We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum mechanics. Our approach nevertheless allows completely reproducing the standard mathematical formalism of quantum mechanics and identifying its applicability limits. We especially attend to the quantum state reduction problem.
A necessary and natural change in our application of quantum mechanics to separated systems is shown to reconcile quantum mechanics and local realism. An analysis of separation and localization justifies the proposed change in application of quantum mechanics. An important EPRB experiment is reconsidered and it is seen that when it is correctly interpreted it supports local realism. This reconciliation of quantum mechanics with local realism allows the axiom sets of quantum mechanics, probability, and special relativity to be joined in a consistent global axiom set for physics.
The semiclassical method is characterized by finite forces and smooth, well-behaved trajectories, but also by multivalued representational functions that are ill-behaved at turning points. In contrast, quantum trajectory methods--based on Bohmian mechanics (quantum hydrodynamics)--are characterized by infinite forces and erratic trajectories near nodes, but also well-behaved, single-valued representational functions. In this paper, we unify these two approaches into a single method that captures the best features of both, and in addition, satisfies the correspondence principle. Stationary eige…
In previous articles [J. Chem. Phys. 121 4501 (2004), J. Chem. Phys. 124 034115 (2006), J. Chem. Phys. 124 034116 (2006), J. Phys. Chem. A 111 10400 (2007)] a bipolar counter-propagating wave decomposition, Psi = Psi+ + Psi-, was presented for stationary states Psi of the one-dimensional Schrodinger equation, such that the components Psi+- approach their semiclassical WKB analogs in the large action limit. The corresponding bipolar quantum trajectories are classical-like and well-behaved, even when Psi has many nodes, or is wildly oscillatory. In this paper, the method is generalized for time-…
In previous articles [J. Chem. Phys. 121 4501 (2004), J. Chem. Phys. 124 034115 (2006), J. Chem. Phys. 124 034116 (2006)] a bipolar counter-propagating wave decomposition, Psi = Psi+ + Psi-, was presented for stationary states Psi of the one-dimensional Schrodinger equation, such that the components Psi+- approach their semiclassical WKB analogs in the large action limit. The corresponding bipolar quantum trajectories are classical-like and well-behaved, even when Psi has many nodes, or is wildly oscillatory. In this paper, the method is generalized for multisurface scattering applications, an…
In a previous paper [J. Chem. Phys. 121 4501 (2004)] a unique bipolar decomposition, Psi = Psi1 + Psi2 was presented for stationary bound states Psi of the one-dimensional Schroedinger equation, such that the components Psi1 and Psi2 approach their semiclassical WKB analogs in the large action limit. The corresponding bipolar quantum trajectories, as defined in the usual Bohmian mechanical formulation, are classical-like and well-behaved, even when Psi has many nodes, or is wildly oscillatory. A modification for discontinuous potential stationary stattering states was presented in a second pap…
The status of locality in quantum mechanics is analyzed from a nonstandard point of view. It is assumed that quantum states are relative, they depend on and are defined with respect to some bigger physical system which contains the former system as a subsystem. Hence, the bigger system acts as a reference system. It is shown that quantum mechanics can be reformulated in accordance with this new physical assumption. There is an important consequence of this dependence: states may not be comparable, i.e., they cannot be checked by suitable measurements simultaneously. This special circumstance i…
In a previous paper [J. Chem. Phys. 121 4501 (2004)] a unique bipolar decomposition, Psi = Psi1 + Psi2 was presented for stationary bound states Psi of the one-dimensional Schroedinger equation, such that the components Psi1 and Psi2 approach their semiclassical WKB analogs in the large action limit. Moreover, by applying the Madelung-Bohm ansatz to the components rather than to Psi itself, the resultant bipolar Bohmian mechanical formulation satisfies the correspondence principle. As a result, the bipolar quantum trajectories are classical-like and well-behaved, even when Psi has many nodes, …
The question of the representation of quantum stationary partially polarized waves as random superpositions of different polarization ellipses is addressed. To this end, the Bohmian formulation of quantum mechanics is considered and extended to quantum optical polarization. As is shown, this approach properly combines definite time-evolving trajectories with rigorous stationary quantum distributions via the topology displayed by the associated phase field.
The Relational Blockworld (RBW) interpretation of non-relativistic quantum mechanics (NRQM) is introduced. Accordingly, the spacetime of NRQM is a relational, non-separable blockworld whereby spatial distance is only defined between interacting trans-temporal objects. RBW is shown to provide a novel statistical interpretation of the wavefunction that deflates the measurement problem, as well as a geometric account of quantum entanglement and non-separability that satisfies locality per special relativity and is free of interpretative mystery. We present RBW's acausal and adynamical resolution …
Several recent attoclock experiments have investigated the fundamental question of a quantum mechanically induced time delay in tunneling ionization via extremely precise photoelectron momentum spectroscopy. The interpretations of those attoclock experimental results were controversially discussed, because the entanglement of the laser and Coulomb field did not allow for theoretical treatments without undisputed approximations. The method of semiclassical propagation matched with the tunneled wavefunction, the quasistatic Wigner theory, the analytical R-matrix theory, the backpropagation metho…
It is shown that the geometric constraint advocated in [R. S. Kaushal, Mod. Phys. Lett. A 15 (2000) 1391] is trivially satisfied. Therefore, such a constraint does not exist. We also point out another flaw in Kaushal's paper.
This paper has been withdrawn by the author. In this short paper I introduce a concept of possibility in order to vindicate Everett's Theory of many worlds. The main idea is that there is only one world: the real. After the wave-collapse, we have again only one world, but many possible worlds which have a different grade of possibility. In this sense 'possible' exclude the 'reality', opposing a long modal tradition.
In this paper we attempt to physically interpret the Modal Kochen- Specker (MKS) theorem. In order to do so, we analyze the features of the possible properties of quantum systems arising from the elements in an orthomodular lattice and distinguish the use of "possibility" in the classical and quantum formalisms. Taking into account the modal and many worlds non-collapse interpretation of the projection postulate, we discuss how the MKS theorem rules the constraints to actualization, and thus, the relation between actual and possible realms.
A recent proof, formulated in the symbolic language of modal logic, shows that a well-defined formulation of the possibility mentioned in the title is answered affirmatively. In the paper being commented upon several proposals were made about how to translate this symbolic proof into prose, and it was concluded, on the basis of those proposed translations, that either the proof was invalid or that an unwarranted reality assumption was made. However, those interpretations deviate in small but important ways from the precise logical path followed in the proof. It is explained here how by staying…
This paper reviews the structure of standard quantum mechanics, introducing the basics of the von Neumann-Dirac axiomatic formulation as well as the well-known Copenhagen interpretation. We review also the major conceptual difficulties arising from this theory, first and foremost, the well-known measurement problem. The main aim of this essay is to show the possibility to solve the conundrums affecting quantum mechanics via the methodology provided by the primitive ontology approach. Using Bohmian mechanics as an example, the paper argues for a realist attitude towards quantum theory. In the s…
It is shown that, with some reasonable assumptions, the theory of general relativity can be made compatible with quantum mechanics by using the field equations of general relativity to construct a Robertson-Walker metric for a quantum particle so that the line element of the particle can be transformed entirely to that of the Minkowski spacetime, which is assumed by a quantum observer, and the spacetime dynamics of the particle described by a Minkowski observer takes the form of quantum mechanics. Spacetime structure of a quantum particle may have either positive or negative curvature. However…
Nonlinear modifications of quantum mechanics have a troubled history. They were initially studied for many promising reasons: resolving the measurement problem, testing the limits of standard quantum mechanics, and reconciling it with gravity. Two results substantially undermined the credibility of non-linear theories. Some have been experimentally refuted, and more importantly, all deterministic non-linear theories can be used for superluminal communication. However, these results are unconvincing because they overlook the fact that the distribution of measurement results predicted by non-lin…
Amplitudes are the major logical object in Quantum Theory. Despite this fact they presents no physical reality and in consequence only observables can be experimetally checked. We discuss the possibility of a theory of Quantum Probabilities capable of give full account to quantum phenomena. Advanteges of this formulation are the evidence of physical processes not described by the orotodox formulation using amplitudes and the possibility of a full algoritimization of Quantum Mechanics.
Some of the so-called imponderables and counterintuitive puzzles associated with the Copenhagen interpretation of quantum mechanics appear to have alternate, parallel explanations in terms of nonlinear dynamics and chaos. These include the mocking up of exponetial decay in closed systems, possible nonlinear extensions of Bell's inequalities, spontaneous symmetry breaking and the existence of intrinsically preferred internal oscillation modes (quantization) in nonlinear systems, and perhaps even the production of diffraction-like patterns by "order in chaos." The existence of such parallel expl…
This study examines Quaternion Dirac solutions for an infinite square well. The quaternion result does not recover the complex result within a particular limit. This raises the possibility that quaternionic quantum mechanics may not be understood as a correction to complex quantum mechanics, but it may also be a structure that can be used to study phenomena that cannot be described through the framework of complex quantum mechanics.
We carry out an investigation into the possibility of developing a Bohmian interpretation based on the continuous motion of point particles for noncommutative quantum mechanics. The conditions for such an interpretation to be consistent are determined, and the implications of its adoption for noncommutativity are discussed. A Bohmian analysis of the noncommutative harmonic oscillator is carried out in detail. By studying the particle motion in the oscillator orbits, we show that small-scale physics can have influence at large scales, something similar to the IR-UV mixing.
Using the formalism of extended $N=4$ supersymmetric quantum mechanics we consider the procedure of the construction of multi--well potentials. We demostrate the form--invariance of Hamiltonians entering the supermultiplet, using the presented relation for integrals, which contain fundamental solutions. The possibility of partial $N=4$ supersymmetry breaking is determined. We also obtain exact forms of multi--well potentials, both symmetric and asymmetric, using the Hamiltonian of harmonic oscillator as initial. The modification of the shape of potentials due to variation of parameters is also…
This paper presents an alternative quantum theory, the Theory of Discrete Extension, which avoids many of the conceptual problems of standard quantum mechanics. It is a deterministic, dynamic collapse theory with a well-defined primitive ontology. In place of the dual, classical concepts of wave and particle, the unitary, non-classical concept of a discretely extended object emerges directly from the theory's dynamic equations as a primitive ontology. Because this ontology is unitary, the theory avoids the dilemmas of wave-particle dualism and complementarity. Furthermore, the theory's dynamic…
The possibility that time can be regarded as a discrete parameter is re-examined. We study the dynamics of the free particle and find in some cases superluminal propagation.
Enforcing the periodicity hypothesis of the "old" formulation of Quantum Mechanics we show the possibility for a new scenario where Special Relativity and Quantum Mechanics are unified in a Deterministic Field Theory [arXiv:0903.3680]. A novel interpretation of the AdS/CFT conjecture is discussed.
A simple experiment using radioactive decay is proposed to test the possibility of a determinsistic, but chaotic, origin of quantum mechanical randomness.
In this paper we analyze and discuss the historical and philosophical development of the notion of logical possibility focusing on its specific meaning in classical and quantum mechanics. Taking into account the logical structure of quantum theory we continue our discussion regarding the Aristotelian Square of Opposition in orthomodular structures enriched with a monadic quantifier. Finally, we provide an interpretation of the Orthomodular Square of Opposition exposing the fact that classical possibility and quantum possibility behave formally in radically different manners.
The notion coexistence of quantum observables was introduced to describe the possibility of measuring two or more observables together. Here we survey the various different formalisations of this notion and their connections. We review examples illustrating the necessary degrees of unsharpness for two noncommuting observables to be jointly measurable (in one sense of the phrase). We demonstrate the possibility of measuring together (in another sense of the phrase) noncoexistent observables. This leads us to a reconsideration of the connection between joint measurability and noncommutativity of…
Recent experimental research with marine algae points towards quantum entanglement at ambient temperature, with correlations between essential biological units separated by distances as long as 20 Angströms. The associated decoherence times, due to environmental influences, are found to be of order 400 fs. This prompted some authors to connect such findings with the possibility of some kind of quantum computation taking place in these biological entities: within the decoherence time scales, the cell "quantum calculates" the optimal "path" along which energy and signal would be transported more…
It is shown, that the only reason for possibility of using microcanonical ensemble is that there are probabilistic processes in microworld, that are not described by quantum mechanic. On a simple example it is demonstrated, that canonical distribution is not independent and equal to microcanonical, but is a result of averaging by microcanonical ensemble.
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical model of physical objects is proposed. This model gives a possibility to unite a description of corpuscular and wave properties of real physical objects, i.e. fields and particles. There are substantiated an approach and a mathematical pattern which give a possibility to describe physical object not only in causal, but also in absolute remote fields of the …
The new interpretation of Quantum Mechanics is based on a complex probability theory. An interpretation postulate specifies events which can be observed and it follows that the complex probability of such event is, in fact, a real positive number. The two-slit experiment, the mathematical formulation of the complex probability theory, the density matrix, Born's law and a possibility of hidden variables are discussed.
A real two-particle experiment is proposed in which one of the particles undergoes two successive impacts on beam-splitters. It is shown that the standard quantum mechanical superposition principle implies the possibility of influences acting backward in time ("retrocausation"), in striking contrast with the principle of causality. It is argued that nonlocality and retrocausation are not necessarily entangled.
We focus on potential mechanisms for `energy-loss-free' transport along the cell microtubules, which could be considered as realizations of Fröhlich's ideas on the role of solitons for superconductivity and/or biological matter. In particular, by representing the MT arrangements as `cavities',we present a novel scenario on the formation of macroscopic (or mesoscopic) quantum-coherent states, as a result of the (quantum-electromagnetic) interactions of the MT dimers with the surrounding molecules of the ordered water in the interior of the MT cylinders. We present some generic order of magnitud…
The problem of defining time (or phase) operator for three-dimensional harmonic oscillator has been analyzed. A new formula for this operator has been derived. The results have been used to demonstrate a possibility of representing quantum-mechanical time evolution in the framework of an extended Hilbert space structure. Physical interpretation of the extended structure has been discussed shortly, too.
Analysis of the logical foundations of quantum mechanics indicates the possibility of constructing a theory using quaternionic Hilbert spaces. Whether this mathematical structure reflects reality is a matter for experiment to decide. We review the only direct search for quaternionic quantum mechanics yet carried out and outline a recent proposal by the present authors to look for quaternionic effects in correlated multi-particle systems. We set out how such experiments might distinguish between the several quaternionic models proposed in the literature.
We consider the possibility that the relative phase in quantum mechanics plays a role in determining measurement outcome and could therefore serve as a "hidden" variable. The Born rule for measurement equates the probability for a given outcome with the absolute square of the coefficient of the basis state, which by design removes the relative phase from the formulation. The value of this phase at the moment of measurement naturally averages out in an ensemble, which would prevent any dependence from being observed, and we show that conventional frequency-spectroscopy measurements on discrete …
Working within the framework of parity-time-symmetric quantum mechanics we look into the possibility of entanglement generation and demonstrate that the feature of non-violation of no-signaling principle may hold for the simplest non-trivial case of bipartite systems. Basically our arguments are based on the computation of the reduced density matrix of one party to justify that the entropy of the other does not change.
Quantum mechanics forces us to reconsider certain aspects of classical causality. The 'central mystery' of quantum mechanics manifests in different ways, depending on the interpretation. This mystery can be formulated as the possibility of selecting part of the initial conditions of the Universe 'retroactively'. This talk aims to show that there is a global, timeless, 'bird's view' of the spacetime, which makes this mystery more reasonable. We will review some well-known quantum effects from the perspective of global consistency.
This is a review-essay on ``Speakable and Unspeakable in Quantum Mechanics'' by John Bell and ``The Undivided Universe: An Ontological Interpretation of Quantum Mechanics'' by David Bohm and Basil Hiley. The views of these authors concerning the character of quantum theory and quantum reality---and, in particular, their approaches to the issues of nonlocality, the possibility of hidden variables, and the nature of and desiderata for a satisfactory scientific explanation of quantum phenomena---are contrasted, with each other and with the orthodox approach to these issues.
Accurate calibration of photodetectors both in analog and in photon-counting regime is fundamental for various scientific applications, which range from "traditional" quantum optics to the studies on foundations of quantum mechanics, quantum cryptography, quantum computation, etc. In this paper we systematically study the possibility of the absolute calibration of analog photo-detectors based on the properties of parametric amplifiers. Our results show that such a method can be effectively developed with interesting possible metrological applications.
We present a brief non-technical introduction to the standing discussion on the relation between Quantum Mechanics and Determinism. Quantum Mechanics inherent randomness in the measurement process is sometimes presented as a door to explain free will. We argue against this interpretation. The possibility that Quantum Mechanics provides just an effective description of Nature which is only valid at our low-energy scales is also discussed.
In this paper we investigate the history of relationalism and its present use in some interpretations of quantum mechanics. In the first part of this article we will provide a conceptual analysis of the relation between substantivalism, relationalism and relativism in the history of both physics and philosophy. In the second part, we will address some relational interpretations of quantum mechanics, namely, Bohr's relational approach, the modal interpretation by Kochen, the perspectival modal version by Bene and Dieks and the relational interpretation by Rovelli. We will argue that all these i…
Several situations, in which an empty wave causes an observable effect, are reviewed. They include an experiment showing ``surrealistic trajectories'' proposed by Englert et al. and protective measurement of the density of the quantum state. Conditions for observable effects due to empty waves are derived. The possibility (in spite of the existence of these examples) of minimalistic interpretation of Bohmian Quantum Mechanics in which only Bohmian positions supervene on our experience is discussed.
Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of many results on the $\h \to 0$ asymptotics, it is not yet clear how to explain within standard quantum mechanics the classical motion of macroscopic bodies. In this paper we shall analyze special cases of classical behavior in the framework of a precise formulation of quantum mechanics, Bohmian mechanics, which contains in its own structure the possibility of describing real objects in an observer-independent way.
We discuss the possibility to formulate the dynamics of spin states described by the Schrodinger equation for pure states and the von Neumann equation (as well as the GKSL equation) for mixed states in the form of quantum kinetic equations for probability distributions. We review an approach to the spin-state description by means of the probability distributions of dichotomic random variables.
Discussions about whether quantum theory is determinism or indeterminism has lasted for a century. A new approach to standard quantum mechanics called many-interacting-worlds method based on many-worlds interpretation and de Broglie-Bohm mechanics provided the possibility to demonstrate probability from deterministic universe.The many-interacting-worlds method has been proved successful in the ground state of harmonic oscillator. In this article we extend this method to one dimensional Coulomb potential and construct a corresponding empirical density function. We also provide a theoretical pro…
A series of recent papers ``Faster than Hermitian Quantum Mechanics'' and related articles made a point of the possibility of a non-Hermitian, but PT-symmetric, operator to play the role of a Hamiltonian. In particular, they show that with an appropriate choice of an inner product, the evolution generated by such an operator will conserve the norm and scalar product. Here we observe that if one chooses such an inner product then the Hamiltonian in question is actually Hermitian, and the whole exercise is to a certain degree redundant.
In the paper we consider an interesting possibility of a time as a stochastic process in quantum mechanics.In order to do it we reconsider time as a mechanical quantity in classical mechanics and afterwards we quantize it. We consider continuous and discrete time.
We present critical arguments against individual interpretation of Bohr's complementarity and Heisenberg's uncertainty principles. Statistical interpretation of these principles is discussed in the contextual framework. We support the possibility to use Statistical Contextual Realist Interpretation of quantum formalism. In spite of all {\bf no-go} theorems (e.g., von Neumann, Kochen and Specker,..., Bell,...), recently (quant-ph/0306003 and 0306069) we constructed a realist basis of quantum mechanics. In our model both classical and quantum spaces are rough images of the fundamental {\bf presp…
Glauber coherent states of quantum systems are reviewed. We construct the tomographic probability distributions of the oscillator states. The possibility to describe quantum states by tomographic probability distributions (tomograms) is presented on an example of coherent states of parametric oscillator. The integrals of motion linear in the position and momentum are used to explicitly obtain the tomogram evolution expressed in terms of trajectories of classical parametric oscillator
An intense effort is being made today to build a quantum computer. Instead of presenting what has been achieved, I invoke here analogies from the history of science in an attempt to glimpse what the future might hold. Quantum computing is possible in principle - there are no known laws of Nature that prevent it - yet scaling up the few qubits demonstrated so far has proven to be exceedingly difficult. While this could be regarded merely as a technological or practical impediment, I argue that this difficulty might be a symptom of new laws of physics waiting to be discovered. I also introduce a…
In this paper I present and defend Rovelli's relation quantum mechanics from some foreseeable objections, so as to clarify its philosophical implications vis a vis rival interpretations. In particular I ask whether RQM presupposes a hidden recourse to both a duality of evolutions and of ontology (the relationality of quantum world and the intrinsicness of the classical world, which in the limit must be recovered from the former). I then concentrate on the pluralistic, antimonistic metaphysical consequences of the theory, due to the impossibility of assigning a state to the quantum universe. Fi…
The behavior of a classical charged point particle under the influence of only a Coulombic binding potential and classical electromagnetic zero-point radiation, is shown to yield agreement with the probability density distribution of Schroedinger's wave equation for the ground state of hydrogen. These results, obtained without any fitting parameters, again raise the possibility that the main tenets of stochastic electrodynamics (SED) are correct, thereby potentially providing a more fundamental basis of quantum mechanics. The present methods should help propel yet deeper investigations into SE…
The transition from classical to quantum mechanics rests on the recognition that the structure of information is not what we thought it was: there are operational, i.e., phenomenal, probabilistic correlations that lie outside the polytope of local correlations. Such correlations cannot be simulated with classical resources, which generate classical correlations represented by the points in a simplex, where the vertices of the simplex represent joint deterministic states that are the common causes of the correlations. The `no go' hidden variable theorems tell us that we can't shoe-horn correlat…
Recently, Elio Conte has commented a paper by the present author devoted to analyze the possibility of checking experimentally whether the perceptual process can lead to the collapse of the wavefunction. Here we answer to the comments by Conte and we show that he has missed to grasp the crucial elements of our proposal. Morever, we discuss some ideas put forward by Conte concerning the occurrence of quantum superpositions of different states of consciousness and we show that they are rather vague and not cogent.
