TWO INTERPRETATIONS OF SPATIO-TEMPORAL COUNTERFACTUALSne general (and straightforward) observation which can be made based on chapters 3 and 4 is that there is more than one way to employ Lewis's semantic framework for counterfactual conditionals in the analysis of quantum entangled states.The main reason is that, as we indicated at the end of chapter 2, there may be various ways to define the similarity relation between possible worlds, and this relation is indispensable for the evaluation of counterfactual statements.To characterize the relation of similarity it is necessary to decide which facts from the actual world are salient with respect to the affinity of possible worlds with it, and which are not.We have already reiterated (and this assessment is unanimously, if mostly tacitly, accepted by all who make use of Lewis's semantics in quantum mechanics) that in the context of the quantummechanical phenomena there is no room for law-breaking possible worlds; therefore Lewis's requirement that the number of unlawful events ("miracles") be minimized cannot act as a criterion of similarity between possible worlds.Only singular, individual and contingent facts can set one possible world apart from another, and only such facts can be taken into account when comparing possible worlds with respect to their affinity with the actual world.But it has already been argued that not all facts taking place in the actual world should count towards similarity.It is imperative, then, to make clear how to tell apart those facts that count from those that do not. "ASYMMETRY BY FIAT" SOLUTION REVIVEDIt seems evident that two dominant intuitions regarding the evaluation of quantum counterfactuals have emerged from the extensive discussion in the two previous chapters.However, it will be much more convenient to describe them in terms of extensions to one of Lewis's alternative approaches to counterfactuals rather than in terms of the similarity relation.As we recall (sec.2.3.3),Lewis indicates that the problem with the temporal asymmetry of counterfactuals can find its solution not only within his O 1 It should be stressed, however, that some authors question the assumed asymmetry of counterfactual dependence.For example H. Price, who defends the idea of backward causation, argues that when evaluating counterfactuals we should hold fixed not the past of the antecedent-event, but rather what is epistemologically accessible to us (see Price 1996, pp.169-170, 178-179).2 It is a matter of choice whether to include or exclude the surface of the light cones in the respective "pasts" of e.We will follow the convention according to which, in the first case, the surface of the forward light cone is excluded from the past, but in the second case the surface of the backward light cone is included in it.
TWO INTERPRETATIONS OF SPATIO-TEMPORAL COUNTERFACTUALSne general (and straightforward) observation which can be made based on chapters 3 and 4 is that there is more than one way to employ Lewis's semantic framework for counterfactual conditionals in the analysis of quantum entangled states.The main reason is that, as we indicated at the end of chapter 2, there may be various ways to define the similarity relation between possible worlds, and this relation is indispensable for the evaluation of counterfactual statements.To characterize the relation of similarity it is necessary to decide which facts from the actual world are salient with respect to the affinity of possible worlds with it, and which are not.We have already reiterated (and this assessment is unanimously, if mostly tacitly, accepted by all who make use of Lewis's semantics in quantum mechanics) that in the context of the quantummechanical phenomena there is no room for law-breaking possible worlds; therefore Lewis's requirement that the number of unlawful events ("miracles") be minimized cannot act as a criterion of similarity between possible worlds.Only singular, individual and contingent facts can set one possible world apart from another, and only such facts can be taken into account when comparing possible worlds with respect to their affinity with the actual world.But it has already been argued that not all facts taking place in the actual world should count towards similarity.It is imperative, then, to make clear how to tell apart those facts that count from those that do not. "ASYMMETRY BY FIAT" SOLUTION REVIVEDIt seems evident that two dominant intuitions regarding the evaluation of quantum counterfactuals have emerged from the extensive discussion in the two previous chapters.However, it will be much more convenient to describe them in terms of extensions to one of Lewis's alternative approaches to counterfactuals rather than in terms of the similarity relation.As we recall (sec.2.3.3),Lewis indicates that the problem with the temporal asymmetry of counterfactuals can find its solution not only within his O 1 It should be stressed, however, that some authors question the assumed asymmetry of counterfactual dependence.For example H. Price, who defends the idea of backward causation, argues that when evaluating counterfactuals we should hold fixed not the past of the antecedent-event, but rather what is epistemologically accessible to us (see Price 1996, pp.169-170, 178-179).2 It is a matter of choice whether to include or exclude the surface of the light cones in the respective "pasts" of e.We will follow the convention according to which, in the first case, the surface of the forward light cone is excluded from the past, but in the second case the surface of the backward light cone is included in it.
This book uses the formal semantics of counterfactual conditionals to analyze the problem of non-locality in quantum mechanics. Counterfactual conditionals (subjunctive conditionals) enter the analysis of quantum entangled systems in that they enable us to precisely formulate the locality condition that purports to exclude the existence of causal interactions between spatially separated parts of a system. They also make it possible to speak consistently about alternative measuring settings, and to explicate what is meant by quantum property attributions. The book develops the possible-world semantics of quantum counterfactuals using David Lewis’s famous approach as a starting point but modifying it significantly in order to achieve compatibility with the demands of the special theory of relativity as well as quantum mechanics. There have been several attempts to use counterfactual semantics to strengthen Bell’s theorem and its cognates such as the GHZ and Hardy theorems. These are critically evaluated in the book. Finally, a counterfactual reconstruction of the EPR argument and Bell’s theorem is proposed that sheds a new light on their philosophical consequences regarding the relations between realism and local causation.
his book's main question-Is quantum mechanics non-local?-stilllooms large.But now we at least know that there can be no hope for a simple and unqualified "yes" or "no" answer to this riddle.There is such an enormous variety of interpretations of what constitutes a violation of the locality intuition, not to mention miscellaneous "degrees of severity" of these violations, that it would be utterly hopeless to expect a quick, onceand-for-all resolution to this problem.Yet we have made some progress.Along the quest to find the best counterfactual formulation of the condition of locality we have uncovered two possible interpretations of counterfactual conditionals which seem to be appropriate for describing quantummechanical phenomena that are in the center of our analysis.We should now take an important step forward and utilize these alternative interpretations to propose a precise formulation of the locality condition that could serve as a tenable explication for various intuitions associated with this notion.As we have already seen throughout this book, philosophers of physics and physicists alike often content themselves with pretty nebulous characterizations of the locality condition, of which the following are a representative sample:An event cannot be influenced by events in space-like separated regions.In particular, the outcome obtained in a measurement cannot be influenced by measurements performed in space-like separated regions; and analogously, possessed elements of physical reality referring to a system cannot be changed by actions taking place in space-like separated regions (Ghirardi & Grassi 1994).Since at the time of measurement the two systems no longer interact, no real change can take place in the second system in consequence of anything that may be done to the first system (Greenberger et al. 1990, p. 1132) For many purposes these descriptions may be considered sufficient, but without a thorough investigation into the possible meanings associated with terms such as "influence", "changed by", "in consequence of", etc. we T
Recent discussions by Mermin [1] and Stapp [2] in this journal on non-locality and counterfactuality are shown to contain linguistic problems that require verification. As such they can at most provide us with two subjective choices for the meaning of 'counterfactual statements' in quantum mechanics. We shall show that the word 'counterfactual' is in fact inappropriate here and should be replaced by the word 'hypothetical'. Mermin's choice imposes a strictly contextual meaning based upon an interpretation of counterfactuality which he used to refute, without proof as we shall see, Stapp's logical proof [3] of non-locality in quantum theory. In linguistic theory both authors' choices of meaning: counterfactual versus hypothetical are equally acceptable and therefore some of the issues they discussed lie outside the domain of physics. The issues they discussed are further confused by the fact that in his reply Stapp [2] seems to have adopted Mermin's counterfactual interpretation against his own original [3] hypothetical interpretation. In the rest of this paper we shall adopt the hypothetical sense of Stapp's original statements but we modify his crucial statement LOC2 appropriately, then following his argumentations, we shall show that there is no conflict between relativity and quantum mechanics. We suggest that this should be the natural (pragmatic) choice of meaning in defining the predictions of events in the Hardy experiment.
I have claimed that it is profitable to distinguish three key questions about causation. The first question, what are causal processes and interactions? , was addressed in Chapter 5. The second question, what is the connection between causes and effects? , was addressed in Chapter 7.The third question, what makes a cause different from an effect? , has not been addressed, and it is to that task that we turn in the present chapter. The question of the directionality and asymmetry of causation has long been an important ingredient in philosophical discussions of causation, although perhaps Reichenbach (1991) was the first to truly appreciate the significance of the question. It is certainly an aspect of folk intuitions. Many philosophers have held that an adequate analysis of causality should provide an explanation or account of causal asymmetry. On the other hand, it is precisely this aspect of causation that is the most common target for elimination from empirical accounts. This chapter looks at the ability of 'process' theories of causality to provide such an account, granting certain constraints. The major constraint, or premise, in the following analysis is the assumption that quantum mechanics reveals the presence of backwards-in-time causation. Thus, in the first instance, the argument presented here will not convince those who hold that there can be no backwards causation. However, I derive an empirical prediction, which, if confirmed, would give those sceptical about backwards causation reason to think again. The chapter begins with an analysis of some of the formal properties of causation. This is followed by a nontechnical presentation of the famous difficulties associated with Bell phenomena in quantum mechanics, and the backwards-in-time solution to those difficulties.
A realist about quantum mechanics must say what unperformed measurements would have shown, and the theorems of Bell and Kochen–Specker forbid the obvious way of saying it: a standing valuation of the unmeasured. Every possible-worlds semantics for counterfactuals evaluates at complete worlds—a valuation by another name—so the realist needs counterfactual substance without counterfactual definiteness, and this paper compresses the framework, Aethic reasoning, built to supply exactly that: evaluation by perturbation of the evaluator’s own information state, the similarity ordering deleted rather than refined—absent as a primitive, and unrecoverable at the consequence-relation level on a reading the companion derives, with the full graded verdict function’s representability posed as the open challenge. The move beneath it: determinacy is a two-place relation between an attribute and an information state, and the openness it relativizes is tense-free—an observer’s unlearned past exactly as open as their unformed future. The chain, run once: blanks are constructive and permanent, so relabeling them wholesale as ignorance forces a single sample space that Bell statistics exclude. From there, mutual exclusivity becomes stated interior content, splitting superposition into a disagreeing regime and an agreeing one—the mixed/coherent regime distinction rendered as a difference in what is written, the continuous phase structure carried by the weighting axiom and nowhere on the attribute side. An information state is valid only if no future record can force a contradiction upon it, which is the collapse law, and run over a powerset of paths it draws the quantum–classical boundary as an exact record partition—recovering, with the weighting installed, Feynman’s indistinguishability rule with a non-circular referent for in principle. Collapse is then an indexing transition; cross-observer objectivity survives—no observer can meet another who contradicts them; and one flagged weighting axiom supplies the quantitative face, Malus and eraser phenomenology included. The price is stated with the claims: the Born-form weights are posited, the bridge from formal invalidity to physical unrealizability is a stated principle rather than a theorem, and one open construction—the irretrievability trigger—is where the framework stakes its divergence from universal unitarity.
formalism, which, like propositional dictum, general and unmarked. In this understanding of interpretation, an interpreta tion always an example of more general preexisting truths, an ex emplary part for whole of truth. Moreover, this conception pre serves our common-sense idea of referential function of interpre tation and sign systems more generally: world to language refers preexists (objectively, substantially) language that de scribes it just as necessities of formal logic preexist phenom ena that exemplify those logical necessities. Interpretation, then, con sists of finding a language conforms to preexisting forms. The second concept of interpretation, Greimas and Courtes argue, is completely different. Within this perspective (which they identify with Saussurian linguistics, Husserlian phenomenology and Freudian psychoanalysis—all intellectual movements contemporaneous with quantum theory), no longer a matter of attributing a given to a would otherwise lack one; rather, it a paraphrase formulates in another fashion equivalent con This downloaded from 157.55.39.144 on Wed, 07 Sep 2016 06:27:46 UTC All use to http://about.jstor.org/terms 300 Ronald Schleifer tent of a element within a given semiotic (Semiot ics and Language, 159). In this second understanding of inter pretation, and are not distinct, but rather every form is, alternatively, a semantic content as well, a signifying form, so that offers an analogical paraphrase of something already within a system of signification. Such para phrases are alternatively and different from their model, and as such raise serious questions about referential truth value that seems to govern linguistic dicta and science. That is, alternativeness of paraphrase offers what Jacques Derrida calls without paradigm ... [in elements are] at once analogous (hence series) and utterly different, offering no guaran tee of (Living On, 130). The opposition between modality and dictum presents just this seriality without paradigm. This espe cially clear in extreme case of negation of modal articulation: negation of a statement taken to be modally inflected—e.g., It not true that atom in left half of box or It not true that multiplication of two negative numbers equals a number—presents metonymic iteration without paradigm, para phrase as Like Heisenberg's between quantum theory and levels of language, this understanding of interpretation presents form of an example, yet, by virtue of fact that what it exempli fies necessarily semanticized, it offers an analogy rather than an example. Even abstract formalism of mathematics, from vantage of classical logic without content, carries meanings that be translated and paraphrased. Although number i operates like any ordinary number, when apprehended modally—when understood as a paraphrase of \J-1—it alternatively seems to be no number at all. All these difficult definitions and dis tinctions, Heisenberg writes, can be avoided if one confines lan guage to description of facts, i.e., experimental results (Physics and Philosophy, 185). In this, Heisenberg suggesting that as soon as one interprets facts—and elsewhere he defines facts of quan tum mechanics positivistically as the black spots on a photographic plate or water droplets in a cloud chamber (Physics and Philoso phy, 179)—one enters realm of dualism of alternation and paraphrase. Positivism—in facts are assumed to be simple entities like water droplets in a cloud chamber—does not admit negation. The droplets are either present or absent, there or not there, and when they are not there nothing signifies. As Jacques La This downloaded from 157.55.39.144 on Wed, 07 Sep 2016 06:27:46 UTC All use to http://about.jstor.org/terms Analogy and Example 301 says, the real, whatever upheaval we it to, always in its place,26 and it so precisely because, unlike symbolic systems (to Lacan opposes real), it does not admit negation. The ab sence of droplets only signifies in logic of semantics in ab sence takes on complex positive meaning within a symbolic system just as unmarked of engagement of vocal chords takes on meaning in phonological system of English in absence of voicing distinguishes phoneme /t/ from /d/. These two traditions of interpretation—one classical, other modernist—themselves present a complex double articulation in same way twentieth-century linguistics and Bohr's description of complementarity do. In this complexity, distinction between these traditions not absolute, but rather alternates as a function of questions asked so that interpretation itself remains undecided. Interpretation and understanding, in Emile Benveniste's terms, are cultural phenomena which have characteristic that they never be taken as simple or defined in order of their own na ture but must always be understood as double from fact that they are to something else, whatever their 'referent' may be.27 In an analogical way, nature of data of physics, at least at subatomic scales, cannot simply be defined in order of their own nature. Instead, in same way that even most straight forward, self-evident literal propositions of a sentence—even pure informative (or non-modalized) utterances Greimas and Courtes describe (Semiotics and Language, 10)—can always also be taken to be a figure for something metonymically of them (such as being behind doing, force behind events, very subject articulating propositions that Nietzsche describes), so of quantum physics also always be taken to be connected to something else outside that data: of (modally in flected) knowledge, quality of spatial and temporal position, semiotic system that governs interpretation.