Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!mnetor!uunet!seismo!gatech!emory!platt From: platt@emory.uucp (Dan Platt) Newsgroups: sci.physics,sci.philosophy.tech Subject: Re: a QM paradox (??) Message-ID: <2201@emory.uucp> Date: Wed, 12-Aug-87 16:52:25 EDT Article-I.D.: emory.2201 Posted: Wed Aug 12 16:52:25 1987 Date-Received: Sat, 15-Aug-87 01:36:57 EDT References: <3794@oberon.USC.EDU> <1938@batcomputer.tn.cornell.edu> Reply-To: platt@emory.UUCP (Dan Platt) Distribution: sci Organization: Math & Computer Science, Emory University, Atlanta Lines: 91 Keywords: Uncertainity Principle Xref: mnetor sci.physics:2028 sci.philosophy.tech:392 In article <1938@batcomputer.tn.cornell.edu> cpf@tcgould.tn.cornell.edu (Courtenay Footman) writes: ... >In article <3794@oberon.USC.EDU> mathur@pollux.usc.edu (Samir Kumar Mathur) writes: >)Here is a thought experiment which seems to violate Uncertainity Principle (UP) >)that came up at a casual discussion with a friend. >) >)Scenario : >) There are two particles A and B and I am trying to measure their >) momentum and positions accurately. >) >)Experiment : >) (1) At time t: >) (a) I measure the momentums p(A,t) & p(B,t) and hence >) p(A&B,t) = p(A,t) + p(B,t) as accurately as I wish. >Possible >) >) (2) At time t+dt: >) (a) I measure the momentum of A, p(A,t+dt) as accurately >) as I wish. >Possible >) (b) I measure the position of B, q(B,t+dt) as accurately >) as I wish. >Possible. However, when dealing with possible violations of the >uncertainty principle, it is best to use the technique Bohr used >in his debates with Einstein: be as concrete as possible. Do not >just say "measure the position"; say how one is doing it. In this >case, say that the measurement is made visually, by shining a light >on it. (Which can be done as accurately as one wishes.) >) (c) I calculate p(B,t+dt) = p(A&B,t) - p(A,t+dt) >) {conservation of momentum} as accurately as I wish. >Oh. At this point, realize that "shining a light on it" is not >the phrase a physicist would use. A physicist would say "scattering >light off it"... >...Bounce off? What does this do to the momentum of particle >B? It changes it by an unknown amount; the uncertainty of your >knowledge of the momentum of particle B will be greater than or equal >to h divided by the uncertainty with which you know its position. This explanation has always left me unsatisfied for the following reason: The Heisenberg Uncertainty Principle must hold for the particles regardless of whether they are being 'measured' or not. The quantum mechanical description implies limitations in the simultaneous resolution of location and momentum even before measurement. Furthermore, QM makes definite statements of how a measurement may affect the momentum of a particle due to measurement (such as scattering amplitudes from S matrices, or linear responses from Kubo formulas, or any other appropriate response of the system to measurement). It is true that the knowlege isn't deterministic in that you get an amplitude as a function of momentum transfer, but you do get a lot more information than just 'measurement of location at resolutions (wavelengths) as small as we want implies a larger and larger momentum transfer which isn't precisely known.' Also, the limitation on the knowlege of location and momentum via scattering with photons is itself based on the wave/particle duality embodied in the relationship between a function and its Fourier transform. In this sense the measurement argument is redundant once you specify the deBroglie relationships; the quantum formalism has the Heisenberg Uncertaity principle built into it one way or the other (even when you do try to determine the effect a measurement would have on the system while you are measuring it - as in the Kubo formalism). It seems to me that the reason for the extreme operationalism of Bohr (there isn't really a particle there unless you measure it) is that it is one of the easiest positions to defend, and therefore to accept, when confronted with the idea that things aren't deterministic: it's easier to say that the act of measuring something messes up the possibility of simultaneous measurement of conjugate measureables, than it is to say that conjugate measureables really aren't simultaneously measureable or even definable. The operational definitions free one from having to say that quantum mechanics is 'really' what 'reality' is doing, it's just a description. However, this means that a particle's location isn't defined except in terms of a measurement (and there isn't really a location unless you measure it) which I find to be a bit extreme. Therefore, I'd suggest that 1) the deBroglie relationships have been supported in all sorts of experiments from scattering, to tunneling, to coherence; 2) The deBroglie relationships have built into it a limitation on the definition of two conjugate measureables. I don't feel I have to know 'why' in the deterministic Newtonian sense any more than an Aristotilian would need to know 'why' a body could keep moving without the application of force... Dan