augeri@regina.DEC (Mike Augeri) (08/08/85)
I imagine that these questions probably have been asked before, but I have not seen them during the time that I have been reading net.physics, so here goes. I can hear the experts saying "Oh boy, here we go again with some more dumb questions." In over-simplified terms Heisenberg's Uncertainty Principle says that we cannot know the simultaneous position and momentum of an individual elementary particle with unlimited accuracy. Yet, we are able to determine the simultaneous position and momentum of conglomerations of these elementary particles. That is, I can determine the position and momentum of my desk to a degree of accuracy limited only by the resolution of the measuring equipment I use, whereas the Uncertainty Principle says that no matter how accurate my measuring equipment, when it comes to the individual particles making up the desk, it is fundamentally impossible to even make the observation. What is different about the individual particles and groups of particles? Is it strictly a case of the measurement process itself disturbing the individual particle, or is something else going on here? For example, it seems to me that if it is simply a matter of the measurement process disturbing the particles we are trying to measure, then we just have to find a measurement process that uses small enough particles so that they won't disturb the particles we are trying to measure. I am not saying that such particles exist. But in my opinion saying that "in principle, it is impossible to measure the simultaneous position and momentum of a particle" is quite different than saying that "the means to measure the simultaneous position and momentum of a particle does not exist". The net result is the same, but the statements are different. Mike Augeri, DEC, Maynard MA USA
rimey@ucbmiro.ARPA (Ken Rimey) (08/08/85)
>In over-simplified terms Heisenberg's Uncertainty Principle says that we >cannot know the simultaneous position and momentum of an individual >elementary particle with unlimited accuracy. Yet, we are able to >determine the simultaneous position and momentum of conglomerations of >these elementary particles. No, you cannot simultaneously determine the exact position and momentum of a conglomeration either. >What is different about the individual particles and groups of particles? Your intuition about groups of particles is really an intuition about relatively massive objects in the relatively large-scale everyday world. The uncertainty principle is (unc. in pos) (unc. in momentum) >= h = 6.6E-34 Js If you want to insure that some object is in its proper place to an accuracy of 1 micrometer, the uncertainty in its momentum will be 6.6E-28 kg m / s. To get the uncertainty in velocity, we divide by the mass. Let's say the thing weighs a milligram. Then it will likely have a velocity of the order of 6.6E-22 m/s - very small. The problem is that everyday distances are large, and that everyday masses are huge, by atomic standards. The mass of an electron is 9.1E-31 kg; experiment with that number. >Is it strictly a case of the measurement process itself disturbing the >individual particle, or is something else going on here? > > Mike Augeri, DEC, Maynard MA USA Something else is going on here. In classical mechanics, a particle has a position and a momentum. You can be uncertain about the position and momentum, but so what? Lack of knowledge doesn't account for the discrete energy levels of a hydrogen atom. In quantum mechanics, what you don't know is also irrelevant. However, the state of particle simply isn't described by a position and a momentum as in classical mechanics. It makes sense to ask, given a particle in some state what might I get if I measure its position or its momentum? Given the state, I could calculate probability distributions describing what I might get. If the distribution for the position measurement is very tightly peaked around a single position, I say that the state has a well-defined position. If I measure the position, I almost always get values very close to that particular one. Similarly, a state might have a well-defined momentum. Can I have a state that has both a well-defined position and a well-defined momentum? No, there is no such thing. Say you have a single particle. It is described by wavefunction, a complex number for every point in space. The Schrodinger equation determines how this wavefunction changes with time. If at some time the wavefunction is zero someplace, looking for the particle there then is guaranteed fruitless. The probability of finding the particle in a given place is given by the magnitude of the complex number there squared. (I should say "The probability of finding it in a given region ..." but you know what I mean.) Take the fourier transform of this wavefunction. This gives you the momentum space wavefunction, a complex number for each momentum. This determines the probability of finding the particle with a given momentum in the same way as the position wavefunction determines the probability of finding the particle with a given position. Note that the momentum wavefunction cannot be chosen independently of the position wavefunction - it is the fourier transform of the latter. Is it possible to have a function that is nonzero only in a very small region, such that its fourier transform is nonzero only in a very small region? No, that is not possible. The electrical engineers among you may recall that the fourier transform of a narrow gaussian is a wide gaussian and vice versa, that the fourier transform of a spike has infinite extent, and so on. This is the uncertainty principle. I'll mention two questions that my explanation above doesn't address. First, does this momentum wavefunction that I have defined really relate to the p=mv we all know and love? Sure. Take a wavefunction with a moderately peaked position distribution, and a moderately peaked momentum distribution. If you calculate how this wavefunction evolves in time according to the Schrodinger equation, you will find that the peak in the position wavefunction moves with a velocity corresponding to the momentum at which the peak in the momentum wavefunction lies. Second, if it is impossible to determine exact position and momentum simultaneously, then what happens if I try? Does lightning strike me or what? The only way I can think of to measure the position of a free particle is to bounce another particle off of it. If that other particle is to have a well-defined position, there will be a large uncertainty in its momentum, and it will transfer some of that momentum to the particle whose position is being determined. Some people's reaction to this thought experiment is "Aha! So that's what's really going on." They are fooling themselves if they think this is a non-mathematical explanation of why the uncertainty principle is true. The argument is circular. The probe particle is a large disturbance only because it itself must satisfy the uncertainty principle. Ken Rimey rimey@berkeley
gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (08/09/85)
> In over-simplified terms Heisenberg's Uncertainty Principle says that we > cannot know the simultaneous position and momentum of an individual > elementary particle with unlimited accuracy. Yet, we are able to > determine the simultaneous position and momentum of conglomerations of > these elementary particles. No, the same constraint holds. Why do you think otherwise? > Is it strictly a case of the measurement process itself disturbing the > individual particle, or is something else going on here? For example, it > seems to me that if it is simply a matter of the measurement process > disturbing the particles we are trying to measure, then we just have to > find a measurement process that uses small enough particles so that they > won't disturb the particles we are trying to measure. But you can't! > But in my opinion saying that "in principle, > it is impossible to measure the simultaneous position and momentum of a > particle" is quite different than saying that "the means to measure the > simultaneous position and momentum of a particle does not exist". Yes, these are different. QM says that you cannot simultaneously determine (the same component) of the position and the momentum of any object with absolute precision; indeed, because the two are Fourier transform pairs, the simultaneous uncertainties have to obey <x> <p sub x> >= (constant on the order of 1) * h, where h is Planck's constant. <quantity> means the RMS uncertainty of a quantity. This is a matter of fundamental principle, not of insufficient cleverness on the part of the measurer.
brooks@lll-crg.ARPA (Eugene D. Brooks III) (08/09/85)
> In over-simplified terms Heisenberg's Uncertainty Principle says that we > cannot know the simultaneous position and momentum of an individual > elementary particle with unlimited accuracy. Yet, we are able to > determine the simultaneous position and momentum of conglomerations of > these elementary particles. That is, I can determine the position and > momentum of my desk to a degree of accuracy limited only by the resolution > of the measuring equipment I use, whereas the Uncertainty Principle says > that no matter how accurate my measuring equipment, when it comes to the > individual particles making up the desk, it is fundamentally impossible to > even make the observation. You can not measure the simultaneous position and momentum of your desk to any degree of accuracy. QM applies to your desk as well and sets appropo limits. There are gravity wave detectors, aluminum bars, that weigh several tons and require QM to correctly describe them. In the case of your desk, the limits set by QM happen to be many orders of magnitude smaller than any measuring device available to measure its position and momentum.
pmk@prometheus.UUCP (Paul M Koloc) (08/09/85)
> > Yet, we are able to > > determine the simultaneous position and momentum of conglomerations of > > these elementary particles. > To measure the conglomerate (a desk) to the absolute accuracy (atomic scale) is just as "uncertain". To measure the conglumerate to the same "percentage of measure" as an atomic particle, of course is not so uncertain. This is simply because 1% of the diameter of a conglomerate (the earth|desk) is a much larger scale than 1% of the diameter of a neutron. What the uncertainty principle seems to say that the information content of a UNIT "space-time cube" is limited. In other words space is "grainy" and not continuous wrt a "point" test particle. It is quasi-continuous in terms of "delta function" test particles. The measuring function also seems to be "grainy". Sort compounds the problem, like trying to read a fuzzy type written word with blurry vision. - - NOTE: MAIL PATH MAY DIFFER FROM HEADER - - +-------------------------------------------------------+--------+ | Paul M. Koloc, President: (301) 445-1075 | FUSION | | Prometheus II Ltd., College Park, MD 20740-0222 | this | | pmk@prometheus.UUCP; ..seismo!prometheus!pmk.UUCP | decade | +-------------------------------------------------------+--------+
john@frog.UUCP (John Woods) (08/09/85)
> In over-simplified terms Heisenberg's Uncertainty Principle says that we > cannot know the simultaneous position and momentum of an individual > elementary particle with unlimited accuracy. Yet, ... I can determine the > position and momentum of my desk to a degree of accuracy limited only by the > resolution of the measuring equipment I use, whereas the Uncertainty > Principle says that no matter how accurate my measuring equipment, when it > comes to the individual particles making up the desk, it is fundamentally > impossible to even make the observation. > OK, the problem is this: Even desks are subject to Heisenberg's Uncertainty Principle (which applies to many measurement pairs, but position and momentum are particularly easy to grasp). Perform the following (canonical) thought experiment: You have an electron under an ideal microscope, and you want to look at it to find its position and/or momentum. You must use a photon to do this, which knocks the electron about, and (look up the experiment for a clear explanation) is the derivation of the Uncertainty Principle: you must interact to measure, and the minimum interaction comes in units of h-bar/2. (I am not doing this justice, sorry). Now, put your desk under the microscope. How do you propose to find out where it is, or how fast it is going? Ask it? No, you bounce photons off of it. It recoils... and if you calculate the amount that your interaction screws up the situation by, it comes out to (ideally) h-bar/2. Why does it seem that desks are perfectly stable objects, that can have perfectly definite positions even when they fly across your office at several feet per second? Because h-bar/2 is so incredibly tiny when compared to sensible desk-measuring units (like furlong-stone-fortnights), that no-one can possibly care about the difference. (For reference, h-bar/2 (which is h over 4*pi), is .527E-34 joule-sec) After all, the photons from your desk lamp don't send your desk flying, do they? I hope this helps. Aggregate particles are bound by the same kinds of behaviour required of sub-atomic particles, but they (and we) are so large that we do not notice. -- John Woods, Charles River Data Systems, Framingham MA, (617) 626-1101 ...!decvax!frog!john, ...!mit-eddie!jfw, jfw%mit-ccc@MIT-XX.ARPA
debray@sbcs.UUCP (Saumya Debray) (08/10/85)
> In over-simplified terms Heisenberg's Uncertainty Principle says that we > cannot know the simultaneous position and momentum of an individual > elementary particle with unlimited accuracy. Yet, we are able to > determine the simultaneous position and momentum of conglomerations of > these elementary particles. That is, I can determine the position and > momentum of my desk to a degree of accuracy limited only by the resolution > of the measuring equipment I use, whereas the Uncertainty Principle says > that no matter how accurate my measuring equipment, when it comes to the > individual particles making up the desk, it is fundamentally impossible to > even make the observation. Not really. Heisenberg's principle states (more or less) that for quantities related in a certain manner ("canonically conjugate"), the product of the uncertainties in their measured values is of the order of Planck's constant. The x-momentum (momentum along the x axis) and x-position of a particle are canonically conjugate quantities, so cannot be simultaneously measured with unlimited accuracy; however, the y-momentum and x-position are not canonically conjugate, so they can be measured simultaneously without any problem. If you could find sufficiently accurate measuring instruments, I suspect you'd find the uncertainty in the x-momentum and x-position of your desk to be, in fact, be of the order of Planck's constant. The magnitude of this is so small, however, that for "all practical purposes", your knowledge of the position and momentum of your desk is accurate. -- Saumya Debray SUNY at Stony Brook uucp: {allegra, hocsd, philabs, ogcvax} !sbcs!debray arpa: debray%suny-sb.csnet@csnet-relay.arpa CSNet: debray@sbcs.csnet
mikes@AMES-NAS.ARPA (08/13/85)
From: mikes@AMES-NAS.ARPA (Peter Mikes) Subject: Re: Heisenberg Uncertainty Principle In-Reply-To: Article(s) <3506@decwrl.UUCP> > Is it strictly a case of the measurement process itself disturbing the > individual particle, or is something else going on there? Can we > find a measurement process that uses small enough particles so that they > won't disturb the particles we are trying to measure? But you can't! gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn@brl-tgr.ARPA>) I would like to prefix my comment to the above by few disclaimers: 1) the opinions are mine, not my employers, his clients etc etc 2) my opinions on QM are unorthodox - but I hope not in conflict with known facts (or even future one's) 3) I agree, in this case (and others) with Gwyn : "You cant" in both accepted and other interpretations of the Quantum Noise, BUT I think that the fact that "there is no measurement process possible" which would determine p&q DOES NOT (necessarily) implies that 'it is strictly a measurement process itself, disturbing the particles..' . Actually I believe that Heisenberg analysis of different measurement setups is secondary and accidental. There is something called the "fluctuations of the vacuum' which has nothing to do with measurement process. There is an 'intristic pressure' of the electron gas, which can be measured (as high pressure limit of conven- tional materials) and which can be calculated from the Uncertainity Principle. There is no measurement involved! This 'quantum pressure' is as real as an osmotic pressure in gas is real - neither is dependent on what WE know about the system. Once you accept the 'existence' of this disturbance, the Uncertain- ty Principle follows naturally as a special case. I consider the typical textbook presentation of Heisenbergs Principle AS CAUSE of the quantum rand- mness as a half-truth which cannot survive a critical analysis. In other words 'even if you could determine p&q at the same time ( some believe that that is a meanigless statement) I believe that you would not be able to make exact predictions - just knowing the MACROSCOPIC potential and those exact initial conditions.' We all agree, I think, that Gwyn:"This is a matter of fundamental principle, not of insufficient cleverness on the part of the measurer." ...that you cannot measure both p&q. The difference of opinion is subtle and easy to be overlooked. The key, once again is the Einstein's definition of what is ' a complete description of reality'. Later developments (Bell's uneqality and Aspects experiments) did not invalidated his remarkably logical definition, they just confirmed that it is indeed a fundamental principle that 'you cant' discover 'hidden parameters' which a clever experimenter can go after to circumvent Heisen- bergs principle. Accepting both Einstein's definition and Bell's analysis, it seems to me that 1) there is both p and q - 2) There is no way we can determine both. That in itself may be disturbing (that are things which WE cannot know) but it's not impossible (actually - it rather natural). The real issue - which I hope somebody will respond to is this: Bells ana- lysis killed the 'Hidden Parameter Theories'. OK - do the concepts of the 'field' (these are related but non-identical concepts: Bohm's/Fenyes's Quantum potential, DeBroglies Pilot Wave, and this concept of the Quantum Fluctuations, taken outside of the context of QED) which is influencing the microscopic particle, which is moving according to the Schrodingers eq. qualify as Hidden Parameters? I do not see how - and I am eager to learn. Peter M.