A formulation of quantum mechanics based on an operational definition of state is presented. This formulation, which includes explicitly the macroscopic systems, assumes the probabilistic interpretation and is nevertheless objective. The classical paradoxes of quantum mechanics are analyzed and their origin is found to be the fictitious properties that are usually attributed to quantum-mechanical states. The hypothesis that any mixed state can always be considered as an incoherent superposition of pure states is found to contradict quantum mechanics. A solution of EPR paradox is proposed. It is shown that entanglement of quantum states is compatible with realism and locality of events, but implies non-local encoding of information.
The role of probability in quantum mechanics is reviewed, with a discussion of the ``orthodox'' versus the statistical interpretive frameworks, and of a number of related issues. After a brief summary of sources of unease with quantum mechanics, a survey is given of attempts either to give a new interpretive framework assuming quantum mechanics is exact, or to modify quantum mechanics assuming it is a very accurate approximation to a more fundamental theory. This survey focuses particularly on the issues of whether probabilities in quantum mechanics are postulated or emergent.
What is called "orthodox" quantum mechanics, as presented in standard foundational discussions, relies on two substantive assumptions --- the projection postulate and the eigenvalue-eigenvector link --- that do not in fact play any part in practical applications of quantum mechanics. I argue for this conclusion on a number of grounds, but primarily on the grounds that the projection postulate fails correctly to account for repeated, continuous and unsharp measurements (all of which are standard in contemporary physics) and that the eigenvalue-eigenvector link implies that virtually all interes…
The prediction of the N-box paradox, that whichever box is opened will contain the record of the particle having passed through it, is traced to a failure to specify whether the other boxes are distinguishable or indistinguishable. These correspond to different ways of lifting the degeneracy of a certain measurement, and have incompatible consequences.
Errors and paradoxes in quantum mechanics, entry in the Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy, ed. F. Weinert, K. Hentschel, D. Greenberger and B. Falkenburg (Springer), to appear
The concept of 'super-indeterminism' captures the notion that the free choice assumption of orthodox quantum mechanics necessitates only the following requirement: an agent's free-choice performance in the selection of measurement settings must not represent an exception to the rule of irreducible quantum indeterminism in the physical universe (i.e, "universal indeterminism"). Any additional metaphysical speculation, such as to whether quantum indeterminism, i.e., intrinsic randomness, implicates the reality of experimenter "freedom", "free will", or "free choice", is redundant in relation to …
The principle of sufficient reason asserts that anything that happens does so for a reason: no definite state of affairs can come into being unless there is a sufficient reason why that particular thing should happen. This principle is usually attributed to Leibniz, although the first recorded Western philosopher to use it was Anaximander of Miletus. The demand that nature be rational, in the sense that it be compatible with the principle of sufficient reason, conflicts with a basic feature of contemporary orthodox physical theory, namely the notion that nature's response to the probing action…
The principle of sufficient reason asserts that anything that happens does so for a reason: no definite state of affairs can come into being unless there is a sufficient reason why that particular thing should happen. This principle is usually attributed to Leibniz, although the first recorded Western philosopher to use it was Anaximander of Miletus. The demand that nature be rational, in the sense that it be compatible with the principle of sufficient reason, conflicts with a basic feature of contemporary orthodox physical theory, namely the notion that nature's response to the probing action…
According to quantum theory, pure physical states correspond to equivalence classes of state vectors, where any two members of one class differ by a complex factor. The point is that such a factor does not change the probability for the occurrence of any measurement result as computed within the formalism of quantum mechanics. In the formalism to be presented here, the state vector does not only determine the probabilities for the occurrence of measurement results, rather it determines the result itself. The information which guides the selection process is obtained from the state vector in a …
Any successful interpretation of quantum mechanics must explain how our empirical evidence allows us to come to know about quantum mechanics. In this article, we argue that this vital criterion is not met by the class of 'orthodox interpretations,' which includes QBism, neo-Copenhagen interpretations, and some versions of relational quantum mechanics. We demonstrate that intersubjectivity fails in radical ways in these approaches, and we explain why intersubjectivity matters for empirical confirmation. We take a detailed look at the way in which belief-updating might work in the kind of univer…
Recently, a geometric embedding of the classical space and classical phase space of an n-particle system into the space of states of the system was constructed and shown to be physically meaningful. Namely, the Newtonian dynamics of the particles was recovered from the Schroedinger dynamics by constraining the state of the system to the classical phase space submanifold of the space of states. A series of theorems related to the embedding and the Schroedinger evolution with a random Hamiltonian was proven and shown to be applicable to the process of measurement in classical and quantum mechani…
We present an analysis of quantum mechanics and its problems and paradoxes taking into account the results that have been obtained during the last two decades by investigations in the field of `quantum structures research'. We concentrate mostly on the results of our group FUND at Brussels Free University. By means of a spin 1/2 model where the quantum probability is generated by the presence of fluctuations on the interactions between measuring apparatus and physical system, we show that the quantum structure can find its origin in the presence of these fluctuations. This appraoch, that we ha…
Referring to the 18th century idealism of George Berkeley in which an object exists if and only if it is observed, this note shows that orthodox quantum mechanics (OQM) entails a Berkelian idealism regarding properties (BIRP): a quantum `has' a property X with quantitative value x if and only if the property X has just been measured with outcome x. It is then impossible to recontextualize GR's principle of curvature in any quantum framework that implies this BIRP, for a quantum cannot curve space-time if it doesn't have a definite energy - which is supposed to be the cause of curvature - in ab…
Many seemingly paradoxical effects are known in the predictions for outcomes of intermediate measurements made on pre- and post-selected quantum systems. Despite appearances, these effects do not demonstrate the impossibility of a noncontextual hidden variable theory, since an explanation in terms of measurement-disturbance is possible. Nonetheless, we show that for every paradoxical effect wherein all the pre- and post- selected probabilities are 0 or 1 and the pre- and post-selected states are nonorthogonal, there is an associated proof of contextuality. This proof is obtained by considering…
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…
For a believer in locality of Nature, the Aharonov-Bohm effect and the Aharonov-Casher effect are paradoxes. I discuss these and other Aharonov's paradoxes and propose a local explanation of these effects. If the solenoid in the Aharonov-Bohm effect is treated quantum mechanically, the effect can be explained via local interaction between the field of the electron and the solenoid. I argue that the core of the Aharonov-Bohm and the Aharonov-Casher effects is that of quantum entanglement: the quantum wave function describes all systems together.
A local realistic model for quantum mechanics of two-particle Einstein-Podolsky-Rosen pairs is proposed. In this model, it is the strict obedience of conservation laws in each event at the quantum level that uphold the perfect correlation of two spatially-separated particles, instead of nonlocality in the orthodox formulation of quantum mechanics. Therefore, one can conclude that all components of the spin of two particles, and the position and momentum of a particle can be measured simultaneously. The proposed model yields the same statistical prediction on an ensemble of individual particles…
Statistical classical mechanics and quantum mechanics are developed and well-known theories that represent a basis for modern physics. The two described theories are well known and have been well studied. As these theories contain numerous paradoxes, many scientists doubt their internal consistencies. However, these paradoxes can be resolved within the framework of the existing physics without the introduction of new laws. To clarify the paper for the inexperienced reader, we include certain necessary basic concepts of statistical physics and quantum mechanics in this paper without the use of …
This short note is an introduction to the slides from our talks given in 2018 during the Advanced School of Quantum Foundations and Quantum Computation in Joao Pessoa , Brazil. In these talks, addressed to participants with a limited knowledge of quantum foundations, we defined locality, causality, randomness, counterfactual definiteness and we explained EPR-Bohm paradoxes. In particular we discussed in great detail various Bell-type inequalities and the implications of their violation in spin polarisation correlation experiments. Finally we explained why and how the predictive completeness of…
Many seemingly paradoxical effects are known in the predictions for outcomes of measurements made on pre- and post-selected quantum systems. A class of such effects, which we call ``logical pre- and post-selection paradoxes'', bear a striking resemblance to proofs of the Bell-Kochen-Specker theorem, which suggests that they demonstrate the contextuality of quantum mechanics. Despite the apparent similarity, we show that such effects can occur in noncontextual hidden variable theories, provided measurements are allowed to disturb the values of the hidden variables.
The classical limit of the Schrodinger equation implies the orthodox statistical interpretation for degrees of freedom in finite-dimensional subspaces of the full Hilbert space, but the argument presented does not imply the Born interpretation for degrees of freedom that have a classical counterpart.
This paper explores the consequences of denying the "emptiness of paths not taken," EPNT, premise of Bernstein, Greenberger, Horne, and Zeilinger (BGHZ) in their paper titled, Bell theorem without inequalities.[ ] Carrying out the negation of EPNT leads to the concept of a "shadow stream." Streams are essentially particle implementations of the paths in Feynman path-integrals, resulting in a simple and consistent extension of the standard axioms for quantum mechanics. The construct provides elegant resolutions of single- and multi-particle interference paradoxes. Moreover, combining the argume…
We present a unified approach, based on the use of quantum uncertainty relations, for arriving at criteria for the demonstration of the EPR paradox and macroscopic superpositions. We suggest to view each criterion as a means to demonstrate an EPR-type paradox, where there is an inconsistency between the assumptions of a form of realism, either macroscopic realism (MR) or local realism (LR), and the completeness of quantum mechanics.
We discuss the hypothesis that the debate about the interpretation of the orthodox formalism of quantum mechanics (QM) might have been misguided right from the start by a biased metaphysical interpretation of the formalism and its inner mathematical relations. In particular, we focus on the orthodox interpretation of the congruence relation, '=', which relates equivalent classes of different mathematical representations of a vector in Hilbert space, in terms of metaphysical identity. We will argue that this seemingly "common sense" interpretation, at the semantic level, has severe difficulties…
The reason why orthodox quantum theory necessarily invokes consciousness is explained. Several procedures whereby the Born probability rule can be introduced are discussed, and reasons are given for prefering one in which consciousness selects a unique realised world. Consciousness is something outside of the laws of physics (quantum mechanics), but it has a real effect upon the experienced world. Finally, orthodox quantum theory is shown to require that consciousness acts non-locally.
The orthodox quantum mechanics has been commonly regarded as being supported decisively by the polarization EPR experiments, in which Bell's inequalities have been violated. The given conclusion has been based, however, on several mistakes that have not been yet commonly known and sufficiently analyzed. The whole problem will be newly discussed and a corresponding solution will be proposed.
In contribution published in AIP Conference Proceedings, No. 1018 (p. 40-5) some discrepancies in Copenhagen quantum mechanics have been summarized and the arguments have been gathered why in the description of microscopic reality the hidden-variable theory should be preferred. It has been shown, too, that the earlier gap in physical descriptions of the microscopic and macroscopic worlds may be practically removed. All corresponding statements have been based on proofs that have been published earlier and reproduced in the given contribution only partially. In the present paper the whole appro…
We present the general Hardy-like quantum pigeonhole paradoxes for \textit{n}-particle states, and find that each of such paradoxes can be simply associated to an un-colorable solution of a specific vertex-coloring problem induced from the projected-coloring graph (a kind of unconventional graph). Besides, as a special kind of Hardy's paradox, several kinds of Hardy-like quantum pigeonhole paradoxes can even give rise to higher success probability in demonstrating the conflict between quantum mechanics and local or noncontextual realism than the previous Hardy's paradoxes. Moreover, not only m…
If the quantum mechanical description of reality is not complete and a hidden variable theory is possible, what arises is the problem to explain where the rates of the outcomes of statistical experiments come from, as already noticed by Landé and Popper. In this paper this problem is investigated, and a new "paradigm" about the nature of dynamical and statistical laws is proposed. This paradigm proposes some concepts which contrast with the usual intuitive view of evolution and of physical law, such as: initial conditions could play no privileged role in determining the evolution of the univer…
It may be possible to empirically discriminate between the predictions of Orthodox Quantum Theory and the deBroglie-Bohm Theory of Quantum Mechanics. An experiment using the measurement methods of Atom Optics is suggested in which an atom trap having evanescent light mirrors in front of each of its walls is used to determine whether trapped atoms are in motion inside the trap. An absence of detected motion would be contrary to the prediction of Orthodox Quantum Theory and would support the deBroglie-Bohm Theory.
The contemporary controversy about the fundamental obscurity in quantum mechanics keeps on the old one about the aim of science, which was between the founders of the quantum theory. The orthodox quantum mechanics could be created only at the cost of renunciation of reality as the aim of natural science. The description only of phenomena, i.e. results of observation, should not be universal if no one believes that these phenomena are manifestation of a unique reality. Such belief concerning quantum mechanics is quite unacceptable because of irremediably conflict with special relativity. Nevert…
Quantum mechanics describes successfully numerous quantum phenomena both microscopic and macroscopic, such as superconductivity. But the controversies about quantum mechanics, in the old days and present day, reveal fundamental obscurity in quantum mechanics. In this work reader attention is drawn first of all to the fact that the orthodox description of superconductivity and some other quantum phenomena uses the realistic interpretation of the wave function proposed by Schrodinger whereas the controversies take place until the present about the positivistic interpretation proposed by Born. Ca…
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.
This work is about Bohmian mechanics, a non-relativistic quantum theory about the motion of particles and their trajectories, named after its inventor David Bohm (Bohm,1952). This mechanics resolves all paradoxes associated with the measurement problem in nonrelativistic quantum mechanics. It accounts for quantum randomness, absolute uncertainty, the meaning of the wave function of a system, collapse of the wave function, and familiar (macroscopic) reality. We review the purpose for which Bohmian trajectories were invented: to serve as the foundation of quantum mechanics, i.e., to explain quan…
We formulate a general principle that supplants a Boolean σ-algebra of intrinsic properties of a classical system by a σ-complex (a union of σ-algebras) of extrinsic properties of a quantum system that are elicited by interactions with other systems. We apply the canonical definitions of the concepts of classical physics of observables, states, combined systems, symmetries, and dynamics to derive the standard quantum characterizations, including the Schrödinger equation and the von Neumann-Lüder's Projection Rule. This manifestly consistent reconstruction of quantum mechanics is then used to d…
We propose that observables in quantum theory are properly understood as representatives of symmetry-invariant quantities relating one system to another, the latter to be called a reference system. We provide a rigorous mathematical language to introduce and study quantum reference systems, showing that the orthodox "absolute" quantities are good representatives of observable relative quantities if the reference state is suitably localised. We use this relational formalism to critique the literature on the relationship between reference frames and superselection rules, settling a long-standing…
An orthodox formulation of quantum mechanics relies on a set of postulates in Hilbert space supplemented with rules to connect it with classical mechanics such as quantisation techniques, correspondence principle, etc. Here we deduce a qubit and its dynamics straightforwardly from a discrete deterministic dynamics and conservation of the classical collision entropy. No Hilbert space is required although it can be inferred from this approach if necessary.
Quantum nonlocality is discussed as an aspect of the quantum formalism that is seriously in need of interpretation. The Transactional Interpretation of quantum mechanics, which describes quantum processes as transactional "handshakes" between retarded $ψ$ waves and advanced $ψ*$ waves, is discussed. Examples of the use of the Transactional Interpretation in resolving quantum paradoxes and in understanding the counter-intuitive aspects of the formalism, particularly quantum nonlocality, are provided.
A local interpretation of quantum mechanics is presented. Its main ingredients are: first, a label attached to one of the virtual paths in the path integral formalism, determining the output for measurement of position or momentum; second, a mathematical model for spin states, equivalent to the path integral formalism for point particles in space time, with the corresponding label. The mathematical machinery of orthodox quantum mechanics is maintained, in particular amplitudes of probability and Born's rule; therefore, Bell's type inequalities theorems do not apply. It is shown that statistica…
Exploring Cognitive Paradoxes in Video Games: A Quantum Mechanical Perspective
Artificial Intelligence and Cyber Futures Institute, Charles Sturt University（查尔斯斯特大学人工智能与网络未来研究所）；The Alan Turing Institute（阿兰·图灵研究所）；The University of Sydney Business School（悉尼大学商学院）
Here we present the most general framework for $n$-particle Hardy's paradoxes, which include Hardy's original one and Cereceda's extension as special cases. Remarkably, for any $n\ge 3$ we demonstrate that there always exist generalized paradoxes (with the success probability as high as $1/2^{n-1}$) that are stronger than the previous ones in showing the conflict of quantum mechanics with local realism. An experimental proposal to observe the stronger paradox is also presented for the case of three qubits. Furthermore, from these paradoxes we can construct the most general Hardy's inequalities…
One of the most central and controversial element of quantum mechanics is the use of non zero vectors of a Hilbert space (or, more generally, of one dimension subspaces) for representing the state of a quantum system. In particular, the question whether such a representation is complete has been debated since almost the early days of quantum mechanics. In this article, we develop an alternate way to formalize knowledge about the state of quantum systems, based solely on experimentally accessible elements, namely on outcomes of finite measurements. We introduce what we call partial description …
It is hypothesized that the Langevin time of stochastic quantum quantization is a physical time over which quantum fields at all values of space and coordinate time fluctuate. The average over paths becomes a time average as opposed to an ensemble average. It is further hypothesized that the Langevin time also paces the motion of particles through coordinate time and is equal to the coordinate time of the present hypersurface in the frame of the Hubble expansion. Despite having a preferred frame, special relativity continues to hold in this formulation as a dynamical symmetry due to the presum…
A new concept of the constitution of Nature is proposed. The constructed submicroscopic quantum mechanics is deterministic and is characterised by elementary excitations of the space net that is treated as the tessellation of balls, or superparticles. Said excitations called "inertons" accompany any canonical particle when it moves. It is shown theoretically that the introduction of inertons obviates all conceptual difficulties of orthodox quantum mechanics. The theory has been verified experimentally. It is argued that just inertons play the role of real carriers in the gravitational interact…
A relativistic version of the (consistent or decoherent) histories approach to quantum theory is developed on the basis of earlier work by Hartle, and used to discuss relativistic forms of the paradoxes of spherical wave packet collapse, Bohm's formulation of Einstein-Podolsky-Rosen, and Hardy's paradox. It is argued that wave function collapse is not needed for introducing probabilities into relativistic quantum mechanics, and in any case should never be thought of as a physical process. Alternative approaches to stochastic time dependence can be used to construct a physical picture of the me…
In this paper we analyze the definition of quantum superpositions within orthodox Quantum Mechanics (QM) and their relation to physical reality. We will begin by discussing how the metaphysical presuppositions imposed by Bohr on the interpretation of QM have become not only interpretational dogmas which constrain the limits of the present Orthodox Line of Research (OLR), but also how these desiderata implicitly preclude the possibility of developing a physical representation of quantum superpositions. We will then continue analyzing how most interpretations of QM argue against the existence of…
Superposition states are at the origin of many paradoxes in quantum mechanics. By unraveling the von Neumann equation for density matrices, we develop a superposition-free formulation of quantum mechanics. Stochastic quantum jumps are a key feature of this approach, in blatant contrast with the continuity of the deterministic Schrödinger equation. We explain how quantum entanglement arises. Our superposition-free formulation results offers a new perspective on quantum mechanics.
In the hidden measurement formalism that we develop in Brussels we explain the quantum structure as due to the presence of two effects, (a) a real change of state of the system under influence of the measurement and, (b) a lack of knowledge about a deeper deterministic reality of the measurement process. We show that the presence of these two effects leads to the major part of the quantum mechanical structure of a theory where the measurements contain the two mentioned effects. We present a quantum machine, where we can illustrate in a simple way how the quantum structure arises as a consequen…
The process approach to NRQM offers a fourth framework for the quantization of physical systems. Unlike the standard approaches (Schrodinger-Heisenberg, Feynman, Wigner-Gronewald-Moyal), the process approach is not merely equivalent to NRQM and is not merely a re-interpretation. The process approach provides a dynamical completion of NRQM. Standard NRQM arises as a asymptotic quotient by means of a set-valued process covering map, which links the process algebra to the usual space of wave functions and operators on Hilbert space. The process approach offers an emergentist, discrete, finite, qu…
It is shown that the statistical conception of quantum mechanics is dynamical but not probabilistic, i.e. the statistical description in quantum mechanics is founded on dynamics. A use of the probability theory, when it takes place, is auxiliary. Attention is drawn to the fact that in the quantum mechanics there are two different objects: an individual object to be statistically described and a statistical average object, which is a result of the statistical description. Identification of the two different objects (a use of the same term for both) is an origin of many known quantum mechanics p…
