A Brief Introduction

Recently, Nature magazine made a survey about how Physicists think of what quantum mechanics says about reality. The survey shows that 47% of respondents consider the wavefunction in the quantum mechanics representing simply a useful tool, and 36% respondents consider the wavefunction representing something real. In this article we show that the double slit experiments support the opinion of 47% of respondents. It is the standard understanding that the double slit experiment shows that the light is waves, not particles. The photoelectric experiment shows that the light is particles. The two experiments show the conceptually different natures of the light and thus led to the wave-particle duality of the light. To thoroughly study the real nature of the light in the double slit experiments, we utilizing the Photon-chamber, Shield, Blocker, Lenses and Metal tubes respectively. We observed the following phenomena in the same double slit experiments: the light is photons, not waves; and it is the photons that produce both the non-interference patterns in Zone-0, Zong-1 and Zone-2, and the interference patterns in Zone-3. We suggest that the observed phenomena: (1) invalidate the wave-particle duality; (2) show that the wavefunction is simply a useful mathematical tool to describe the wave phenomena in Zone-3; (3) show that the wavefunction cannot be utilized to describe the no-wave phenomena in Zone-0, Zong-1 and Zone-2; (4) support the particle reality of quantum mechanics.

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.

Quantum interference, manifest in the two slit experiment, lies at the heart of several quantum computational speed-ups and provides a striking example of a quantum phenomenon with no classical counterpart. An intriguing feature of quantum interference arises in a variant of the standard two slit experiment, in which there are three, rather than two, slits. The interference pattern in this set-up can be written in terms of the two and one slit patterns obtained by blocking one, or more, of the slits. This is in stark contrast with the standard two slit experiment, where the interference pattern cannot be written as a sum of the one slit patterns. This was first noted by Rafael Sorkin, who raised the question of why quantum theory only exhibits irreducible interference in the two slit experiment. One approach to this problem is to compare the predictions of quantum theory to those of operationally-defined ‘foil’ theories, in the hope of determining whether theories that do exhibit higher-order interference suffer from pathological—or at least undesirable—features. In this paper two proposed extensions of quantum theory are considered: the theory of Density Cubes proposed by Dakić, Paterek and Brukner, which has been shown to exhibit irreducible interference in the three slit set-up, and the Quartic Quantum Theory of Życzkowski. The theory of Density Cubes will be shown to provide an advantage over quantum theory in a certain computational task and to posses a well-defined mechanism which leads to the emergence of quantum theory—analogous to the emergence of classical physics from quantum theory via decoherence. Despite this, the axioms used to define Density Cubes will be shown to be insufficient to uniquely characterise the theory. In comparison, Quartic Quantum Theory is a well-defined theory and we demonstrate that it exhibits irreducible interference to all orders. This feature of Życzkowski’s theory is argued not to be a genuine phenomenon, but to arise from an ambiguity in the current definition of higher-order interference in operationally-defined theories. Thus, to begin to understand why quantum theory is limited to a certain kind of interference, a new definition of higher-order interference is needed that is applicable to, and makes good operational sense in, arbitrary operationally-defined theories.

This thesis develops a new way of modelling atoms that behave quantum mechanically on the inside, but classically on the outside. Doing so makes modelling the salient physics tractable. Prior to this technique, treating the outside of an atom classically failed to reproduce a bedrock experiment of quantum mechanics—the Stern–Gerlach experiment. I also report on the conception and flourishing of a control and analysis software suite for experiments in quantum science. This open-source project empowers experimenters to compose human-readable narratives upon their apparatus and has been adopted by a dozen groups worldwide.

Games are useful tools for introducing new concepts to students. This paper describes a competitive two-player game for sophomore students in a modern physics survey course or junior/senior students in an introductory quantum mechanics course to build intuition and quantitative understanding of the probabilistic nature of quantum measurements in two-level systems such as qubits or the Stern–Gerlach experiment. The goal of the game is to guess a quantum state secretly chosen from a given set in the fewest number of measurements. It uses 20-sided dice or other classical random number generators to simulate quantum measurements. The Bloch vector formalism is introduced to give a geometric description of the quantum states and measurement outcomes. Several ready-to-use sets of quantum states are given, so readers can jump right in and try the game themselves without any prior knowledge of quantum mechanics. More advanced students can also use the game in suggested follow-up exercises to deepen students' understanding of quantum measurements and their statistical description.

Emergence of classicality from quantum mechanics, a hotly debated topic, has had no satisfactory resolution so far. Various approaches including decoherence and gravitational interactions have been suggested. In the present work, the Schrödinger–Newton model is used to study the role of semi‐classical self‐gravity in the evolution of massive spin‐1/2 particles in a Stern‐Gerlach experiment. For small mass, evolution of the initial wavepacket in a spin superposition shows a splitting in the magnetic field gradient into two trajectories as in the standard Stern–Gerlach experiment. For larger mass, the deviations from the central path are less than in the standard Stern–Gerlach case, while for high enough mass, the wavepacket does not split, and instead follows the classical trajectory for a magnetic moment in inhomogeneous magnetic field. This indicates the emergence of classicality due to self‐gravitational interaction when the mass is increased. In contrast, decoherence which is a strong contender for emergence of classicality, leads to a mixed state of two trajectories corresponding to the spin‐up and spin‐down states, and not the classically expected path. The classically expected path of the particle probably cannot be explained even in the many‐worlds interpretation of quantum mechanics. Stern–Gerlach experiments in the macroscopic domain are needed to settle this question.

Many quantum phenomena, traditionally described by quantum electrodynamics, can be calculated within the framework of so-called semiclassical theory, in which atoms are described by the wave equations of quantum mechanics (Schrödinger, Dirac, etc.), while light is described by classical electrodynamics without quantization of the radiation. These phenomena include the photoelectric effect, the Compton effect, the Lamb shift, radiative effects, spontaneous emission, the Hanbury Brown and Twiss effect, etc. In this paper, I show that the double-slit experiment can also be calculated in detail in terms of semiclassical theory if we take into account the discrete (atomic) structure of matter. I show that the results of a semiclassical simulation of the “linear” double-slit experiment coincide with predictions of wave theory only for low-intensity light and for short exposure time, while stricter dependences exist for long-term exposure. The semiclassical theory is used for calculation of the “nonlinear” double-slit experiment with an intense laser beam in which multiphoton and tunnel excitation of atoms on a photographic plate occurs. The Born rule for light is derived from the semiclassical theory.

It is an often repeated claim in the literature that quantum mechanics is indeterministic and that it has put an end to the classical notion of causality. From the impossibility of determining the exact spatio-temporal trajectory of an atomic system, for instance, Heisenberg infers ‘the invalidity of the causal law’ in quantum mechanics [1]. What is tacitly assumed in such views is a chain of reasoning, which leads from determinism to causality. One form of determinism – predictive determinism – is the view that a sufficient knowledge of the laws of nature and appropriate boundary conditions will enable a superior intelligence to predict the future states of the physical world and to retrodict its past states with infinite precision. Laplace attributes this capacity to his famous demon: for the demon the physical world stretches out like the frames of a filmstrip. Each frame is caused by an earlier frame and in its turn causes a later frame. From the present frame the Laplacean demon is capable of predicting and retrodicting all other frames. Hence the demon identifies determinism and causality. ‘We ought to regard the present state of the universe as the effect of its antecedent state and as the cause of the state that is to follow’ [9]. Laplace assumes that these states are unique and can be determined with mathematical precision such that prediction and retrodiction become possible. The laws of physics are typically expressed in differential equations which describe the evolution of some physical parameter, P , as a function of time, t . As one state of a system, S1, evolves to another state, S2, where this temporal evolution is made precise by the employment of differential equations, it becomes easy to think of differential equations as precise mathematical representations of causal laws [10]. This is indeed how Einstein presented the matter: ‘The differential law is the only form which completely satisfies the modern physicist’s demand for causality’ [2]. Although Russell [11] had argued that the ‘law of causality (. . .) is the product of a bygone age’ he nevertheless admitted causal laws in the form of functional relations and differential equations into physics. This functional model of causality enjoyed great popularity amongst physicists. But the experimental results from quantum mechanics – like the double-slit experiments – seemed to threaten the Laplacean identification of determinism and causality. Physicists reacted to this threat in three different ways.

The Stern–Gerlach experiment was one of the early illustrative examples of the Bohr view of quantum mechanics. In the Bohr view, a measurement is an interaction between a quantum object and an apparatus which acts in a classical fashion. There are still open problems with this concept, many of which enter into the discussion of the original Stern–Gerlach measurement.

When both slits of the double slit experiment are open, closing one paradoxically increases the detection rate at some points on the detection screen. Feynman famously warned that temptation to understand such a puzzling feature only draws us into blind alleys. Nevertheless, we gain insight into this feature by drawing an analogy between the double slit experiment and a time reversed fire alarm. Much as closing the slit increases probability of a future detection, ruling out fire drill scenarios, having heard the fire alarm, increases probability of a past fire (using Bayesian inference). Classically, Bayesian inference is associated with computing probabilities of past events. We therefore identify this feature of the double slit experiment with a time reversed thermodynamic arrow. We believe that much of the enigma of quantum mechanics is simply due to some variation of time's arrow. In further support of this, we employ a plausible formulation of the thermodynamic arrow to derive an uncertainty in classical mechanics that is reminiscent of quantum uncertainty.

The [formula omitted]-Adic Schrödinger equation and the two-slit experiment in quantum mechanics

Summary form only given. Complementarity is one of the most basic principles of quantum mechanics. A quantum mechanical object, be it a photon or a massive particle, shows position (particle-like) or momentum (wave-like) attributes exclusively depending on the experimental situation. Over the years, Young's two-slit experiment has been emphasized as a good example of complementarity. We report two two-slit experiments in which complementarity is enforced by availability of which-path information at the measurement stage of the quantum, which is different from the traditional understanding. A type-II BBO crystal is pumped by a CW UV laser generating spontaneous parametric down-conversion (SPDC). Entangled signal and idler photons are then sent in different directions. A double slit is placed in the idler beam and the idler detectors are scanned in the transverse direction.

As is well known, the two–slit experiment is related, within Quantum Mechanics (Q.M.), to the dualistic character of radiation (for instance light), whose behavior is correctly represented as a wave-like phenomenon during its passage from the source, through the slits, up to the screen; and by a particle model (for instance, photons) when it impinges on the screen causing the extraction of electrons.KeywordsClassical LogicQuantum LogicClassical PhysicClassical ParticleLogical ConnectiveThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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.

Inter-relation between quantum and classical probability models is one of the most fundamental problems of quantum foundations. Nowadays this problem also plays an important role in quantum technologies, in quantum cryptography and the theory of quantum random generators. In this letter, we compare the viewpoint of Richard Feynman that the behavior of quantum particles cannot be described by classical probability theory with the viewpoint that quantum–classical inter-relation is more complicated (cf, in particular, with the tomographic model of quantum mechanics developed in detail by Vladimir Man'ko). As a basic example, we consider the two-slit experiment, which played a crucial role in quantum foundational debates at the beginning of quantum mechanics (QM). In particular, its analysis led Niels Bohr to the formulation of the principle of complementarity. First, we demonstrate that in complete accordance with Feynman's viewpoint, the probabilities for the two-slit experiment have the non-Kolmogorovian structure, since they violate one of basic laws of classical probability theory, the law of total probability (the heart of the Bayesian analysis). However, then we show that these probabilities can be embedded in a natural way into the classical (Kolmogorov, 1933) probability model. To do this, one has to take into account the randomness of selection of different experimental contexts, the joint consideration of which led Feynman to a conclusion about the non-classicality of quantum probability. We compare this embedding of non-Kolmogorovian quantum probabilities into the Kolmogorov model with well-known embeddings of non-Euclidean geometries into Euclidean space (e.g., the Poincaré disk model for the Lobachvesky plane).