As argued in Hellman (1993), the theorem of Pour-El and Richards (1983) can be seen by the classicist as limiting constructivist efforts to recover the mathematics for quantum mechanics. Although Bridges (1995) may be right that the constructivist would work with a different definition of 'closed operator', this does not affect my point that neither the classical unbounded operators standardly recognized in quantum mechanics nor their restrictions to constructive arguments are recognizable as objects by the constructivist. (...) Constructive substitutes that may still be possible necessarily involve additional 'incompleteness' in the mathematical representation of quantum phenomena. Concerning a second line of reasoning in Hellman (1993), its import is that constructivist practice is consistent with a 'liberal' stance but not with a 'radical', verificationist philosophical position. Whether such a position is actually espoused by certain leading constructivists, they are invited to clarify. (shrink)

We discuss a generalization of the standard notion of probability space and show that the emerging framework, to be called operational probability theory, can be considered as underlying quantal theories. The proposed framework makes special reference to the convex structure of states and to a family of observables which is wider than the familiar set of random variables: it appears as an alternative to the known algebraic approach to quantum probability.

The formula for the differential scattering cross section in quantum mechanics is derived without the usual assumption that the square of the ψ-function is a position probability density for particles. It is argued that position, like time, may be basically a macroscopic parameter rather than a random variable for microparticles.

We generalize the modal interpretation of quantum mechanics so that it may be applied to composite systems represented by arbitrary density operators. We discuss the interpretation these density operators receive and relate this to the discussion about the interpretation of proper and improper mixtures in the standard interpretation.

I pedagogically show that the momentum operator in quantum mechanics, in the position representation, commonly known to be a derivative with respect to a spatial x-coordinate, can be derived by identifying momentum as the generator of space translations.

This paper analyses Richard Bader’s ‘operational’ view of quantum mechanics and the role it plays in the the explanation of chemistry. I argue that QTAIM can partially be reconstructed as an ‘austere’ form of quantum mechanics, which is in turn committed to an eliminative concept of reduction that stems from Kemeny and Oppenheim. As a reductive theory in this sense, the theory fails. I conclude that QTAIM has both a regulatory and constructive function in the (...) theories of chemistry. (shrink)

Quantum mechanics has recently indicated that, at the fundamental level, temporal order is not fixed. This phenomenon, termed Indefinite Causal Order, is yet to receive metaphysical or theological engagement. We examine Indefinite Causal Order, particularly as it emerges in a 2018 photonic experiment. In this experiment, two operations A and B were shown to be in a superposition with regard to their causal order. Essentially, time, intuitively understood as fixed, flowing, and fundamental, becomes fuzzy. We argue that if (...) Indefinite Causal Order is true, this is good evidence in favor of a B‐theory of time, though such a B‐theory requires modification. We then turn to theology, suggesting that a B‐theoretic temporal ontology invites serious reconsideration of the doctrine of salvation. This paper concludes that the best explanation for salvation given a B‐theory is mind‐dependent salvific becoming, a type of psychological soteriological change that occurs through downward causation. (shrink)

The effect of short disturbances on nonrelativistic motion is formulated in terms of operators. Analogies with quantum mechanics are developed and some disparities noted. For the one-dimensional particle we obtain analogues of the de Broglie wave commonly associated with particle motion, Heisenberg's commutation relation, Schrödinger's equation, and the statistical interpretation. Whether these results have any bearing on quantum mechanics itself is left an open question.

Quantum mechanics may be formulated as Sensible Quantum Mechanics (SQM) so that it contains nothing probabilistic except conscious perceptions. Sets of these perceptions can be deterministically realized with measures given by expectation values of positive-operator-valued awareness operators. Ratios of the measures for these sets of perceptions can be interpreted as frequency- type probabilities for many actually existing sets. These probabilities gener- ally cannot be given by the ordinary quantum “probabilities” for a single set of alternatives. (...) Probabilism, or ascribing probabilities to unconscious aspects of the world, may be seen to be an aesthemamorphic myth. (shrink)

Is quantum mechanics about ‘states’? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to ‘classical’ instantiations of a probability calculus. Its providing a general framework for prediction accounts for its distinctive traits, which one should be careful not to mistake for reflections of any strange ontology. The suggestion is also made that quantum theory unwittingly emerged, in Schrödinger’s formulation, as (...) a ‘lossy’ by-product of a quantum-mechanical variant of the Hamilton-Jacobi equation. As it turns out, the effectiveness of quantum theory qua predictive algorithm makes up for the computational impracticability of that master equation. (shrink)

We study the process of observation (measurement), within the framework of a “perspectival” (“relational,” “relative state”) version of the modal interpretation of quantum mechanics. We show that if we assume certain features of discreteness and determinism in the operation of the measuring device (which could be a part of the observer's nerve system), this gives rise to classical characteristics of the observed properties, in the first place to spatial localization. We investigate to what extent semi-classical behavior of the (...) object system itself (as opposed to the observational system) is needed for the emergence of classicality. Decoherence is an essential element in the mechanism of observation that we assume, but it turns out that in our approach no environment-induced decoherence on the level of the object system is required for the emergence of classical properties. (shrink)

In orthodox quantum mechanics, it has virtually become the custom to identify properties of a physical system with operationally testable propositions about the system. The causes and consequences of this practice are explored mathematically in this paper. Among other things, it is found that such an identification imposes severe constraints on the admissible states of the physical system.

There have been many claims that quantum mechanics plays a key role in the origin and/or operation of biological organisms, beyond merely providing the basis for the shapes and sizes of biological molecules and their chemical affinities. These range from Schr¨odinger’s suggestion that quantum fluctuations produce mutations, to Hameroff and Penrose’s conjecture that quantum coherence in microtubules is linked to consciousness. I review some of these claims in this paper, and discuss the serious problem of decoherence. (...) I advance some further conjectures about quantum information processing in bio-systems. Some possible experiments are suggested. © 2004 Elsevier Ireland Ltd. All rights reserved. (shrink)

Recently, new types of independence of a pair of C *- or W *-subalgebras (1,2) of a C *- or W *-algebra have been introduced: operational C *- and W *-independence (Rédei and Summers, http://arxiv.org/abs/0810.5294, 2008) and operational C *- and W *-separability (Rédei and Valente, How local are local operations in local quantum field theory? 2009). In this paper it is shown that operational C *-independence is equivalent to operational C *-separability and that (...) class='Hi'>operational W *-independence is equivalent to operational W *-separability. Specific further sub-types of both operational C *- and W *-separability and operational C *- and W *-independence are defined and the problem of characterization of the logical interdependencies of the independence notions is raised. (shrink)

I show that the quantum state ω can be interpreted as defining a probability measure on a subalgebra of the algebra of projection operators that is not fixed (as in classical statistical mechanics) but changes with ω and appropriate boundary conditions, hence with the dynamics of the theory. This subalgebra, while not embeddable into a Boolean algebra, will always admit two-valued homomorphisms, which correspond to the different possible ways in which a set of “determinate” quantities (selected by ω (...) and the boundary conditions) can have values. The probabilities defined by ω (via the Born rule) are probabilities over these two-valued homomorphisms or value assignments. So any universe of interacting systems, including those functioning as measuring instruments, can be modelled quantum mechanically without the projection postulate. (shrink)

The relevance of symmetry to today's physics is a widely acknowledged fact. A significant part of recent physical inquiry – especially the physics concerned with investigating the fundamentalbuilding blocks of nature – is grounded on symmetry principles andtheir many and far-reaching consequences. But where these symmetries come from and what their real meaning is are open questions, at the center of a developing debate among physicists and philosophers of science. To tackle the problems arising in considering the symmetry issue is (...) the main purpose of this paper. Starting with briefly recalling the bases for the discussion – how symmetry enters and operates in physics, its special effectiveness in the quantum domain and the many relevant functions it performs (Sections 1–3), the paper then focus on the general interpretative questions that arise and the sorts of answers that have been given (Section 4). (shrink)

These lecture notes present a concise and introductory, yet as far as possible coherent, view of the main formalizations of quantum mechanics and of quantum field theories, their interrelations and their theoretical foundations. The "standard" formulation of quantum mechanics (involving the Hilbert space of pure states, self-adjoint operators as physical observables, and the probabilistic interpretation given by the Born rule) on one hand, and the path integral and functional integral representations of probabilities amplitudes on the (...) other, are the standard tools used in most applications of quantum theory in physics and chemistry. Yet, other mathematical representations of quantum mechanics sometimes allow better comprehension and justification of quantum theory. This text focuses on two of such representations: the algebraic formulation of quantum mechanics and the "quantum logic" approach. Last but not least, some emphasis will also be put on understanding the relation between quantum physics and special relativity through their common roots - causality, locality and reversibility, as well as on the relation between quantum theory, information theory, correlations and measurements, and quantum gravity. Quantum mechanics is probably the most successful physical theory ever proposed and despite huge experimental and technical progresses in over almost a century, it has never been seriously challenged by experiments. In addition, quantum information science ha s become an important and very active field in recent decades, further enriching the many facets of quantum physics. Yet, there is a strong revival of the discussions about the principles of quantum mechanics and its seemingly paradoxical aspects: sometimes the theory is portrayed as the unchallenged and dominant paradigm of modern physical sciences and technologies while sometimes it is considered a still mysterious and poorly understood theory, waiting for a revolution. This volume, addressing graduate students and seasoned researchers alike, aims to contribute to the reconciliation of these two facets of quantum mechanics. (shrink)

A time-symmetric formulation of nonrelativistic quantum mechanics is developed by applying two consecutive boundary conditions onto solutions of a time- symmetrized wave equation. From known probabilities in ordinary quantum mechanics, a time-symmetric parameter P0 is then derived that properly weights the likelihood of any complete sequence of measurement outcomes on a quantum system. The results appear to match standard quantum mechanics, but do so without requiring a time-asymmetric collapse of the wavefunction upon measurement, (...) thereby realigning quantum mechanics with an important fundamental symmetry. (shrink)

Starting from the formal expressions of the hydrodynamical (or “local”) quantities employed in the applications of Clifford algebras to quantum mechanics, we introduce—in terms of the ordinary tensorial language—a new definition for the field of a generic quantity. By translating from Clifford into tensor algebra, we also propose a new (nonrelativistic) velocity operator for a spin- ${\frac{1}{2}}$ particle. This operator appears as the sum of the ordinary part p/m describing the mean motion (the motion of the center-of-mass), and (...) of a second part associated with the so-called Zitterbewegung, which is the spin “internal” motion observed in the center-of-mass frame (CMF). This spin component of the velocity operator is nonzero not only in the Pauli theoretical framework, i.e., in the presence of external electromagnetic fields with a nonconstant spin function, but also in the Schrödinger case, when the wavefunction is a spin eigenstate. Thus, one gets even in the latter case a decomposition of the velocity field for the Madelung fluid into two distinct parts, which constitutes the nonrelativistic analogue of the Gordon decomposition for the Dirac current. Explicit calculations are presented for the velocity field in the particular cases of the hydrogen atom, of a spherical well potential, and of an electron in a uniform magnetic field. We find, furthermore, that the Zitterbewegung motion involves a velocity field which is solenoidal, and that the local angular velocity is parallel to the spin vector. In the presence of a nonuniform spin vector (Pauli case) we have, besides the component of the local velocity normal to the spin (present even in the Schrödinger theory), also a component which is parallel to the curl of the spin vector. (shrink)

The principal results of Schrödinger's paper are reviewed and a possible extension of his formalism for diffusion processes to general quantum mechanical processes is given. The formalism is not in accord with the general theory of transformation of quantum mechanics and violates the basic assumption of the unpredictable change of a system due to a measurement. Nevertheless, the formalism leads to a density operator which is constructed according to accepted quantum mechanical rules.

In talking about the compatibility of quantum observables, discussions often center on the question of whether the corresponding operators commute—even though commutativity is a coarse-grained notion that largely fails to capture the salient “nonclassical” features of quantum theory. Often, too, such discussions involve the issue of whether the operators in question satisfy a Heisenberg-like inequality, of the form ΔA·ΔB≥r>0—even though such inequalities are specific to unbounded operators and (for this and other reasons) are typically not a useful way (...) to discuss joint uncertainty in quantum mechanics. In the present paper we emphasize a simpler dichotomy, in which operator pairs (A, B) are classified according to whether or not states can be found with arbitrarily small dispersions in both A and B. If A and B cannot be made arbitrarily dispersionless simultaneously, then we call A and B an uncertainty pair. Otherwise, we call A and B a certainty pair. An interesting feature of uncertainty pairs in particular is that they are stable, in the sense that if A and B form an uncertainty pair, then slight enough perturbations of A and B must also form an uncertainty pair. This stability, obvious in the finite-dimensional case, follows in general from an operator inequality derived herein. A consequence of this inequality is that perturbed position and momentum operators X+δX and P+δP cannot share an eigenvector unless |δX|·|δP|≥ℏ/2. (Here vertical bars denote the operator norm.) This, despite the fact that (as we show) arbitrarily slight perturbations of X and P can fail to satisfy a Heisenberg inequality—a fact which raises interesting measurement issues in its own right. (shrink)

Traditionally, “the operator calculus of Born and Wiener” has been considered one of the four formulations of quantum mechanics that existed in 1926. The present paper reviews the operator calculus as applied by Max Born and Norbert Wiener during the last months of 1925 and the early months of 1926 and its connections with the rise of the new quantum theory. Despite the relevance of this operator calculus, Born–Wiener’s joint contribution to the topic is generally bypassed in (...) historical accounts of quantum mechanics. In this study, we analyse the paper that epitomises the contribution, and we explain the main reasons for the apparent lack of interest in Born and Wiener’s work. We argue that they did not solve the main problem for which the tool was intended, that of linear motion, because of their reluctance to use Dirac delta functions. (shrink)

A relativistic one-particle, quantum theory for spin-zero particles is constructed uponL 2(x, ct), resulting in a positive definite spacetime probability density. A generalized Schrödinger equation having a Hermitian HamiltonianH onL 2(x, ct) for an arbitrary four-vector potential is derived. In this formalism the rest mass is an observable and a scalar particle is described by a wave packet that is a superposition of mass states. The requirements of macroscopic causality are shown to be satisfied by the most probable trajectory (...) of a free tardyon and a nontrivial framework for charged and neutral particles is provided. The Klein paradox is resolved and a link to the free particle field operators of quantum field theory is established. A charged particle interacting with a static magnetic field is discussed as an example of the formalism. (shrink)

Quantum Mechanics has faced deep controversies and debates since its origin when Werner Heisenberg proposed the first mathematical formalism capable to operationally account for what had been recently discovered as the new field of quantum phenomena. Today, even though we have reached a standardized version of QM which is taught in Universities all around the world, there is still no consensus regarding the conceptual reference of the theory and, if or if not, it can refer to something (...) beyond measurement outcomes. In this work we will argue that the reason behind the impossibility to reach a meaningful answer to this question is strictly related to the 20th Century Bohrian-positivist re-foundation of physics which is responsible for having introduced within the theory of quanta a harmful combination of metaphysical dogmatism and naive empiricism. We will also argue that the possibility of understanding QM is at plain sight, given we return to the original framework of physics in which the meaning of understanding has always been clear. (shrink)

A proof is presented that a form of incompleteness in Quantum Mechanics follows directly from the use of unbounded operators. It is then shown that the problems that arise for such operators are not connected to the non- commutativity of many pairs of operators in Quantum Mechanics and hence are an additional source of incompleteness to that which allegedly flows from the..

Recently we have studied quantum mechanics of bounded operators with a discrete spectrum. In particular, we derived an expression for the commutator[Q, P] of two bounded operators whose spectrum is discrete, and we showed that in the limit of a continuous spectrum the commutator becomes the standard one of Heisenberg. In this paper we show that the angular momentum operator and the phase operator satisfy the new commutation relation. We also briefly discuss the problem of the canonical phase (...) operator conjugate to the number operator. (shrink)

The purpose of this book is to initiate a new discipline, namely a formalized epistemological method drawn from the cognitive strategies practised in the most effective among the modern scientific disciplines, as well as from general philosophical thinking. Indeed, what is lacking in order to improve our knowledge and our domination of the modes which nowadays are available for the generation and communication of knowledge, thoroughly and rapidly and with precision and detail? It is a systematic explication of the epistemological (...) essence encrypted in the specialized languages and algorithms of the major modern scientific approaches, a systematic cross-referencing of the explicated results, and a final elaboration of a new coherent whole. Quantum mechanics, like a diver, can take us down to the level of the very first actions of our conceptualization of reality. And starting from there, it can induce an explicit understanding of certain fundamental features of the new scientific thinking. A formalized epistemology should not be mistaken for a crossdisciplinary or a multidisciplinary project. The latter projects are designed to offer to nonspecialists access to information, to results obtained inside specialized disciplines, as well as a certain understanding of these results; whereas a formalized epistemology should equip anyone with a framework for conceptualizing himself in whatever domain and direction he or she might choose. A formalized epistemology should not be mistaken either for an approach belonging to the modern cognitive sciences. These try to establish as neutrally as possible descriptions of how the human body-and-mind work spontaneously when knowledge is generated; whereas a method of conceptualization should establish what conceptual-operational deliberate procedures have to be applied in order to represent and to achieve processes of generation of knowledge optimized accordingly to any definite aims. This book addresses philosophers of science, physicists, mathematicians, logicians, computer scientists, researchers in cognitive sciences, and biologists, as well as any intellectual who is interested in scientific and philosophical thinking. (shrink)

Problems related to the operator form of the generalized canonical momenta in quantum mechanics are resolved by use of the general quantum mechanical canonical point transformation method. This method can be applied to any general canonical point transformation irrespective of the relationship between the domains of the original and transformed variables. The differential representation of the original canonical momenta pi in the original coordinate space is −i $\begin{array}{*{20}c} / \\ h \\ \end{array}$ ∂/∂x i and of the (...) transformed canonical momentap i ′ in the transformed coordinate space is −i $\begin{array}{*{20}c} / \\ h \\ \end{array}$ ∂/∂x i ′. Relationships are derived between the eigenvalues of the original and transformed momenta in either space. The ordering problem for general point transformations is discussed and is shown to be solved. As an example of the generality of the method, it is demonstrated on the point transformation in three dimensions from Cartesian rectilinear to spherical rectilinear coordinates. (shrink)

A formulation of relativistic quantum mechanics is presented independent of the theory of Hilbert space and also independent of the hypothesis of spacetime manifold. A hierarchy is established in the nondistributive lattice of physical ensembles, and it is shown that the projections relating different members of the hierarchy form a semigroup. It is shown how to develop a statistical theory based on the definition of a statistical operator. Involutions defined on the matrix representations of the semigroup are interpreted (...) in terms ofCPT conjugations. The theory of particles of spin one-half and systems with higher spin is developed from first principles. Methods are also developed for defining energy, momentum, orbital angular momentum, and weighted spacetime coordinates without reference to a manifold. (shrink)

Standard canonical quantum mechanics makes much use of operators whose spectra cover the set of real numbers, such as the coordinates of space, or the values of the momenta. Discrete quantum mechanics uses only strictly discrete operators. We show how one can transform systems with pairs of integer-valued, commuting operators $P_i$ and $Q_i$ , to systems with real-valued canonical coordinates $q_i$ and their associated momentum operators $p_i$ . The discrete system could be entirely deterministic while the (...) corresponding (p, q) system could still be typically quantum mechanical. (shrink)

In the framework of the topos approach to quantum mechanics we give a representation of physical properties in terms of modal operators on Heyting algebras. It allows us to introduce a classical type study of the mentioned properties.

The language of manuals may be used to discuss inference in measurement in a general experimental context. Specializing to the context of the frame manual for Hilbert space, this inference leads to state dominance of the inferred state from partial measurements; this in turn, by Sakai's theorem, determines observables which are described by positive operator-valued measures. Symmetries are then introduced, showing that systems of covariance, rather than systems of imprimitivity, are natural objects to study in quantum mechanics. Experiments (...) measuring different polarization components simultaneously are reexamined in this language. Finally, implications of the Naimark extension theorem for the manual approach are investigated. (shrink)

In previous works we have established that the spacetime probabilistic organization of the quantum theory is determined by the spacetime characteristics of the operations by which the observer produces the objects to be studied (“states” of microsystems) and obtains qualifications of these. Guided by this first conclusion, we have then built a “general syntax of relativized conceptualization” where any description is explicitly and systematically referred to the two basic epistemic operations by which the conceptor introduces the object to be (...) qualified and then obtains qualifications of it. Inside this syntax there emerges a general typology of the relativized descriptions. Here we show that with respect to this typology the type of the predictive quantum mechanical descriptions acquires a precise definition. It appears that the quantum mechanical formalism has captured and has expressed directly in a mathematical language the most complex form in which can occur a first descriptional phase that lies universally at the bottom of any chain of conceptualization. The main features of the Hilbert-Dirac algorithms are decoded in terms of the general syntax of relativized conceptualization. This renders explicit the semantical contents of the quantum mechanical representations relating each one of these to its mathematical quantum mechanical expression. Basic insufficiencies are thus identified and, correlatively, false problems as well as answers to these, or guides toward answers. Globally the results obtained provide a basis for future attempts at a general mathematical representation of the processes of conceptualization. “Il pourrait, en effet, être dangereux pour l'avenir de la Physique qu'elle se contente trop facilement de purs formalismes, d'images floues et d'explications toutes verbales s'exprimant par des mots à signification imprécise”—Louis de Broglie,Certitudes et Incertitudes de la Science (Albin Michel, Paris, 1965). (shrink)

A foundation of quantum mechanics based on the concepts of focusing and symmetry is proposed. Focusing is connected to c-variables—inaccessible conceptually derived variables; several examples of such variables are given. The focus is then on a maximal accessible parameter, a function of the common c-variable. Symmetry is introduced via a group acting on the c-variable. From this, the Hilbert space is constructed and state vectors and operators are given a definite interpretation. The Born formula is proved from weak (...) assumptions, and from this the usual rules of quantum mechanics are derived. Several paradoxes and other issues of quantum theory are discussed. (shrink)

In the article the possibility of breaking the eigenvalue-eigenstate link in quantum mechanics is considered. An argument is presented to the effect that there are some non-maximal observables for which the implication from eigenstates to eigenvalues is not valid, i.e. such that although the probability of revealing certain value upon measurement is one, they don't possess this value before the measurement. It is shown that the existence of such observables leads to contextuality, i.e. the thesis that one Hermitean (...) operator can represent more than one physical observable. Finally, contextuality brought about by these considerations is compared with contextuality suggested by the Kochen-Specker paradox. (shrink)

Although a few new results are presented, this is mainly a review article on the relationship between finite-dimensional quantum mechanics and finite groups. The main motivation for this discussion is the hidden subgroup problem of quantum computation theory. A unifying role is played by a mathematical structure that we call a Hilbert *-algebra. After reviewing material on unitary representations of finite groups we discuss a generalized quantum Fourier transform. We close with a presentation concerning position-momentum measurements (...) in this framework. (shrink)

In this paper it will be argued that any realist interpretation of quantum mechanics intending to preserve the objectivity of the set of the definite-valued observables should require such a set to be invariant under the symmetry group of the theory. In particular, it will be shown that the natural way to reach this goal is to appeal to the Casimir operators of the Galilean group. Additionally, this idea will be generalized in two ways: by selecting the definite-valued (...) observables of a system in quantum field theory as those represented by the Casimir operators of the Poincaré group, and by extending the strategy to gauge symmetries. (shrink)

The aim of this paper is to consider in what sense the modal-Hamiltonian interpretation of quantum mechanics satisfies the physical constraints imposed by the Galilean group. In particular, we show that the only apparent conflict, which follows from boost-transformations, can be overcome when the definition of quantum systems and subsystems is taken into account. On this basis, we apply the interpretation to different well-known models, in order to obtain concrete examples of the previous conceptual conclusions. Finally, we (...) consider the role played by the Casimir operators of the Galilean group in the interpretation. (shrink)

We construct a world model consisting of a matter field living in 4 dimensional spacetime and a gravitational field living in 11 dimensional spacetime. The seven hidden dimensions are compactified within a radius estimated by reproducing the particle–wave characteristics of diffraction experiments. In the presence of matter fields the gravitational field develops localized modes with elementary excitations called gravonons which are induced by the sources. The final world model treated here contains only gravonons and a scalar matter field. The gravonons (...) are localized in the environment of the massive particles which generate them. The solution of the Schrödinger equation for the world model yields matter fields which are localized in the 4 dimensional subspace. The localization has the following properties: There is a chooser mechanism for the selection of the localization site. The chooser selects one site on the basis of minor energy differences and differences in the gravonon structure between the sites, which at present cannot be controlled experimentally and therefore let the choice appear statistical. The changes from one localization site to a neighbouring one take place in a telegraph-signal like manner. The times at which telegraph like jumps occur depend on subtleties of the gravonon structure which at present cannot be controlled experimentally and therefore let the telegraph-like jumps appear statistical. The fact that the dynamical law acts in the configuration space of fields living in 11 dimensional spacetime lets the events observed in 4 dimensional spacetime appear non-local. In this way the phenomenology of CQM is obtained without the need of introducing the process of collapse and a probabilistic interpretation of the wave function. Operators defining observables need not be introduced. All experimental findings are explained in a deterministic way as a consequence of the time development of the wave function in configuration space according to Schrödinger’s equation without the need of introducing a probabilistic interpretation. (shrink)

It is shown that below the threshold of pair creation, a consistent quantum mechanical interpretation of relativistic spin-0 and spin-1 particles (both massive and mussless) ispossible based an the Hamiltonian-Schrödinger form of the firstorder Kemmer equation together with a first-class constraint. The crucial element is the identification of a conserved four-vector current associated with the equation of motion, whose time component is proportional to the energy density which is constrainedto be positive definite for allsolutions. Consequently, the antiparticles must be (...) interpreted as positive-energy states traveling backward in time. This also makes it possible to define hermitian position operators with localized eigensolutions (δ-functions) as well as Bohmian trajectories for bosons. The exact theory is obtained by “second quantization” and is mathematically completely equivalent to conventional quantum field theory. The classical field emerges in the high mean number limit of coherent states of the exact theory. The formalism provides a new basis for computing tunneling times for photons and chaotic phenomena in optics. (shrink)

In an article by Margenau and Cohen various correspondence principles were described in connection with Weyl, Born-Jordan, and symmetrized ordering of quantum mechanical operators. In this article we make an interesting comparison between the aforementioned ordering process and our previous prescriptions.

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)

A model is described in which subjective consciousness is generated through an unusual property of quantum non-locality. Chaos and bifurcation serve to link quantum transactions to global brain dynamics through the fractal architecture and dynamics of the central nervous system. The resulting process operates at the boundary between quantum computation and wave-particle reduction, thus combining optimality and free-choice. It is concluded that subjective consciousness has an evolutionary role as a non-computational predictive faculty, first emerging from chaotic excitations (...) in single-celled organisms; and that conscious anticipation, rather than computation, has been the principal factor promoting selective advantage in the development of the brain. (shrink)

We point out that, when the dimension of the Hilbert space is greater than two, Bell’s operators entering the Bell-CHSH inequality do exhibit inequivalent unitary matrix representations. Although the Bell-CHSH inequality turns out to be violated, the size of the violation is different for different representations, the maximum violation being given by Tsirelson’s bound. The feature relies on a pairing mechanism between the modes of the Hilbert space of the system.

I argue against a general time observable in quantum mechanics except for quantum gravity theory. Then I argue in support of case specific arrival time and dwell time observables with a cautionary note concerning the broad approach to POVM observables because of the wild proliferation available.

Although quantum mechanics can accurately predict the probability distribution of outcomes in an ensemble of identical systems, it cannot predict the result of an individual system. All the local and global hidden variable theories attempting to explain individual behavior have been proved invalid by experiments (violation of Bell’s inequality) and theory. As an alternative, Schrodinger and others have hypothesized existence of free will in every particle which causes randomness in individual results. However, these free will theories have failed (...) to quantitatively explain the quantum mechanical results. In this paper, we take the clue from quantum biology to get the explanation of quantum mechanical distribution. Recently it was reported that mutations (which are quantum processes) in DNA of E. coli bacteria instead of being random were biased in a direction such that the chance of survival of the bacteria is increased. Extrapolating it, we assume that all the particles including inanimate fundamental particles have a will and that is biased to satisfy the collective goals of the ensemble. Using this postulate, we mathematically derive the correct spin probability distribution without using quantum mechanical formalism (operators and Born’s rule) and exactly reproduce the quantum mechanical spin correlation in entangled pairs. Using our concept, we also mathematically derive the form of quantum mechanical wave function of free particle which is conventionally a postulate of quantum mechanics. Thus, we prove that the origin of quantum mechanical results lies in the will (or consciousness) of the objects biased by the collective goal of ensemble or universe. This biasing by the group on individuals can be called as “coherence” which directly represents the extent of life present in the ensemble. So, we can say that life originates out of establishment of coherence in a group of inanimate particles. (shrink)