Until recently Jeffrey Bub and Itamar Pitowsky, in the framework of an information theoretic view of quantum mechanics, claimed first that to the measurement problem in its ordinary formulation there correspond in effect two measurement problems (simply called the big and the small measurement problems), with a different degree of relevance and, second, that the analysis of a quantum measurement is a problem only if other assumptions, taken by Pitowsky and Bub to be unnecessary 'dogmas', are assumed. Here I critically discuss this unconventional stance on the measurement problem and argue that the Bub and Pitowsky arguments are inconclusive, mainly because they rely on an unwarranted extension to the quantum realm of a distinction concerning the foundations of special relativity which is in itself rather controversial.
According to the Received View identical quantum particles are a previously unknown kind of objects that do not possess individuality. In this Chapter we discuss this view, criticize it, and propose an alternative. According to this alternative view so-called identical quantum particles should in many cases not be seen as objects (particles) at all. However, there are situations in which a particle picture does become applicable. But the particles that emerge in these cases are distinguishable individuals, unlike the particles of the Received View.
Foundational investigations in quantum mechanics, both experimental and theoretical, gave birth to the field of quantum information science. Nevertheless, the foundations of quantum mechanics themselves remain hotly debated in the scientific community, and no consensus on essential questions has been reached. Here, we present the results of a poll carried out among 33 participants of a conference on the foundations of quantum mechanics. The participants completed a questionnaire containing 16 multiple-choice questions probing opinions on quantum-foundational issues. Participants included physi…
In this article, we develop quantum mechanics upon the framework of the quantum mechanical Hamilton-Jacobi theory. We will show, that the Schroedinger point of view and the Hamilton-Jacobi point of view are fully equivalent in their description of physical systems, but differ in their descriptive manner. As a main result, a wave function in Hamilton-Jacobi theory can be decomposed into travelling waves in any point in space, not only asymptotically. The well known WKB-theory will be a special result of the more general theory, we will develop below. By the example of the linear potential and t…
The author's opinion on the interpretation of quantum mechanics is further elucidated. Not only may quantum mechanics be a description of the sub-microscopic world that is profoundly different from what is often asserted, particularly concerning 'what is really going on', but questions such as these may well be essential for finding new ways of constructing models beyond what is now called the Standard Model of the sub-atomic particles.
The so-called Received View (RV) on quantum non-individuality states, basically, that quantum particles are not individuals. It has received an amount of criticism in the recent literature, most of it concerning the relation between the RV and the relation of identity. In this chapter we carefully characterise a family of concepts involved in clarifying the view, indicating how the very idea of failure of identity, commonly used to define the RV, may be understood. By doing so, we hope to dissipate some misunderstandings about the RV, which shall also be seen as evidence of its tenability.
A recent phase transition in the relational interpretation of quantum mechanics (RQM) is situated in its historical context, and the novelty of the post-transition viewpoint is questioned.
Drawing inspiration from Dirac's work on functions of non commuting observables, we develop a fresh approach to phase space descriptions of operators and the Wigner distribution in quantum mechanics. The construction presented here is marked by its economy, naturalness and more importantly, by its potential for extensions and generalisations to situations where the underlying configuration space is non Cartesian.
A view of emission and absorption of photons by atoms, which was proposed by Max Planck, is recalled. A direct experiment that could corroborate or refute that view is defined.
We compute rigorously the ground and equilibrium states for Kitaev's model in 2D, both the finite and infinite version, using an analogy with the 1D Ising ferromagnet. Next, we investigate the structure of the reduced dynamics in the presence of thermal baths in the Markovian regime. Special attention is paid to the dynamics of the topological freedoms which have been proposed for storing quantum information.
The goal of this paper is to explain how the views of Albert Einstein, John Bell and others, about nonlocality and the conceptual issues raised by quantum mechanics, have been rather systematically misunderstood by the majority of physicists.
In a previous preprint (quant-ph/0012122) we introduced a ``contextual objectivity" formulation of quantum mechanics (QM). A central feature of this approach is to define the quantum state in physical rather than in mathematical terms, in such a way that it may be given an "objective reality". Here we use some ideas about the system dimensionality, taken from quant-ph/0101012, to propose a possible axiomatic approach to QM. In this approach the structure of QM appears as a direct consequence of the non-commutative character of the (classical geometrical) group of "knobs transformations", that …
In this paper I propose a new way for counting the microstates of a system out of equilibrium. As, according to quantum mechanics, things happen as if a given particle can be found in more than one state at once, I extend this concept to propose the coherent access by a particle to the available states of a system. By coherent access I mean the possibility for the particle to act as if it is populating more than one microstate at once. This hypothesis has experimental implications, since the thermodynamical probability and, as a consequence, the Bose-Einstein distribution as well as the argume…
A survey probing respondents' views on various foundational issues in quantum mechanics was recently created by Schlosshauer, Kofler, and Zeilinger [arXiv:1301.1069] and then given to 33 participants at a quantum foundations conference. Here we report the results of giving this same survey to the attendees at another recent quantum foundations conference. While it is rather difficult to conclude anything of scientific significance from the poll, the results do strongly suggest several interesting cultural facts -- for example, that there exist, within the broad field of "quantum foundations", …
We analyse a proposition which considers quantum theory as a mere tool for calculating probabilities for sequences of outcomes of observations made by an Observer, who him/herself remains outside the scope of the theory. Predictions are possible, provided a sequence includes at least two such observations. Complex valued probability amplitudes, each defined for an entire sequence of outcomes, are attributed to Observer's reasoning, and the problem of wave function's collapse is dismissed as a purely semantic one. Our examples include quantum "weak values", and a simplified version of the "dela…
In the 80 years since the seminal Einstein, Podolsky, and Rosen (EPR) paper, physicists and philosophers have mused about the `spooky action at a distance' aspect of quantum mechanics that so bothered Einstein. In his formal analysis of EPR-type entangled quantum states, Bell (1964) concluded that any hidden variable theory designed to reproduce the predictions of quantum mechanics must necessarily be nonlocal and allow superluminal interactions. This doesn't immediately imply that nonlocality is a characteristic feature of quantum mechanics let alone a fundamental property of nature; however,…
In this paper, we demonstrate novel relationships between quantum mechanics and the electromagnetic wave equation. In our approach, an invariant interference-dependent electromagnetic quantity, which we call "quantum rest mass", replaces the conventional role of the inertial rest mass. In the ensuing results, photons, during interference, move slower than the speed of light in vacuum, and possess de Broglie wavelength. Further, we use our electromagnetic approach to examine double-slit photon trajectories, and to arrive at the Schrodinger equation's results for a particle in an infinite square…
There are considered some corollaries of certain hypotheses on the observation process of microphenomena. We show that an enlargement of the phase space and of its motion group and an account for the diffusion motions of microsystems in the enlarged space, the motions which act by small random translations along the enlarged group, lead to observable quantum effects. This approach enables one to recover probability distributions in the phase space for wave functions. The parameters of the model considered here are estimated on the base of Lamb's shift in the spectrum of the hydrogen's atom.
A non-local hidden variables theory for non-relativisitic quantum theory is presented, which gives a realist completion of quantum mechanics, in the sense of a complete description of individual events. The proposed fundamental theory is an extension of an energetic causal set theory, which assumes that time, events, causal structure, momentum and energy are fundamental. But space and the wave function are emergent. The beables of the theory are the views of the events, which are a subset of their causal pasts. Thus, this theory asserts that the universe is a causal network of events, which co…
The concept of supersymmetry in a quantum mechanical system is extended, permitting the recognition of many more supersymmetric systems, including very familiar ones such as the free particle. Its spectrum is shown to be supersymmetric, with space-time symmetries used for the explicit construction. No fermionic or Grassmann variables need to be invoked. Our construction extends supersymmetry to continuous spectra. Most notably, while the free particle in one dimension has generally been regarded as having a doubly degenerate continuum throughout, the construction clarifies taht there is a sing…
Brukner and Pienaar have critiqued the Relational Quantum Mechanics of Rovelli, and together with Di Biagio, the latter has replied. I point out a few places where, in my view, that reply needs clarification.
We propose a version of the non-relativistic quantum mechanics in which the pure states of a quantum system are described as sections of a Hilbert (generally infinitely-dimensional) fibre bundle over the space-time. There evolution is governed via (a kind of) a parallel transport in this bundle. Some problems concerning observables are considered. There are derived the equations of motion for the state sections and observables. We show that up to a constant the matrix of the coefficients of the evolution operator (transport) coincides with the matrix of the Hamiltonian of the investigated quan…
Multiparametric statistical model providing stable reconstruction of parameters by observations is considered. The only general method of this kind is the root model based on the representation of the probability density as a squared absolute value of a certain function, which is referred to as a psi function in analogy with quantum mechanics. The psi function is represented by an expansion in terms of an orthonormal set of functions. It is shown that the introduction of the psi function allows one to represent the Fisher information matrix as well as statistical properties of the estimator of…
Since its inception Bohmian mechanics has been generally regarded as a hidden-variable theory aimed at providing an objective description of quantum phenomena. To date, this rather narrow conception of Bohm's proposal has caused it more rejection than acceptance. Now, after 65 years of Bohmian mechanics, should still be such an interpretational aspect the prevailing appraisal? Why not favoring a more pragmatic view, as a legitimate picture of quantum mechanics, on equal footing in all respects with any other more conventional quantum picture? These questions are used here to introduce a discus…
The Einstein, Podolski and Rosen (EPR) argument aiming to prove the incompleteness of quantum mechanics (QM) was opposed by most EPR's contemporary physicists and is not accepted within the standard interpretation of QM, which maintains that QM is a complete theory. An analysis of the semantic implications of the opponent positions shows that they imply different notions of truth. The introduction of a nonclassical notion of truth within the standard interpretation is usually justified by referring to known theorems that should prove that QM is a contextual and nonlocal theory. However, these …
The common-sense view of reality is expressed logically in Boolean subset logic (each element is either definitely in or not in a subset, i.e., either definitely has or does not have a property). But quantum mechanics does not agree with this "properties all the way down" picture of micro-reality. Are there other coherent alternative views of reality? A logic of partitions, dual to the Boolean logic of subsets (partitions are dual to subsets), was recently developed along with a logical version of information theory. In view of the subset-partition duality, partition logic is the alternative t…
In 19th century (in the process of transition from mechanics to the field theory) the German school of theoretical physics confronted problems similar to the basic problems in the foundations of quantum mechanics (QM). Hertz tried to resolve such problem through analysis of the notion of a scientific theory and interrelation of theory and experiment. This analysis led him to the Bild (image) conception of theory (which was latter essentially developed, but also modified by Boltzmann). In this paper we claim that to resolve the basic foundational problems of QM, one has to use the Bild concepti…
This article was written in response to a request from an editor of American Vedantist. It is shown that the idea that consciousness is essential to understanding quantum mechanics arises from logical fallacies. This may be welcome news to those who share the author's annoyance at consciousness being dragged into discussions of physics, but beware: The same fallacies may underlie the reader's own way of making sense of quantum mechanics. The article ends up embracing a Vedantic world view, for two reasons. For one, such a world view seems to the author to be the most sensible alternative to a …
It is argued that the nature of probability is essentially informational rather than physical and that quantum mechanical predictions should be viewed as logical inferences made on the basis of the information content of a given experimental situation. By implementing such a viewpoint, it is possible to maintain a sharp distinction between the physical and statistical aspects of quantum mechanics. The idea is applied to the double-beam interference experiment, reproducing the results of the standard formulation of quantum mechanics in a manner that renders the notion of wave-particle duality s…
A suitable unified statistical formulation of quantum and classical mechanics in a *-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's information regarding a physical system. This is seen as the main difference from classical mechanics, where an observer's information regarding a physical system obeys classical probability theory. Quantum mechanics is then viewed purely as a mathematical framework for the probabilistic description of noncommutative information, with the projection postulate being …
In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative point of view in which quantum mechanics emerges as a limiting case of classical mechanics in which the classical system is decoupled from its environment.
Recently, the problem of the infinite spherical well was solved by the group-theoretical method to resolve all the peculiarities in the currently accepted solution [DOI: 10.13140/RG.2.2.18172.44162 (Researchgate, 2017)]. With a view to further justifying the group-theoretical method, the problem is first studied from the viewpoint of classical mechanics. Then the radial probability densities predicted by classical mechanics are compared with those predicted from solutions of the problem obtained by the group-theoretical method. The comparisons clearly indicate the convergence of predictions of…
Taking into account the results that we have been obtained during the last decade in the foundations of quantum mechanic we put forward a view on reality that we call the 'creation discovery view'. In this view it is made explicit that a measurement is an act of a macroscopic physical entity on a microphysical entity that entails the creation of new elements of reality as well as the detection of existing elements of reality. Within this view most of the quantum mechanical paradoxes are due to structural shortcomings of the standard quantum theory, which means that our analysis agrees with the…
Everett's interpretation of quantum mechanics was proposed to avoid problems inherent in the prevailing interpretational frame. It assumes that quantum mechanics can be applied to any system and that the state vector always evolves unitarily. It then claims that whenever an observable is measured, all possible results of the measurement exist. This assertion of multiplicity has been understood in many ways by proponents of Everett's theory. Here we shall illustrate how different views on multiplicity carry onto different views on spacetime.
We sketch a group-theoretical framework, based on the Heisenberg-Weyl group, encompassing both quantum and classical statistical descriptions of mechanical systems. We re-define in group-theoretical terms the kinematical arena and the state-space of the system, achieving a unified quantum-classical language and a novel version of the correspondence principle. We briefly discuss the structure of observables and dynamics within our framework.
The view exists that the Bell inequality is a mere inconsistent application of classical concepts to a well-established quantum world. In the article, ``Nonlocality claims are inconsistent with Hilbert-space quantum mechanics'' [Phys. Rev. A, 101, 022117, (2020)], Robert B. Griffiths advocates for quantum theory's locality. Although R. B. Griffiths presents valuable insights in favor of quantum mechanics' local character, he argues the Bell inequality is an inconsistent application of classical physics to quantum mechanics. We explain why a correct assessment of the Bell inequality does not in…
In this work we consider non-relativistic quantum mechanics, obtained from a classical configuration space Q of indistinguishable particles. Following an approach proposed by one of the authors, wave functions are regarded as elements of suitable projective modules over C(Q). We take furthermore into account the G-Theory point of view, where the role of group action is particularly emphasized. As an example illustrating the method, the case of two particles is worked out in detail. Previous works aiming at a proof of a spin-statistics theorem for non-relativistic quantum mechanics are re-consi…
A new ontological view of the quantum measurement processes is given, which has bearings on many broader issues in the foundations of quantum mechanics as well. In this scenario a quantum measurement is a non-equilibrium phase transition in a ``resonant cavity'' formed by the entire physical universe including all of its material and energy content. A quantum measurement involves the energy and matter exchange among not only the system being measured and the measuring apparatus but also the global environment of the universe resonant cavity, which together constrain the nature of the phase tra…
We present a formal geometric framework for the study of adiabatic quantum mechanics for arbitrary finite-dimensional non-degenerate Hamiltonians. This framework generalizes earlier holonomy interpretations of the geometric phase to non-cyclic states appearing for non-Hermitian Hamiltonians. We start with an investigation of the space of non-degenerate operators on a finite-dimensional state space. We then show how the energy bands of a Hamiltonian family form a covering space. Likewise, we show that the eigenrays form a bundle, a generalization of a principal bundle, which admits a natural co…
Using classical statistics, Schrodinger equation in quantum mechanics is derived from complex space model. Phase-space probability amplitude, that can be defined on classical point of view, has connections to probability amplitude in internal space and to wave function in quantum mechanics. In addition, the physical entity of wave function in quantum mechanics is confirmed once again.
In the previous paper (quant-ph/0204037) we proved that the quantum mechanics not only has statistic interpretation, but also the specific electromagnetic form. Here, from this point of view we show that all the formal particularities of Dirac's equation have also the known electromagnetic sense.
The causal interpretation of quantum mechanics, as originally stated by deBroglie and Bohm, had several attractive features. Among these is the possibility that it could address some of the most fundamental questions on quantum phenomena. However, subsequent theoretical conjectures, which have now been included in the orthodox view of the deBroglie Bohm theory, are unphysical and have done much to undermine the original theory's appeal. We, therefore, return to the original theory as our starting point and address one of its perplexing areas: the quantum potential. By avoiding the unphysical c…
Why does the $i=\sqrt{-1}$ appear essentially in the quantum mechanics? Why are there operators and noncommutativity (the uncertainty relation) in the quantum mechanics? Why are these two aspects closely related and indivisible? In probing these problems, a new point of view is proposed tentatively.
Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Classical mechanics can now be viewed as a deformation of quantum mechanics. The forms of semiquantum approximations to classical mechanics are indicated.
In this note, I try to accomplish two things. First, I fulfill Andrei Khrennikov's request that I comment on his "Vaxjo Interpretation of Quantum Mechanics," contrasting it with my own present view of the subject matter. Second, I try to paint an image of the hopeful vistas an information-based conception of quantum mechanics indicates.
taking aside the review part, a finite-cardinality's set of new ideas concerning algorithmic information issues in Quantum Mechanics is introduced and analyzed
This paper is an introduction to the ideas of Bohmian mechanics, an interpretation of quantum mechanics in which the observer plays no fundamental role. Bohmian mechanics describes, instead of probabilities of measurement results, objective microscopic events. In recent years, Bohmian mechanics has attracted increasing attention by researchers. The form of a dialogue allows me to address questions about the Bohmian view that often arise.
I criticize the widely-defended view that the quantum measurement problem is an example of underdetermination of theory by evidence: more specifically, the view that the unmodified, unitary quantum formalism (interpreted following Everett) is empirically indistinguishable from Bohmian Mechanics and from dynamical-collapse theories like the GRW or CSL theories. I argue that there as yet no empirically successful generalization of either theory to interacting quantum field theory and so the apparent underdetermination is broken by a very large class of quantum experiments that require field theo…
