that he understood QM very well, but that in 1982 some 50 years later, he still couldn't reconcile himself to it. That is why Einstein spent the entire rest of his life trying to disprove the Uncertainty Principle so that if anyone does say "screw the theory" after reading this article, then they better be smarter than Einstein and invent a better theory because at present, this one is working.--Voyajer 21:39, 22 December 2005 (UTC)

The uncertainty principle in all of its quantum weirdness

To explain further QM, especially the uncertainty principle, I will use a simplified anthropomorphic illustration of electrons in orbits around the atom applying the principles of uncertainty and QM to show how "strange" strange really is. First, let's start with the retained QM features of the Bohr atom model. Imagine an electron as a person, in fact, say you are the electron and you are running around a circular track about 10 feet wide. There is another inside track in further from your track by another few yards. This inside track is also 10 feet wide. There is a refreshment stand at the center of the track which is the nucleus and although you are attracted to it, the probability of you ever being able to get to the refreshment stand is zero. No can do. You are using up more energy to do laps running on the outside track, so you want to move to the inside track. However, the probability of you being able to cross those few yards to the inside track is zero. Therefore, you pull out your handy triquarter and say, "Beam me up Scotty," and you are instantaneously transported to the inside track. (quantum leaping) Another weird thing is that if someone is looking at you (but not measuring where you are), they think they have very blurred vision because you seem to be blurred across the whole ten feet of the track. Most of your body is concentrated at your position, but the rest of you is stretched out across the track.

user:kevin aylward this is simply not correct. Objects are not "smeared" out. Such an assumption disagrees with experiment. I won’t go on, other than that you need to read some graduate level text books. Unfortunately, popular writings for laymen invariable talk waffle.

(uncertainty) Now there is another guy who comes along and wants to run on the inside track with you. You look at him and you see that he is identical to you in every way. In fact, no one looking at either of you can ever tell you apart. (indistinguishable particles) Now he starts running on the inside track with you but in the opposite direction. (spin) He is also spread out over the 10 foot width of the track and is fuzzier and less distinct toward the edges of the track. All of a sudden, you decide to turn around and run in the same direction he is running. But as you turn around, he turns around too as if reading your mind. This happens every time. (quantum entanglement) --- I could go on, but this should be weird enough. The true facts are that the track would describe a sphere and you would be stretched out all over the sphere at once which is even harder to imagine. Not only that, but you would be standing still (standing wave) and moving at the same time (angular momentum). That is why Bohr said "if you don't think QM is strange, you haven't understood a single word."

I love what Einstein had to say about all this:

• (after Heisenberg's 1927 lecture) "Marvelous, what ideas the young people have these days. But I don't believe a word of it."
• "The Heisenberg-Bohr tranquilizing philosophy - or religion? - is so delicately contrived that, for the time being, it provides a gentle pillow for the true believer from which he cannot very easily be aroused. So let him lie there.

Further, the fact that Einstein didn't like uncertainty didn't mean he wasn't still a brilliant genius. In fact, the challenges that Einstein brought to QM have transformed it and tweaked it and refined it.

My personal favorite anachronistic quote about QM is the ironic fact that it came out of Copenhagen in Denmark and Shakespeare said in Hamlet as if speaking of QM itself:

• "There is something rotten in the state of Denmark...There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy."

--Voyajer 16:51, 23 December 2005 (UTC)

Why Heisenberg's microscope is not used in article

It was said above:

While I agree with this quotation, this is not how the article is currently written. It spends several paragraph talking about "experiments" and not theory. Insofar as its focused on experiments and measurement, you objections are obviated. If instead the article was re-written to focus on the theory, then this would be a legit complaint.

FWIW, I have a PhD in quantum mechanics, and more precisely in quantum field theory, and have spent a bit of time on the history of quantum mechanics, including Einstein and EPR, and the measurement problem, and so feel very comfortable with these things. From that perspective, I felt that the the chit-chat in the introduction about "experimental errors" and "experimentally measuring" things is mis-leading. It can be fixed by removing these paragraphs entirely, and replacing them by a theoretical discussion of Pontryagin duality, which is the "modern" understanding of the uncertainty principle. The other tack is to add discussions of actual experiments. Larmor precession is a great example of the uncertainty principle at work; however, it is far too complicated an example for this introduction; that's why the Heisenberg microscope, despite the protestions above, is a good example. linas 17:37, 23 December 2005 (UTC)

The first argument above is that since the article focuses on experiments and not theory and therefore Heisenberg's microscope should be used. This is a non sequitur argument. Heisenberg's microscope is theory in the form of a thought experiment whereas Heisenberg's Uncertainty Principle was based on actual experiments of actual measurements. It was through spectroscopic analysis that Heisenberg invented matrix mechanics which for the first time expressed the uncertainty principle in the form of the famous commutation relation of matrix mechanics. And as linas has said that he agrees with the statement that Heisenberg's microscope "is not itself part of current understanding" as he says above, yet he still insists on using it in the article which he himself says is not based on theory whereas Heisenberg's microscope is wholly based on theory and is not a real experiment in any sense of the word.

Linas says above that 'the introduction about "experimental errors" and "experimentally measuring" things is mis-leading'.

However, it is exactly due to experimental errors that Heisenberg came up with the uncertainty principle. Historically it arose from errors in experimentation. Heisenberg took these errors as not to be indicative of imprecisions in the instrument, but fundamental.

Quote from origins of Uncertainty Principle:

"After Schrödinger showed the equivalence of the matrix and wave versions of quantum mechanics, and Born presented a statistical interpretation of the wave function, Jordan in Göttingen and Paul Dirac in Cambridge, England, created unified equations known as "transformation theory." These formed the basis of what is now regarded as quantum mechanics. The task then became a search for the physical meaning of these equations in actual situations showing the nature of physical objects in terms of waves or particles, or both. As Bohr later explained it, events in tiny atoms are subject to quantum mechanics, yet people deal with larger objects in the laboratory, where the "classical" physics of Newton prevails. What was needed was an "interpretation" of the Dirac-Jordan quantum equations that would allow physicists to connect observations in the everyday world of the laboratory with events and processes in the quantum world of the atom.

"Studying the papers of Dirac and Jordan, while in frequent correspondence with Wolfgang Pauli, Heisenberg discovered a problem in the way one could measure basic physical variables appearing in the equations. His analysis showed that uncertainties, or imprecisions, always turned up if one tried to measure the position and the momentum of a particle at the same time. (Similar uncertainties occurred when measuring the energy and the time variables of the particle simultaneously.) These uncertainties or imprecisions in the measurements were not the fault of the experimenter, said Heisenberg, they were inherent in quantum mechanics. Heisenberg presented his discovery and its consequences in a 14-page letter to Pauli in February 1927. The letter evolved into a published paper in which Heisenberg presented to the world for the first time what became known as the uncertainty principle."--[2]

Therefore, it was experimental imprecision that led to the uncertainty principle NOT theory. Therefore, Heisenberg's microscope thought experiment came after the uncertainty principle and was developed later as an attempt to explain and simplify and illustrate the imprecision already observed in a theory empirically derived from data and the idea behind the Heisenberg microscope thought experiment was not present in its development.

Heisenberg's Uncertainty Principle is about imprecision of measurement that should be applied to actual experiments and actual observations. It was derived from from experiment and data and is to be applied to experiment and data. So whether an article on HUP is written from the point of view of the development of the theory or from the point of view of experimentation, it still should be written about HUP as imprecision in measurement.

Although the analogy to Heisenberg's microscope is used in simple models of the uncertainty principle as those in Stephen Hawking's popular interpretation of cosmology and quantum mechanics, it does not present a clear picture of the development of the uncertainty principle and as Linas has agreed with the paragraph that said, Heisenberg's microscope "is not itself part of current understanding", it should not be included in introductory information about the uncertainty principle which is based upon imprecision of measurement as first seen in matrix mechanics and later developed therefrom.--Voyajer 20:02, 1 January 2006 (UTC)

further reason why the Heisenberg microscope is not used

Niels Bohr is actually said in some sources to have originated the thought experiment of a gamma-ray microscope which suggests that, since a microscope's light “disturbs” the motion of small objects under observation in an intractable way, exact simultaneous knowledge of the position and momentum of elementary particles is impossible. This thought experiment has repeatedly been deemed a poor proof of the uncertainty principle because

• 1. Heisenberg's microscope is stating that uncertainty is an error in measurement, when the uncertainty principle itself is not about there being an error in measurement caused by an instrument like a microscope, but about there being a fundamental deviation between position and momentum of observables.

and

• 2. Heisenberg's microscope suffers from the same problematic assumptions about locality as Einstein's analysis of the EPR experiment.

Thirdly, the uncertainty principle did not arise from observations of a single particle. The uncertainty principle arose from spectroscopy. In spectroscopy, no one is looking at subatomic particles through a microscope. In spectroscopy a single light source is illuminating an element. Therefore that single light source is disturbing all the particles to the same degree and the spectrum created is therefore all disturbed to the same degree so no particle is more or less disturbed than another. Yet, even in this case, Heisenberg is saying that there is still a deviation in measurement between position and momentum of a moving particle. This therefore cannot be due to a collision of a photon under a microscope, but is inherent in nature. Therefore, it is a fallacy to say that the act of measurement disturbs the particle. This is a leftover from the HM thought experiment. Nothing disturbs the particle. Heisenberg's uncertainty principle arose from inaccuracy in measurement where there was nothing to disturb the measurement. He saw this as not the fault of the spectroscope, but an inherent characteristic of the universe.--Voyajer 00:48, 3 January 2006 (UTC)

Rewrote the overview

I rewrote the overview. A couple things I noticed:

• I liked the approach of discussing measurement immediately since it is a somewhat natural pedagogical way to introduce uncertainty. However, it's not ideal because it leads to the misconception that the uncertainty can be due to the poor quality of an instrument. I tried to make it clear that this works for an infinitely precise/accurate instrument (note that there may be some disambiguation required between when accuracy and precision are used -- right now the overview and new section are correct in their formulation, but the novice reader might not appreciate the distinction), but other editors may think of better ways to improve on this formulation.

• Whoever put the stuff in about standard deviations was barking up the wrong tree. Not all wavefunctions are normal distributions.

Standard deviations do not imply the normal distribution. SD is simply the rms of an ensemble of measurements. To wit, sqrt(sum((value_i-mean)^2/N))

• The waveparticle duality parts (now a new section) are important but might be overstated. After all, it's not at all obvious that the Heisenberg Uncertainty Principle implies wave-particle duality since it can be formulated exclusively in terms of observable properties (that is, independent on what the nature of the object is that you are observing).

• The sound signal analogy is a good way to introduce Fourier Analysis without bogging down the reader in technicalities. However, the analogy cannot be taken too far lest the reader get the impression that there is something about signal processing that determines the uncertainty principle. Nevertheless, the relationship between position and momentum space is well-illustrated by this example and it is also a natural lead-in to the time-energy corrollary for the HUP.

• I didn't mess with the interpretations paragraph too much as it seemed fairly good. It may be too detailed for a lead-off like that, but I don't have a strong enough opinion on the matter.

--ScienceApologist 09:33, 16 January 2006 (UTC)

about Wilson-Sommerfeld's Quatization

I've read Modern Physics about Wilson-Sommerfeld's Quatumzation Theory. I don't understand:

1.Why did they consider that $\oint {Pdx}$?

Because it is the action (physics)

2.By 1.,I think that was just correct with some limit of

Uncertainty Principle if P represents(ed) "Poition". I said

right? Or it obeyed U.P.?

No, P is the momentum.

Thanks for correction. Previously I wanted to show was that P stands for "Period",not for "Positon". Actually I know it stands for momentum.--HydrogenSu 11:34, 27 January 2006 (UTC)

3.Why does $\oint {Pdx}=nh$? Then we by this to solve A

(amplitude)? And however,by what theory? See please

File:Modern physics.jpg

That snapshot of the whiteboard shows that P is the momentum. You may also choose to think of the action as if it were the total angular momentum; the Bohr-Sommerfeld quantization condition states that the total angular momentum is quantized. The theory is thier own: they invented it in order to try to explain atomic spectra. linas 22:00, 26 January 2006 (UTC)

For the reason of I rarely coming here,so email me: coralieiloveu@yahoo.com.tw as any new reply about this question appears. --HydrogenSu 10:31, 25 January 2006 (UTC)

Wider usage

There is a wider usage of this principle that basically says in any given observation, the observer affects the observed, and hence affects the reality (or variable) they are supposedly trying to measure. An example would be, say Dian Fossey observing gorilla behavior: she observed a lot of behavior, but how much can you trust her observations given that her presence among the gorillas may itself have had an effect that would normally not be there?

This may be mentioned in the article somewhere, but I think the article could be improved with a more accessible mention with a non-physics example, such as the one above. However, if anyone thinks I'm wrong about this, please let me know. I know I have read more than one author citing the HUP in non-physics examples. Is the "observer effect" part of another "principle" I've missed?

I hope you physics guys will indulge a peon of the non-physics world to help me understand this a little better. For all I know there could be a whole article on it somewhere... Thanks for your time. --DanielCD 01:45, 5 February 2006 (UTC)

This article is very explicitly about the Hiesberg uncertainty principle, and should not be expanded to include other principles. Also, there already is an article on the observer effect, which could be considerably improved. (Its lacking in references, among other things). linas 04:04, 5 February 2006 (UTC)

I just added a few sentences about the observer effect to this article. linas 04:14, 5 February 2006 (UTC)

OK, thanks. That's what I was looking for. I haven't read your article additions yet, but I'm right in assuming the HUP is not the same thing...? I'll probably find my answer in the OE article or your additions. Thanks. --DanielCD 05:30, 5 February 2006 (UTC)

Wow that is messy. I'll see if I can't tidy it up. --DanielCD 05:31, 5 February 2006 (UTC)

OK, my questions are totally answered. Thanks a lot for the help! --DanielCD 05:42, 5 February 2006 (UTC)

Uncertainty + the butterfly effect = ?

I don't understand the uncertainty principle very well, but most descriptions I've read seem to say that uncertainty effects don't come into play on the human scale (or any larger scale). However, I would expect uncertainty effects to grow as the scale gets larger (especially with long periods of time, even with small distances and small numbers of particles). Take the following example:

Two particles in an otherwise empty universe. Each has a small uncertainty in its position. Each has no charge but a large mass (so that they interact very strongly by gravity). Neither particle affects the uncertainty of the other instantaneously, but if you give some time for them to interact, the uncertainty of the position of particle 1 grows, because it is attracted gravitationally to P2, but since P2's position in uncertain, there is no certainty of where P1 is gravitating to. (if P2 is further away, the attraction is weaker, if closer it's stronger, if slightly to the left it's towards a different position, etc.) Because every force has an equal and opposite force, the same effects apply to P2's gravitation to P1. I would expect uncertainties to grow very quickly with time. If you add more particles, it gets worse. I suspect distance might actually slow down the growth of uncertainty (the uncertainties in the position of particles would be less compared to the distance between them), but it wouldn't stop it, so I'd expect anything at the macroscopic scale to be even more fuzzy than the quantum scale.

I'm especially concerned with the fuzziness in the positions of electrons orbiting atoms. The descriptions I've seen spread the possible positions of the electrons pretty evenly on all sides of the nucleus. But if that holds, there can be no certainty whether the forces the nucleus exerts are in one direction or the other. If the electron is on one side the forces are in one direction: e....n F-> , if on the other, the forces are in the opposite direction: n....e <-F

But if the position is uncertain, the forces are uncertain: e?...n...e?  ?<-F->?

What am I not understanding here?

12.37.33.3 17:58, 21 February 2006 (UTC)

The uncertainty principle and chaos theory are two very different things. In QM we learn things don't have exact positions and energies at exact times - not a measurement problem - it just isn't the way reality is. In chaos theory we learn that even if it did - even if we lived in a Newtonian clock like universe, critical sensitivity to initial conditions means even deterministic systems can have behavior that appears to be random. WAS 4.250 18:30, 21 February 2006 (UTC)

I know they're different, but what I'm talking about is how they do relate. If small differences in initial conditions create large differences in final conditions in the most precise of universes, shouldn't small uncertainties in the initial conditions create large uncertainties in final conditions in universes that are less "clock like"

12.37.33.3 23:11, 21 February 2006 (UTC)

There is no simple answer. This is studied in the field of quantum chaos. Its relatively sleepy as a research field, but quite interesting. To understand it, however, you need ot understand quantum mechanics first. And also plain-old chaos theory too. I can only suggest embarking on a coure of study. By the way, the wave functions in quantum-chaotic systems end up being fractals that fit together like perfect jigsaw puzzles. And while attempting to understand that, I've wandered off into p-adic analysis, but that's a different story. linas 01:47, 22 February 2006 (UTC)

After more thought I think the best example of what I'm asking is Schroedingers cat. A small uncertainty in the initial conditions creates a large uncertainty in the final conditions (1 atom determines whether a great number of other atoms form a living, breathing cat, or a dead, inert one). Apparently observation forces the system into one state or the other, but that brings up another question: wouldn't any interaction with another particle constitute an observation, and since every particle in the universe is constantly interacting with every other, wouldn't that mean that every particle is always observed?

Yes, more or less. Except that the last sentence should read "almost all particles are observed most of the time". You can certainly create "nobody is looking now" conditions in the lab: for example, you can put a thin vapor of atoms in a vacuum chamber, and throw some electrons at them, and you will see the full glory of quantum mechanics manifest itself. After reflecting on this for a while, you will soon discover that similar "no one is looking now" conditions exist in lots of places, from interstellar gasses, to the gas of electrons in a transistor, or to atomic nuclei, which are pretty damn-lonely isolated from just about everything, sitting in a cushiony-soft springy electron cloud there at the center of an atom, with these immense distances to the next nearest nucleus (at least, at earthly matter densities). linas 16:46, 22 February 2006 (UTC)

But "somebody" is always looking. The mass of a particle always bends spacetime, and other particles always follow these bends. Gravity is always there. Same with electromagnetism, charged particles (as I understand it) are always exchanging photons, creating forces between those particles. If this isn't happening, and you have a "nobody's looking" scenario, your thin vapor of atoms should fly off in a straight line (or as close to it as possible given uncertainties in position and momentum), ignoring the Earth's gravity, any solid objects, and everything else in the universe until someone is once again looking. I agree that the uncertainty principle gives a very good prediction of what unknowns in your system and errors in measurement will do, but the state of every paritcle must be exact and precise or else everything turns to mush. 12.37.33.3 04:33, 18 March 2006 (UTC)

You say "the state of every paritcle must be exact and precise or else everything turns to mush". It may seem that way, but a quantum state actually doesn't have a determinate position and time. It's not just a problem of measurement. This doesn't create a problem for the electrodynamic field, since that field can also exist in a quantum state. It is a problem for spacetime; if mass-energy is in a quantum superposition of states, then the spacetime metric must also be in a superposition. Modelling this requires a quantum theory of gravity, which is an active area of research at the moment. -lethe ^{talk +} 05:16, 18 March 2006 (UTC)

My problem is not with understanding that a quantum state doesn't have a determinate position or time, but with understanding how anything without said determinism can be anything but fuzzy mush on every scale. Relativity may not be imaginable, I might not be able to get my mind around it, but at least it makes sense: I can connect the dots even though I can't see the whole picture. Quantum indeterminancy just doesn't make sense. Linguofreak 02:34, 19 March 2006 (UTC)

Two things can help you get used to fuzzy mush: first, realize that fuzziness is a general phenomenon of waves. Even water waves in the ocean don't have well-defined position. Second, stuff is not really so bad as long as you don't try to do bad things like measure two nincompatible observables. A particle can have a definite energy and a definite angular momentum, for instance. No fuzziness need arise there. -lethe ^{talk +} 17:35, 21 March 2006 (UTC)

There is fuzzy mush on every scale. But its only very slightly fuzzy on large scales, because it works probabilistically. In probability, the more trials you have, the closer you come to your expected value. Macroscopic objects involve millions of particles - in effect, millions of trials. So you get very close to your expected value the vast majority of the time - resulting in apparent determinism. dolph 16:56, 21 March 2006 (UTC)

Ocean waves may not have a well defined position, but they have a very definite set of positions and heights at each position. And they have a very well defined crest too. You can determine exactly how two waves will interact with each other. Linguofreak 05:12, 22 March 2006 (UTC)

Quantum theory is not "fuzzy mush". Its mostly linear algebra, and the uncertainty principle has to do with how matrix multiplication is not commutative. The matricies involved are quite "sharp", its just that position and momentum correspond to different basis. Read about the Fourier transform for more info. Also, you probably want to take this discussion to the wikipedia science reference desk, where you might find a broader set of folks willing to explain all this. linas 15:25, 22 March 2006 (UTC)

You're right: water waves have a set of well-defined positions for the crests. This set may be infinite. The same may be said of electrons. If you're willing to abandon "position" as a single number, and instead view it as an infinite set of crests, then all mushiness disappears. This is exactly the view that modern physics takes about this issue: quantum particles are completely characterized by their wavefunctions. But you still cannot ask for a single number to specify position, neither for an electron, nor for a water wave. -lethe ^{talk +} 19:56, 22 March 2006 (UTC)

So would a given particle gravitate towards the "average" position of another particle? In other words, take the particle's complete set of positions, give a weight to each position according to the "height" of the wavefunction at that position, and then find a "center of gravity" so to speak. (Arrgh I keep remembering to sign only two seconds after I save my edit) Linguofreak 16:12, 26 March 2006 (UTC)

Instead of gravitation, let's ask the same question about electrostatic repulsion: does the electron get attracted to the weighted average position positron? (By the way, this weighted average is called the expectation value). The answer is no, the attraction between the two depends on the total overlap of their wavefunctions. Roughly speaking, little pieces of overlap of wavefunctions are called matrix elements, and to know the force between the two particles requires a summation over all matrix elements, and consequently the force has to be represented as a spectrum of values as well. However, the force, averaged with weight over all the matrix elements (that is to say, the expectation value of the force) is indeed given by the expectation values of the particle's position. If you think only of expectation values, then things behave in the way you're used to from classical mechanics. This result is known as Ehrenfest's theorem. But note that if you think of electrons only in terms of their expectation values, then it is impossible to understand all the effects of interference (which is everything that makes quantum mechanics interesting).

Now if you want to ask the same question about gravitational attraction, I'll just say that I expect things to be qualitatively similar. There should be a correspondence between classically expected results and quantum expectation values. However, things get complicated because the spacetime metric should probably be fuzzy mush as well, which makes it impossible to define for decide when things commute and when they don't. But we could probably do a semiclassical approximation and so as long as quantum gravitational effects could be neglected, then the answer would be the same. -lethe ^{talk +} 16:47, 26 March 2006 (UTC)

PS I haven't forgotten about your spin question. I think the answer is that the angular momentum does not become unbounded as the rate of rotation approaches c. Stated another way, yes, the relativistic moment of inertia increases as the speed goes up, but not enough to get enough angular momentum before we reach c. I'll post my thoughts on the matter eventually, but I want to find a nice calculation first to back it up, which has been surprisingly difficult. -lethe ^{talk +} 16:50, 26 March 2006 (UTC)

OK, if the force comes from the expectation values of the positions of the particles, then I don't suppose that things are much different from the attraction between two bodies that are not point masses (such as planets), where the force averages out to being between the planets' centers of mass. Except for the fact that planets tend to collide if they overlap, whereas electrons pass straight through each other. Maybe it's better not to use the concept of a particle having an uncertain position but rather being spread out over a range of positions. As to the question of spin, you don't have to give me a concrete answer immediately, but I'll collect my thoughts on the appropriate talk page so you can see why I think that angular (or any other) momentum must be infinite at c. In fact, I think I already have it there, so I'll just add a bit, and then we can go from there. Linguofreak 20:53, 26 March 2006 (UTC)

To reiterate: only the expecation of the forces come from the expectation values of the positions. The full spectrum of the forces requires knowledge of the full spectrum of the position. Also, about bodies passing through each other, when the electrons pass too near, the wavefunctions exhibit interference, which leads to purely quantum mechanical effects, like the degeneracy pressure, something that simply has no analogy for classical particles, which is one example why thinking solely in terms of expectation values is not sufficient to understand the full dynamics. Finally, regarding your last point "maybe it's better not to use the concept of a particle having an uncertain position, but rather being spread out over a range of positions", that's almost exactly right. In the beginning days of quantum mechanics, Heisenberg thought of particles as having position which could only be measured with a limited precision. But after the revolution of the EPR paradox, Bell's theorem, etc, we now know that that is simply not correct. The particle must be understood to simply not have a single position, but rather be spread out. -lethe ^{talk +} 22:41, 26 March 2006 (UTC)

Ok. So actually when particles do pass through each other they do have forces related to the collision. Would I be right to say that they "bounce off each other"? But the whole "uncertainty" thing needs a new name. I totally misunderstood the concept because of the name. I thought that particles had distinct positions, but the positions were uncertain, fuzzy, and determined (tongue in cheek) by flip of a coin. But now I understand that the positions are certain but not distinct, which clears everything up. The position/momentum relationship now makes perfect sense too. The more closely you gather a water wave towards one position, the higher it gets, so when you let it go, the higher it was stacked, the faster everything falls away, so the greater the distribution of momentums. And the only way to get all the momentums the same is to not have a wave, i.e. flatten the surface out, so you have a greater distribution of positions. Wakarimasu!! After a short break I will begin working on Quantum entanglement or something. Linguofreak 03:36, 27 March 2006 (UTC)

Now you've got it exactly right. About the name, I agree it's a bit misleading. It is so named, because that's how the founding fathers originally understood it, and we're stuck with the name, even though we know better now. -lethe ^{talk +} 05:06, 27 March 2006 (UTC)

Just to clarify one thing: when two electrons pass near/through each other, there are degeneracy forces that act on them because of interference, as well as the electrostatic forces which happen also for classical particles. I would call the latter "forces related to the collision", and the former "forces related to the quantum effects". Whether or not the resulting collision can be called a "bounce" is a matter of taste. -lethe ^{talk +} 05:19, 27 March 2006 (UTC)

Another question: Do two particles that are antiparticles of each other annihilate when there is any overlap in the set of possible positions for the two, or is there some other criterion?

This shouldn't be taken too literally, it's not the entire story, but it might be at least qualitatively accurate to say that the probability of annihilation is proportional to the amount of overlap between the two wavefunctions. -lethe ^{talk +} 23:12, 2 April 2006 (UTC)

Editor war?

On March 3 the user "DV8 2XL" unwisely reverted my changes without explanation. It is not good. .. The text removed by me was really erroneous. J_x and J_y are not "conjugate". And time is not an operator.

I also want to change the following: "joule" to "Joule", "a exact" to "an exact", "He wrote in a 1925 letter" to "He wrote in 1925 a letter", "form—but" to "form — but", "curviture" to "curvature".

Also I want to remove "Many cats have been named "Schrodinger" as an allusion to Schrodinger's thought experiment involving a cat which illustrates the uncertainty principle." That cat is not really an illustration of the uncertainty principle. It is an illustration of the level, where projection principle works.

I ask "DV8 2XL" to make these corrections him(er)self.

Sorry, sorry I'm a little trigger-happy to-day with a lot of vandal blanking by annons in the articles I watch. I didn't take the time to look if this was a valid edit, which I agree I was. Please accept my apologies. I will revert back at once.

Please consider opening an account here, it's easy and it's free. --DV8 2XL 21:50, 3 March 2006 (UTC)

First image

I just changed the caption on the first image to conform with what I think is the proper description for this thing. Talk about a complicated image. I think it is a particle in a 1-D box in the third energy level unconfined in the other two dimensions with a gaussian wavefunction (thus the standard deviation comment) Now that I'm finished editting this caption, I think that this image may be completely un-useful. What if, instead, we just gave the 1-D wavefunction vs. position and wavefunction vs. momentum for a gaussian wavefunction in free space? This might be more conceptually illustrative of the uncertainty concept. The graphic is, in fact, patently incorrect as well because it represents a sinuosoid as circles. A "circular" wavefunction is impossible since it would have an infinite derivative (and therefore momenta) at each node. I think the image needs to go, but I would like a replacement image before we trash it completely. Thoughts, concerns, issues? --ScienceApologist 02:40, 11 April 2006 (UTC)

(Amendment to above statement) On second thought, since the sinusoidal wavefunction is actually valued along the horizontal axis, the image may be technically correct since you cannot see how the standard deviation matches exactly in that direction. The circle is therefore an artifact of a conspiracy between the gaussianity and the sinusoidality in perpendicular directions. I stick by my assertion, however, that the image is probably too confusing for its own good. --ScienceApologist 02:43, 11 April 2006 (UTC)

I agree about the image. This article has accumulated a lot of cruft. In particular, the stuff on measurement error I do not find helpful. The other element which seems superfluous is to bring up wave-particle duality. The basic idea of Heisenberg is not that esoteric. By all means, have at it.--CSTAR 02:52, 11 April 2006 (UTC)

I support deleting the image. And I also do not understand the statement "The standard deviation is 1/2 of h-bar where h-bar is the quantization of one radian". The standard deviation of what? And how radian (measure of angle?) is quantized? And how it gets the dimensionality of action? Rcq 00:33, 22 May 2006 (UTC)

As per this discussion, the image has been nominated for deletion at Wikipedia:Images and media for deletion. Please comment there. --ScienceApologist 02:23, 22 May 2006 (UTC)

Fisher information and all that

• I have visited the articles mentioned in the "Expression of finite available amount of Fisher information" paragraph and have not found there anything directly relevant to the HUP.
• On the page Fisher information I have found a link to an "essay" by R. Frieden (who, probably, makes self-promotion here) with topics like "Vital role of the probe particle". Such topics are currently deprecated in the discussions of the HUP: they are the remainders of the outdated approaches.
• There is no reasonable explanation here that the book of Stam contains something important about the HUP.
• The section talks about "the mean-squared momentum", not about "the mean-squared deviation of momentum". This seems to be strange.
• So, now I delete the section. Sorry.
• If somebody feels that information approach is really important for the HUP, I recommend to write something in the articles devoted to information first.

Observer Effect

I'm not convinced that the uncertainty principle and the observer effect are entirely unrelated. The uncertainty principle does refer to the precision of measurements , but taking measurements effects the state of the particles.

One example is the old two slit diffraction. initially the momentum of particles in a beam are well known, and position uncertain. Once the particle has passed through one of the slits, the position is temporaily well known, causing the momentum to be uncertain which leads to diffraction.

Though not related to the uncertainty principle, it's not controversial that measurements of quantum states does effect these states. An example is in determining the z-direction of spin of a particle, if a particle is initially in a superposition of z-directions, taking a measurement will effect the spin of the particle by causing the collapse of the wavefunction to a single value.

In reference to the section on common misconceptions, its seems the the EPR experiment is used to justify fact that an observation does not need to use a particle to obtain a measurement. I believe this relates to a possibly incorrect interpretation that the EPR applies to two quantum state, when as they are entangled they belong to the same quantum state. One of the particles is disturbed, and so the quantum state of the particles in changed.

I propose a small edit to the statement that it's not related to the oberver effect. Dougleduck15/5/06

Richard P. Feynman's lecture from the 1960's clearly describes the uncertainty principle as the observer effect. Jones 08/05/06

That's strange, because in QED (The Strange Theory of Light and Matter) he describes it completely differently. Furby100 03:35, 3 June 2007 (UTC)

Introduction of the article

Dear friends,

• I think that introduction needs to be improved.
• The word "conjugate" implies forming pair. It does not mean "non-commuting". And I cannot agree with the conjugate quantities article. Conjugate quantities are the notion of classical mechanics only. This notion can be brought (in some sense) to quantum mechanics in the case when semiclassical limit exists (and this is the case when uncertainty principle is applied). But in our days there is no necessity in this complication.
• Some time ago I removed a paragraph, which called J_x and J_y "conjugate" (see "Editor war?" above). The case of J_x and J_y (though, possibly, of little importance) clearly shows that the uncertainty principle does not necessarily imply any conjugacy.
• Why not use modern formulation, suggested by Arbatsky? It is general, up-to-date, and easy to understand.
• I am going to rewrite the introduction in the near future. Rcq 19:47, 30 May 2006 (UTC)

The certainty principle war is coming

Dear friends,

It seems we are going to have a war for the certainty principle here. I do not want it, but I see no choice. Some people, who are incompetent in the subject, fight with this topic, because papers about the CP were published in a journal, which they do not consider "reputable". I understand their concern and support it in some sense. I understand that from their incompetent point of view they try to make WP better. But, in fact, they violate WP policy. And what can I do, if this case is truely unique, and the certainty principle is not "rubbish" (as they rudely call it)? Are all editors here so incompetent in QM that they cannot judge the topic? I cannot believe it. I hope that the Truth will win here, not obscurantism. And without war. What do you think? Hryun 23:19, 6 June 2006 (UTC)

Threatening an edit war is a sure way to get you and all of your sockpuppets blocked. Wikipedia's content guidelines are very clear about not letting in original research; if you do not agree with that as a way of operating you are invited to go elsewhere. --Fastfission 20:54, 7 June 2006 (UTC)

I would recommend that you accept the consensus view. An edit war would probably end badly, probably with a block. -lethe ^{talk +} 22:55, 7 June 2006 (UTC)

B. Roy Frieden's anonymous POV-pushing edits

B. Roy Frieden claims to have developed a "universal method" in physics, based upon Fisher information. He has written a book about this. Unfortunately, while Frieden's ideas initially appear interesting, his claimed method is highly controversial:

• Binder, Philippe M. (2000). "Physics from Fisher Information: A Unification (a review)". American Journal of Physics. 68: 1064–1065.
• Kibble, T. W. B. (1999). "Physics from Fisher Information: A Unification (a review)". Contemporary Physics. 40: 1999. (the reviewer has some positive comments but concludes that Frieden's work is "misguided")
• Case, James (2000). "An Unexpected Union---Physics and Fisher Information". SIAM News. July 17. eprint (highly favorable)
• Matthews, Robert (1999). "Physics and Fisher Information (a review)". New Scientist. January. unauthorized electronic reprint
• Physics from Fisher Information: A Unification (a review) from Cosma Shalizi (Computer Science, University of Michigan) (highly critical)
• Physics from Fisher Information (a review) from R. F. Streater (Mathematics, Kings College, London) (highly critical)
• Physics from Fisher Information thread from sci.physics.research, May 1999 (mostly critical)
• Fisher Information - Frieden unification Of Physics thread from sci.physics.research, October 1999 (mostly critical)

Note that Frieden is Prof. Em. of Optical Sciences at the University of Arizona. The data.optics.arizona.edu anon has used the following IPs to make a number of questionable edits:

1. 150.135.248.180 (talk · contribs)
   1. 20 May 2005 confesses to being Roy Frieden in real life
   2. 6 June 2006: adds cites of his papers to Extreme physical information
   3. 23 May 2006 adds uncritical description of his own work in Lagrangian and uncritically cites his own controversial book
   4. 22 October 2004 attributes uncertainty principle to Cramer-Rao inequality in Uncertainty Principle, which is potentially misleading
   5. 21 October 2004 adds uncritical mention of his controversial claim that the Maxwell-Boltzmann distribution can be obtained via his "method"
   6. 21 October 2004 adds uncritical mention of his controversial claim that the Klein-Gordon equation can be "derived" via his "method"
2. 150.135.248.126 (talk · contribs)
   1. 9 September 2004 adds uncritical description of his work to Fisher information
   2. 8 September 2004 adds uncritical description of his highly dubious claim that EPI is a general approach to physics to Physical information
   3. 16 August 2004 confesses IRL identity
   4. 13 August 2004 creates uncritical account of his work in new article, Extreme physical information
   5. 11 August 2004 creates his own wikibiostub, B Roy Frieden

These POV-pushing edits should be modified to more accurately describe the status of Frieden's work.---CH 21:54, 16 June 2006 (UTC)

Humor as a magnet

The humor subsection appears to be a magnet for nonnotable and lame jokes. I'd like to delete it, but invite your views. --Lambiam^Talk 06:23, 27 June 2006 (UTC)

So deleted, and pray that some bot not blindly restore it. --Lambiam^Talk 05:56, 28 July 2006 (UTC)

What is being evaluated in One of the theorems?

In the section One of the theorems, I currently find the following quote:

It may be evaluated not only for pairs of conjugate operators (e.g. those defining measurements of distance and of momentum, or of duration and of energy) but generally for any pair of Hermitian operators. There is also an uncertainty relation between the field strength and the number of particles which is responsible for the phenomenon of virtual particles.

What exactly is being "evaluated" here? The statistical interpretation of uncertainty? If this is the case, I don't think it is fair to speak of "any pair of Hermitian operators." There are serious problems for the given statistical measure of uncertainty for finite dimensional Hermitian operators. Some of the problems with the uncertainty principle in the finite dimensional case can easily be seen by noting that hermitian matrices can not have a commutator similar to the identity. 19:09, 12 July 2006 (UTC)

Humor

RE:

"An episode of Matt Groening's Futurama features the show's characters at a racetrack. After his favored horse loses in a "quantum finish," the professor shouts angrily, "No fair! You changed the outcome by measuring it!" and tears up his ticket."

This has nothing to do with the Uncertainty Principle. This is actually referring to the (apparent) collapse of the wave function.

I am going to remove that part. Gagueci 23:16, 27 July 2006 (UTC)

Reffering to the previous post by user Lambiam, I also motion the deletion of the humor section. Gagueci 23:20, 27 July 2006 (UTC)

RE:

"How many physicists does it take to change a light bulb?" "Only one – all the physicist has to do is observe the light bulb, and he changes it."

Again, observation/measurment to change the out come and the Uncertainty Principle are two seperate ideas. Gagueci 23:22, 27 July 2006 (UTC)

Common observables which obey the uncertainty principle

Standard deviations are calculated from making repeated measurements. The measurement resolution and measurement errors requires to be much better than the rms for the standard deviations. HUP is a statement on standard deviations, not individual measurements. Measurements of observables can be much better than HUP. — Preceding unsigned comment added by 217.155.191.217 (talk • contribs) 14:11, 11 August 2006 (UTC)

Note: moved from article space to talk page. Mike Peel 13:14, 11 August 2006 (UTC)

First Paragraph Isn't Very Good

The first paragraph is as a clear and interesting as mud.

I've made some edits to try to make it more accessible. Hope they helped :-) --75.83.140.254 18:56, 31 December 2006 (UTC)

HUP was Classically Determined

In the introduction, I don't like to see the quantum mechanical descriptions, notations, and arguments for this principle which was classically determined. Therefore, I created the section called, "The Basis.."

derivation

Should the derivation be clarified? Is what I wrote too much for Wikipedia?

I just think it is amazing that the uncertainty principle is derived with the Schwarz-inequality (and I am happy that I could make use of my linear algebra course). It is all there now I think but not quite in the right order to be easily understandable. The notation changes using x first and then Ψ --FelixP 20:46, 2 October 2006 (UTC)

I like this section, it should stay; I think the change in notation is troulblesome, but it does make it's own point: that you are leaving the purely mathematical world behind for the physical one.--Charlesrkiss 02:13, 9 October 2006 (UTC)

I am thinking about rearranging this section some more. Maybe I can make a first paragraph that kind of explains what's happening and the importance of commuting operators, i.e. that they share eigenfunctions and therefore the values of the corresponding observables are clearly defined. And I want to point out how it's all linear algebra. In my eyes only using Ψ would make sense even though of course it might make you forget that the derivation is pure linear algebra without any actual functions needed. FelixP 16:40, 9 October 2006 (UTC)

The Basis of the Uncertainty Principle

Does anyone agree with me and consider the following a "modern" understanding of HUP.

To measure the frequency of a wave one must compare the wave with a reference signal of known frequency, such as the beats of a standard clock. This is the same as to allow the two signals to interfere with each other. One will not know if the two frequencies are, or are not, exactly, precisely, the same, if one does not have an infinite amount of time to measure both and be certain.

If one attempts to measure the difference in frequencies over a finite period of time, however, to be relatively certain with ones comparison, one would have to

1. allow at least one beat of the clock, and
2. the frequency of the measured wave, for it to be observed within the given time interval, must be greater than or equal to the frequency of the clock, that is to say: have an equal or smaller period.

In other words, this corresponds to one or more beats of the wave per unit time of the standard clock: $1/\Delta t$, which will be less than or equal to the minimum observeable frequency $\Delta v$, or:

${\frac {1}{\Delta t}}\leq \Delta v$

It follows that if $\Delta v$ is close to zero $\Delta t$ must be nearly infinite, and the uncertainty large if measured over a short time interval.

$\Delta t\Delta v\geq 1$

The corresponding uncertainty in wavelength is easily deduced if given the speed of the wave. The Uncertainty Principle, as it pertains to the momentum of a material particle, is inferred from experiment that confirms the wavelength of a material particle is equal to $h/mV$ ; where $h$ is Planck's constant, and $mV$ its momentum. See Planck's law of black body radiation.

$\lambda ={\frac {h}{mV}}$

—The preceding unsigned comment was added by 68.48.244.84 (talk • contribs) 05:08, October 8, 2006 (UTC).

I read this prove in Skoog and Leary, Instrumental Analysis. It's a good description for the special case of time and frequency. I would prefer the general derivation because it covers everything. FelixP 10:55, 8 October 2006 (UTC)

While the section was still there I renamed it from "Basis" to "Basic explanation" – which is what I think it was. Such a section need not be in competition with the general derivation, but to understand the latter you need a background most readers don't have. The section was removed altogether with edit summary removed this misleading section. I don't know what specifically was misleading about it and if some less drastic remedy wouldn't have sufficed. In my opinion the article would be better if it had some basic explanation that can be followed by anyone with a high-school algebra background, and if, as suggested above, such an explanation can be sourced, all the better.  --Lambiam^Talk 16:40, 8 October 2006 (UTC)

The reason I removed the analysis above on the grounds that it's misleading, is that it could lead a beginner (i.e. its target readership) into thinking that the uncertainty principle is necessarily either an epistemic limitation, or some sort of practical measurement deficiency — when, in fact, it is commonly interpreted to be an ontological feature of quantum mechanics. I also don't think that including concepts like "unless one has an infinite time to conduct the measurement" is either paedogogically edifying or even absolutely correct...it brings too many other issues into the mix. But if everyone else thinks I'm being a frightful pedant, I won't make a fuss! I just feel that if we are to provide a basic explanation, we should be sure that we won't be forming concepts in the minds of beginners that they will battle to shed later, should it prove necessary for them to do so... Byrgenwulf 17:01, 8 October 2006 (UTC)

I think this could be a subsection of derivation. But it should be mentioned that things aren't still well defined even without an observer. This fact is mathematically better represented with wave functions than with classical movement. FelixP 18:19, 8 October 2006 (UTC)

If we have such a (sub)section at all, it should precede the current derivation: the readers who it aims at will suffer from their eyes glazing over before they reach the end of that derivation. Setting aside for a moment the intriguing issue of whether our esteemed editor Byrgenwulf is an insufferable pedant, the question we need to agree on is this: Will such a basic explanation (if done well) enhance the value of the article? (It's even better if we can agree on the answer!) I see a definite value in blowing away the mist of mystic mystery hanging around the UP. Can we do that by an entirely elementary derivation (even if only for a special case) without compromising the integrity of that derivation with respect to a higher level of understanding of the UP? Unfortunately, I am insufficiently familiar with the matter to judge the latter aspect; what I can judge is whether an existing exposition is internally conistent and comprehensible.  --Lambiam^Talk 22:15, 8 October 2006 (UTC)

I agree that the use of the word "infinite" is weak. The word "approaching infinite" would be more easily understood, though incorrect. I will do a work around and post it sometime over the next few days. I'm not sure, either, where the subsection should go.

I do know that I would not use the word "quantum physics" in the opening sentence. It could just as well read "In physics.." I imagine you want to link people to quantum physics, but UP is more general that QP. Overall it'a pretty decent article, but I wouldn't mind seeing it grow to several pages, the importance of the topic deserves careful attention and expansion, even if a little redundant.--Charlesrkiss 02:07, 9 October 2006 (UTC)

Popular culture revisited

I'm not a physicist; I just wanted to mention yet another usage of HUP in popular culture: In the 1985 movie Creator (a romantic comedy about cloning) Peter O'Toole uses HUP quite charmingly in giving Vincent Spano advice about women. Personally, I like popular culture references in scientific articles; they render the articles more accessible to non-scientists like me. :D

Strange sentence

This unsigned comment by 84.58.240.210, 21:12, October 19, 2006 (UTC), has been moved here from the text of the article

I feel that this sentence does not make sense (grammatically) and is therefore confusing:

"But it is now understood that no treatment of any scientific subject, experiment, or measurement is said to be accurate without disclosing the nature of the probability distribution (sometimes called the error) of the measurement."

I guess they mean:

"But it is now understood that no treatment of any scientific subject, experiment, or measurement CAN BE said to be accurate without disclosing the nature of the probability distribution (sometimes called the error) of the measurement."

Request for clarification

Hi, this is just to fill a gap in my understanding. Can someone explain to me if there is a relationship between this principle and the calculus notion of limits and infinitesimals? Assuming that we know the mass of the object (pretty common for electrons, etc.) then the uncertainty comes down to not knowing simultaneously the position and velocity. Well, that makes perfect sense to me, because velocity is change in position over time, so a particle doesn't have a velocity at all at an instant, and so it has none at the instant of measurement - it is in a specific position, and if it has a velocity then its position is an interval (no matter how small). Is this right? Or possibly, correct but just unrelated to the uncertainty principle? This intuitive understanding also works for mass, since as it turns out mass is also (from the KE) velocity (change in position) plus a large constant (the rest mass). Kybernetikos 08:24, 26 October 2006 (UTC)

The short answer is: This is not what the UP is about. This way you will not get a finite bound ħ/2 on the uncertainty. There used to be a section that gave a better basic explanation, but it was removed as being misleading. You can see it in the history here.  --Lambiam^Talk 10:12, 26 October 2006 (UTC)

Wave frequency analogy

I am unconvinced about the HUP and it, along with most of quantum physics, is one of several reasons that I gave up plans to become a physicist and turned to pure maths. Anyway.

The wave frequency analogy is very, very unconvincing. It seems as foolish as saying "we can't know what the gradient of a function is at a point, since the gradient is determined by many points over an interval". Sure, we can't calculate it given only information about a single point that lies on the curve. That doesn't mean it doesn't exist. For any f(x), f'(x) is perfectly well-defined and returns a a perfectly good value. Just because we can't measure a quantity accurately doesn't mean the quantity is meaningless. The frequency still exists at a single point in time and it's entirely meaningful, we just can't calculate it without knowledge of the rest of the wave. Am I wrong? Maelin (Talk | Contribs) 13:47, 2 November 2006 (UTC)

You are right, and I think that section could be better written. Suppose you have a function of time f(t) and its fourier transform g(ω). What the section is trying to say is that if you want to estimate g(ω) from some measurements of f(t) you need a number of points of f(t) to do that, one won't work. Suppose you measure f(t) inside a time interval ∆t. The larger ∆t is, the better you can estimate g(ω). However, the larger ∆t gets, the less you can make a definitive statement about the value of f(t) inside ∆t. NOT that f(t) doesn't take on various values inside ∆t, but that you cannot characterize it as a single fixed value. Conversely, the smaller ∆t is, the better you can specify f(t) by a fixed value, but the less you know about the frequency spectrum g(ω).

The equivalent of the HUP in this time-frequency analogy is that if f(t) is very bunched up around a particular value of t (a delta function being the most extreme example), then the frequency spectrum g(ω) is very spread out. On the other hand, if f(t) is very spread out, then it tends to have a very specific frequency. That is, g(ω) is very bunched up around a particular value of ω. Check out the localization property section in the Fourier transform article for a quantitative description. PAR 16:31, 2 November 2006 (UTC)

I have to say, that pure maths is great. The perspective of HUP, however, is that one "can't measure a quantity accurately" despite the fact that the quantity might be "perfectly well-defined." Though its "perfectly well-defined[ness]" cannot be proved.

For greater accuracy, I suppose one can use something other than a standard clock, such as one's "extra sensory perception," but how many times is the result using that method going to be wrong?

HUP doesn't claim that "a perfectly good value" doesn't exist, it just proves that using a standard clock over a finite time period to measure an unknown frequency will contain a probability for error. That alone doesn't make it logical, rational, or even meaningful to abandon the study of physics because there are still much greater unknowns in the physical sciences than those circumscribed by HUP. --Charlesrkiss 04:46, 3 November 2006 (UTC)

I'm more confused now than ever. This seems like a failure of conventional instrumentation, not some Golden Law of Ineffability. The HUP should say, "no device we can think of could measure both the momentum and position of a particle, given our current understanding of quantum mechanics," not "it's impossible to know them both at once". Also, the dodgy paragraph is still in the article. I'm not going to fix it myself because I don't understand the HUP, but someone ought to. Maelin (Talk | Contribs) 12:21, 20 November 2006 (UTC)

Yes please elaborate specifically in the article. If you could measure without using waves or whatever, couldn't you know then? If you could measure the effect on space time itself or something like that for example. -Z 28 Nov 06

Excuse me. As far as I know, instruments, measuring devices, measuring instruments, devices, etc. contain particles; essentially they are collections of particles for the purpose of examining another, totally "unrelated" set of particles ("unrelated" unless you measure every other particle in the Universe simultaneously and have total knowledge of all the laws of physics, ofcourse).

So, if to your satisfaction, one can't measure a simple frequency with another frequency, what the heck else are you going to measure? And how??

The whole principle of Heisenberg is based on our ability to measure "things" with "other things." In other words, we are not God and reality isn't a mathematics text, like you might wish. --Charlesrkiss 04:36, 7 December 2006 (UTC)

Bell's inequality and hidden variables

I'm not sure about this (from the History and Interpretations Section):

"For the greater part of the twentieth century, there were many such hidden variable theories proposed, but in 1964 John Bell theorized the Bell inequality to counter them, which postulated that although the behavior of an individual particle is random, it is also correlated with the behavior of other particles".

I am not sure that John Bell formulated his inequalities with the specific view in mind *to "counter"* hidden variables views-- everything I've read about his view, and that he himself has written and said interviews shows that he supported them, with special sympathies for the deBroglie pilot-wave / Bohmian mechanical interpretation of QM.

Unless it can be substantiated that John Bell formulated his inequality *to counter hidden* variables, I think this section should be removed.

Whether people (other than Bell) *think* on the whole that his inequality refutes hidden variables interpretations is another story, but there's no reason his intentions at the time of arriving at his results should have conformed to what *other people would have later thought* of his results. DivisionByZer0 06:50, 3 November 2006 (UTC)

Help

Okay it often talks of how even with infinitly precise tools you could not measure somethings exact position and velocity and that this has been proven. I would like more on that because it never explains why and what proof. Also it states that it is possible to observe something without disturbing it through quantum entanglement, how is that possible and why wouldn't you be able to be certain of somethings position and velocity at the same time through those means?

Another question, I know its impossible to know velocity and position of an object at the same time, but wouldn't it be possible to measure an onjects exact position, and then later measuring a particle's exact velocity? And if it were travelling in a vacuum at a constant speed you should be able to calculate its exact position at any given time by knowing which way it was going, how fast, and where it was before?

I admit I have a hard time understanding anything to do with quantum physics, so in your explanations to my questions could you do it in laymen's terms? Thanks for any help in advance! --Justaperson117 01:26, 7 December 2006 (UTC)

I must admit the article could be clearer: I may try to improve it if I can. --Michael C. Price ^talk 09:34, 8 December 2006 (UTC)

Try looking at it this way: the measure of momentum contains a velocity vector, it has an orientation, moving in some direction. You couldn't get just one set of coordinates (x₁,y₁,z₁) to measure it's motion; you'd need another set (x₂,y₂,z₂). To get the first set isn't a problem; but to get the first set you have to have interacted with the particle, that's the problem.

Basically, to have a particle you want to look at, you hit the particle with a photon, say; once you hit it, and measure the reflected photon, you get the first set of coordinates; but you've also changed the particles momentum (direction), you have little idea where it's going now; In fact, you had little idea where it was coming from either. It's sort of like that. --Charlesrkiss 21:34, 7 December 2006 (UTC)

You can prove the uncertainty principle if you start out with the basic assumptions of quantum mechanics, but its kind of complicated.

Regarding the entanglement, you measure the other particle by measuring the entangled particle instead, which does not disturb the other particle. But you still disturb the entangled particle. You cannot measure the entangled particle's position and momentum simultaneously, so you can't infer all the other particles properties either.

You can't measure position and then momentum to get both because when you measure position, you disturb the momentum. Then when you measure momentum, you disturb the position, so you never get both at once. PAR 15:25, 8 December 2006 (UTC)

You don't need to start with any quantum mechanical assumptions to undertand the uncertainty principle; HUP predates QP. If you want something convenient to read, scroll up this discussion to "The Basis of the Uncertainty Principle." It writes about the implicit error in comparing two frequencies, and can be sourced in many texts!! It was deleted from the main body of the article, maybe when I have time to work on it, I can make it more concise, emphatic, and universal. The problem is, once one starts expaining it too much it just gets more complicated, ie. dot product/angle, mass-energy, etc. —The preceding unsigned comment was added by Charlesrkiss (talk • contribs) 19:43, 8 December 2006 (UTC).

Actually, that is sort of true. In the restricted case of classical waves (electromagnetic, acoustic, etc) there is an uncertainty principle which is (at least for the electromagnetic case) the same as the quantum principle. But if we interpret the Heisenberg uncertainty principle as the universal application of the principle to include even massive particles, then it must involve the quantum mechanical wave function, in which case the HUP does not predate QP. PAR 20:20, 8 December 2006 (UTC)

Yes, the uncertainty relations exist in classical fields/signal theory, but it requires the De Broglie hypothesis E = hf for matter, not just photons, to turn

$\Delta t\Delta f\geq 1$

into

$\Delta t\Delta E\geq h$

where E = energy, f = frequency, t= time. Ditto for x, p --Michael C. Price ^talk 23:07, 8 December 2006 (UTC)

True, I had it backwards, HUP does not predate QP. But it's Heisenberg's Blackbody Theory, publsihed in 1901, where E = hf that De Broglie extended to massive particles, p and $\lambda ,$ about the year 1925. The Uncertainty Relation was published in 1927, but I've seen credit given to it as early as 1924, I've read. Anyway. --Charlesrkiss 06:26, 9 December 2006 (UTC)

Heisenberg Blackbody theory, published 1901? This is outrageous. Heisenberg was born in 1901 !! The Blackbody theory you mention was due to Max Planck and the year is 1900, 14-th of December to more exact. --Dextercioby 10:32, 15 December 2006 (UTC)

Ooops, yeah, that's what I mean. Sorry. --Charlesrkiss 05:45, 16 December 2006 (UTC)

grammar and punctuation

User Khukri reverted some corrections I made to the article's grammar and punctuation. I think my corrections were right, so I've re-reverted. I'll post on Khukri's user talk page inviting more discussion here, so we don't get into a revert war.--75.83.140.254 18:54, 31 December 2006 (UTC)

Probably most of your corrections were correct (I didn't check), but I did see one edit summary that stood out: you changed "particle state" to "particle's state" with the edit summary "particle" is a noun, which can't modify another noun. That's not true; nouns can be adjectives if they feel like it (see Adjective#Adjectival use of nouns, noun-as-adjective)), e.g. particle physics, mountain bike. That said, both are fine in general. —Quarl ^(talk) 2007-01-02 11:01Z

Also: Verbing weirds language. :) —Quarl ^(talk) 2007-01-02 11:19Z

Landau measurements

The term "Landau measurement" is not defined. The linked article on Landau, while well-written, does not cover this term at all. Neither does the von Neumann bio cover the term "von Neumann measurement." So maybe this article is the right place to define these two terms and explain the distinction, at least briefly. I am not in any position to contribute this, so this is a request for someone capable to do so. Birdbrainscan 17:30, 17 January 2007 (UTC)

Single Particle vs. ensemble

The introduction of the article misinterprets the uncertainty principle to my knowledge by placing it in the context of a single particle. While Heisenberg himself my have put this view forth, I believe modern physicists interpret the uncertainty in the context of the measurement of an ensemble of particles all in the same initial state. Furthermore, the introduction indicates that the more precise we make our position measurements, the less precise we make our momentum measurements- but this is incorrect to my knowledge. If we measure an arbitrary particles position, no matter our "sloppy" our measurement is, is the particle collapses to a position eigenstate and the following momentum "measurement" will be infinitely imprecise-that is, all momentum eigenstates are equally likely after any position measurement has been made. Again, this emphasizes the importance of talking about ensembles and not individual particles- the variance in position, the variance in momentum, or their product is determined by the ensemble of particles all in the same initial state, not by our measurement on one individual particle.

h-bar or h-bar/2 ?

Although every mention of the uncertainty principle on this site suggests dP*dX >= h-bar/2, several sites and my text book state that it is simply dP*dX >= h-bar. Why the discrepancy, and which is correct?

[3] [4]

Peterarmitage 00:31, 5 March 2007 (UTC)

hbar/2 is correct, if you define dP as the standard deviation of P and dX as the standard deviation of X. Rafael Garcia —The preceding unsigned comment was added by 68.118.245.199 (talk) 09:02, 1 May 2007 (UTC).

Intersting Thought

Could not the universe be deterministic in quantum mechanics, not scientifically deterministic though. The particle appears to be in one position due to a faulty measurement, it is affected by a field, its new location appears to have a touch of randomness because of the error in measurement.

Or, does this conflict with the Bell inequality? Ozone 20:48, 21 March 2007 (UTC)

Reading it

I really don't like that this article is so pedantic; there's no other way to put it. I'd think in the unique environment Wikipedia provides, topics such as these should be available to the layman student, but one look at the lead destroys any hope of wading through the rest of it. Of course, I don't think the complicated subject should be 'dumbed' down or anything, but for the same reason that newcomers fail to read policy even when given a direct link to it, this article is inherently untouchable by anyone unfamiliar with it. If it is any real admission of my intellectual statute, I admit it is much easier to read through the articles on Queen and Pokémon, and I think that is because they are written by people who want their subject to be understood. I'm not in a position to offer another rewrite or propose anything, but I'm a little disappointed. ALTON .ıl 07:52, 8 May 2007 (UTC)

I have to agree with this. Having read the article and the talk page, I'm still a little unclear as to why knowing position more accurately necessarily precludes accurate knowledge of velocity. The article makes it clear that uncertainty can be predicted mathematically, and that the UP is not synonymous with the act of observation changing that which is observed. The formulae that are given later are not particularly accessible to laypersons such as myself, but I would really like to understand this concept. Is it possible to describe the underlying idea in conceptual terms? Ethidium 17:39, 11 May 2007 (UTC)

I also agree with the above. There are more laymen in the audience than students, probably (pun-pun). While the subject is understandably technical, the text doesn't have to be so academic. One of the differences between an encyclopedia and a student's subject book. Preroll 00:39, 31 July 2007 (UTC)

Momentum=mass times velocity. Aside from relativistic effects, mass is constant. So uncertainty in momentum is uncertainty in velocity. Mathchem271828 14:18, 31 July 2007 (UTC)

Statistical Ensembles?

The article states: "However, the Robertson-Schrödinger uncertainty relation is not the uncertainty as stated in the Heisenberg uncertainty principle. That is, this derivation is inherently only applicable to measurements on a statistical ensemble of systems, and says nothing, contrary to most popular statements, about the simultaneous measurements of individual systems."

I'm almost certain that that's not right -- that the uncertainty relation between any two non-commuting operators does not pertain only to a statistical ensemble of systems, any more than the standard position-momentum uncertainty does. Can anyone confirm or deny this? --Steve 15:20, 16 May 2007 (UTC)

I went ahead and fixed thisSteve 05:46, 25 May 2007 (UTC)

Question about scalar product and norm

The article says

$\left\langle \psi |X\psi \right\rangle =\|X\psi \|^{2}$

This is obviously wrong if, for instance, we consider $R^{n}$ with the natural scalar product and $X\psi =2\psi$. Could someone clarify on this point please? Avatariks 03:02, 22 May 2007 (UTC)

I fixed thisSteve 05:46, 25 May 2007 (UTC)

Also, what is meant by $\langle A\rangle$ for an Operator $A$? Is it the same as $\left\langle A\right\rangle _{\psi }$ defined in the article? Avatariks 20:23, 23 May 2007 (UTC)

Rewrite of Derivation section

I just rewrote the derivation section, making the following changes: 1) Assuming A:H->H and B:H->H, and x in H, we don't need to worry about Ax, Bx, ABx, or BAx being defined. 2) Took out the comment that the Robertson-Schrödinger uncertainty relation only pertains to statistical ensembles, not an individual quantum system. 3) Removed the incorrect assertion :$\left\langle \psi |X\psi \right\rangle =\|X\psi \|^{2}$. 4) Took out comment giving examples, as these belong in a different section.Steve 05:46, 25 May 2007 (UTC)

Gabor-Weyl Uncertainty Principle

There seems not to be anything on this uncertainty principle. I think it uses a similar Cauchy-Schwartz inequality argument to relate the uncertainty in a function and its Fourier transform. Furby100 04:02, 3 June 2007 (UTC)

Is that the "theorem in functional analysis that the standard deviation of a function, times the standard deviation of its Fourier transform, is at least 1/2."? (from "wave-particle duality" section) I put that in knowing the theorem (from a math problem-set) but not its name. If so, it would be great if you could add the theorem's name, and a reference where it's stated (and ideally proved), to the article. Steve 02:58, 21 June 2007 (UTC)

New opening paragraph?

Enormousdude has added an opening paragraph: "In quantum physics, the HUP is a mathematical property of a pair of canonical conjugate quantities - namely the reciprocity of spans of their spectra. It therefore mathematically limits the accuracy with which it is possible to define and thus to measure such pairs."

Now I'm all for having articles be precise and mathematically correct, but first, the article already has a precise and mathematically correct statement (see, among other places, the "derivation" section), second, Wikipedia policy is that the opening of an article should be accessible to a layman, and this is absolutely not ("reciprocity", "span", and "spectrum" are all incomprehensible to non-experts), third, it's inaccurate to say it's a "mathematical property": it's a physical property, in the sense that its truth is contingent on the laws of physics being a certain way, unlike mathematical theorems, which follows from logic alone, and fourth, a term like "uncertainty" can be just as precise as a term like "span", as long as we give it a precise definition, so why not (in the opening section) use a term that makes it easier to parse?

If there's some relevent mathematical formulation of HUP that isn't already addressed in the article, by all means add a section on it, but this is not an appropriate opening paragraph. I am reverting it. Steve 03:47, 21 June 2007 (UTC)

Uncertainty vs Observer

I have been looking through the article, and while I agree that Uncertainty Principle is independent of the Observer Theory, I fail to see any solid references to back this statement up. I'm sure there are plenty out there, and I was wondering if it would be worth including one or two in the article.

Thanks in advance, Glooper 02:21, 7 July 2007 (UTC)

That entire section is erroneous. It is a closed subject and the article shows a bias towards a flawed outlook. If anyone cares enough to start an edit war, it should be changed. I am sure there will be many people who will favor it's current form, as some textbooks in modern physics for undergraduates include the same erroneous outlook. Mathchem271828 20:16, 17 July 2007 (UTC)

As a writer of (some of) that section, I'll respond a bit. First, I agree that there should be sources. I have loads of books on quantum mechanics, but none that talk about popular misconceptions thereof, so I can't help there.

Second, I agree that the section could use improvement. (For example, I don't think bringing up EPR is helpful.) I think a great idea would be to include specific quotes which make this (alleged?) mistake, to say exactly what it is that the section is (and is not) refuting. In fact, I'd bet that after doing that, the disagreements about content would go away too.

For example, the World Book (1989 ed.) encyclopedia entry on HUP says it "holds true because even the best methods used to measure the position and momentum of a moving particle disturb the particle. For example, physicists might scatter photons...off a moving electron to 'see' its position. But, in a collision, a photon transfers momentum to the electron.... As a result, physicists cannot verify precisely both the position and momentum of the electron at the same time." Now a reasonable non-physicist reading this would understand it to mean that measuring the momentum disturbs the electron's position and vice versa, and that's why HUP is true. Of course, it's very true that measuring momentum disturbs position and vice versa, due to wave function collapse (and this could rightly be called an observer effect), but that has nothing to do with HUP, which as the section laboriously explains, holds even if you do not measure position and momentum subsequently (or simultaneously) on the same particle.

Here's a second example (although I guess this is the same as the first example, but in more detail). The textbook "Modern Physics" by Tipler and Llewellyn (p224) goes through the gamma-ray microscope argument in detail, showing that for aperture angle θ and gamma-ray photon wavelength λ, you get Δx≥λ/(2 sin θ) and Δp_x≥(h sin θ)/λ, so the product is at least h/2. They conclude, "Thus, even though the electron prior to our observation may have had a definite position and momentum, our observation has unavoidably introduced an uncertainty in the measured values of those quantities. This illustrates the essential point of the uncertainty principle—that this product of uncertainties cannot be less than about h in principle, that is, even in an ideal situation." Now a reasonable person reading this would say, "well, if you had prepared two identical copies of that electron, and measured the x-position of the first copy with a tiny wavelength and huge aperture, and measured the x-momentum of the second copy with a huge wavelength and tiny aperture, then there's no reason that the product of uncertainties couldn't get arbitrarily small." The fact that this reasoning doesn't work is proof that what we're talking about is not, in fact, the heart of the uncertainty principle. (It's just a neat, tangentially-related, exercise in semi-classical quantum mechanics.)

Update: I think I was being too harsh in that last, snarky, parenthetical comment: The gamma-ray microscope argument is more than tangentially related the HUP -- it's a special case. The HUP guarantees that it's impossible to construct a measuring apparatus that will simultaneously collapse the position and momentum wavefunctions to the extent that their post-collapse product exceeds hbar/2. So the statement, "Any apparatus that tries to measure position and momentum will satisfy thus-and-such uncertainty bounds, just like the gamma-ray microscope here does" is equivalent to the statement, "the HUP applies immediately after any measurement." So this is a special case of the HUP. But it's no more than a special case, since, for example, HUP applies equally well to the very different wavefunction which was there immediately before a measurement, and this fact cannot be understood just by thinking about the measurement. Steve 02:59, 1 August 2007 (UTC)

So that's what I think the section should be about (again, I agree that the current incarnation could use some improvement). Agree or disagree? Steve 03:14, 18 July 2007 (UTC)

Steve, I am going to re-read the section. Maybe I was in error in my rush to judgement. I would like to think about what it says and what you have put here and get back to you! Mathchem271828 23:14, 18 July 2007 (UTC)

I have added a very solid reference that describes the distinction and gives an example experiment.Teply 19:00, 9 September 2007 (UTC)

What is measurement?

See my user page. --Pateblen 12:36, 1 August 2007 (UTC)

Steve, your comment was well taken so I moved the discussion to my user page. But there certainly seems to be excessive "musings" remaining on this talk page that are not directed toward improvement of this important article (not including yours, which are). I would be interested to know your views on absolute supression of wave function collapse which is required for EPR and Bell experiments. --FP Eblen 14:40, 1 August 2007 (UTC)

Some confusion

First of all, the opening paragraph is unnecessarily complicated. The first sentence alone requires a layman to look up deterministic, probability distribution and standard deviation, nor is it clear what is meant by a ‘system’. Would it not be better to start with a more general sentence or two, like The uncertainty principle is an important concept in quantum physics. It claims that there will always be some uncertainty about the position or momentum of a particle, and that both of these values cannot be accurately measured at the same time.?

More to the point I am having trouble understanding the equation. Presumably delta-x is the standard deviation of the probability distribution of position, and delta-p likewise for momentum (though this is never stated). As I understand it, a standard deviation of zero would indicate certainty. (Wrong?) But it cannot be zero because the equation says their product will never be less than h-bar over 2, which I take to be about 0.527 (wrong?). That doesn't seem to gel with the figure given in the article of 10 to the -35 joule-seconds. Also, if I am reading it rightly it would imply that neither value can be known with certainty (otherwise the product would still be zero) whereas I thought the point was that both cannot be known with certainty. Widsith 16:38, 28 August 2007 (UTC)

The clarity of the opening always has room for improvement I suppose, and your suggestion seems reasonably on-track. I encourage you to look at previous versions of the article if you want to see how impenetrable the opening used to be :-) Yes, Δx and Δp are standard deviations; this is reasonably expressed in the statement "the product of the standard deviations $\Delta x\Delta p\geq \hbar /2$". Or perhaps it's only a clear sentence for people like me who are used to reading math and know how it fits into a grammatical sentence. I'm not sure where you get that hbar over 2 is .527; it is 5*10^-35 Joule-seconds. You're quite correct that neither Δx nor Δp can be precisely equal to zero (or else the other is "infinity", which is physically impossible). Is it implied otherwise somewhere? If so, we should fix it. --Steve 05:18, 29 August 2007 (UTC)

The number confusion was me being stupid. But the article should probably explain this idea in words as well as in the form of an equation. I studied maths till I was 18 but many people are not aware, for example, that ΔxΔp means that they are being multiplied, nor is it actually explained what x or p are or that the delta is designating a standard deviation. What is not clear enough is the point that if this product were zero then the values would be certain, and that the equation makes this theoretically impossible. You explain the numerical value of the right-hand side of the equation - eventually - but you don't explain the significance of its being higher than zero. On your final question, the article says it is impossible to have a particle that has an arbitrarily well-defined position and momentum - am I right then in thinking that and should be or? Don't get me wrong, this article is better than most maths/physics pages in Wikipedia, but the vast majority that I use are still of more use to mathematicians than interested laymen. Widsith 10:33, 29 August 2007 (UTC)

Regarding the last point, "and" is definitely better. Claims that "neither Δx nor Δp can be precisely equal to zero" do not seem well founded.--Michael C. Price ^talk 05:20, 30 August 2007 (UTC)