Following the argument of Pusey et al. (in Nature Phys. 8:476, 2012), new interest has been raised on whether one can interpret state-vectors (pure states) in a statistical way (ψ-epistemic theories), or if each one of them corresponds to a different ontological entity. Each interpretation of quantum theory assumes different ontology and one could ask if the PBR argument carries over. Here we examine this question for histories formulations in general with particular attention to the co-event formulation. (...) class='Hi'>State-vectors appear as the initial state that enters into the quantum measure. While the PBR argument goes through up to a point, the failure to meet some of the assumptions they made does not allow one to reach their conclusion. However, the author believes that the “statistical interpretation” is still impossible for co-events even if this is not proven by the PBR argument. (shrink)

Copenhagen interpretation of quantum mechanics deals with these problems is reviewed. A new interpretation of the formalism of quantum mechanics, the transactional interpretation, is presented. The basic element of this interpretation is the transaction describing a quantum event as an exchange of advanced and retarded waves, as implied by the work of Wheeler and Feynman, Dirac, and others. The transactional interpretation is explicitly nonlocal and thereby consistent with recent tests of the Bell inequality, yet is (...) relativistically invariant and fully causal. A detailed comparison of the transactional and Copenhagen interpretations is made in the context of well-known quantum-mechanical Gedankenexperimenre and "paradoxes." The transactional interpretation permits quantum-mechanical wave functions to be interpreted as real waves physically present in space rather than as "mathematical representations of knowledge" as in the Copenhagen interpretation. The transactional interpretation is shown to provide insight into the complex character of the quantum-mechanical state vector and the mechanism associated with its "collapse." It also leads in a natural way to justification of the Heisenberg uncertainty principle and the Born probability law (P = ii iij*), basic elements of the Copenhagen interpretation. (shrink)

In the proposed article by Maxim Isaenko "Ukrainian Christian tradition of state creation... "on the question of application A comparative methodological approach is presented in the analysis conceptual dispositions available in Ukrainian, Polish, and Russian types of state-building and organization of power institutions. Studying socio-legal models that are characteristic of three Slavic peoples, vectors of kinship and distance are outlined understanding of the phenomena of the state, power, law.

Any realist interpretation of quantum theory must grapple with the measurement problem and the status of state-vector collapse. In a no-collapse approach, measurement is typically modeled as a dynamical process involving decoherence. We describe how the minimal modal interpretation closes a gap in this dynamical description, leading to a complete and consistent resolution to the measurement problem and an effective form of state collapse. Our interpretation also provides insight into the indivisible nature of measurement—the (...) fact that you can't stop a measurement part-way through and uncover the underlying 'ontic' dynamics of the system in question. Having discussed the hidden dynamics of a system's ontic state during measurement, we turn to more general forms of open-system dynamics and explore the extent to which the details of the underlying ontic behavior of a system can be described. We construct a space of ontic trajectories and describe obstructions to defining a probability measure on this space. (shrink)

A drastic resolution of the quantum paradoxes is proposed, combining (I) von Neumann's postulate that collapse of the state vector is due to the act of observation, and (II) my reinterpretation of von Neumann's quantal irreversibility as an equivalence between wave retardation and entropy increase, both being “factlike” rather than “lawlike” (Mehlberg). This entails a coupling of the two de jure symmetries between (I) retarded and (II) advanced waves, and between Aristotle's information as (I) learning and (II) willing (...) awareness. Symmetric acceptance of cognizance as a source of retarted waves, and of will as a sink of advanced waves, is submitted as a central “paradox” of the Copernican or Einsteinian sort, out of which new light is shed upon previously known paradoxes, such as the EPR paradox, Schrödinger's cat, and Wigner's friend. Parapsychology is thus found to creep into the picture. (shrink)

The analysis, with the use of two state vectors, of a quantum system, during the time interval between two measurements, leads to some amazing results, which seem to contradict our usual “quantum common sense.” We explore the questions of compatibility with the conventional quantum theory, uniqueness of pre- and post-selected ensembles, commutativity, simultaneity and reality of strong and weak values in the intermediate time, and the meaning of the weak value. Common criticisms are shown to be unfounded.

A new interpretation of quantum theory is proposed. It coincides in a number of points with the orthodox interpretation, the main difference being that the projection of the state vector can occur without the intervention of any observer.

Recently it has been shown that transformations of Heisenberg-picture operators are the causal mechanism which allows Bell-theorem-violating correlations at a distance to coexist with locality in the Everett interpretation of quantum mechanics. A calculation to first order in perturbation theory of the generation of EPRB entanglement in nonrelativistic fermionic field theory in the Heisenberg picture illustrates that the same mechanism leads to correlations without nonlocality in quantum field theory as well. An explicit transformation is given to a representation in (...) which initial-condition information is transferred from the state vector to the field operators, making the locality of the theory manifest. (shrink)

Within many approaches to the interpretation of quantum mechanics, especially modal interpretations, one singles out a particular decomposition of the state vector in order to fix the properties that are well-defined for the system. We present a novel proposal for this preferred decomposition. Given a distinguished factorization of the Hilbert space, it is the decomposition that minimizes the Ingarden–Urbanik entropy from among all product decompositions with respect to the distinguished factorization. We incorporate this choice of preferred decomposition (...) into a framework for modal interpretations and investigate in detail the extent to which it provides a solution to the measurement problem and the extent to which it ensures that measurements whose outcomes are predictable with probability 1 reveal pre-existing properties of the system under investigation. (shrink)

This paper presents a new Symmetrical Interpretation (SI) of relativistic quantum mechanics which postulates: quantum mechanics is a theory about complete experiments, not particles; a complete experiment is maximally described by a complex transition amplitude density; and this transition amplitude density never collapses. This SI is compared to the Copenhagen Interpretation (CI) for the analysis of Einstein’s bubble experiment. This SI makes several experimentally testable predictions that differ from the CI, solves one part of the measurement problem, resolves (...) some inconsistencies of the CI, and gives intuitive explanations of some previously mysterious quantum effects. (shrink)

The central problem in the quantum theory of measurement, how to describe the process of state reduction in terms of the quantum mechanical formalism, is solved on the basis of the relativity of quantal states, which implies that once the apparatus is detected in a well-defined state, the object state must reduce to a corresponding one. This is a process termed by Schrödinger disentanglement. Here, it is essential to observe that Renninger's negative result does constitute an actual (...) measurement process. From this point of view, Heisenberg's interpretation of his microscope experiment and the Einstein-Podolsky-Rosen arguments are reinvestigated. Satisfactory discussions are given to various experimental situations, such as the Stern-Gerlach-type experiment, successive measurements, macroscopic measurements, and Schrödinger's cat. Finally it is proposed to regard a state vector in quantum mechanics as an irreducible physical construct, in Margenau's sense, that is not further analyzable both mathematically and conceptually. (shrink)

The argument laid out in this book discusses and interprets the work of Hobbes in relation to religion. It compares a traditional interpretation of Hobbes where Hobbes’ use of conventional terminology when talking about natural law is seen as ironic or merely convenient despite an atheist viewpoint, with the view that Hobbes’ morality is truly traditional and Christian. The book considers other thinkers of the age in tandem with Hobbes and discusses in detail his theology inspired by corporeal mechanics. (...) The position is that there are significant senses in which Hobbes can be said to be a traditional natural law theorist. (shrink)

The argument laid out in this book discusses and interprets the work of Hobbes in relation to religion. It compares a traditional interpretation of Hobbes where Hobbes’ use of conventional terminology when talking about natural law is seen as ironic or merely convenient despite an atheist viewpoint, with the view that Hobbes’ morality is truly traditional and Christian. The book considers other thinkers of the age in tandem with Hobbes and discusses in detail his theology inspired by corporeal mechanics. (...) The position is that there are significant senses in which Hobbes can be said to be a traditional natural law theorist. (shrink)

The argument laid out in this book discusses and interprets the work of Hobbes in relation to religion. It compares a traditional interpretation of Hobbes where Hobbes’ use of conventional terminology when talking about natural law is seen as ironic or merely convenient despite an atheist viewpoint, with the view that Hobbes’ morality is truly traditional and Christian. The book considers other thinkers of the age in tandem with Hobbes and discusses in detail his theology inspired by corporeal mechanics. (...) The position is that there are significant senses in which Hobbes can be said to be a traditional natural law theorist. (shrink)

Elementary particles are considered as local oscillators under the influence of zeropoint fields. Such oscillatory behavior of the particles leads to the deviations in their path of motion. The oscillations of the particle in general may be considered as complex rotations in complex vector space. The local particle harmonic oscillator is analyzed in the complex vector formalism considering the algebra of complex vectors. The particle spin is viewed as zeropoint angular momentum represented by a bivector. It has been (...) shown that the particle spin plays an important role in the kinematical intrinsic or local motion of the particle. From the complex vector formalism of harmonic oscillator, for the first time, a relation between mass $m$ and bivector spin $S$ has been derived in the form $\varvec{\sigma }_3 mc^2{\mathcal {J}}_{\pm } =\lambda \Omega _{\mathbf{s}} \cdot \mathrm{{S}} {\mathcal {J}}_{\pm }$ . Where, $\Omega _{s}$ is the angular velocity bivector of complex rotations, $c$ is the velocity of light. The unit vector $\varvec{\sigma }_3$ acts as an operator on the idempotents ${\mathcal {J}}_{+}$ and ${\mathcal {J}}_{-}$ to give the eigen values $\lambda =\pm 1.$ The constant $\lambda $ represents two fold nature of the equation corresponding to particle and antiparticle states. Further the above relation shows that the mass of the particle may be interpreted as a local spatial complex rotation in the rest frame. This gives an insight into the nature of fundamental particles. When a particle is observed from an arbitrary frame of reference, it has been shown that the spatial complex rotation dictates the relativistic particle motion. The mathematical structure of complex vectors in space and spacetime is developed. (shrink)

Some interpretations of quantum mechanics regard a mixed quantum state as a ensemble, each individual member of which has a definite but unknown state vector. Other interpretations ascribe a state vector only to anensemble of similarly prepared systems, but not to anindividual. Previous attempts to detect the hypothetical individual state vectors have failed, essentially because the state operator enters the relevant equations linearly. An example from nonlinear dynamics, in which a density matrix enters (...) nonlinearly, is examined because it might appear to circumvent this difficulty. However, it is shown that the hypothetical individual state vectors can not be detected this way, so the adequacy of theensemble interpretation survives a critical test. (shrink)

In this paper I provide an ontology for the co‐variant vectors, contra‐variant vectors and tensors that are familiar from General Relativity. This ontology is developed in response to a problem that Timothy Maudlin uses to argue against universals in the interpretation of physics. The problem is that if vector quantities are universals then there should be a way of identifying the same vector quantity at two different places, but there is no absolute identification of vector quantities, (...) merely a path‐relative one.My solution to the problem is to use the mathematical characterization of vectors as differential operators on scalar fields. On the proposed hypothesis a scalar field is a conjunctive state of affairs, and vector and tensor fields are relations instantiated by scalar fields. (shrink)

The purpose of this paper is to show that the mathematics of quantum mechanics is the mathematics of set partitions linearized to vector spaces, particularly in Hilbert spaces. That is, the math of QM is the Hilbert space version of the math to describe objective indefiniteness that at the set level is the math of partitions. The key analytical concepts are definiteness versus indefiniteness, distinctions versus indistinctions, and distinguishability versus indistinguishability. The key machinery to go from indefinite to more (...) definite states is the partition join operation at the set level that prefigures at the quantum level projective measurement as well as the formation of maximally-definite state descriptions by Dirac’s Complete Sets of Commuting Operators. This development is measured quantitatively by logical entropy at the set level and by quantum logical entropy at the quantum level. This follow-the-math approach supports the Literal Interpretation of QM—as advocated by Abner Shimony among others which sees a reality of objective indefiniteness that is quite different from the common sense and classical view of reality as being “definite all the way down”. (shrink)

In quantum mechanics, the state of an individual particle (or system) is unobservable, i.e., it cannot be determined experimentally, even in principle. However, the notion of “measuring a state” is meaningful if it refers to anensemble of similarly prepared particles, i.e., the question may be addressed: Is it possible to determine experimentally the state operator (density matrix) into which a given preparation procedure puts particles. After reviewing the previous work on this problem, we give simple procedures, in (...) the line of Lamb's operational interpretation of quantum mechanics, for measuring a translational state operator (whether pure or mixed), via its Wigner function. These procedures closely parallel methods that might be used in classical mechanics to determine a true phase space probability distribution; thus, the Wigner function simulates such a distribution not only formally, but operationally also. There is no way to determine what the wave function (or state vector) of a system is—if arbitrarily given, there is no way to “measure” its wave function. Clearly, such a measurement would have to result in afunction of several variables, not in a relatively small set ofnumbers .... In order to verify the [quantum] theory in its generality, at least a succession of two measurements are needed. There is in general no way to determine the original state of the system, but having produced a definite state by a first measurement, the probabilities of the outcomes of a second measurement are then given by the theory.E. P. Wigner(1). (shrink)

Eugene Wigner and others have speculated that the “collapse of the state vector” during an observation might be a physically real process so that some modification of current quantum theory would be required to describe the interaction with a conscious observer appropriately.Experimental reports on the “psychokinetic effect” as a mental influence on the outcome of quantum jumps suggest that perhaps this effect might be vital for an understanding of the observer's role in quantum mechanics.Combining these two speculations we (...) introduce a reduction principle that provides for the gradual reduction of a macroscopically ambiguous state and allows simultaneously for the occurrence of some psychokinetic effect in the process of observation.The resulting model leads to many of the paradoxical, but logically consistent, features of the psychokinetic effect that have been reported, and makes further testable predictions.The model does not touch on the more profound questions of consciousness. But the model implies that the result of a conscious observation, the collapse of the state vector, becomes accessible to the experimenter, with the psychokinetic effect as probe: Whether Schrödinger's cat has not or has collapsed the state vector determines whether or not the later human observer can still exert a psychokinetic influence on the result. (shrink)

The paper contains a discussion on two kinds of coincidence experiments. First, a standard two-photon coincidence experiment is considered and it is shown that its outcomes are incompatible with any classical radiation theory because of the role of the state vector reduction phenomenon in such an experiment. In the second part of the paper a proposed new kind of photon coincidence experiment is discussed. The classical and quantum predictions for the outcomes of this experiment differ dramatically and therefore (...) the experiment should constitute a new limitation to the classical radiation theories. The proposed experiment should also yield information about the kinematics of the reduction of the state vector process. (shrink)

Time-symmetric formulation of quantum mechanics—the two-state vector formalism—is presented as a tool for studying past behaviour of quantum systems. A role of weak measurement and weak values in the Cheshire Cat effect and a nested (Vaidman) three-path interferometer are discussed. Interpretation of a particle’s faint trace indicating possibility of discontinuous paths of particles passing the Vaidman interferometer is given. Consistent histories are presented as one of alternative approaches. Multitude of controversial issues is briefly reviewed and discussed.

We develop a vector space semantics for verb phrase ellipsis with anaphora using type-driven compositional distributional semantics based on the Lambek calculus with limited contraction of Jäger. Distributional semantics has a lot to say about the statistical collocation based meanings of content words, but provides little guidance on how to treat function words. Formal semantics on the other hand, has powerful mechanisms for dealing with relative pronouns, coordinators, and the like. Type-driven compositional distributional semantics brings these two models together. (...) We review previous compositional distributional models of relative pronouns, coordination and a restricted account of ellipsis in the DisCoCat framework of Coecke et al. :1079–1100, 2013). We show how DisCoCat cannot deal with general forms of ellipsis, which rely on copying of information, and develop a novel way of connecting typelogical grammar to distributional semantics by assigning vector interpretable lambda terms to derivations of LCC in the style of Muskens and Sadrzadeh Logical aspects of computational linguistics, Springer, Berlin, 2016). What follows is an account of ellipsis in which word meanings can be copied: the meaning of a sentence is now a program with non-linear access to individual word embeddings. We present the theoretical setting, work out examples, and demonstrate our results with a state of the art distributional model on an extended verb disambiguation dataset. (shrink)

To experience is to undergo a process, to be in a state of receiving input which affords information about our environment. For highly developed beings like ourselves, the inputs determining states of conscious sensory perception are among the most important for our survival. At first glance, these states seem relational, each being a situation wherein a percipient X is passively conscious of something Y--its object, subject-matter, or content--without any apparent effort. Of course, the briefest reflection convinces us that despite (...) a seemingly passive reception of data from without, a good deal of interpretation goes into the making of perceptual judgments, as evidenced by their wide variance in the face of like sensory stimulation. One person looking at the slope of a mountain notices a patch of whitish stones; another sees a flock of sheep grazing. They are distinguished by their different reactions to similar input, whether or not these are best construed as inferences, interpretations, or, simply, differing degrees of attentiveness. (shrink)

The grounding of semiotics in the finiteness of cognition is extended into constructs and methods for analysis by incorporating the assumption that cognition can be similar within and between agents. After examining and formalizing cognitive similarity as an ontological commitment, the recurrence of cognitive states is examined in terms of a “cognitive set.” In the individual, the cognitive set is seen as evolving under the bidirectional, cyclical determination of thought by the historical environment. At the population level, the distributed “global” (...) cognitive set is argued to be constrained to a manifold in which the cognition of individuals is determined only when their cognitive sets meet certain conditions in the world: a result seen as consistent with Lotman’s semiosphere. With these foundations in place, dimensional modelling of the semiosic field is inaugurated. Firstly, measures of cognitive similarity are formalized as cognitive “distance” and on this basis the concept of a semiotic vector is defined. Secondly, semiotic vectors are seen to shape a general pattern of oscillation in semiosis, and thus to imply zero points in semiosic potential. Thirdly, semiosic oscillation in individual agents is shown to be consistent with a novel diachronic or longitudinal interpretation of Greimas’ semiotic square expanded into a “semiotic pipe” in which cognition traverses an n-dimensional space structured by axes of oscillation. Finally, the expanded theory of finite semiotics is advanced as a useful basis for two new complementary disciplines: a computational, mathematical science of “natural semiotic processing” to trace and model semiotic vectors and oscillation; and an ethical, rhetorical art of “technological influencing” to guide its inputs and applications. (shrink)

The subject of the study is the mystical experience as a kind of altered states of consciousness. The purpose of the article is to solve at the conceptual level the problem of distinguishing genuine mystical experience and various kinds of surrogate states with quasi-mystical content. The theoretical basis for solving this problem was the study of the panorama of moments of divergence and convergence of discourses of the humanities and natural sciences, as well as theology. In the course of the (...) conducted research, the infra-personal processes going on in the vector of the dissolving and spreading "I" were revealed. They correspond to both mystical (dissolution in the Deity, in emptiness, in cosmic consciousness, etc.) and clinical states (confused or floating consciousness). The authors also consider in detail the ultrapersonal processes occurring within the framework of the dissemination of personal consciousness and which correspond to both mystical (the scattering of reality into many spirits, souls, astral projections and quasi-persona) and clinical conditions (schizophrenic type disorders). The novelty of the article lies in revealing the diverse directions of inauthentic mystical experience based on the systematic study of altered states of consciousness, as well as in determining the range in which an outlet to authentic forms of mystical experience can open. It has been established that in the spectrum of infra-personal and ultra-personal states there is such a feature of mystical and occult practices with the prefix "neo" as the achievement of mystical states according to the "accelerated course" programs. However, due to the inversion of the view characteristic of modern consciousness, in the ideology of neo-mysticism, destructive processes are often perceived as a new, higher stage in the evolution of mankind. With this interpretation, conditions arise for the perception of science as a "new religion", as well as the desire to find in scientific concepts a support for modern occultism and neo-mysticism. (shrink)

The interpretation of quantum mechanics is discussed from the viewpoint of quantum logic (QL). QL is understood to concern the possible properties that can be ascribed to a physical system SYS. The micro-state of SYS at any given moment t is identified with the set of all properties actualized by SYS at time t. Minimal adequacy requirements are proposed for all interpretations of micro-states. A strict interpretation is defined to be one according to which the properties ascribable (...) to SYS are individuated by the projection operators on the associated Hilbert space. Two strict interpretations are examined. Kochen's interpretation is also discussed, and it is argued that it is not a strict interpretation. (shrink)

David Deutsch and others have suggested that the Many-Worlds Interpretation of quantum mechanics is the only interpretation capable of explaining the special efficiency quantum computers seem to enjoy over classical ones. I argue that this view is not tenable. Using a toy algorithm I show that the Many-Worlds Interpretation must crucially use the ontological status of the universal state vector to explain quantum computational efficiency, as opposed to the particular ontology of the MWI, that is, (...) the computational histories of worlds. As such, any other interpretation that treats the state vector as representing real ontological features of a system can explain quantum speedup too. ‡Thanks to Soazig Le Bihan for her critical comments on this paper. †To contact the author, please write to: Department of Philosophy, Liberal Arts 101, University of Montana, Missoula, MT 59812; e-mail: armond. duwell @umontana.edu. (shrink)

We consider a representation of the state reduction which depends neither on its reality nor on the details of when and how it emerges. Then by means of the representation we find necessary conditions, even if not the sufficient ones, for a decomposition of the state vector space to be a solution to the basis problem. The conditions are that the decomposition should be Lorentz invariant and orthogonal and that the associated projections should be continuous. They are (...) shown to be able to determine a decomposition in each of a few examples considered if the other circumstances are taken into account together. (shrink)

The development of quantum information theory has renewed interest in the idea that the state vector does not represent the state of a quantum system, but rather the knowledge or information that we may have on the system. I argue that this epistemic view of states appears to solve foundational problems of quantum mechanics only at the price of being essentially incomplete.

By following the analysis of De Caro and Garuccio [Phys. Rev. A 54, 174 (1996)], we show that the factorable state vector produced with a beam-splitter set on the paths of parametric down-converted photons violates some new inequalities that we deduce from local realism. These inequalities are more stringent than those used up to now in the discussion of such phenomena.

The 2017 codetection of electromagnetic radiation and gravitational waves was the first of its kind and marked the beginning of multimessenger astronomy. But this event has been treated within recent literature as something of an end as well. The 2017 detection is often regarded as an instance of falsification for all theories of modified gravity which postulate gravitational waves propagate along separate geodesics from electromagnetic radiation, perhaps most notably Jacob Bekenstein’s Tensor-Vector-Scalar gravity. I critically examine this explicit endorsement of (...) falsification by astronomers and astrophysicists. While the current state of multimetric modified gravity theories is dim, recent developments in multimessenger observation do not offer a deductive falsification. Rather such evidence should be regarded as a corroboration of the null hypothesis, following Deborah Mayo's error-statistical account. (shrink)