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. Fresheneesz08:30, 20 April 2006 (UTC)[reply]
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. linas15:53, 22 December 2005 (UTC)[reply]
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. linas17:37, 23 December 2005 (UTC)[reply]
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. --Voyajer21:28, 22 December 2005 (UTC)[reply]
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. linas17:37, 23 December 2005 (UTC)[reply]
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.--Voyajer21:39, 22 December 2005 (UTC)[reply]
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. (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."
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. linas17:37, 23 December 2005 (UTC)[reply]
---
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.--Voyajer20:02, 1 January 2006 (UTC)[reply]
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.--Voyajer00:48, 3 January 2006 (UTC)[reply]
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.
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.
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. linas22:00, 26 January 2006 (UTC)[reply]
For the reason of I rarely coming here,so email me: coralieiloveu@yahoo.com.tw as any new reply about this question appears.
--HydrogenSu10:31, 25 January 2006 (UTC)[reply]
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. --DanielCD01:45, 5 February 2006 (UTC)[reply]
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). linas04:04, 5 February 2006 (UTC)[reply]
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. --DanielCD05:30, 5 February 2006 (UTC)[reply]
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->?
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 4.25018:30, 21 February 2006 (UTC)[reply]
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"
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. linas01:47, 22 February 2006 (UTC)[reply]
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). linas16:46, 22 February 2006 (UTC)[reply]
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. 12.37.33.304:33, 18 March 2006 (UTC)[reply]
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. -lethetalk+05:16, 18 March 2006 (UTC)[reply]
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. Linguofreak02:34, 19 March 2006 (UTC)[reply]
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. -lethetalk+17:35, 21 March 2006 (UTC)[reply]
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. dolph16:56, 21 March 2006 (UTC)[reply]
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. Linguofreak05:12, 22 March 2006 (UTC)[reply]
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. linas15:25, 22 March 2006 (UTC)[reply]
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. -lethetalk+19:56, 22 March 2006 (UTC)[reply]
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) Linguofreak16:12, 26 March 2006 (UTC)[reply]
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. -lethetalk+16:47, 26 March 2006 (UTC)[reply]
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. -lethetalk+16:50, 26 March 2006 (UTC)[reply]
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. Linguofreak20:53, 26 March 2006 (UTC)[reply]
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. -lethetalk+22:41, 26 March 2006 (UTC)[reply]
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. Linguofreak03:36, 27 March 2006 (UTC)[reply]
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. -lethetalk+05:06, 27 March 2006 (UTC)[reply]
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. -lethetalk+05:19, 27 March 2006 (UTC)[reply]
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. -lethetalk+23:12, 2 April 2006 (UTC)[reply]
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.
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? --ScienceApologist02:40, 11 April 2006 (UTC)[reply]
(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. --ScienceApologist02:43, 11 April 2006 (UTC)[reply]
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.--CSTAR02:52, 11 April 2006 (UTC)[reply]
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? Rcq00:33, 22 May 2006 (UTC)[reply]
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
