From stapp@thsrv.lbl.gov Wed Jul 22 17:41:30 1998 Date: Wed, 22 Jul 1998 17:38:06 -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? On Wed, 22 Jul 1998, Jerry Finkelstein wrote: > > Dear Henry, > > Thank you for your (second) reply. I think that we are so > nearly in agreement that there is no need for me to reproduce most of your > reply here! In particular, while I like to emphasize that the definition > of counterfactual is a matter of choice, you point out that "The conditions... > on hypothetical worlds...(are) constrained by the nature of the theoretical > project at hand." I am happy to adopt the definition you feel constrained > to make, namely the one under which (to quote from your first reply to me) > "The condition on the passage from the real/actual world to this hypothetical > world is that c be left unchanged." > That is the condition which is relevant to the matter at hand. But let > me record here what I think we would agree upon in a more general > context: For a counterfactual beginning "If R1 instead of R2," > everything not within the forward light cone of R should be > left unchanged. > > My only quibble is with what you write at the end of your reply: > > > 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. > > I think that there is a reference to the Left buried within the phrase > "...then the outcome f would have appeared.." The word "would" indicates > a counterfactual, and we have agreed, I believe, that (part of) the meaning > of the counterfactual is that the outcome on the Left is held fixed. > No! That is no part of the meaning of SR. The meaning of SR has to do exclusively with `facts' located in R: this meaning would be unaffected of there were no experiment at all set up on the left. SR , by itself, is a general statement about possible worlds, and it makes no reference or allusion, or implicit reference to anything at all except for a configuration of `facts' each of which is located in R in some possible world. Of course, SR asserts a very strong condition, which would not in general be expected to hold true: in general the `possible worlds' would not be restricted in this very restrictive way. But I prove that if we impose some very strong conditions on the set of possible worlds then this very restrictive condition SR that pertains exclusively to `facts' located in R must hold true if L2 is performed. For example, the assertion A that every male human being on earth is named `Tom' is a strong condition that is surely not true in the actual world, but the assertion X->A is true if X is the assertion ``If every male human being on earth not named `Tom' is destoyed''. Likewise, one must distinguish the MEANING of SR from certain conditions that entail that it is true. In the case of SR the strong condition that entails it is QM^LOC1^L2. > To put it another way: we have agreed that the phrase > > "If R1 were performed, outcome f would appear" > > does NOT mean "f appears in all worlds (which taken by themselves obey > quantum mechanics) in which R1 is performed" > and in particular does not mean "f appears in Hworld2." > "If R1 were performed, outcome f would appear" DOES mean "f appears in all possible worlds in which R1 is performed" (I consider this statement to be issued from the actual world, in which R2 is performed) > Rather, this phrase "If R1 were performed, outcome f would appear" means > "f appears in all worlds (which taken by themselves obey quantum mechanics) > in which R1 is performed and in which the outcome on the Left is the same as > in the actual world" > > and that is where the reference to the Left comes in. > > Jerry > The phrase "If R1 were performed, the outcome f would appear" means that "f appears in all possible worlds in which R1 is performed" The words "were" and "would" do carry meaning: they tell us that the statement does not refer to the one actual world, or to all possible actual worlds, if that makes any sense. The statement is explicitly about some `possible worlds', and it is specifically about those possible worlds that differ from the actual world only by `physical' consequences of the explicitly mentioned counterfactual condition: otherwise the assertion "would appear" would be too strong, for physics. Now the statement "If R1 were performed, the outcome f would appear" is only about `facts' in R. But it is about these `facts' in the set of possible worlds v' that differs from the actual world v in which the statement is issued only by the consequences of the changes needed to accommodate the counterfactual condition R1. This statement is issued from a world in which R2 is performed, and g appears. So the meaning of the assertion SR: R2^g->[R1[]-->f] is that: If R2 is performed and outcome g appears to the observers in R, then in any possible world that differs from one in which R2^g holds only by the consequences of the switch from R2 to R1 the outcome appearing in R must be f. Of course, that is a strong condition on these possible world, and it is not expected to hold in general. But absolutely no reference is made to the Left: one could apply it to a completely different case in which there is no measurement on the Left. The intuitive meaning is that if one were to extract from some giant ensemble of cases the particular ones in which R2^g hold then in the worlds that "would occur" if the choice of R2 had been reversed, but nothing was allowed to change except for the consequences of that change, the outcome of R1 would be f. Of course, this connection is not expected to hold in general. But the MEANING is specified, within the general context "possible worlds", exclusively by `facts' that are located in R I prove QM^LOC1^L2-> SR. In this context there is an experiment on the Left, and the demand is made that L2 be performed. The MEANING of SR, as specified above, can be applied, and the truth of SR establihed. You might try to argue that the Left comes into the meaning of SR through the notion of "possible worlds". But the only features of those possible worlds that enter into the determination of the truth-value of SR are the `facts' located in R. The PROOF of QM^LOC1^L2->SR certainly uses the occurrence of c, but c is eliminated by the use of the syllogism, {[(g->c)^(c->f)]->(g->f)}, justified by LOC1. Indeed, it is only by virtue of the fact that c can be eliminated in this way that one is able to deduce that the truth conditions for SR are satified: if one could not get rid of the c then one could not establish that the defining conditions for the truth of SR, which say nothing about anything outside R, are satisfied. Henry