This paper is devoted to clarification of the notion of entanglement through decoupling it from the tensor product structure and treating as a constraint posed by probabilistic dependence of quantum observable _A_ and _B_. In our framework, it is meaningless to speak about entanglement without pointing to the fixed observables _A_ and _B_, so this is _AB_-entanglement. Dependence of quantum observables is formalized as non-coincidence of conditional probabilities. Starting with this probabilistic definition, we achieve the Hilbert (...) space characterization of the _AB_-entangled states as amplitude non-factorisable states. In the tensor product case, _AB_-entanglement implies standard entanglement, but not vise verse. _AB_-entanglement for dichotomous observables is equivalent to their correlation, i.e., $\langle AB\rangle _{\psi} \not = \langle A\rangle _{\psi} \langle B\rangle _{\psi}.$ We describe the class of quantum states that are $A_{u} B_{u}$ -entangled for a family of unitary operators (_u_). Finally, observables entanglement is compared with dependence of random variables in classical probability theory. (shrink)

In this note we demonstrate that the results of observations in the EPR–Bohm–Bell experiment can be described within the classical probabilistic framework. However, the “quantum probabilities” have to be interpreted as conditional probabilities, where conditioning is with respect to fixed experimental settings. Our approach is based on the complete account of randomness involved in the experiment. The crucial point is that randomness of selections of experimental settings has to be taken into account within one consistent framework (...) covering all events related to the experiment. This approach can be applied to any complex experiment in which statistical data are collected for various experimental settings. (shrink)

In the framework of the histories approach to quantum mechanics developed by Griffiths and Omnès, we consider the question of the uniqueness of the probability assigned to the histories; the question was solved by Omnès only in special cases. We find conditions which ensure uniqueness of such probability in the general case.

The well-known proposal to consider the Lüders-von Neumann measurement as a non-classical extension of probability conditionalization is further developed. The major results include some new concepts like the different grades of compatibility, the objective conditional probabilities which are independent of the underlying state and stem from a certain purely algebraic relation between the events, and an axiomatic approach to quantum mechanics. The main axioms are certain postulates concerning the conditional probabilities and own intrinsic probabilistic interpretations (...) from the very beginning. A Jordan product is derived for the observables, and the consideration of composite systems leads to operator algebras on the Hilbert space over the complex numbers, which is the standard model of quantum mechanics. The paper gives an expository overview of the results presented in a series of recent papers by the author. For the first time, the complete approach is presented as a whole in a single paper. Moreover, since the mathematical proofs are already available in the original papers, the present paper can dispense with the mathematical details and maximum generality, thus addressing a wider audience of physicists, philosophers or quantum computer scientists. (shrink)

Emilio Santos has argued (Santos, Studies in History and Philosophy of Physics http: //arxiv-org/abs/quant-ph/0410193) that to date, no experiment has provided a loophole-free refutation of Bell’s inequalities. He believes that this provides strong evidence for the principle of local realism, and argues that we should reject this principle only if we have extremely strong evidence. However, recent work by Malley and Fine (Non-commuting observables and local realism, http: //arxiv-org/abs/quant-ph/0505016) appears to suggest that experiments refuting Bell’s inequalities could at most (...) confirm that quantum mechanical quantities do not commute. They also suggest that experiments performed on a single system could refute local realism. In this paper, we develop a connection between the work of Malley and Fine and an argument by Bub from some years ago [Bub, The Interpretation of Quantum Mechanics, Chapter VI(Reidel, Dodrecht,1974)]. We also argue that the appearance of conflict between Santos on the one hand and Malley and Fine on the other is a result of differences in the way they understand local realism. (shrink)

Popper's idea of propensities constituting the physical background of predictable probabilities is reviewed and developed by introducing a suitable formalism compatible with standard probability calculus and with its frequency interpretation. Quantum statistical ensembles described as pure cases (“eigenstates”) are shown to be necessarily not homogeneous if propensities are actually at work in nature. An extension of the theory to EPR experiments with local propensities leads to a new and more general proof of Bell's theorem. No joint probabilities (...) for incompatible observables need to be introduced. (shrink)

Motivated by a recent proof of free choices in linking equations to the experiments they describe, I clarify some relations among purely mathematical entities featured in quantum mechanics (probabilities, density operators, partial traces, and operator-valued measures), thereby allowing applications of these entities to the modeling of a wider variety of physical situations. I relate conditional probabilities associated with projection-valued measures to conditional density operators identical, in some cases but not in others, to the usual reduced (...) density operators. While a fatal obstacle precludes associating conditional density operators with general non-projective measures, tensor products of general positive operator-valued measures (POVMs) are associated with conditional density operators. This association together with the free choice of probe particles allows a postulate of state reductions to be replaced by a theorem. An application shows an equivalence between one form of quantum key distribution and another with respect to certain eavesdropping attacks. (shrink)

We present a derivation of the third postulate of relational quantum mechanics from the properties of conditional probabilities. The first two RQM postulates are based on the information that can be extracted from interaction of different systems, and the third postulate defines the properties of the probability function. Here we demonstrate that from a rigorous definition of the conditional probability for the possible outcomes of different measurements, the third postulate is unnecessary and the Born’s rule naturally (...) emerges from the first two postulates by applying the Gleason’s theorem. We demonstrate in addition that the probability function is uniquely defined for classical and quantum phenomena. The presence or not of interference terms is demonstrated to be related to the precise formulation of the conditional probability where distributive property on its arguments cannot be taken for granted. In the particular case of Young’s slits experiment, the two possible argument formulations correspond to the possibility or not to determine the particle passage through a particular path. (shrink)

In the present paper, I shall argue that quantum theory can contribute to reconciling evolutionary biology with the creation hypothesis. After giving a careful definition of the theological problem, I will, in a first step, formulate necessary conditions for the compatibility of evolutionary theory and the creation hypothesis. In a second step, I will show how quantum theory can contribute to fulfilling these conditions. More precisely, I claim that (1) quantum probabilities are best understood in terms (...) of ontological indeterminism, but (2) reflect nevertheless causal openness rather than divine indifference or arbitrariness, and (3) such a genuinely creative universe can be considered as the work of a loving Creator. I ask subsequently whether these necessary conditions are also sufficient for the compatibility of evolutionary theory and the creation hypothesis. Finally, I will show that relating evolutionary biology with theology via quantum theory could also shed some light on the nature of life. (shrink)

The concepts of joint probability as implied by the Copenhagen and realist interpretations of quantum mechanics are examined in relation to (a) the rules for manipulation of probabilistic quantities, and (b) the role of the Bell inequalities in assessing the completeness of standard quantum theory. Proponents of completeness of the Copenhagen interpretation are required to accept a modification of the classical laws of probability to provide a mechanism for complementarity. A new formulation of the locality postulate is given, (...) not involving factorizability or conditional probabilities, which clarifies the role of locality in the derivation of the Bell inequalities. (shrink)

It is pointed out that the probabilistic character of a theory does not indicate by itself a distancing with respect to the norms of objectification. Instead, the very structure of the calculation of probabilities utilised by this theory is capable of bearing the trace of a constitution of objectivity in Kant’s sense. Accordingly, the procedure of the constitution of objectivity is first studied in standard and in quantum cases with due reference to modern cognitive science. Then, an examination (...) of the differences between classical and quantum probabilities is performed. It is shown that the form of the quantum calculation of the probabilities carries the mark of the contextuality of the phenomena on which it bears. Conversely, certain conditions that have the form of Bell’s inequalities carry the mark of decontextualization. (shrink)

The probabilities a Bayesian agent assigns to a set of events typically change with time, for instance when the agent updates them in the light of new data. In this paper we address the question of how an agent's probabilities at different times are constrained by Dutch-book coherence. We review and attempt to clarify the argument that, although an agent is not forced by coherence to use the usual Bayesian conditioning rule to update his probabilities, coherence does (...) require the agent's probabilities to satisfy van Fraassen's [1984] reflection principle (which entails a related constraint pointed out by Goldstein [1983]). We then exhibit the specialized assumption needed to recover Bayesian conditioning from an analogous reflection-style consideration. Bringing the argument to the context of quantum measurement theory, we show that "quantum decoherence" can be understood in purely personalist terms---quantum decoherence (as supposed in a von Neumann chain) is not a physical process at all, but an application of the reflection principle. From this point of view, the decoherence theory of Zeh, Zurek, and others as a story of quantum measurement has the plot turned exactly backward. (shrink)

Quantum information science is a source of task-related axioms whose consequences can be explored in general settings encompassing quantum mechanics, classical theory, and more. Quantum states are compendia of probabilities for the outcomes of possible operations we may perform on a system: ''operational states.'' I discuss general frameworks for ''operational theories'' (sets of possible operational states of a system), in which convexity plays key role. The main technical content of the paper is in a theorem that (...) any such theory naturally gives rise to a ''weak effect algebra'' when outcomes having the same probability in all states are identified and in the introduction of a notion of ''operation algebra'' that also takes account of sequential and conditional operations. Such frameworks are appropriate for investigating what things look like from an ''inside view,'' i.e., for describing perspectival information that one subsystem of the world can have about another. Understanding how such views can combine, and whether an overall ''geometric'' picture (''outside view'') coordinating them all can be had, even if this picture is very different in structure from the perspectives within it, is the key to whether we may be able to achieve a unified, ''objective'' physical view in which quantum mechanics is the appropriate description for certain perspectives, or whether quantum mechanics is truly telling us we must go beyond this ''geometric'' conception of physics. (shrink)

Quantum probability is used to provide a new organization of basic quantum theory in a logical, axiomatic way. The principal thesis is that there is one fundamental time evolution equation in quantum theory, and this is given by a new version of Born’s Rule, which now includes both consecutive and conditional probability as it must, since science is based on correlations. A major modification of one of the standard axioms of quantum theory allows the implementation (...) of various mathematically distinct models (commonly called ‘pictures’) of them. A natural definition of isomorphism of models is presented next. For a given Hamiltonian the standard ‘pictures’ of quantum theory (e.g., Schrödinger, Heisenberg, interaction) are isomorphic models, whose probabilities are nonetheless model independent. The Schrödinger equation remains valid in one model of the axioms, even though it is no longer the fundamental equation of time evolution. All the usual calculations of standard, textbook quantum theory remain valid, but they are put in a new light. For example, the ‘collapse’ of the state is now viewed in the Schrödinger model as _one_ step in a _two_ step algorithm for calculating _one_ conditional probability. In the isomorphic Heisenberg model, where states are constant in time, one has the same conditional probability given by the same formula. Also, entanglement is defined in a new, more general model independent way as an aspect of quantum probability without using ‘collapse’ or tensor products. (shrink)

We argue that quantum theory does not allow for a generalization of the notion of classical conditional probability by showing that the probability defined by the Lüders rule, standardly interpreted in the literature as the quantum-mechanical conditionalization rule, cannot be interpreted as such.

The use of probability theory is widespread in our daily life as well as in scientific theories. In virtually all cases, calculations can be carried out within the framework of classical probability theory. A special exception is given by quantum mechanics, which gives rise to a new probability theory: quantum probability theory. This dissertation deals with the question of how this formalism can be understood from a philosophical and physical perspective. The dissertation is divided into three parts. In (...) the first part, the formalism of quantum probability theory and its relation to quantum mechanics is presented. The second part considers the possibility of reformulating quantum probability theory to embed it within classical probability. Mathematically, this possibility overlaps with the possibility of the existence of hidden variables theories of quantum mechanics: theories that attempt to solve fundamental problems in quantum mechanics by introducing additional physical properties of systems. The conclusion of this part is that, although classical reformulations of quantum probability theory are formally possible, they offer little insight into the formalism of quantum probability theory itself. The third part regards a more direct investigation of quantum probability theory. A reformulation of quantum probability theory is obtained by constructing a quantum logic on the basis of empirical non-probabilistic predictions of quantum mechanics. In this reformulation quantum probability functions are conditional probability functions on an algebra of propositions about measurements and measurement outcomes. (shrink)

In previous work, a non-standard theory of probability was formulated and used to systematize interference effects involving the simplest type of quantum systems. The main result here is a self-contained, non-trivial generalization of that theory to capture interference effects involving a much broader range of quantum systems. The discussion also focuses on interpretive matters having to do with the actual/virtual distinction, non-locality, and conditional probabilities.

It is argued that quantum mechanics does not have merely a predictive function like other physical theories; it consists in a formalisation of the conditions of possibility of any prediction bearing upon phenomena whose circumstances of detection are also conditions of production. This is enough to explain its probabilistic status and theoretical structure.

Friedman and Putnam have argued (Friedman and Putnam 1978) that the quantum logical interpretation of quantum mechanics gives us an explanation of interference that the Copenhagen interpretation cannot supply without invoking an additional ad hoc principle, the projection postulate. I show that it is possible to define a notion of equivalence of experimental arrangements relative to a pure state φ , or (correspondingly) equivalence of Boolean subalgebras in the partial Boolean algebra of projection operators of a system, which (...) plays a role in the Copenhagen explanation of interference analogous to the role played by the material equivalence, given φ , of certain propositions in the Friedman-Putnam quantum logical analysis. I also show that the quantum logical interpretation and the Copenhagen interpretation are equally capable of avoiding the paradoxical conclusion of the Einstein-Podolsky-Rosen argument (Einstein, Podolsky, and Rosen 1935). Thus, neither interference phenomena nor the correlations between separated systems provide a test case for distinguishing between the relative acceptability of the Copenhagen interpretation and the quantum logical interpretation as explanations of quantum effects. (shrink)

An interesting link between two very different physical aspects of quantum mechanics is revealed; these are the absence of third-order interference and Tsirelson’s bound for the nonlocal correlations. Considering multiple-slit experiments—not only the traditional configuration with two slits, but also configurations with three and more slits—Sorkin detected that third-order (and higher-order) interference is not possible in quantum mechanics. The EPR experiments show that quantum mechanics involves nonlocal correlations which are demonstrated in a violation of the Bell or (...) CHSH inequality, but are still limited by a bound discovered by Tsirelson. It now turns out that Tsirelson’s bound holds in a broad class of probabilistic theories provided that they rule out third-order interference. A major characteristic of this class is the existence of a reasonable calculus of conditional probability or, phrased more physically, of a reasonable model for the quantum measurement process. (shrink)

The Conditional Probability Interpretation of Quantum Mechanics replaces the abstract notion of time used in standard Quantum Mechanics by the time that can be read off from a physical clock. The use of physical clocks leads to apparent non-unitary and decoherence. Here we show that a close approximation to standard Quantum Mechanics can be recovered from conditional Quantum Mechanics for semi-classical clocks, and we use these clocks to compute the minimum decoherence predicted by the (...) Conditional Probability Interpretation. (shrink)

This paper relates both to the metaphysics of probability and to the physics of time asymmetry. Using the formalism of decoherent histories, it investigates whether intuitions about intrinsic time directedness that are often associated with probability can be justified in the context of no-collapse approaches to quantum mechanics. The standard approach to time symmetry in the decoherent histories literature is criticised, and an alternative approach is proposed, based on two decoherence conditions within the one-vector formalism. In turn, considerations (...) of forwards and backwards decoherence and of decoherence and recoherence suggest that a time-directed interpretation of probabilities, if adopted, should be both contingent and perspectival. (shrink)

A classical probabilistics explanation for a typical quantum effect in Hardy's paradox is demonstrated.

In the Bayesian approach to quantum mechanics, probabilities—and thus quantum states—represent an agent’s degrees of belief, rather than corresponding to objective properties of physical systems. In this paper we investigate the concept of certainty in quantum mechanics. Particularly, we show how the probability-1 predictions derived from pure quantum states highlight a fundamental difference between our Bayesian approach, on the one hand, and Copenhagen and similar interpretations on the other. We first review the main arguments for (...) the general claim that probabilities always represent degrees of belief. We then argue that a quantum state prepared by some physical device always depends on an agent’s prior beliefs, implying that the probability-1 predictions derived from that state also depend on the agent’s prior beliefs. Quantum certainty is therefore always some agent’s certainty. Conversely, if facts about an experimental setup could imply agent-independent certainty for a measurement outcome, as in many Copenhagen-like interpretations, that outcome would effectively correspond to a preexisting system property. The idea that measurement outcomes occurring with certainty correspond to preexisting system properties is, however, in conflict with locality. We emphasize this by giving a version of an argument of Stairs [(1983). Quantum logic, realism, and value-definiteness. Philosophy of Science, 50, 578], which applies the Kochen–Specker theorem to an entangled bipartite system. (shrink)

Nobel Laureate in physics Wolfgang Pauli studied philosophy and the history of ideas intensively, especially in his later years, to form an accurate ontology vis-à-vis quantum theory. Pauli's close contacts with the Swiss psychiatrist C.G. Jung gave him special qualifications for also understanding the basic problems of empirical knowledge. After Pauli's sudden death in 1958, this work was maintained mainly in his posthumously published correspondence, which so far extends only to 1939. Because Pauli's view differs essentially from the (...) direction physics research took after the deaths of the founding fathers of quantum theory, this article attempts to describe the main features in Pauli's revolutionary thought, which is based on nature's “epistemological lesson” as revealed by Pauli's atomic research. Pauli's conclusions have important implications for various issues in Western culture, not least with the limits of science and the relation of science to religion. (shrink)

We present a procedure which allows us to recover classical and nonclassical logical structures as concrete logics associated with physical theories expressed by means of classical languages. This procedure consists in choosing, for a given theory ${{\mathcal{T}}}$ and classical language ${{\fancyscript{L}}}$ expressing ${{\mathcal{T}}, }$ an observative sublanguage L of ${{\fancyscript{L}}}$ with a notion of truth as correspondence, introducing in L a derived and theory-dependent notion of C-truth (true with certainty), defining a physical preorder $\prec$ induced by C-truth, and finally selecting (...) a set of sentences ϕ V that are verifiable (or testable) according to ${{\mathcal{T}}, }$ on which a weak complementation ⊥ is induced by ${{\mathcal{T}}. }$ The triple $(\phi_{V},\prec,^{\perp})$ is then the desired concrete logic. By applying this procedure we recover a classical logic and a standard quantum logic as concrete logics associated with classical and quantum mechanics, respectively. The latter result is obtained in a purely formal way, but it can be provided with a physical meaning by adopting a recent interpretation of quantum mechanics that reinterprets quantum probabilities as conditional on detection rather than absolute. Hence quantum logic can be considered as a mathematical structure formalizing the properties of the notion of verification in quantum physics. This conclusion supports the general idea that some nonclassical logics can coexist without conflicting with classical logic (global pluralism) because they formalize metalinguistic notions that do not coincide with the notion of truth as correspondence but are not alternative to it either. (shrink)

Twenty five years ago, Sir John Carew Eccles together with Friedrich Beck proposed a quantum mechanical model of neurotransmitter release at synapses in the human cerebral cortex. The model endorsed causal influence of human consciousness upon the functioning of synapses in the brain through quantum tunneling of unidentified quasiparticles that trigger the exocytosis of synaptic vesicles, thereby initiating the transmission of information from the presynaptic towards the postsynaptic neuron. Here, we provide a molecular upgrade of the Beck and (...) Eccles model by identifying the quantum quasiparticles as Davydov solitons that twist the protein α-helices and trigger exocytosis of synaptic vesicles through helical zipping of the SNARE protein complex. We also calculate the observable probabilities for exocytosis based on the mass of this quasiparticle, along with the characteristics of the potential energy barrier through which tunneling is necessary. We further review the current experimental evidence in support of this novel bio-molecular model as presented. (shrink)

Although Wittgenstein’s influence on logic and foundations of mathematics is well recognized, nonetheless, his legacy concerning other sciences is much less elucidated, and in this article we aim at shedding new light on physics, artificial intelligence, and cognitive science from a Wittgensteinian perspective. We focus upon three issues amongst other things: the Chosmky versus Norvig debate on the nature of language; a Neo-Kantian parallelism between Bohr’s philosophy of physics and Hilbert’s philosophy of mathematics; the relationships between cognitive contextuality (...) and physical contextuality as shown by recent Bell-type results. The Chosmky versus Norvig debate may be seen as a battle between Wittgenstein’s earlier and later conceptions of meaning, i.e., picture theory and use theory. From a Wittgensteinian point of view, quantum physics may be seen as a physical version of the Linguistic Turn. The parallelism between Bohr’s philosophy of classical concepts and Hilbert’s philosophy of finitism builds upon transcendental philosophy in the Kantian tradition, both Bohr and Hilbert having been influenced by Neo-Kantian thinkers, such as Hertz, whose sign theory is actually a common root of Wittgenstein’s picture theory and Hilbert’s axiomatics. Wittgenstein is considered a root of contextualism in contemporary philosophy. Contextuality has different manifestations in physics and cognitive science, and contextuality studies across the sciences are rapidly developing in cutting-edge research. We elucidate both analogies and disanalogies between contextuality of reality and contextuality of reason in terms of the nature of probabilities involved. In passing, we also give a reformulation of Penrose’s quantum mind thesis. (shrink)

There is another meeting place for quantum physics and psychology, both within and outside of cognitive modeling. In physics it is known as the issue of classical (probabilistic) determinism, and in psychology it is known as the issue of selective influences. The formalisms independently developed in the two areas for dealing with these issues turn out to be identical, opening ways for mutually beneficial interactions.

Although Wittgenstein’s influence on logic and foundations of mathematics is well recognized, nonetheless, his legacy concerning other sciences is much less elucidated, and in this article we aim at shedding new light on physics, artificial intelligence, and cognitive science from a Wittgensteinian perspective. We focus upon three issues amongst other things: the Chosmky versus Norvig debate on the nature of language; a Neo-Kantian parallelism between Bohr’s philosophy of physics and Hilbert’s philosophy of mathematics; the relationships between cognitive contextuality (...) and physical contextuality as shown by recent Bell-type results. The Chosmky versus Norvig debate may be seen as a battle between Wittgenstein’s earlier and later conceptions of meaning, i.e., picture theory and use theory. From a Wittgensteinian point of view, quantum physics may be seen as a physical version of the Linguistic Turn. The parallelism between Bohr’s philosophy of classical concepts and Hilbert’s philosophy of finitism builds upon transcendental philosophy in the Kantian tradition, both Bohr and Hilbert having been influenced by Neo-Kantian thinkers, such as Hertz, whose sign theory is actually a common root of Wittgenstein’s picture theory and Hilbert’s axiomatics. Wittgenstein is considered a root of contextualism in contemporary philosophy. Contextuality has different manifestations in physics and cognitive science, and contextuality studies across the sciences are rapidly developing in cutting-edge research. We elucidate both analogies and disanalogies between contextuality of reality and contextuality of reason in terms of the nature of probabilities involved. In passing, we also give a reformulation of Penrose’s quantum mind thesis. (shrink)

Quantum mechanics and probability theory share one peculiarity. Both have well established mathematical formalisms, yet both are subject to controversy about the meaning and interpretation of their basic concepts. Since probability plays a fundamental role in QM, the conceptual problems of one theory can affect the other. We first classify the interpretations of probability into three major classes: inferential probability, ensemble probability, and propensity. Class is the basis of inductive logic; deals with the frequencies of events in repeatable experiments; (...) describes a form of causality that is weaker than determinism. An important, but neglected, paper by P. Humphreys demonstrated that propensity must differ mathematically, as well as conceptually, from probability, but he did not develop a theory of propensity. Such a theory is developed in this paper. Propensity theory shares many, but not all, of the axioms of probability theory. As a consequence, propensity supports the Law of Large Numbers from probability theory, but does not support Bayes theorem. Although there are particular problems within QM to which any of the classes of probability may be applied, it is argued that the intrinsic quantum probabilities are most naturally interpreted as quantum propensities. This does not alter the familiar statistical interpretation of QM. But the interpretation of quantum states as representing knowledge is untenable. Examples show that a density matrix fails to represent knowledge. (shrink)

In this work, we focus on the philosophical aspects and technical challenges that underlie the axiomatization of the non-Kolmogorovian probability framework, in connection with the problem of quantum contextuality. This fundamental feature of quantum theory has received a lot of attention recently, given that it might be connected to the speed-up of quantum computers—a phenomenon that is not fully understood. Although this problem has been extensively studied in the physics community, there are still many philosophical questions (...) that should be properly formulated. We analyzed different problems from a conceptual standpoint using the non-Kolmogorovian probability approach as a technical tool. (shrink)

: Probably the crux of quantum science is the relationship between consciousness and reality. The name for that relation is varied, and points out to a most fundamental problem, namely the possibility to overcome dualism. In science and philosophy at large, determinism and reductionism have already been tackled, if not superseded. The trouble though remains with dualism. This paper argues in favor of a radical relationship between reality and consciousness based on quantum theory. Such a relation is panpsychism, (...) which can be translated and grasped in various other forms. The arguments are provided and some conclusions are drawn. Resumo: Provavelmente, o cerne da ciência quântica é a relação entre consciência e realidade. O nome dado a dessa relação varia, o que aponta para um problema fundamental, a saber, a possibilidade de se superar o dualismo. Na ciência e na filosofia em geral, o determinismo e o reducionismo já foram abordados, se não superados. O problema permanece com o dualismo. Este artigo argumenta em favor de uma relação radical entre realidade e consciência baseada na teoria quântica: o panpsiquismo, que pode ser descrito e apreendido em várias formas. Os argumentos são fornecidos e algumas conclusões são tiradas. (shrink)

The paper makes a case for there being causation in the form of causal properties in the domain of fundamental physics. That case is built on an interpretation of quantum theory in terms of state reductions so that there really are both entangled states and classical properties (although that case does not necessarily depend on such an interpretation). GRW is the most elaborate physical proposal for such an interpretation. I show how this interpretation suggests a commitment to entangled (...) states being dispositions for spontaneous localizations, more precisely being causal properties or structures that are the power to bring about classical properties through state reductions in the form of spontaneous localizations. That commitment implies conceiving quantum probabilities as propensities and accepting a fundamental law that is not time-reversal invariant. The paper indicates several arguments for these commitments. (shrink)

We show that the so-called quantum probabilistic rule, usually introduced in the physical literature as an argument of the essential distinction between the probability relations under quantum and classical measurements, is not, as it is commonly accepted, in contrast to the rule for the addition of probabilities of mutually exclusive events. The latter is valid under all experimental situations upon classical and quantum systems. We discuss also the quantum measurement situation that is similar to the (...) classical one, described by the Bayes formula. We show the compatibility of the description of this quantum measurement situation in the frame of purely classical and experimentally justified straightforward frequency arguments and in the frame of the quantum stochastic approach to the description of generalized quantum measurements. In view of derived results, we argue that even under experiments upon classical systems the classical Bayes formula describes particular experimental situations that are specific for context-independent measurements. The similarity of the forms of the relation between the transformation of probabilities, which we derive in the frame of the quantum stochastic approach and in the frame of the approach, based on straightforward frequency arguments, underlines once more that the projective (von Neumann) measurements represent only a special type of measurement situations in quantum physics. (shrink)

This paper investigates the kind of empiricism combined with an operationalist perspective that, in the first decades of our Century, gave rise to a turning point in theoretical physics and in probability theory. While quantum mechanics was taking shape, the classical (Laplacian) interpretation of probability gave way to two divergent perspectives: frequentism and subjectivism. Frequentism gained wide acceptance among theoretical physicists. Subjectivism, on the other hand, was never held to be a serious candidate for application to physical theories, (...) despite the fact that its philosophical back-ground strongly resembles that underlying quantum mechanics, at least according to the Copenhagen interpretation. The reasons for this are explored. (shrink)

This paper offers a critique of the Bayesian interpretation of quantum mechanics with particular focus on a paper by Caves, Fuchs, and Schack containing a critique of the “objective preparations view” or OPV. It also aims to carry the discussion beyond the hardened positions of Bayesians and proponents of the OPV. Several claims made by Caves et al. are rebutted, including the claim that different pure states may legitimately be assigned to the same system at the same time, and (...) the claim that the quantum nature of a preparation device cannot legitimately be ignored. Both Bayesians and proponents of the OPV regard the time dependence of a quantum state as the continuous dependence on time of an evolving state of some kind. This leads to a false dilemma: quantum states are either objective states of nature or subjective states of belief. In reality they are neither. The present paper views the aforesaid dependence as a dependence on the time of the measurement to whose possible outcomes the quantum state serves to assign probabilities. This makes it possible to recognize the full implications of the only testable feature of the theory, viz., the probabilities it assigns to measurement outcomes. Most important among these are the objective fuzziness of all relative positions and momenta and the consequent incomplete spatiotemporal differentiation of the physical world. The latter makes it possible to draw a clear distinction between the macroscopic and the microscopic. This in turn makes it possible to understand the special status of measurements in all standard formulations of the theory. Whereas Bayesians have written contemptuously about the “folly” of conjoining “objective” to “probability,” there are various reasons why quantum-mechanical probabilities can be considered objective, not least the fact that they are needed to quantify an objective fuzziness. But this cannot be appreciated without giving thought to the makeup of the world, which Bayesians refuse to do. Doing this on the basis of how quantum mechanics assigns probabilities, one finds that what constitutes the macroworld is a single Ultimate Reality, about which we know nothing, except that it manifests the macroworld or manifests itself as the macroworld. The so-called microworld is neither a world nor a part of any world but instead is instrumental in the manifestation of the macroworld. Quantum mechanics affords us a glimpse “behind” the manifested world, at stages in the process of manifestation, but it does not allow us to describe what lies “behind” the manifested world except in terms of the finished product—the manifested world, for without the manifested world there is nothing in whose terms we could describe its manifestation. (shrink)

Question order effects are commonly observed in self-report measures of judgment and attitude. This article develops a quantum question order model (the QQ model) to account for four types of question order effects observed in literature. First, the postulates of the QQ model are presented. Second, an a priori, parameter-free, and precise prediction, called the QQ equality, is derived from these mathematical principles, and six empirical data sets are used to test the prediction. Third, a new index is derived (...) from the model to measure similarity between questions. Fourth, we show that in contrast to the QQ model, Bayesian and Markov models do not generally satisfy the QQ equality and thus cannot account for the reported empirical data that support this equality. Finally, we describe the conditions under which order effects are predicted to occur, and we review a broader range of findings that are encompassed by these very same quantum principles. We conclude that quantum probability theory, initially invented to explain order effects on measurements in physics, appears to be a powerful natural explanation for order effects of self-report measures in social and behavioral sciences, too. (shrink)

This work is a conceptual analysis of certain recent developments in the mathematical foundations of Classical and Quantum Mechanics which have allowed to formulate both theories in a common language. From the algebraic point of view, the set of observables of a physical system, be it classical or quantum, is described by a Jordan-Lie algebra. From the geometric point of view, the space of states of any system is described by a uniform Poisson space with transition probability. Both (...) these structures are here perceived as formal translations of the fundamental twofold role of properties in Mechanics: they are at the same time quantities and transformations. The question becomes then to understand the precise articulation between these two roles. The analysis will show that Quantum Mechanics can be thought as distinguishing itself from Classical Mechanics by a compatibility condition between properties-as-quantities and properties-as-transformations. -/- Moreover, this dissertation shows the existence of a tension between a certain "abstract way" of conceiving mathematical structures, used in the practice of mathematical physics, and the necessary capacity to specify particular states or observables. It then becomes important to understand how, within the formalism, one can construct a labelling scheme. The “Chase for Individuation” is the analysis of different mathematical techniques which attempt to overcome this tension. In particular, we discuss how group theory furnishes a partial solution. (shrink)

Any attempt to introduce probabilities into quantum mechanics faces difficulties due to the mathematical structure of Hilbert space, as reflected in Birkhoff and von Neumann's proposal for a quantum logic. The (consistent or decoherent) histories solution is provided by its single framework rule, an approach that includes conventional (Copenhagen) quantum theory as a special case. Mermin's Ithaca interpretation addresses the same problem by defining probabilities which make no reference to a sample space or event algebra (...) (“correlations without correlata”). But this leads to severe conceptual difficulties, which almost inevitably couple quantum theory to unresolved problems of human consciousness. Using histories allows a sharper quantum description than is possible with a density matrix, suggesting that the latter provides an ensemble rather than an irreducible single-system description as claimed by Mermin. The histories approach satisfies the first five of Mermin's desiderata for a good interpretation of quantum mechanics, including Einstein locality, but the Ithaca interpretation seems to have difficulty with the first (independence of observers) and the third (describing individual systems). (shrink)

Taking as starting point two familiar interpretations of probability, we develop these in a perhaps unfamiliar way to arrive ultimately at an improbable claim concerning the proper axiomatization of probability theory: the domain of definition of a point-valued probability distribution is an orthomodular partially ordered set. Similar claims have been made in the light of quantum mechanics but here the motivation is intrinsically probabilistic. This being so the main task is to investigate what light, if any, this sheds on (...) quantum mechanics. In particular it is important to know under what conditions these point-valued distributions can be thought of as derived from distribution-pairs of upper and lower probabilities on boolean algebras. Generalising known results this investigation unsurprisingly proves unrewarding. In the light of this failure the next topic investigated is how these generalized probability distributions are to be interpreted. (shrink)

In early 1927, Pascual Jordan published his version of what came to be known as the Dirac-Jordan statistical transformation theory. Later that year and partly in response to Jordan, John von Neumann published the modern Hilbert space formalism of quantum mechanics. Central to both formalisms are expressions for conditional probabilities of finding some value for one quantity given the value of another. Beyond that Jordan and von Neumann had very different views about the appropriate formulation of problems (...) in the new theory. For Jordan, unable to let go of the analogy to classical mechanics, the solution of such problems required the identification of sets of canonically conjugate variables, i.e., p’s and q’s. Jordan ran into serious difficulties when he tried to extend his approach from quantities with fully continuous spectra to those with wholly or partly discrete spectra. For von Neumann, not constrained by the analogy to classical physics and aware of the daunting mathematical difficulties facing the approach of Jordan ), the solution of a problem in the new quantum mechanics required only the identification of a maximal set of commuting operators with simultaneous eigenstates. He had no need for p’s and q’s. Related to their disagreement about the appropriate general formalism for the new theory, Jordan and von Neumann stated the characteristic new rules for probabilities in quantum mechanics somewhat differently. Jordan was the first to state those rules in full generality, von Neumann rephrased them and then sought to derive them from more basic considerations. In this paper we reconstruct the central arguments of these 1927 papers by Jordan and von Neumann and of a paper on Jordan’s approach by Hilbert, von Neumann, and Nordheim. We highlight those elements in these papers that bring out the gradual loosening of the ties between the new quantum formalism and classical mechanics. (shrink)

Through the introduction of his ‘common cause principle’ [The Direction of Time, 1956], Hans Reichenbach was the first to formulate a precise link relating causal claims to statements of probability. Despite some criticism, the principle has been hugely influential and successful—a pillar of scientific practice, as well as guiding our reasoning in everyday life. However, Bell’s theorem, taken in conjunction with quantum theory, challenges this principle in a fundamental sense at the microscopic level. For the same reason, the celebrated (...) causal model framework pioneered by Pearl, as well as by Spirtes, Glymour and Scheines, defies satisfactory causal explanations of quantum correlations—the role of the ‘causal Markov condition’ in this framework amounts to a generalisation of Reichenbach’s principle. Much effort has been devoted to the development of quantum causal models to overcome this challenge and to study whether a principled way of causal reasoning, albeit adjusted in its terms, can be maintained when it comes to quantum physics. A clarification of what quantum causal relations are supposed to be is also a much needed step in light of the hotly debated topic of causality in foundations of quantum theory, e.g. in the study of ‘indefinite causal structures’. This paper reports and discusses a framework of quantum causal models and argues that it is promising and interesting for two main reasons. First, it can be seen as a prime example of a recent research programme that took direct and fruitful inspiration from ideas first formulated by Reichenbach—it began by asking, and giving an answer to, how the common cause principle could be generalised appropriately to quantum theoretical terms. Second, the framework did not only facilitate generalisations of the core theorems of the classical framework of causal models, but, above all, it has a theorem at its center that justifies the ‘quantum causal Markov condition’ on the basis of what arguably is a natural definition of causal relations in quantum theory. This provides a conceptually clear grounding of the framework, as well as a proposal for the needed clarification of quantum causal relations in the foundations of quantum theory more generally. (shrink)

Correlation meaning interaction for physical occurrences, the joint probability formalizes this interaction and conceptualizes a stochastic causality. Bayesian reversibility then expresses action-reaction symmetry for spacelike, und cause-effect symmetry for timelike, separations. Information-negeutropy equivalence (that is. reversibility of the twin-faced information concept) extends Mehlberg's “lawlike reversibility” and vindicates Wigner's claim that psychokinesis is reciprocal to gain in knowledge. A covariant axiomatization of probabilities as expressing physical interaction, and displaying the spacetime propagation of information, is proposed. Its correspondence (but essential difference) (...) with the quantum calculation recipe is evidenced. The unfolding paradigm of a twin-faced reality- and- representation universe is stressed, and Pauli's hints in this direction are mentioned. (shrink)

We prove that if the physical entity S consisting of two separated physical entities S1 and S2 satisfies the axioms of orthodox quantum mechanics, then at least one of the two subentities is a classical physical entity. This theorem implies that separated quantum entities cannot be described by quantum mechanics. We formulate this theorem in an approach where physical entities are described by the set of their states, and the set of their relevant experiments. We also show (...) that the collection of eigenstate sets forms a closure structure on the set of states, which we call the eigen-closure structure. We derive another closure structure on the set of states by means of the orthogonality relation, and call it the ortho-closure structure, and show that the main axioms of quantum mechanics can be introduced in a very general way by means of these two closure structures. We prove that for a general physical entity, and hence also for a quantum entity, the probabilities can always be explained as being due to a lack of knowledge about the interaction between the experimental apparatus and the entity. (shrink)

Everettian quantum mechanics faces the challenge of how to make sense of probability and probabilistic reasoning in a setting where there is typically no unique outcome of measurements. Wallace has built on a proof by Deutsch to argue that a notion of probability can be recovered in the many worlds setting. In particular, Wallace argues that a rational agent has to assign probabilities in accordance with the Born rule. This argument relies on a rationality constraint that Wallace calls (...) state supervenience. I argue that state supervenience is not defensible as a rationality constraint for Everettian agents unless we already invoke probabilistic notions. (shrink)

In the quest and search for a physical theory of everything from the macroscopic large body matter to the microscopic elementary particles, with strange and weird concepts springing from quantum physics discovery, irreconcilable positions and inconvenient facts complicated physics – from Newtonian physics to quantum science, the question is- how do we close the gap? Indeed, there is a scientific and mathematical fireworks when the issue of quantum uncertainties and entanglements cannot be explained with (...) classical physics. The Copenhagen interpretation is an expression of few wise men on quantum physics that was largely formulated from 1925 to 1927 namely by Niels Bohr and Werner Heisenberg. From this point on, there is a divergence of quantum science into the realms of indeterminacy, complementarity and entanglement which are principles expounded in Yijing, an ancient Chinese knowledge constructed on symbols, with a vintage of at least 3 millennia, with broken and unbroken lines to form stacked 6-line structure called the hexagram. It is premised on probability development of the hexagram in a space-time continuum. The discovery of the quantization of action meant that quantum physics could not convincingly explain the principles of classical physics. This paper will draw the great departure from classical physics into the realm of probabilistic realities. The probabilistic nature and reality interpretation had a significant influence on Bohr’s line of thought. Apparently, Bohr realized that speaking of disturbance seemed to indicate that atomic objects were classical particles with definite inherent kinematic and dynamic properties (Hanson, 1959). Disturbances, energy excitation and entanglements are processual evolutionary phases in Yijing. This paper will explore the similarities in quantum physics and the methodological ways where Yijing is pivoted to interpret observable realities involving interactions which are uncontrollable and probabilistic and forms an inseparable unity due to the entanglement, superposition Transgressing disciplinary boundaries in the discussion of Yijing, originally from the Western Zhou period (1000-750 BC), over a period of warring states and the early imperial period (500-200 BC) which was compiled, transcribed and transformed into a cosmological texts with philosophical commentaries known as the “Ten Wings” and closely associated with Confucius (551- 479 BC) with the Copenhagen Interpretation (1925-1927) by the few wise men including Niel Bohr and Werner Heisensberg would seem like a subversive undertaking. Subversive as the interpretations from Yijing is based on wisdom derived from thousands of years from ancient China to recently discovered quantum concepts. The subversive undertaking does seem to violate the sanctuaries of accepted ways in looking at Yijing principles, classical physics and quantum science because of the fortified boundaries that have been erected between Yijing and the sciences. Subversive as this paper may be, it is an attempt to re-cast an ancient framework where indeterminism, complementarity, non-linearity entanglement, superposition and probability interpretation is seen in today quantum’s realities. (shrink)

The article is devoted to the problem of interpreting of the several consequences that derive from multi-world concepts of modern physics. The inflation scenario and the associated string landscape model are the objects of analysis. The reviewed multi-world concepts are exposed to presume the existence of a plenitude (possibly infinite) of various fundamental principles (laws of nature) that govern the physics of one or another possible reality. The research is based on the hermeneutical method, comparative method, dialectical method, (...) formal translation method, and scientific modeling method. The author represents specifics of physical theories (the criteria and requirements for them) that claim to describe all possible worlds in the conclusions. In this regard, the issues of the status of “possible” and “impossible” worlds and practicable ways to determine them are discussed. The main result of the study is the justification (based on the assumption of many fundamentally different worlds scenario possibility) that each type of world must correspond to a certain structure of consciousness defined by its basic physical principles (and probably other mathematics). This possibly means that a unified “theory of everything” that includes all possible mathematical and physical fundamental structures cannot exist since every one of them determines a specific type of consciousness (where it is possible). (shrink)

The Hilbert space formalism describes causality as a statistical relation between initial experimental conditions and final measurement outcomes, expressed by the inner products of state vectors representing these conditions. This representation of causality is in fundamental conflict with the classical notion that causality should be expressed in terms of the continuity of intermediate realities. Quantum mechanics essentially replaces this continuity of reality with phase sensitive superpositions, all of which need to interfere in order to produce the correct conditional (...) probabilities for the observable input-output relations. In this paper, I investigate the relation between the classical notion of reality and quantum superpositions by identifying the conditions under which the intermediate states can have real external effects, as expressed by measurement operators inserted into the inner product. It is shown that classical reality emerges at the macroscopic level, where the relevant limit of the measurement resolution is given by the variance of the action around the classical solution. It is thus possible to demonstrate that the classical notion of objective reality emerges only at the macroscopic level, where observations are limited to low resolutions by a lack of sufficiently strong intermediate interactions. This result indicates that causality is more fundamental to physics than the notion of an objective reality, which means that the apparent contradictions between quantum physics and classical physics may be resolved by carefully distinguishing between observable causality and unobservable sequences of hypothetical realities “out there”. (shrink)