From: naturman@uctvax.uct.ac.za
Newsgroups: sci.physics
Subject: Re: Value Rule is sometimes false
Keywords: Calm down Benjamin
Date: 11 Oct 92 19:10:17 GMT
Article-I.D.: uctvax.1992Oct11.171017.203059
Organization: University of Cape Town

In article <Oct.7.22.00.12.1992.2563@ruhets.rutgers.edu>, bweiner@ruhets.rutgers.edu (Benjamin Weiner) writes:
> naturman@uctvax.uct.ac.za writes:
>>Only reply to this if you are deeply familiar with Locality and Realism
>>paradoxes.
> 
> Such arrogance ...

No arrogance intended. Since the subject is quite touchy and could have led to
a lengthy thread with hundreds of people posting, I hoped that by trying to
limit replies to experts on the topic, a lot of unnecessary arguments could be
avoided.

 
>>The VR in interpretations of QM formalism says that
>>if the probability of an observable Q having a value q in state Psi is zero,
>>then Q cannot have value q in Psi.
>>It is certainly agreed that VR is false for observables corresponding to
>>operators with an uncountable spectrum of eigenvalues, since any such
>>eigenvalue has prob. zero in a non-eigenstate.
> 
> This doesn't make any sense.  How about the superposition 
>  |psi> = ( |x=0.4> + |x=0.5> ) / sqrt(2) ?  It's not an eigenstate of
> x, but ...

Ok Ok, delta functions do funny things which I forgot to take into account.

>>Now consider a
>>state Psi where prob(r>0) = prob(r<0), i.e a probability density amplitude
>>symmetric about r=0. Then if p:E-->[0,1] is the probability function for Q
>>having particular values in E in state Psi. Then p(-1) = p(1) = 0.5 while
>>p(0) = 0. 
> 
> Barring a delta function at X=0, fine.

Right, I forgot those delta functions again.
 
>>If we accept VR then we must conclude that Q cannot have value 0 in
>>state Psi. This is false since X can have value 0, and consequently Q
>>has value q = s(0) = 0.
> 
> As you know, though (or should know given that you used "probability
> density") the probability of measuring X and getting *exactly* zero,
> is zero.  One can only measure X to be within some interval dx
> (the probability density has to be under an integral sign, in 
> other words, and we ruled out delta functions above.)

I know, this is precisely the point I'm making.
 
>>If BI [Bell Inequality] needs VR ... [realism carries the day].
>  ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> Burden of proof's on you, bud.

I was hoping that someone familiar with the these interpretation problems would
be able to tell me the answer. If you check my followup, I later went and
looked at the proof of BI myself and found that VR failure doesn't affect BI.
 
>>Please only reply if you are really familiar with the subject. Don't reply if
>>you have free-will hangups or a fetish for retaining Nonlocality at all costs.
>>
>>* Baby Doc Naturman 
> 
> Big, fat, hairy deal.  Not even the guru-est of the gurus ask people
> not to respond to their posts!  This is Usenet, not Phys Rev Letters.
> I do have a free-will hangup, which is why I'm responding.  I figure
> in a wholly deterministic world you would be have no choice but to
> post this drivel, and it would be unfair for me to criticize what was
> essentially foreordained.  (This is a well-known ethical problem with
> strong determinism: how do you justify penalties for criminal acts
> which the criminal was foredoomed to commit?  Think about it, twice.)

This exactly the kind of philosophical argument I wanted to avoid!!
 
> I have no idea why I am talking to someone who calls himself "Baby Doc."
> Are you really trying to call up images of the Haitian dictator
> Baby Doc Duvalier or are you just dense?

No, its a nickname I got because I finished my PhD research at 23. (Not quite
the characteristic of a dense person even if I say so myself.)
 
*****************************************************************************
* Baby Doc Naturman                                                         *
* USS Enterprise                           "It's life Jim,                  *
* Final Frontier                                  but not as we know it."   *
* naturman@uctvax.uct.ac.za                                                 *
*                                                       Spock of Vulcan     *
*****************************************************************************

Hey, I like Star Trek, so what!?
Newsgroups: sci.physics,sci.math