From: muttiah@thistle.ecn.purdue.edu (Ranjan S Muttiah)
Subject: Re: The instantaneous transfer of information in QM calculations
Organization: Purdue University Engineering Computer Network
Date: Tue, 12 Jan 1993 00:48:53 GMT

In article <482@mtnmath.UUCP> paul@mtnmath.UUCP (Paul Budnik) writes:
>In article <1993Jan10.005707.11410@noose.ecn.purdue.edu>, muttiah@thistle.ecn.purdue.edu (Ranjan S Muttiah) writes:
>> Paul, I'm not a quantum mechanic (I wish most of the time I was one
>> with a 50% polarization :-), but I don't think the projection postulate
>> necessarily requires this collapse thing.  I think it states that
>> after an experimentation the system will be in state given by: P_a|H>
>> function etc either. Are you questioning whether |H|^2 is really a probability ?
>The linear propagation of the wave function is the evolution of the
>wave function as defined by the Shrodinger equation. I am certainly not
>questioning the interpretation of the wave function as a probability
>question the assumption that wave function changes *instantaneously*
>when an observation is made.

Paul you said that the projection postulate doesn't involve some sort 
of "collapse." On second reading of Anthony Sudbery, I have to eat my words as 
well as your's and say that we were both wrong.  Here's why (from page 186):


Projection Postulate:

	If the result of the experiment is a immediately after the experiment
the system will be in the state described by the state vector
	P_a|PSI>.

Say a quantum object is in state space S (for us Engineers state space=vector
				space :- Why the extra cost of the terminology :).

Say experimental apparatus in state space A.

Let the Eigenstates [*] |PSI1> |PSI2> be in S that correspond to two different
results of the experiment, with corresponding apparatus states |Q1> and |Q2>.
Let the intial state of the appartus be |Q0>.

During experimentation:
 				   theta (phase), courtesy of Dr. Sarfartti.
				  /
	e^-iHt/h(|PSI1>|Q1>) = e^i@1|PSI1>|Q1>
        e^-iHt/h(|PSI2>|Q2>) = e^i@2|PSI2>|Q2>

Now, 
	|PSI0> = c1|PSI1> + c2|PSI2>

	e^-iHt/h(|PSI0>|Q0>) = e^-iHt/h(c1|PSI1>|Q1> + e^-iHt/h(c2|PSI2>|Q2>
			     = e^i@1 c1 |PSI1>|Q1> + e^i@2 c2 |PSI2>|Q2>


Now quoting almost verbatim: "if experiment is done to determine position of
pointer |Q1> with probability |c1|^2, then state of the object + apparatus
is |PSI1>|Q1>  => Object is in state |PSI1>." Similarly for object 2.  This
shows that applying projection postulate to object alone is equivalent to
applying the Schrodinger equation to object + apparatus.  Now remembering that
the Schrodinger equation only applies to an undistrubed system, if there's someone
else watching the experiment, then we would have to apply S. to object+apparatus
+obser which is equivalent to applying projection postulate to object alone etc.  
Funny but true :-).  Actually, there's another invocation of a postulate in the 
above reasoning.


>alters the probability distribution that you use in the second invocation
>of the projection postulate.  This is the *only* way to get predictions of
>nonlocal macroscopic effects from the postulates of quantum mechanics.
>All other laws of physics are local.
>Paul Budnik

I'm having a little difficulty following you here.  The EPR paradox was
based on a contradiction of the uncertainty principle.  Someone should post
a FAQ on the EPR as written (and watchout for the capitals) in the EPR paper!
There are tons of interpretations of that paper that the real message in
the paper is lost (I don't claim to understand their argument BTW).  I think
"locality" in EPR sense meant != FTL. Now Bell's in inequality, locality is 
defined in terms of the independence of probability events i.e., given two results
of experiments, a and b, with state vectors A and B:

	P   (a . b| A . B) = P (a|A) P (b|B)
	 E&F                  E       F

I don't think this necessarily precludes less than speed of light (please 
explain to me if you think otherwise).  Now to be sure (but _only_ to be sure), 
you might want the measurements E and F to be seperated such that there
is no speed of light communication (what you call space-like seperation I believe).
And that's it.  I don't know what else to say.  If Bell's inequality is
violated then the assumptions about probability must be wrong (I think Daryl
M. pointed this out as well).  The information about spins could have been 
exchanged before the experiment had even begun/during/any fancy you want.

__________
[*]
An Eigenstate |phi_x> of a particle is given by the the state of particle after
it passes through a polaroid oriented along the x-axis.  If there's only one way 
of achieving an Eigenstate then that is called a non-degenerate state.