From stapp@thsrv.lbl.gov Fri Jun 26 11:00:01 1998 Date: Fri, 26 Jun 1998 10:33:40 -0700 (PDT) From: Henry Stapp To: Bill Unruh 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 Subject: Re: reply to unruh sent to Phys. Rev. A On Thu, 25 Jun 1998, Bill Unruh wrote: > > > > > > > > On Wed, 24 Jun 1998, Bill Unruh wrote: ... > > > To summarise, You say that the following chain of reasoning is valid. > > > > > > L2^R2^g -> L2^c^R2^g-> L2^c^R2 -> L2^c^R1->L2^c^R1^f->L2^R1^f > > > 1 2 3 4 5 > > > Where 1 follows from the Hardy state property, 2 from more specific > > > implies less specific, 3 from LOC1, 4from Hardy state, and 5 from more > > > specific to less again. (You condense this whole chain in your > > > proposition 5 going just from the first to the last in one step) > > > I say that if all of R1, R2 and L2 were really measured then these steps > > > would be valid. > > > > Of course, the whole purpose of the argument leading to line 5 is to use > > the assumption that the choice between R1 and R2 is supposed to be a free > > choice between alternative possibilities only one of which, namely R2, > > actually occurs. I have been very explicit in emphasizing that the > > possible world in which R1 occurs is purely hypothetical, and the issue > > being examined is whether it is possible to construct a rationally > > coherent theoretical idea in which the laws of nature hold also in the > > theoretical world in which R1 is performed, instead of R2, and nothing > > else is changed in that hypothetical world except for consequences of the > > change, in the later region R, of R2 to R1. > > > > > Furthermore, if one had some nothion of realism, then > > > they would again be valid. > > > > Even in classical thinking one does not imagine that R1 and R2 are both > > real: that both could be performed. And the only realities in the logical > > universe that I consider are the measurements in mutually > > exclusive possible worlds and the appearance to the observers in some > > such world of an outcome of a measurement that is performed in that world. > > There is no simultaneous existence of outcomes that exist in alternative > > possible worlds. > > > > This reality structure is in full accord with quantum > > philosophy. I stress again that I make no reality assumptions that are > > alien to what quantum philosophy allows. The only allowed *correlations* > > between outcomes in alternative possible worlds are ones strictly entailed > > by the explicitly stated theoretical conditions. > > No disagreement here. I never claimed that you do something else. > > > > > However, R1 is not actaully measured. step 4 > > > is an inference about the value R1 would have if it were (although it > > > has not been) measured, > > > > Yes! It is an inference drawn---within a reality structure that is > > completely in line with quantum philosophy---from several explicitly > > stated assumptions. > > > > We agree. > > > > or is an inference drawn from treating L2 as the > > > measuring apparatus for R1. > > > > > However in either case step 5 is invalid. > > > because R1 having value f is an inference drawn from the acutual > > > measurement make on L2, and is not the outcome of an actual independent > > > meansurement of R1 , you cannout drop the determining condition (c) > > > which leads to the inference that R1 would have value f. > > > ... > > I agree that `R1 having value f is an inference drawn from actual > > measurement made on L2, and that f is not the outcome of an actual > > measurement of R1'. Certainly the proof that the outcome f would appear > > to the observers of R1 does involve the fact that c appears to the > > observers of L2. You claim that therefore the conclusion that > > ``L2 implies SR'' is not valid. > > > > But what is the basis of that claim? > > > > The basis is that step 5 in my expansion of your argument above is > invalid. L2^c implies SR, but L2 does not imply SR. > > > I am using a reality structure that is completely in line with > > quantum philosophy, and have deduced the existence of a certain > > correlation pertaining to possible outcomes in R in two alternative > > possible worlds on the basis of a locality assumption LOC1 that does > > assert the existence of *another* correlation (namely an identify of > > an *earlier* outcome) between these two alternative possible worlds. > > Fine, agreed. > > > > You reject my proof on the basis of the following argument. > > > > I reject your proof on the basis that step 5 above does not follow from > your assumptions. > > > > (by general to specific I mean that in ordinary discourse, if two or more > > > conditions are asserted as jointly true, then any subset is also true. > > > However in quantum mechanics, this is not admissable if one of the set > > > is asserted as true only because of the truth of another. Truth is more > > > conditional. This is why, since f is true only because c is true, > > > removing c also removes f since R1 has, by assumption, not actually been > > > measured. It is a counterfactual and has in fact not been measured > > > (except perhaps by the apparatus L2). f is an inferred value rather than > > > a truely measured value. The assumption that the truth of the value f is > > > , once established, independent of the evidence for its truth (namely c) > > > is what I call an assumption of realism. Of course, the claim is not that f is true. Statement f does not stand alone. The claim is that, under the stated assumptions, L2 implies SR. > > > Without that assumption, step 5 > > > is invalid. You have agreed that the reality structure in my argument is in accord with quantum philosophy. > > > > > > Note that in your statement of the properties of the hardy state you > > > state that L2^c^R1->L2^R1^f. The general statement that one can make is > > > that L2^c^R1->L2^c^R1^f. IF L2 and R1 are actually measured > > > independently, then your statement follows. However, that I would claim > > > is the only situation in which your statement is asserted by quantum > > > mechanics and the Hardy state. *************************************************************************** *> > > Quantum mechaics does not assert that in * *> > > the Hardy state, L2^c^R1->L2^R1^f is always true, ie, even if R1is *> > > counterfactually asserted. * ************************************************************************** > > > > My stated intention was to find out whether it was possible to > > construct a theoretical idea in which there was not only the actual > > world but also a hypothetical world that also obeyed the predictions of > > QM, and which was connected to the actual world in accordance with > > condition LOC1. If one does not impose the condition that the hypothetical > > world conforms to the predictions of QM the there is no longer any > > question: the whole situation becomes completely flabby. > > I have never claimed that I believe the hypothetical world violates the > predictions of quantum mechanics. Where in my argument have you deduced > this? Well, the statement in the box that I have outlined by asterisks is a prediction of quantum theory that would be true if R1 were the experiment actually performed in R. If R1 and L2 were both actually performed this prediction of quantum theory could be written in various equivalent forms: (L2^R1^c)->f, or (L2^R1)->(c->f), or (L2^c)->(R1->f), or (L2^c^R1)->f, or (L2^c^R1)->(R1^f). I choose to include the condition R1 with f in order to keep manifestly on display the fact that the outcome f is claimed to appear only under the condition that R1 is performed. I included L2 in the conclusion in order to keep manifestly on display what the freely chosen conditions were, but the inclusion of these two conditions, L2 and R1, would, if they were both actual, be completely gratuitous. The assumption that this prediction of quantum theory, (L2^R1^c)->(L2^R1^f), is true also in the *hypothetical* world in which L2 and R1 are performed allows one to pass from the statement L2^c^R1 directly to L2^R1^f: steps 4 and 5 are thereby replaced by the single step 4', L2^c^R1--> L2^R1^f. So I completely circumvent step 5. > Quanum mechanics does assert that L2^c^R1-> L2^c^R1^f. However, if > R1 is not measured independently, then L2^c^R1^f does not imply L2^R1^f. > This is the statement about quantum mechanics I am making. This claim is > entirely within your demand that the hypothetical world satisfy the > rules of quantum mechanics. Using my explicitly stated assumption that the prediction of quantum theory L2^R1^c->L2^R1^f is satisfied in the hypothetical world allows me to by-pass the assertion L2^c^R1^f->L2^R1^f that you are challenging: I never use that statement. That fact already is enough to dispose of your challenge. But, in any case, you have agreed that my reality structure is completely compatible with the principles of quantum theory. So what is the basis of your claim that within quantum theory this most basic principle of logic---that the truth of a conjunction of statements implies the truth of each individual statement---fails: that application of this principle constitutes a reality assumption that violates quantum philosophy. I hardly think that Bohr would sanction the casting out of this basic principle of logic in the name of quantum philosophy, in a discussion that is confined to assertions about possible measurements and the possible outcomes appearing to the observers. Your justification for going to such extreme lengths to reject my argument is this: > One of the features of quantum mechanics, > which you have agreed with, is that the truth of proposition is not > independent of the evidence used to prove that truth. f is not > independent of c if c is the only evidence for the truth of f. > The key statement in this argument, `f is not independent of c ...', is ambiguous: it is stated in a loose and overly compactified way that blurs out important distinctions. The fact that under condition L2^c the statement `f appears to the observers in R under condition R1' would be true does indeed depend on the fact that c appears to the observers in L. But this meaning of the statement `f is not independent of c' does not entail that the statement `f appears to the observers in under R condition R1' could not be true also under other conditions. The meaning of this statement `f appears to the observers in R under conditions R1' depends on the defining conditions for it to be true, not upon some *particular condition* that entail that these defining conditions are satisfied. Your implicit suggestion that f is somehow inseparably tied to c does not take into account the distinctions that arise when the meaning of the symbol f in `f is not independent of c' is spelled out. The logical structure that I employ does satisfy---for reason that I have described above, which you have accepted---all the reality requirements imposed by quantum philosophy. Most specifically, there is never any implication that an unperformed measurement has a well defined outcome. Clear thinking requires making the important distinctions, and by making the distinctions described above---within the unproblematic logical framework that I employ---one sees that f need not be inseparably tied to c, and that quantum reality conditions do not require rejecting the basic law of logic A^B->A. > > So if you reject this whole problem that I am posing then there is no > > basis of discussion. Certainly in normal reasoning about `what would > > happen if...' there is the presumption that one does not contemplate > > wholesale abandonment of every physical law: that goes even beyond > > science fiction, and we are trying to stay within scientific theory. > > > > I (as opposed to some of your critics) am perfectly willing to consider > counterfactual arguments. I also believe that any such arguments are > strongly dependent on the theoretical framework (in this case the > valididty of quantum mechanics). The dispute is over which aspects of > quantum mechanics survive their trip to the hypothetical world. > > > I repeatedly emphasized that a key condition for the problem was that the > > laws of QM hold not only in the actual world, which is all that quantum > > theory demands, but also in the hypothetical worlds. If you are willing to > > say that it is impossible to uphold THAT condition, together with LOC1, > > then we have no disagreement. > > The laws of QM hold. The questionis what are those laws. I mean the usual predictions of quantum theory in the actual world, and the very same assertions for the hypothetical worlds under consideration. > Your conditions > 2 and 3 are conditions which hold for actually independently measured > situations. They do not hold for cases in which the values are infered > rather than independently measured. > > > > > > I would agree that quantum mechanics does > > > allow oneoto assert L2^c^R1->L2^c^R1^f since one can regard L2 as a > > > measuring apparatus for R1, and the value c does, by the standard von > > > Neuman argument allow one to deduce vale f for R1 even if R1 has not > > > been actually measured (eg in the counterfactual situation). HOwever it > > > does not in general allow the dropping of c from the right hand side of > > > this relation.) > > > > > > > We agree, finally, that the problem as I posed it, which demands that the > > predictions of QM hold not only in the actual world but also in the > > hypothetical worlds under consideration, is what my argument applies to: > > one can maintain LOC1 and not get line 5 if one relinquishes, instead of > > LOC1. all other conditions on the hypothetical worlds, and in particular > > the demand that they conform to the predictions of QM. > > > I guess we disagree on what the predictions of quantum mechanics are > then. I say that in general > L2^c^R1-> L2^c^R1^f > under some conditions L2^c^R1^f -> L2^R1^f, but those conditions do not > survive the trip to the hypothetical world, because R1 is not actually > and independently measured in that hypothetical world. > > > > > I hope this clarifies my argument to you. > > > > Yes! I am glad that we have isolated the source of disagreement, and that > > it in no way negates or undermines my explicitly stated claims. > > > In particular, the problem that I pose explicitly asserts that the hypothetical worlds under consideration satisfy the predictions that quantum theory would impose if they were the actual world, and this includes *the specifically stated* prediction L2^c^R1-> L2^R1^f. The reality structure I use is compatible with quantum philosophy, and, if the essential necessary distinctions are made, then examination reveals no need to reject the logical principle that the truth of a conjunction implies the truth, individually, of each of its component elements. Yours sincerely, Henry