The electron double-slit interference is re-examined from the point of view of temporal topos. Temporal topos (or t-topos) is an abstract algebraic (categorical) method using the theory of sheaves. A brief introduction to t-topos is given. When the structural foundation for describing particles is based on t-topos, the particle-wave duality of electron is a natural consequence. A presheaf associated with the electron represents both particle-like and wave-like properties depending upon whether an object in the site (t-site) is specified (...) (particle-like) or not (wave-like). It is shown that the localization of the electron at one of the slits is equivalent to choosing a particular object in the t-site and that the electron behaves as a wave when it passes through a double-slit because there are more than one object in the t-site. Also, the single-slit diffraction is interpreted as a result of the possibility of many different ways of factoring a morphism between two objects. (shrink)

We discuss the possible nature and role of non-physical entanglement, and the classical vs. non-classical interface, in models of human decision-making. We also introduce an experimental setting designed after the double-slit experiment in physics, and discuss how it could be used to discriminate between classical and non-classical interference effects in human decisions.

The question of some of the friends is: -/- How is it possible to explain “Double slit experiment” by “Fuzzy time-Particle Interpretation”?

The paradoxes of the double-slit experiment with an electron are shown to originate in the implicit assumption that the electron is always located in the classical space. It is demonstrated that there exists a natural substitute for this assumption that provides a method of resolving the paradoxes.

In Calosi and Wilson (Phil Studies 2019/2018), we argue that on many interpretations of quantum mechanics (QM), there is quantum mechanical indeterminacy (QMI), and that a determinable-based account of metaphysical indeterminacy (MI), as per Wilson 2013 and 2016, properly accommodates the full range of cases of QMI. Here we argue that this approach is superior to other treatments of QMI on offer, both realistic and deflationary, in providing the basis for an intelligible explanation of the interference patterns in the (...) class='Hi'>double-slit experiment. We start with a brief overview of the motivations for QMI and for a determinable-based account of MI (§1). We then apply a developed 'glutty' implementation of determinable-based QMI to the superposition-based QMI present in the double-slit experiment, and positively compare the associated explanation of double-slit interference with that available on a metaphysical supervaluationist account of QMI (§2). We then present and respond to objections, due to Glick (2017) and Torza (2017), either to QMI (§3) or to our specific account of QMI (§4); in these sections we also positively compare our treatment of double-slit interference to that available on Glick's deflationary treatment of QMI. We conclude with some dialectical observations (§5). (shrink)

In this study, we solve analytically the Schrödinger equation for a macroscopic quantum oscillator as a central system coupled to two environmental micro-oscillating particles. Then, the double-slit interference patterns are investigated in two limiting cases, considering the limits of uncertainty in the position probability distribution. Moreover, we analyze the interference patterns based on a recent proposal called stochastic electrodynamics with spin. Our results show that when the quantum character of the macro-system is decreased, the diffraction pattern becomes more (...) similar to a classical one. We also show that, depending on the size of the slits, the predictions of quantum approach could be apparently different with those of the aforementioned stochastic description. (shrink)

Shahriar S. Afshar claimed that his 2007 modified version of the double-slit experiment violates complementarity. He makes two modifications to the standard double-slit experiment. First, he adds a wire grid that is placed in between the slits and the screen at locations of interference minima. The second modification is to place a converging lens just after the wire grid. The idea is that the wire grid implies the existence of interference minima, while the lens can simultaneously (...) obtain which-way information. More recently, Cramer argued that the experiment bolstered the Transactional Interpretation of Quantum mechanics. His argument scrutinizes Bohr’s complementarity in favor of TIQM. We analyze this experiment by simulation using the path integral formulation of quantum mechanics and find that it agrees with the wave-particle duality relation given by Englert, Greenberg and Yasin. We conclude that the use of Afshar’s experiment to provide a testbed for quantum mechanical interpretations is limited. (shrink)

Quasi-set theory $\cal Q$ allows us to cope with certain collections of objects where the usual notion of identity is not applicable, in the sense that $x = x$ is not a formula, if $x$ is an arbitrary term. $\cal Q$ was partially motivated by the problem of non-individuality in quantum mechanics. In this paper I discuss the range of explanatory power of $\cal Q$ for quantum phenomena which demand some notion of indistinguishability among quantum objects. My main focus is (...) on the double-slit experiment, a major physical phenomenon which was never modeled from a quasi-set-theoretic point of view. The double-slit experiment strongly motivates the concept of degrees of indistinguishability within a field-theoretic approach, and that notion is simply missing in $\cal Q$. Nevertheless, other physical situations may eventually demand a revision on quasi-set theory axioms, if someone intends to use it in the quantum realm for the purpose of a clear discussion about non-individuality. I use this opportunity to suggest another way to cope with identity in quantum theories. (shrink)

In this work we show that, within the framework of double-slit experiment, it is possible to ascertain simultaneously more incompatible properties together with the measurement of the position of the final impact-point. A wide family of solutions is concretely found and an ideal experiment realizing such a detection is designed, relatively to the detection of two incompatible properties. In the case of three incompatible properties, general conditions for the existence of solutions are singled out and a particular family (...) of solutions is provided. (shrink)

A new probability interpretation of interference phenomena in the double-slit experiment is proposed. It differs from the standard interpretation (based on elementary events happening in complementary, mutually exclusive setups—arrivals of waves to the screen when one of the slits is closed) which encounters the “paradox” that the law of total probability is violated. This new interpretation is free of such difficulties and paradoxes since it is based on compatible elementary events (events happening in the same setup in which (...) happenall events considered—arrivals of quantons to the screen when both slits are open). Quantum objects—quantons—possess simultaneously particle and wave properties. Compatible statistical interpretation synthesizes in a consistent way the superposition principle for waves and the law of total probability applied to compatible events. Such synthesis is a theoretical expression of de Broglie's observation, now fully confirmed by experiments, that the interference fringes obtained on a photographic plate result from an infinite number of tiny local spots which display arrival of quantons, while the set of fringes is a statistical effect of the wave aspect. (shrink)

Simultaneous observation of the wave-like and particle-like aspects of the photon in the double-slit experiment is unallowed. The underlying reason behind this limitation is not understood. In this paper, we explain this unique behavior by considering the communicational properties of the photons. Photons have three independently adjustable properties (energy, direction, and spin) that can be used to communicate messages. The double-slit experiment setup fixes two of these properties and confines the single photon’s capacity for conveying messages (...) to no more than one message. With such a low communication capacity, information theory dictates that measurements associated only with one proposition can obtain consistent results, and a second measurement associated with an independent proposition must necessarily lead to randomness. In the double-slit example, these are the wave or particle properties of the photon. The interpretation we offer is based on the formalism of information theory and does not make use of Heisenberg’s uncertainty relation in any form. (shrink)

By probability theory the probability space to underlie the set of statistical data described by the squared modulus of a coherent superposition of microscopically distinct (sub)states (CSMDS) is non-Kolmogorovian and, thus, such data are mutually incompatible. For us this fact means that the squared modulus of a CSMDS cannot be unambiguously interpreted as the probability density and quantum mechanics itself, with its current approach to CSMDSs, does not allow a correct statistical interpretation. By the example of a 1D completed scattering (...) and double slit diffraction we develop a new quantum-mechanical approach to CSMDSs, which requires the decomposition of the non-Kolmogorovian probability space associated with the squared modulus of a CSMDS into the sum of Kolmogorovian ones. We adapt to CSMDSs the presented by Khrennikov (Found. Phys. 35(10):1655, 2005) concept of real contexts (complexes of physical conditions) to determine uniquely the properties of quantum ensembles. Namely we treat the context to create a time-dependent CSMDS as a complex one consisting of elementary (sub)contexts to create alternative subprocesses. For example, in the two-slit experiment each slit generates its own elementary context and corresponding subprocess. We show that quantum mechanics, with a new approach to CSMDSs, allows a correct statistical interpretation and becomes compatible with classical physics. (shrink)

The purpose of this work is to carry out a systematic, detailed analytical study, together with the direct interpretations, as they follow from the analytical expressions obtained, of three basic “experiments” which have been classical examples in our understanding of quantum mechanics. The experiments considered are: the single- and double-slit (-hole) experiments, and the final one, which, in particular, deals with the situation where a particle is “reflected off” the detection screen in the single-slit experiment. Special emphasis (...) is put on pointing out some purely quantum mechanical results, which follow from the analytical expressions, as well as on making a comparison with classical physics. Needless to say, the analysis of such experiments has been extremely important in laying the foundations of quantum physics. (shrink)

In spite of the interference manifested in the double-slit experiment, quantum theory predicts that a measure of interference defined by Sorkin and involving various outcome probabilities from an experiment with three slits, is identically zero. We adapt Sorkin’s measure into a general operational probabilistic framework for physical theories, and then study its relationship to the structure of quantum theory. In particular, we characterize the class of probabilistic theories for which the interference measure is zero as ones in which (...) it is possible to fully determine the state of a system via specific sets of ‘two-slit’ experiments. (shrink)

One can often encounter claims that classical (Kolmogorovian) probability theory cannot handle, or even is contradicted by, certain empirical findings or substantive theories. This note joins several previous attempts to explain that these claims are unjustified, illustrating this on the issues of (non)existence of joint distributions, probabilities of ordered events, and additivity of probabilities. The specific focus of this note is on showing that the mistakes underlying these claims can be precluded by labeling all random variables involved contextually. Moreover, contextual (...) labeling also enables a valuable additional way of analyzing probabilistic aspects of empirical situations: determining whether the random variables involved form a contextual system, in the sense generalized from quantum mechanics. Thus, to the extent the Wang-Busemeyer QQ equality for the question order effect holds, the system describing them is noncontextual. The double-slit experiment and its behavioral analogues also turn out to form a noncontextual system, having the same probabilistic format (cyclic system of rank 4) as the one describing spins of two entangled electrons. (shrink)

The assertion that an experiment by Afshar et al. demonstrates violation of Bohr’s Principle of Complementarity is based on the faulty assumption that which-way information in a double-slit interference experiment can be retroactively determined from a future measurement.

We report on the simultaneous determination of complementary wave and particle aspects of light in a double-slit type “welcher-weg” experiment beyond the limitations set by Bohr’s Principle of Complementarity. Applying classical logic, we verify the presence of sharp interference in the single photon regime, while reliably maintaining the information about the particular pinhole through which each individual photon had passed. This experiment poses interesting questions on the validity of Complementarity in cases where measurements techniques that avoid Heisenberg’s uncertainty (...) principle and quantum entanglement are employed. We further argue that the application of classical concepts of waves and particles as embodied in Complementarity leads to a logical inconsistency in the interpretation of this experiment. (shrink)

There exist several phenomena breaking the classical probability laws. The systems related to such phenomena are context-dependent, so that they are adaptive to other systems. In this paper, we present a new mathematical formalism to compute the joint probability distribution for two event-systems by using concepts of the adaptive dynamics and quantum information theory, e.g., quantum channels and liftings. In physics the basic example of the context-dependent phenomena is the famous double-slit experiment. Recently similar examples have been found (...) in biological and psychological sciences. Our approach is an extension of traditional quantum probability theory, and it is general enough to describe aforementioned contextual phenomena outside of quantum physics. (shrink)

The potential for scalable quantum computing depends on the viability of fault tolerance and quantum error correction, by which the entropy of environmental noise is removed during a quantum computation to maintain the physical reversibility of the computer’s logical qubits. However, the theory underlying quantum error correction applies a linguistic double standard to the words “noise” and “measurement” by treating environmental interactions during a quantum computation as inherently reversible, and environmental interactions at the end of a quantum computation as (...) irreversible measurements. Specifically, quantum error correction theory models noise as interactions that are uncorrelated or that result in correlations that decay in space and/or time, thus embedding no permanent information to the environment. I challenge this assumption both on logical grounds and by discussing a hypothetical quantum computer based on “position qubits.” The technological difficulties of producing a useful scalable position-qubit quantum computer parallel the overwhelming difficulties in performing a double-slit interference experiment on an object comprising a million to a billion fermions. (shrink)

The double slit problem is idealized by simplifying each slit by a point source. A composite reduced action for the two correlated point sources is developed. Contours of the reduced action, trajectories and loci of transit times are developed in the region near the two point sources. The trajectory through any point in Euclidean 3-space also passes simultaneously through both point sources.

The double slit experiment for a massive scalar particle is described using intuitionistic logic with quantum real numbers as the numerical values of the particle's position and momentum. The model assigns physical reality to single quantum particles. Its truth values are given open subsets of state space interpreted as the ontological conditions of a particle. Each condition determines quantum real number values for all the particle's attributes. Questions, unanswerable in the standard theories, concerning the behaviour of single particles (...) in the experiment are answered. (shrink)

Recent double-slit type neutron experiments (1) and their theoretical implications (2) suggest that, since one can tell through which slit the individual neutrons travel, coherent wave packets remain nonlocally coupled (with particles one by one), even in the case of wide spatial separation. Following de Broglie's initial proposal, (3) this property can be derived from the existence of the persisting action of real superluminal physical phase waves considered as building blocks of the real subluminal wave field packets (...) which surround individual particle paths in the Einstein-de Broglie-Bohm interpretation of quantum mechanics. (shrink)

A modified Young double-slit experiment proposed by Wootters and Zurek is considered in which a system P of parallel plates covered with a photographic emulsion has been set up in the region where we would normally expect the central interference fringes. Because under certain conditions P makes it possible to conclude with much more than50% certainty through which of the two slits each particular photon passed, the relevant interference pattern becomes blurred. It is proved that this implies a (...) retroactive effect because the setup of P and the interaction of photons with P appear to influence the momentum transferred to the photons by the edges of the slits at an earlier stage of the experiment. (shrink)

Two luminaries of 20th century astrophysics were Sir James Jeans and Sir Arthur Eddington. Both took seriously the view that there is more to reality than the physical universe and more to consciousness than simply brain activity. In his Science and the Unseen World Eddington speculated about a spiritual world and that "conscious is not wholly, nor even primarily a device for receiving sense impressions." Jeans also speculated on the existence of a universal mind and a non-mechanical reality, writing in (...) his The Mysterious Universe "the universe begins to look more like a great thought than like a great machine." In his book QED Feynman discusses the situation of photons being partially transmitted and partially reflected by a sheet of glass: reflection amounting to four percent. In other words one out of every 25 photons will be reflected on average, and this holds true even for a "one at a time" flux. The four percent cannot be explained by statistical differences of the photons nor by random variations in the glass. Something is "telling" every 25th photon on average that it should be reflected back instead of being transmitted. Other quantum experiments lead to similar paradoxes. To explain how a single photon in the two-slit experiment can "know" whether there is one slit or two, Hawking and Mlodonow write: In the double-slit experiment Feynman's ideas mean the particles take paths that thread through the first slit, back out though the second slit, and then through the first again; paths that visit the restaurant that serves that great curried shrimp, and then circle Jupiter a few times before heading home; even paths that go across the universe and back. This, in Feynman's view, explains how the particle acquires the information about which slits are openŠ. It is hard to imagine a more absurd physical explanation. We can think of no way to hardwire the behavior of photons in the glass reflection or the two-slit experiments into a physical law. On the other hand, writing a software algorithm that would yield the desired result is really simple. A digital reality whose laws are software is an idea that has started to gain traction in large part thanks to an influential paper in Philosophical Quarterly by Oxford professor Nick Bostrom. Writing in the New York Times John Tierney had this to say: Until I talked to Nick Bostrom, a philosopher at Oxford University it never occurred to me that our universe might be somebody else's hobby. But now it seems quite possible. In fact, if you accept a pretty reasonable assumption of Dr. Bostrom's, it is almost a mathematical certainty that we are living in someone else's computer simulation. An alternate view is that there exists a great consciousness whose mind is the hardware, and whose thoughts are the software creating a virtual universe in which we as beings of consciousness live. Normal 0 false false false EN-US X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;} Normal 0 false false false EN-US X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;}. (shrink)

All statements describing physical reality are derived through interpretation of measurement results that requires a theory of the measuring instruments used to make the measurements. The ultimate measuring instrument is our body which displays its measurement results in our mind. Since a physical theory of our mind-body is unknown, the correct interpretation of its measurement results is unknown. The success of the physical sciences has led to a tendency to treat assumption in physics as indisputable facts. This tendency hampers the (...) development of new theories capable of addressing the foundations of mind. To show the possibility that false interpretations of experimental results have lead to equally false projections onto physical reality may have happened, the double slit experiment and special relativity experiments are examined in detail. I will show that strongly held a-priory beliefs characterizing measurement instruments have lead to unjustified but widely held concepts in physical theories. For example the assumption that material bodies have minds can change the interpretation of experiments to produce alternative physical theories. Since some material bodies have minds this paper calls for a review of the conscious observer’s role in the execution and interpretation of fundamental physics experiments in order to verify or challenge the basic beliefs adopted in standard physical theories. (shrink)

A geometric approach to quantum mechanics with unitary evolution and non-unitary collapse processes is developed. In this approach the Schrödinger evolution of a quantum system is a geodesic motion on the space of states of the system furnished with an appropriate Riemannian metric. The measuring device is modeled by a perturbation of the metric. The process of measurement is identified with a geodesic motion of state of the system in the perturbed metric. Under the assumption of random fluctuations of the (...) perturbed metric, the Born rule for probabilities of collapse is derived. The approach is applied to a two-level quantum system to obtain a simple geometric interpretation of quantum commutators, the uncertainty principle and Planck’s constant. In light of this, a lucid analysis of the double-slit experiment with collapse and an experiment on a pair of entangled particles is presented. (shrink)

Nelson’s stochastic quantum mechanics provides an ideal arena to test how the Born rule is established from an initial probability distribution that is not identical to the square modulus of the wavefunction. Here, we investigate numerically this problem for three relevant cases: a double-slit interference setup, a harmonic oscillator, and a quantum particle in a uniform gravitational field. For all cases, Nelson’s stochastic trajectories are initially localized at a definite position, thereby violating the Born rule. For the (...) class='Hi'>double slit and harmonic oscillator, typical quantum phenomena, such as interferences, always occur well after the establishment of the Born rule. In contrast, for the case of quantum particles free-falling in the gravity field of the Earth, an interference pattern is observed before the completion of the quantum relaxation. This finding may pave the way to experiments able to discriminate standard quantum mechanics, where the Born rule is always satisfied, from Nelson’s theory, for which an early subquantum dynamics may be present before full quantum relaxation has occurred. Although the mechanism through which a quantum particle might violate the Born rule remains unknown to date, we speculate that this may occur during fundamental processes, such as beta decay or particle-antiparticle pair production. (shrink)

Recent experiments have shown that certain fluid-mechanical systems, namely oil droplets bouncing on oil films, can mimic a wide range of quantum phenomena, including double-slit interference, quantization of angular momentum and Zeeman splitting. Here I investigate what can be learned from these systems concerning no-go theorems as those of Bell and Kochen-Specker. In particular, a model for the Bell experiment is proposed that includes variables describing a ‘background’ field or medium. This field mimics the surface wave that accompanies (...) the droplets in the fluid-mechanical experiments. It appears that quite generally such a model can violate the Bell inequality and reproduce the quantum statistics, even if it is based on local dynamics only. The reason is that measurement independence is not valid in such models. This opens the door for local ‘background-based’ theories, describing the interaction of particles and analyzers with a background field, to complete quantum mechanics. Experiments to test these ideas are also proposed. (shrink)

Introduction: The law of causality and its methodology -- Recent causal realism in quantum physics -- The law of causality : Hume, Quine and quantum physics -- Ontological and probabilistic causalisms -- Laplacean causalism in quantum physics -- Ontological commitment in quantum physics -- Causality in some quantum experiments -- Interpretations of important results in quantum physics -- Causality in the EPR paradox: Part 1. The physics -- Causality in the EPR paradox: Part 2. The physical ontology -- Causality in (...) a new double slit experiment and in EPR -- Causality in the special theory of relativity -- Micro-physical and cosmic causal continuity -- Conclusion: Causal ubiquity in the micro-world. (shrink)

Relativizing Newton" is a first step towards a simple and beautiful theory of everything. The theory, termed "Information Relativity" (IR) takes a novel approach to physics that overlooks all post-Newtonian physics. It stands on the shoulders of Newtonian dynamics, but modifies it by accounting for the time-travel of information from one reference-frame to another, a fact which somehow was ignored by Galileo Galilee and Isaac Newton, and which remained ill-treated by the all post-Newtonian theories, including Einstein's relativity and quantum theories. (...) Except for the aforementioned correction of classical physics, IR has no axiomatic presumptions, nor arbitrary free parameters. Astonishingly, accounting for the aforementioned delays in information results in a set of simple and beautiful transformations, which explain and predict a great deal of physical phenomena. Most importantly, IR's transformations reveal the mysteries of dark matter, dark energy, and gravity. They also provide a unifying platform for the physics of the too-big (astrophysics and cosmology), and the too-small (small particles dynamics and quantum mechanics). The phenomena explained and predicted successfully by IR include The Michelson-Morley's null-result, "time-dilation" of decaying muons, the neutrino velocities measured by OPERA and other collaborations, particle diffraction in the double-slit experiment, Sagnac Effects, the quantization of orbits in Bohr's hydrogen atom, entanglement, quantum criticality, confinement, asymptotic freedom, solar light bending, gravitational redshift, the Pioneer anomaly, dark matter in galaxies, and the Schwarzschild's black hole. (shrink)

In this article we discuss the problem of finding an interpretation of quantum mechanics which provides an objective account of physical reality. In the first place we discuss the problem of interpretation and analyze the importance of such an objective account in physics. In this context we present the problems which arise when interpreting the quantum wave function within the orthodox formulation of quantum mechanics. In connection to this critic, we expose the concept of ‘entity’ as an epistemological obstruction. In (...) the second part of this paper we discuss the relation between actuality and potentiality in classical and quantum physics, and continue to present the concept of ontological potentiality which is distinguished from the generic Aristotelian notion of potentiality in terms of ‘becoming actual’. In this paper our main aim is to provide an objective interpretation of quantum mechanics which allows us to discuss the meaning of physical reality according to the theory. For this specific propose we present the concept of faculty in place of the concept of ‘entity’. Within our theory of faculties, we continue to discuss and interpret two paradigmatic experiments of quantum mechanics such as the double-slit and Schrodinger’s cat. (shrink)

A presentation showing how the statements which relate to microphysical objects as they are different from the statements of classical mechanics is made. The determinism of classical and of quantum-mechanical theories is qualified. A (crucial) distinction between causality and determinism is given. Detailed analyses of diffraction as a result of single and double-slit demonstrations point to paradoxes arising from the use of particle or wave models, respectively, for photons and electrons. The compromising wave-packet model is underscored. The meanings (...) for the Psi-function and for |ψ|2 are presented, with an explanation of the limitations that arise from giving an interpretation of |ψ|2 as a probability. The meaning of ψ -waves is analyzed. A case is made for the ψ -function's describing a well-ordered list of betting odds, based on previous statistical experiences, for the different results of specific experiments of a microscopic object of study with macroscopic apparatus. The Schrödinger wave equation is evaluated for meaning and judged as a deterministic expression. (shrink)

The traditional analysis of the basic version of the double-slit experiment leads to the conclusion that wave-particle duality is a fundamental fact of nature. However, such a conclusion means to imply that we are not only required to have two contradictory pictures of reality but also compelled to abandon the objectiveness of the truth values, “true” and “false”. Yet, even if we could accept wave-like behavior of quantum particles as the best explanation for the build-up of an interference (...) pattern in the double-slit experiment, without the objectivity of the truth values we would never have certainty regarding any statement about the world. The present paper discusses ways to reconcile the correct description of the double-slit experiment with the objectiveness of “true” and “false”. (shrink)

Nonobjectivity of physical properties enters physics with the standard interpretation of quantum mechanics (QM), and a number of paradoxes of this theory follow from it. It seems, however, based on sound physical arguments (double slit experiment, Heisenberg's principle, Bell–Kochen–Specker theorem, etc.), so that most physicists think that avoiding it is impossible. We discuss these arguments here and show that they can be criticized from a physical viewpoint. Our criticism proves that nonobjectivity must be considered an epistemological choice rather (...) than an unavoidable feature of QM, so that an objective interpretation of QM is not a priori impossible, which justifies our attempt at providing it in some previous papers. This interpretation is based on a classical language in which the language of the standard interpretation (Quantum Logic) is embedded as a subset of statements that are directly testable according to QM. (shrink)

Quantum trajectory-based descriptions of interference between two coherent stationary waves in a double-slit experiment are presented, as given by the de Broglie–Bohm and modified de Broglie–Bohm formulations of quantum mechanics. In the dBB trajectory representation, interference between two spreading wave packets can be shown also as resulting from motion of particles. But a trajectory explanation for interference between stationary states is so far not available in this scheme. We show that both the dBB and MdBB trajectories are capable (...) of producing the interference pattern for stationary as well as wave packet states. However, the dBB representation is found to provide the ‘which-way’ information that helps to identify the hole through which the particle emanates. On the other hand, the MdBB representation does not provide any which-way information while giving a satisfactory explanation of interference phenomenon in tune with the de Broglie’s wave particle duality. By counting the trajectories reaching the screen, we have numerically evaluated the intensity distribution of the fringes and found very good agreement with the standard results. (shrink)

It is shown that any hidden variable model that reproduces quantum mechanics for a single particle must either be nonlocal or violate conservation of momentum. This is established by deriving an inequality which must hold in any local, momentum-conserving hidden variable model for a modified form of the double-slit experiment. It is then shown that any hidden variable model that reproduces quantum mechanics must violate the inequality. The inconsistency between the classical and quantum views of the world is (...) therefore demonstrated in a new way. (shrink)

This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or toy model of quantum mechanics over sets (QM/sets). There have been several previous attempts to develop a quantum-like model with the base field of ℂ replaced by ℤ₂. Since there are no inner products on vector spaces over finite fields, the problem is to define the Dirac brackets and the probability calculus. The previous attempts (...) all required the brackets to take values in ℤ₂. But the usual QM brackets <ψ|ϕ> give the "overlap" between states ψ and ϕ, so for subsets S,T⊆U, the natural definition is <S|T>=|S∩T| (taking values in the natural numbers). This allows QM/sets to be developed with a full probability calculus that turns out to be a non-commutative extension of classical Laplace-Boole finite probability theory. The pedagogical model is illustrated by giving simple treatments of the indeterminacy principle, the double-slit experiment, Bell's Theorem, and identical particles in QM/Sets. A more technical appendix explains the mathematics behind carrying some vector space structures between QM over ℂ and QM/Sets over ℤ₂. (shrink)

Consider the case of the double slit expt where a single photon lands on the film and twenty years later the film gets developed and a human observer looks at it. Question: What is the state of the universe during those twenty years ? (The Schrodinger cat business).

It is generally believed that the uncertainty relation Δq Δp≥1/2ħ, where Δq and Δp are standard deviations, is the precise mathematical expression of the uncertainty principle for position and momentum in quantum mechanics. We show that actually it is not possible to derive from this relation two central claims of the uncertainty principle, namely, the impossibility of an arbitrarily sharp specification of both position and momentum (as in the single-slit diffraction experiment), and the impossibility of the determination of the (...) path of a particle in an interference experiment (such as the double-slit experiment). (shrink)

Recently quantum probability theory started to be actively used in studies of human decision-making, in particular for the resolution of paradoxes (such as the Allais, Ellsberg, and Machina paradoxes). Previous studies were based on a cognitive metaphor of the quantum double-slit experiment—the basic quantum interference experiment. In this paper, we report on an economics experiment based on a triple-slit experiment design, where the slits are menus of alternatives from which one can choose. The test of nonclassicality is (...) based on the Sorkin equality (which was only recently tested in quantum physics). Each alternative is a voucher to buy products in one or more stores. The alternatives are obtained from all disjunctions including one, two or three stores. The participants have to reveal the amount for which they are willing to sell the chosen voucher. Interference terms are computed by comparing the willingness to sell a voucher built as a disjunction of stores and the willingness to sell the vouchers corresponding to the singleton stores. These willingness to sell amounts are used to estimate probabilities and to test both the law of total probabilities and the Born Rule. Results reject neither classical nor quantum probability. We discuss this initial experiment and our results and provide guidelines for future studies. (shrink)

Quantum mechanics implies many paradoxes (e.g. Schrödinger's cat, double-slit experiment, non-locality) which are in contradiction to our ordinary experience. To comprehend quantum theory we must revise our understanding of such matters as the objective nature of reality, the nature of causality, and the nature of a complex system and its relation to its components. Finally, common sense seems to be an epistemo-logical obstacle in our understanding of the quantum picture of the world.

The paper, in Part 1, is devoted to discussing the underlying logic and algebra of the classical mechanics and quantum mechanics, their syntax and semantics, the reasons for their differences and the diagrammatic representations of the two. This part of the paper also demonstrates that there are several puzzling characters of microphysical phenomena by alluding to the relevant details of the double-slit experiment. These counterintuitive results of the experiment make it difficult to explain the empirical success and realist (...) commitments of quantum mechanics. The second part, Part 2, of the paper is concerned with the question as to how conceptual schemes of scientists interact with the world such that the problem of new meaning and reference of the microphysical terms could be determined. The paper refrains from having a general discussion on Realism and do not venture into a comprehensive survey and critique of all known varieties of realistic interpretations. It selects only a few forms of realism (based on the reasons given) in investigating microphysical phenomena forming part of QM. These selected forms of realism explain how does conceptual scheme/terms in scientific theory hookup to the objects and their relations in the world based on the model-theoretic character of the scientific theory and causal rigidified descriptivism of scientific terms (vide Putnam) as well as scientist’s interaction with the world, say, in the “instrumental context of laboratory” (vide Heelan) such that the problem of meaning and reference could be resolved. The paper claims that convergence of the two views may result in a particular form of realism, the Hermeneuticized Internal Realism, appropriate for the science of microphysical phenomena. (shrink)

Although there is good experimental evidence for the Aharonov–Bohm phase shift occurring when a solenoid is placed between the beams forming a double-slit electron interference pattern, there has been very little analysis of the relevant classical electromagnetic forces. These forces between a point charge and a solenoid involve subtle relativistic effects of order v 2 /c 2 analogous to those discussed by Coleman and Van Vleck in their treatment of the Shockley–James paradox. In this article we show that (...) a treatment exactly analogous to that given by Coleman and Van Vleck predicts classical electromagnetic forces which provide the basis for the Aharonov–Bohm phase shift. The magnetic force on the solenoid due to the passing charge leads to a displacement of the solenoid center of energy which must be balanced by the displacement of the passing charge. This classical displacement of the passing charge is exactly what is required to account for the Aharonov–Bohm phase shift. Also, we discuss a magnetic moment model which appears frequently in the literature and note that although the model provides conservation of linear momentum, it does not satisfy the general requirements for relativistic theories. We give an example suggesting that the new equation of motion for a magnetic moment proposed by Aharonov, Pearle, and Vaidman based upon the hidden momentum of the magnetic moment is completely inappropriate. Finally, we emphasize that the Aharonov–Casher phase shift is also explained by classical electromagnetic forces exactly parallel to those explaining the Aharonov–Bohm phase shift. (shrink)

How can electrons behave sometimes like particles and sometimes like waves? How does an atom know, when it passes through one slit of a double-slit apparatus, that the other slit is also open, so that it should behave so as to contribute to an interference pattern? How does a radioactive atom know when to decay? How can electrons tunnel across classically forbidden regions? How can Schrödinger's cat be simultaneously dead and alive - but only until we (...) look at it and find that it is one or the other? (shrink)