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From: mathur@pollux.usc.edu (Samir Kumar Mathur)
Newsgroups: sci.physics,sci.philosophy.tech
Subject: a QM paradox (??)
Message-ID: <3794@oberon.USC.EDU>
Date: Sun, 2-Aug-87 17:31:52 EDT
Article-I.D.: oberon.3794
Posted: Sun Aug  2 17:31:52 1987
Date-Received: Sun, 2-Aug-87 22:36:33 EDT
Sender: nobody@oberon.USC.EDU
Reply-To: mathur@pollux.usc.edu (Samir Kumar Mathur)
Distribution: sci
Organization: University of Southern California, Los Angeles, CA
Lines: 63
Keywords: Uncertainity Principle
Xref: mnetor sci.physics:1957 sci.philosophy.tech:340

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.

	(2) At time t+dt:
		(a) I measure the momentum of A, p(A,t+dt) as accurately
			as I wish.
		(b) I measure the position of B, q(B,t+dt) as accurately
			as I wish.
		(c) I calculate p(B,t+dt) = p(A&B,t) - p(A,t+dt) 
			{conservation of momentum} as accurately as I wish.

Conclusion:
	From steps 2(b),(c) I conclude that I can measure p(B,t+dt),q(B,t+dt)  
	as accurately as I wish. This obviously violates Heisenberg's UP.

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I could come up with the following possible explanations for the above
paradox(??) :

1. In the act of observing the two momentums p(A,t),p(B,t) accurately,
	I will always disturb the total momentum of the system and thus 
	I cannot calculate 2(c) from the principle of conservation of
	momentum.

2. The two events 2(b) & 2(c) are not independent and doing one of them
	*instantaneously* effects the other, ie. the two cannot be 
	carried out simultaneously with arbitrary accuracy.

3. My step 2(c) is incorrect because I am assuming some kind of *objectivity*
	(is it the right word in this context ?) in this experiment which
	leads to a wrong conclusion. ie. unless I actually observe p(B,t+dt),
	I can never say that p(B,t+dt) = p(A&B,t) - p(A,t+dt) and that I 
	cannot claim that conservation of momentum holds unless I directly
	measure all the component momentums. But of course, if I do that,
	step 2(b) will not be possible.

------------------------------------------------------------------------------

I would welcome any knowledgeble/reasonable comments on the subject.

Cheers,
Samir.

ps. I am relatively new on this net and in case an isomorph of this question
	has already been discussed, I apologise for reposting it.

*****************************************************************************
	Thought for the day :       Mu.
	
	Samir K. Mathur     (213)-743-2746 (off)
	CS dept., USC.      (213)-748-2524 (Res)
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