---------- Forwarded message ----------
Date: Tue, 19 May 1998 17:31:53 -0700 (PDT)
From: Henry Stapp <stapp@thsrv.lbl.gov>
To: William Unruh <unruh@silias.as.huji.ac.il>
Cc: finkel@thsrv.lbl.gov, mermin@msc.cornell.edu,
    peres@photon.technion.ac.il, RGRIF@cmu.edu, shimony@buphy.bu.edu,
    vaidman@post.tau.ac.il, sofia@techunix.technion.ac.il
Subject: Re: Reply to Unruh's Revised version

Dear Bill, 

Thank you for clarifying your position. I think these clarifications
do allow me to pinpoint our differences, and to make quite clear why
your arguments, or at least the one's that you have described here, do not
apply to my proof. I reproduce below all of your note, with my comments
interleafed and appended.

On Tue, 19 May 1998, William Unruh wrote:

> 
> Thanks again for your response. However, I think that it still misses the
> point I was making. Under your interpretation L1 was actually and
> independently measured. 

No! I assume L2 is actually measured: From the standpoint of the *actual
situation* in which L2 and R2 are measured, and outcome g appears to the
observers stationed in R, one considers some hypothetical situations in
which certain free choices are imagined to be other than what they
actually are. The issue is whether one can consistently assume (i.e.,
imagine) that the changes in these free choices have absolutely no
faster-than-light effects of any kind.

To proceed, I assume that you meant to write L2, instead of L1.

> Under that assumption then if R2 is measured to
> have value g, then one can legitimately infer that the actually measured
> value of L2 is c, and furthermore, one can separate the truth of that
> of the statement that L2 has value c from the evidence that R2 has value
> g, because one now has a separate line of evidence, namely that L2 was
> actually and independently measured. However, as I state in my paper, one
> then cannot do the same for R1, since R1 was NOT independently measured.

The status of the outcome of R1 is indeed very different from the status
of the outcome of L2: L2 is actually measured and the observers in L must,
by virtue of the asserted facts, and a result from QT, observe outcome c.
But R1 is not actually measured and the claim regarding which outcome 
would be observed if R1 had been performed rests directly upon a
locality assumption LOC1 that is more open to question here than the
validity of the predictions of QT.

> (That is the essense of the counterfactual-- that it was R2 not R1 taht
> was actually measured.) Now one can use the value of L2, namely c, to
> infer that if R1 HAD been measured, its value would have been f.  

Agreed!

> But now
> the truth of the statement R1 is f cannot be seperated from the evidence
> used to infer that value, namely that L2 is c. Ie, under the assumption
> that L2 is actually measured, then I believe that your argument falls when
> you seperate the truth of R1 is f from the evidence that L2 is c, and try
> to state that R1 is f follows only from L2 having been measured. 

I do not claim that ``f follows only from L2 having been measured.''

My claim in line 4 is that if the actual situation is one in which L2 and
R2 are performed, and the observers in R observe outcome g, then if we
imagine that a change in R at the later time can have no effect on what
the observers in L have already observed, and that the predictions of QT
hold also in the hypothetical situation, then one can conclude that if R1
were performed in the hypothetical situation then in that hypothetical
situation the observers in R must observe outcome f.

You say you believe that my argument fails, but you did not
correctly state my argument. My argument, stated above, is more
complex, and it follows the normal canons of reason.  So you must
show how or why it conflicts with the principles of QT.
You argue as follows:

> Ie, the
> step
> (L2^c^R1^f)->(L2^R1^f)
> is false when the only evidence for counterfactual R1 being f is L2^c.
> 
> Now usually in logic, a subset of a true statement which is a conjunction
> of statements is also true.--ie statement (A^B) is true only if A and B
> are also true seperately. However, in this case, the true of R1^f depends
> on the truth of L2^c and does not have any truth value (as a
> counterfactual) from the truth value of L2^c. In particular R1^f is not
> true under just the truth of L2 having been measured. One must adjoin to
> L2 the truth of its value as c as well before one can deduce that the
> counterfactual R1 is f.
> 

I have already answered that argument: My statement 4 is 

(L2^R2^g) =>[(R1/R2)--> (L2^R1^f)]

where => is normal implication (the strict conditional) and (R1/R2)-->
means `If, hypothetically, R1 is performed instead of (the actual) R2,
then, in this hypothetical situation, it is true that...'.

This is not an assertion that R1^f is true ``under just the truth of
L2 having been measured'': there is the crucial further condition
R2^g that is needed before one can claim R1^f.
 
The arrow -> in your statement needs to be defined. In reasoning one
generally wants to pass from some assumptions to some perhaps simple
conclusion. One needs, therefore, to simplify the statements, and not
carry along the entire proof. The meanings of => and ^ are thus generally
defined so that the step A^B => A is valid. It is certainly advantagous
to define the meanings of the symbols (or the words corresponding to them)
so that this normal rule of logic works, and this is achieved in modal
logic. Your claim is evidently that quantum strictures cast some cloud
on the possibility of doing this in a quantum context.  

Of course, words (symbols) and their meanings can be defined in various
ways. The issue therefore is not whether there is some way to interpret
words (or symbols) in such a way as to make my argument fail in a
quantum context. It is rather whether my way of interpreting my words and
symbols, which *is* compatible with the normal rules of logic, contravenes
any strictures on reasoning imposed by quantum philosophy. 

Normally one has the rule A^B => A, and I retain that
rule. Obviously your claim that A^B->A is false means that you are
adopting some other rules. The question is whether the strictures imposed
by normal quantum philosophy force me to adopt your meanings.

Your argument for the failure of L2^c^R1^f to imply L2^R1^f is this:  

> Your statement 3 of course does have L2^c^R1->L2^R1^f
> as a statement of the Hardy state. But this is true of the hardy state
> only if L2 and R1 have been seperately measured, and not if R1^f is simply
> infered from L2^c. Doing so I still argue is to appeal to some notion of
> the reality of R1^f- ie that the truth can be seperated from the evidence.  
> 
> 
> Bill
 
	
In my argument R1^f is not a reality: it is a hypothetical result that
would, by virtue of a number of theoretical assumptions about a certain
realm of hypothetical worlds that is deliniated by those assumptions,
occur in such a hypothetical world. I stay far far away from any notion
that R1^f is a reality. 

The reality is L2^R2^g, which entails also the fact that in the real world
the observers in L do in fact observe the outcome c: the predictions
of quantum theory in the actual word specified by L2^R2^g ensure that the
observers in L do observe the outcome c (in complete agreement with the
von Neumann argument that you agree must be preserved).

The inference that under those actual conditions the hypothetical R1 would
have outcome f is not dependent upon any notion of the reality of R1^f:
quite to the contrary it is explicitly made clear in my argument that R1^f
is purely hypothetical. 

But I explicitly emphasized the fact that an important theoretical
constraint upon the allowed hypothetical worlds is that the
laws of physics are supposed to hold in those hypothetical worlds: if the
laws of nature are allowed to fail in the hypothetical worlds then no
rigorous results of the kind being sought here would be derivable.

This clearly stated crucial assumption is what allows one to invoke
the quantum laws (L2^R1^c)=> (L2^R1^f) in the hypothetical world in which
R1 is performed. There is no need to, or tendency to, confuse the hypothetical 
R1^f with reality: rather I carefully maintain throughout the  argument a 
clear distinction between the real and the hypothetical, and explictly
state, and emphasize, the crucial assumption that allows the quantum laws
to be applied to the hypothetical world.

Nor has the truth of R1^f in the hypothetical world, under the
explicitly stated condition, been separated from the evidence.
You have accepted as evidence the actual observations of the observers in
L, namely L2^c: this is the evidential basis for concluding that
in the hypothetical world in which R1 is performed instead of R2 the
observers in R would observe outcome f. This crucial linkage between
the outcome f in the hypothetical world and the outcome c in the actual
world comes, in part, from the basic assumption in this argument, namely
LOC1, which asserts that in the hypothetical worlds under consideration,
which are supposed to differ from the actual worlds only by a change in
the free choice made by the experimenter in the later region R, and by the
consequences of that change, the outcome actually observered earlier by
the observers stationed in L is unchanged.

Nowhere in this argument is there an assumption, or intimation, of the
existence of any reality except for one actually existing one that
meets the conditions  that L2 and R2 are performed and the outcome g
appears to the observers stationed in R.

Best regards, Henry