Is David Bohm’s Quantum Mechanics Interpretation Irrefutable?

The theoretical bases of the so-called “pilot-wave” concept interpretation of quantum mechanics, as well as the performed and possible experiments to test its adequacy are considered.     

On Epstein’s Trajectory Model of Non-Relativistic Quantum Mechanics

In 1952 Bohm presented a theory about non-relativistic point-particles that move deterministically along trajectories and showed how it reproduces the predictions of standard quantum theory. This theory was actually presented before by de Broglie in 1926, but Bohm’s particular formulation of the theory inspired Epstein to come up with a different trajectory model. The aim of this paper is to examine the empirical predictions of this model. It is found that the trajectories in this model are in general very different from those in the de Broglie-Bohm theory. In certain cases they even seem bizarre and rather unphysical. Nevertheless, it is argued that the model seems to reproduce the predictions of standard quantum theory (just as the de Broglie-Bohm theory).     

Quantum Mechanics and Information Security

After a short review of the background and main theoretical results of quantum key distribution, I shall then introduce the existing problems for secure QKD in practice. Ishall then forus on the security problem of QKD with an imperfect source, in particular, the recently developed theory of the decoy-state method which can help to implement the secure QKD without a single-photon source. Basically, if the single-photon source is replaced by the weak coherent light, the protocol can betotally insecure due to the photon-number-splitting attack given a lossy channel. However, if werandomly change the intensity of each pulses among a few different values （ e. g. , 3 ） we can thenal- most exactly verify the fraction of bits generated by those single-photonpulses. This, together with the prior art theo- retical result, can raise the secure distance of QKD with currently existing technologies from less than 20 kms to more than 120 kms. Experimental implementation of decoy-state QKD have been done.     

Randomness in Classical Mechanics and?Quantum Mechanics

The Copenhagen interpretation of quantum mechanics assumes the existence of the classical deterministic Newtonian world. We argue that in fact the Newton determinism in classical world does not hold and in the classical mechanics there is fundamental and irreducible randomness. The classical Newtonian trajectory does not have a direct physical meaning since arbitrary real numbers are not observable. There are classical uncertainty relations: Δq>0 and Δp>0, i.e. the uncertainty (errors of observation) in the determination of coordinate and momentum is always positive (non zero).     

What’s Wrong with Einstein’s 1927 Hidden-Variable Interpretation of Quantum Mechanics?

Einsteins unpublished 1927 deterministic trajectory interpretation of quantum mechanics is critically examined, in particular with regard to the reason given by Einstein for rejecting his theory. It is shown that the aspect Einstein found objectionable—the mutual dependence of the motions of particles when the (many-body) wavefunction factorises—is a generic attribute of his theory but that this feature may be removed by modifying Einsteins method in either of two ways: using a suggestion of Grommer or, in a physically important special case, using a simpler technique. It is emphasized though that the presence or absence of the interdependence property does not determine the acceptability of a trajectory theory. It is shown that there are other grounds for rejecting Einsteins theory (and the two modified theories), to do with its domain of applicability and compatibility with empirical predictions. That Einsteins reason for rejection is not a priori grounds for discarding a trajectory theory is demonstrated by reference to an alternative deterministic trajectory theory that displays similar particle interdependence yet is compatible with quantum predictions.PACS: 03.65.Bz.Essay written in memory of J.T. Cushing.     

Is Quantum Mechanics Incompatible with Newton’s First Law?

Quantum mechanics (QM) clearly violates Newton’s First Law of Motion (NFLM) in the quantum domain for one of the simplest problems, yielding an effect in a force-free region much like the Aharonov-Bohm effect. In addition, there is an incompatibility between the predictions of QM in the classical limit, and that of classical mechanics (CM) with respect to NFLM. A general argument is made that such a disparity may be found commonly for a wide variety of quantum predictions in the classical limit. Alternatives to the Schrödinger equation are considered that might avoid this problem. The meaning of the classical limit is examined. Critical views regarding QM by Schrödinger, Bohm, Bell, Clauser, and others are presented to provide a more complete perspective.     

Background Independent Quantum Mechanics, Classical Geometric Forms and Geometric Quantum Mechanics—I

The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert space has been discussed for the chosen Quantum states. Since the theory of classical gravity is basically geometric in nature and Quantum Mechanics is in no way devoid of geometry, the explorations pertaining to more and more geometry in Quantum Mechanics could prove to be valuable for larger objectives such as understanding of gravity.     

Quantum Simulation of Generalized Hardy’s Paradox and Corresponding Hardy’s Inequality via Quantum Programming

International Journal of Theoretical Physics - Hardy’s paradox can demonstrate the conflict between quantum mechanics and local realism. Experimental testing of Hardy’s paradox has been...     

Bell’s Theorem without Inequalities and without Unspeakable Information

A proof of Bell’s theorem without inequalities is presented in which distant local setups do not need to be aligned, since the required perfect correlations are achieved for any local rotation of the local setups.     

Quantum Computing’s Classical Problem,Classical Computing’s Quantum Problem

Tasked with the challenge to build better and better computers, quantum computing and classical computing face the same conundrum: the success of classical computing systems. Small quantum computing systems have been demonstrated, and intermediate-scale systems are on the horizon, capable of calculating numeric results or simulating physical systems far beyond what humans can do by hand. However, to be commercially viable, they must surpass what our wildly successful, highly advanced classical computers can already do. At the same time, those classical computers continue to advance, but those advances are now constrained by thermodynamics, and will soon be limited by the discrete nature of atomic matter and ultimately quantum effects. Technological advances benefit both quantum and classical machinery, altering the competitive landscape. Can we build quantum computing systems that out-compute classical systems capable of some \(10^{30}\) logic gates per month? This article will discuss the interplay in these competing and cooperating technological trends.     

Quantum Perfect Correlations and Hardy’s Nonlocality Theorem

In this paper the failure of Hardy's nonlocality proof for the class of maximally entangled states is considered. A detailed analysis shows that the incompatibility of the Hardy equations for this class of states physically originates from the fact that the existence of quantum perfect correlations for the three pairs of two-valued observables (D ₁₁, D ₂₁), (D ₁₁, D ₂₂), and (D ₁₂, D ₂₁) [in the sense of having with certainty equal (different) readings for a joint measurement of any one of the pairs (D ₁₁, D ₂₁), (D ₁₁, D ₂₂), and (D ₁₂, D ₂₁)], necessarily entails perfect correlation for the pair of observables (D ₁₂, D ₂₂) [in the sense of having with certainty equal (different) readings for a joint measurement of the pair (D ₁₂, D ₂₂)]. Indeed, the set of these four perfect correlations is found to satisfy the CHSH inequality, and then no violations of local realism will arise for the maximally entangled state as far as the four observables D _ij, i,j = 1 or 2, are concerned. The connection between this fact and the impossibility for the quantum mechanical predictions to give the maximum possible theoretical violation of the CHSH inequality is pointed out. Moreover, it is generally proved that the fulfillment of all the Hardy nonlocality conditions necessarily entails a violation of the resulting CHSH inequality. The largest violation of this latter inequality is determined.     

Hiding Information in Theories Beyond Quantum Mechanics,and It’s Application to the Black Hole Information Problem

The black hole information problem provides important clues for trying to piece together a quantum theory of gravity. Discussions on this topic have generally assumed that in a consistent theory of gravity and quantum mechanics, quantum theory is unmodified. In this review, we discuss the black hole information problem in the context of generalisations of quantum theory. In this preliminary exploration, we examine black holes in the setting of generalised probabilistic theories, in which quantum theory and classical probability theory are special cases. We are able to calculate the time it takes information to escape a black hole, assuming that information is preserved. In quantum mechanics, information should escape pure state black holes after half the Hawking photons have been emitted, but we find that this get’s modified in generalisations of quantum mechanics. Likewise the black-hole mirror result of Hayden and Preskill, that information from entangled black holes can escape quickly, also get’s modified. We find that although information exits the black hole as predicted by quantum theory, it is fairly generic that it fails to appear outside the black hole at this point—something impossible in quantum theory due to the no-hiding theorem. The information is neither inside the black hole, nor outside it, but is delocalised.     

Quantum Circuits and Schr?dinger’s Cat States

Quantum systems that are confined to circuit geometries are called quantum circuits. Macroscopic superconducting circuits are quantum circuits which can be modelled using a Quantisation by Parts scheme based on the macroscopic wave function approach of Feynman. This paper studies the circuit composed of an input wire and an output plate. We find that in order to achieve a consistent theory of supercurrent flow we have to generalize the quantisation by parts scheme to quantise in a path space. The generalized theory predicts a current flow down the wire into the plane. In addition to a current flowing radially outwards in the plane, the theory allows a circulating current round the origin. Strikingly, the circulating current can flow clockwise or anti-clockwise in such a way as to generate a magnetic moment of magnitude half of a Bohr magneton for an orbiting electron in an atom and a magnetic flux half that of the magnetic flux quantum of a superconducting ring. There is also the possibility of a macroscopic superposition of the two states of opposing circulating currents resembling a Schr?dinger’s cat situation. Furthermore, we outline a setup involving an external magnetic field that may allow experimental tests of the theory.     

Quantum Teleportation and Grover’s Algorithm Without the Wavefunction

In the same way as the quantum no-cloning theorem and quantum key distribution in two preceding papers, entanglement-assisted quantum teleportation and Grover’s search algorithm are generalized by transferring them to an abstract setting, including usual quantum mechanics as a special case. This again shows that a much more general and abstract access to these quantum mechanical features is possible than commonly thought. A non-classical extension of conditional probability and, particularly, a very special type of state-independent conditional probability are used instead of Hilbert spaces and wavefunctions.     

Fractional Green’s Function for the Time-Dependent Scattering Problem in the Space-Time-Fractional Quantum Mechanics

Integral form of the space-time-fractional Schrödinger equation for the scattering problem in the fractional quantum mechanics is studied in this paper. We define the fractional Green’s function for the space-time fractional Schrödinger equation and express it in terms of Fox’s H-function and in a computable series form. The asymptotic formula of the Green’s function for large argument is also obtained, and applied to study the fractional quantum scattering problem. We get the approximate scattering wave function with correction of every order.     

Time Symmetric Quantum Mechanics and Causal Classical Physics ?

A two boundary quantum mechanics without time ordered causal structure is advocated as consistent theory. The apparent causal structure of usual “near future” macroscopic phenomena is attributed to a cosmological asymmetry and to rules governing the transition between microscopic to macroscopic observations. Our interest is a heuristic understanding of the resulting macroscopic physics.     

Unreasonable and “Unreasonable” in Quantum Mechanics?

The particles of quantum mechanics (QM) are discrete undulatory entities which are described in terms of the complex state vectors of the theory in full agreement with experiment. The wave-particle paradox stems from the fact that undulation and discreteness are inconsistent within the classical theory which was historically the point of departure for the canonical foundation. The author describes his prolonged efforts of anchoring the state vector of QM in experiment rather in obsolete theory.     

Bell’s Inequalities and Methods of Quantifying Measures of Entanglement Correlations

Bell inequalities provide a specific setting for investigating the physics of entanglement in quantum mechanics. They give a basis for providing an experimental realization of these kinds of quantum phenomena and exhibit some of its more unusual consequences. Some useful ways to look at entanglement quantitatively are presented. It is intended that the presentation and results will provide insights which make effective experimental observation easier.     

Heisenberg’s Uncertainty Relation and Bell Inequalities in High Energy Physics

An effective formalism is developed to handle decaying two-state systems. Herewith, observables of such systems can be described by a single operator in the Heisenberg picture. This allows for using the usual framework in quantum information theory and, hence, to enlighten the quantum features of such systems compared to non-decaying systems. We apply it to systems in high energy physics, i.e. to oscillating meson–antimeson systems. In particular, we discuss the entropic Heisenberg uncertainty relation for observables measured at different times at accelerator facilities including the effect of CP\mathcal{CP} violation, i.e. the imbalance of matter and antimatter. An operator-form of Bell inequalities for systems in high energy physics is presented, i.e. a Bell-witness operator, which allows for simple analysis of unstable systems.