From stapp@thsrv.lbl.gov Wed Jul 22 08:05:25 1998
Date: Tue, 21 Jul 1998 20:46:34 -0700 (PDT)
From: Henry Stapp
To: JLFinkelstein@lbl.gov
Cc: Bill Unruh , Lev Vaidman ,
mermin@msc.cornell.edu, RGRIF@cmu.edu, shimony@buphy.bu.edu
Subject: Re: (non)locality?
I comment on Jerry's comment.
On Tue, 21 Jul 1998, Jerry Finkelstein wrote:
>
>
> On Mon, 20 Jul 1998, Henry Stapp wrote:
>
> >
> > Dear Jerry, 20 July 1998
> >
> > Your intervention is helpful, Let me carry it one step further.
> >
> > For convenience I include your letter in full.
>
> (deleted)
>
> >
> > I think it may be helpful to compare the counterfactual situation
> > under consideration here to a corresponding non-counterfactual
> > one: Supposed for a moment that R1 and R2 could actually both be measured.
> > And suppose we have the two predictions of the theory:
> >
> > 1) L2^R2^g -> c
> > 2) L2^R1^c -> f
> >
> > Then ordinary logic would allow one to conclude that
> >
> > L2 -> [R2^g -> (R1 -> f)]
> >
> > This is a deduced result of the form
> >
> > L2 -> SR~,
> >
> > where the truth of SR~ is fully determined by the truth of statements
> > whose truth-values are determined by the facts located in the region R.
> >
> > If the region R is located (much) earlier that the region L in which
> > the free choice between L1 and L2 is made then I do not think that
> > anyone would deny that if SR~ could be proved to fail in case L1 were to
> > choosen, rather than L2, then the condition of no influence backward in
> > time would fail.
> >
> > The fact that the ``proof'' of SR~ under condition L2 does involve the
> > outcome c in region L would not alter the fact that a nontrivial
> > dependence of the truth-value of SR~ upon which free choice is made at a
> > time later than all the facts that determine the truth of SR~ would mean
> > a failure of the notion of no influence backward in time.
> >
> > Jerry's final statement was:
> >
> > > However, it does not
> > > show that the truth of a statement which has NOTHING to do with the Left can
> > > depend on a choice made on the Left.
> >
> > The point at issue is not about ``NOTHING to do with the Left''.
> >
> > It is about a statement whose truth-value is determined by facts located
> > at an earlier time.
> >
> > One does not say that the truth of SR~ has ``NOTHING to do with the
> > Left'': it was proved to be true only by explicit reference to c on
> > the left. But the MEANING of SR~ (the defining conditions for the truth of
> > SR~) depends only on the facts in region R. The laws of logic
> > allowed one eliminate the middle term of the syllogism, namely the
> > reference to c, and prove. under condition L2 that SR~ must be true.
> > Because the condtions for SR~ to be true depend only on facts in the
> > earlier region, it SR~ were then to fail to be true under condition L1
> > then locality must fail.
>
> I agree with everything up to this point. In fact let me re-emphasize one
> thing you have just said: The MEANING of SR~ has nothing to do with the
> left.
>
> > In comparing our case involving the counterfactual conditional SR to the
> > case of SR~ just considered we see that the reality of R2 and g and of c
> > is not disrupted. The whole difference is in the hypothetical world in
> > which R1 is performed, instead of R2. The condition on the passage from
> > the real/actual world to this hypothetical world is that c be left
> > unchanged: that is assumption LOC1. So instead of simply []-->
> > one might wish to write [A]-->, where A reminds us that the predictions
> > of QM and LOC1 are understood to be included among the premises.
> >
>
> Here I would like to be a little more careful, at least with the
> wording. In my previous message, in the context of LOC1 I defined
>
> > > Aworld: L2 measured, result c found; R2 measured.
> > > Hworld1: L2 measured, result c found; R1 measured.
> > > Hworld2: L2 measured, result d found; R1 measured.
>
> When you say "...c be left unchanged; that is assumption LOC1," it sounds
> as if you are assuming a physical principle called LOC1, and that
> principle implies that Hworld1 (rather than Hworld2) is the correct world
> to associate with Aworld. I would say instead that there is no question
> of "correctness" here, but I am certainly willing to adopt with you the
> definition of counterfactual which results from declaring Hworld1 closer
> to Aworld than is Hworld2. That is the definition which I represented by
> the notation [F]--> (which you seem to be writing [A]-->).
>
I would say that there IS a correct meaning here, in the context of my
announced intention, which is itself within the context of placing
upon physical theories that imbed QT, and that explicity encompass the
notion that the choices by the experimenters are to be treated as free
variables, a constraint that expresses the idea that no effect of these
free choices can act backward in time.
The conditions that one wishes to place on hypothetical worlds is indeed
a matter of theoretical choice. But that choice is constrained by the
nature of the theoretical project at hand.
The project at hand requires imposing a theoretical condition LOC1
that is supposed to restrict the theory by imposing the idea that
the free choice in R is not supposed to have any effect at any
earlier time, and in particular in L. There is, in fact, one actual
course of events, but the idea that the choice made by the
experimenter in R is "free" means that we are supposed to imagine
"possible worlds" in which the choice goes the other way.
And we want to impose upon this extension the locality condition that
the choice has no bachward-in-time effects. But then the locality
condition should rule out your Hworld2: what ``would happen'' if the
choice in R went the other way is that outcome in region L
``would be'' the same no matter which choice is made (later) in R.
The locality idea is a ``physical principle'' in the sense that before the
choice is actually made one is supposed, according to quantum ideas,
to imagine that either of the choices, R1 or R2, is possible: once the
choice is made one of the two possibilities become nonactual. But the
theoretical locality condition can, I think, be viewed as our theoretical
formulation of the ``physical principle'' that this physical free choice
between R1 and R2 is somehow freely made in region R, and has no effects
on anything that lies earlier in time.
> > But the effect of the change to this situation involving counterfactual
> > conditionals is that it means that the nonlocality
> > property that is proved here has consequences only in the context
> > of the theoretical problem of devising a theoretical picture of nature
> > that will accommodate the idea that each experimenter can be considered
> > to be free to choose which experiment he will perform. But even though one
> > is then led to consider mutually exclusive possiblities, there is no
> > assumption alien to orthodox QM because orthodox QM certainly allows one
> > the assume that experimenters can freely choose in this way. I do point
> > out that I have not made any ASSUMPTION that a hypothetical experiment
> > has a definite outcome: such outcomes become definite only insofar as
> > they can be deduced from postulated QM plus LOCALITY.
> >
> >
>
> Good. We agree that the meaning of SR~ has nothing to do with the Left.
> However, I tried to indicate that the MEANING of the counterfactual DOES
> somehow involve the left, by writing
>
> > >
> > > The string of symbols I am writing "(R1) [F]--> (f)" can be expanded
> > > to read "If R1 were measured, and if the result on the Left were the
> > > same as in the actual world, then the result of R1 would be f."
>
> Let me now put it another way. If I look at the definition of SR~, namely
>
> R2^g -> (R1 -> f ),
>
> I understand what that means without having to say anything about the
> Left. But if I look at the corresponding statement SR, namely
>
> R2^g -> (R1 []--> f),
>
> in order to understand the meaning I have to know what the counterfactual
> implication means. Well "R1 []--> f" means " f is true in those worlds
> closest to Aworld in which R1 is true," but in order to evaluate the
> distance of a given hypothetical world from Aworld, I have to say what is
> going on at the Left.
>
> If you do not agree with this, Henry, here is a challenge: can you give a
> complete definition of SR (including, of course, saying exactly what the
> counterfactual means) without making any reference whatsoever to any
> position other than the Right?
>
> In conclusion, I think that the meaning of SR (with the definition of
> counterfactual that we have agreed upon) has something to do with the
> left, in a sense in which the meaning of SR~ does not. And I agree with
> you that the truth of SR does depend upon the choice made at the Left.
>
> Jerry
>
>
>
The way that I understand SR is based on the premise that we are suppose
to accept the idea that the choice made by the experimenter in R is
"free": this choice is not determined or fixed by anything that is earlier
in time, but it could in principle have consequences anywhere in
spacetime.
SR asserts that if the free choice by the experimenter in R happens to
be R2, and if, moreover, the outcome that then appears to the observers
in R turns out to be g, then if that choice had gone the other
way---so that the actual world would have been one in which R1 is
performed, then the outcome f would have appeared to the observers in this
region R.
This meaning of SR makes no reference to any position other than the
Right!
In order to PROVE that this property---which refers only to `facts'
located in R---is in fact true, under some condition pertaining to L, one
must bring in assumptions about QM and LOCALITY, and considerations
pertaining to region L. But the MEANING of SR has nothing at all to do
with L: it is well defined even if there is no measurement at all set
up in L.