Relation Between Relativistic and Non-Relativistic Quantum Mechanics as Integral Transformation

A formulation of quantum mechanics (QM) in the relativistic configurational space (RCS) is considered. A transformation connecting the non-relativistic QM and relativistic QM (RQM) has been found in an explicit form. This transformation is a direct generalization of the Kontorovich–Lebedev transformation. It is shown also that RCS gives an example of non-commutative geometry over the commutative algebra of functions.     

Search for a possible variation of the fine structure constant

The determination of the fine structure constant α and the search for its possible variation are considered. We focus on the role of the fine structure constant in modern physics and discuss precision tests of quantum electrodynamics.Different methods of a search for possible variations of fundamental constants are compared and those related to optical measurements are considered in detail.     

Quantum Mechanics: Modal Interpretation and Galilean Transformations

The aim of this paper is to consider in what sense the modal-Hamiltonian interpretation of quantum mechanics satisfies the physical constraints imposed by the Galilean group. In particular, we show that the only apparent conflict, which follows from boost-transformations, can be overcome when the definition of quantum systems and subsystems is taken into account. On this basis, we apply the interpretation to different well-known models, in order to obtain concrete examples of the previous conceptual conclusions. Finally, we consider the role played by the Casimir operators of the Galilean group in the interpretation.     

磁单极与磁洛伦兹力

概述了磁单极概念的历史发展,从洛伦兹变换出发,利用电磁场张量和四维力的协变性以及电荷相对论不变,直接证明了运动磁单极受磁洛伦兹力,建议了一个磁洛伦兹力的验证方案,并用磁洛伦兹力公式导出狄拉克电荷量子化条件．证明了磁洛伦兹力公式具有与库仑定律相同的精确度．     

Atom‐Interferometry Measurement of the Fine Structure Constant

Using an atom interferometer to measure the quotient of the reduced Planck's constant and the mass of a cesium‐133 atom $?/m_{\mathrm{Cs}}$, the most accurate measurement of the fine structure constant $\alpha =1/137.035999046(27)$ is recorded, at an accuracy of 0.20 parts per billion (ppb). Using multiphoton interactions (Bragg diffraction and Bloch oscillations), the largest phase (12 million radians) of any Ramsey–Bordé interferometer and controlled systematic effects at a level of 0.12 ppb are demonstrated. Comparing the Penning trap measurements with the Standard Model prediction of the electron gyromagnetic anomaly $a_e$ based on the α measurement, a 2.5 $\sigma$ tension is observed, rejecting dark photons as the reason for the unexplained part of the muon's gyromagnetic moment discrepancy at a 99% confidence level according to frequentist statistics. Implications for dark‐sector candidates (e.g., scalar and pseudoscalar bosons, vector bosons, and axial‐vector bosons) may be a sign of physics beyond the Standard Model. A future upgrade of the cesium fountain atom interferometer is also proposed to increase the accuracy of $?/m_{\mathrm{Cs}}$ by 1 to 2 orders of magnitude, which would help resolve the tension.     

Relating the Quantum Mechanics of Discrete Systems to Standard Canonical Quantum Mechanics

Standard canonical quantum mechanics makes much use of operators whose spectra cover the set of real numbers, such as the coordinates of space, or the values of the momenta. Discrete quantum mechanics uses only strictly discrete operators. We show how one can transform systems with pairs of integer-valued, commuting operators $P_i$ and $Q_i$ , to systems with real-valued canonical coordinates $q_i$ and their associated momentum operators $p_i$ . The discrete system could be entirely deterministic while the corresponding (p, q) system could still be typically quantum mechanical.     

Precision spectroscopy of the helium atom

Persistent efforts in both theory and experiment have yielded increasingly precise understanding of the helium atom. Because of its simplicity, the helium atom has long been a testing ground for relativistic and quantum electrodynamic effects in few-body atomic systems theoretically and experimentally. Comparison between theory and experiment of the helium spectroscopy in 1s2p³P _J can potentially extract a very precise value of the fine structure constant á. The helium atom can also be used to explore exotic nuclear structures. In this paper, we provide a brief review of the recent advances in precision calculations and measurements of the helium atom.      

Testing the variation of the fine structure constant with strongly lensed gravitational waves

The possible variation of the electromagnetic fine structure constant, αe, at cosmological scales has aroused great interest in recent years. Strongly lensed gravitational waves(GWs) and their electromagnetic counterparts could be used to test this variation. Under the assumption that the speed of a photon can be modified,whereas the speed of a GW is the same as predicted by general relativity, and they both propagate in a flat FriedmanRobertson-Walker universe, we investigated the difference in time delays of the images and derived the upper bound of the variation of αe. For a typical lensing system in the standard cosmological models, we obtained B cosθ 1.85×10~(-5),where B is the dipolar amplitude and θ is the angle between observation and the preferred direction. Our result is consistent with the most up-to-date observations on αe. In addition, the observations of strongly lensed GWs and their electromagnetic counterparts could be used to test which types of alternative theories of gravity can account for the variation of α_e.     

Hamilton's Turns for the Lorentz Group

Hamilton in the course of his studies on quaternions came up with an elegant geometric picture for the group SU(2). In this picture the group elements are represented by “turns,” which are equivalence classes of directed great circle arcs on the unit sphere S ², in such a manner that the rule for composition of group elements takes the form of the familiar parallelogram law for the Euclidean translation group. It is only recently that this construction has been generalized to the simplest noncompact group SU(1, 1)=Sp(2, R)=SL(2, R), the double cover of SO(2, 1). The present work develops a theory of turns for SL(2, C), the double and universal cover of SO(3, 1) and SO(3, C), rendering a geometric representation in the spirit of Hamilton available for all low dimensional semisimple Lie groups of interest in physics. The geometric construction is illustrated through application to polar decomposition, and to the composition of Lorentz boosts and the resulting Wigner or Thomas rotation. PACS numbers: 02.20.-a     

洛伦兹力可看作静止电荷所受电场力的相对论效应——兼论洛伦兹力公式具有与库仑定律相同的精确度

从洛伦兹变换出发,利用电磁场张量和四维力的协变性及电荷相对论不变,直接证明:在一个惯性参考系内的静止电荷所受电场力,转换到另一个惯性参考系就是运动电荷受的洛伦兹力.证明洛伦兹力公式具有与库仑定律相同的精确度.     

Foundations of the Quaternion Quantum Mechanics

We show that quaternion quantum mechanics has well-founded mathematical roots and can be derived from the model of the elastic continuum by French mathematician Augustin Cauchy, i.e., it can be regarded as representing the physical reality of elastic continuum. Starting from the Cauchy theory (classical balance equations for isotropic Cauchy-elastic material) and using the Hamilton quaternion algebra, we present a rigorous derivation of the quaternion form of the non- and relativistic wave equations. The family of the wave equations and the Poisson equation are a straightforward consequence of the quaternion representation of the Cauchy model of the elastic continuum. This is the most general kind of quantum mechanics possessing the same kind of calculus of assertions as conventional quantum mechanics. The problem of the Schrödinger equation, where imaginary ‘i’ should emerge, is solved. This interpretation is a serious attempt to describe the ontology of quantum mechanics, and demonstrates that, besides Bohmian mechanics, the complete ontological interpretations of quantum theory exists. The model can be generalized and falsified. To ensure this theory to be true, we specified problems, allowing exposing its falsity.     

Emergent Quantum Mechanics and the Origin of Quantum Non-local Correlations

International Journal of Theoretical Physics - A geometric interpretation for quantum correlations and entanglement according to a particular framework of emergent quantum mechanics is developed....     

Quantum Mechanics of Neutrino Oscillations

We present a simple but general treatment of neutrino oscillations in the framework of quantum mechanics, using plane waves and intuitive wave packet principles when necessary. We attempt to clarify some confusing statements that have recently appeared in the literature.     

On the Classical Limit of Quantum Mechanics

Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of many results of the standard approach, it is not yet clear how to explain within standard quantum mechanics the classical motion of macroscopic bodies. In this paper, we shall formulate the classical limit as a scaling limit in terms of an adimensional parameter ε. We shall take the first steps toward a comprehensive understanding of the classical limit, analyzing special cases of classical behavior in the framework of a precise formulation of quantum mechanics called Bohmian mechanics which contains in its own structure the possibility of describing real objects in an observer-independent way.     

Q-spaces and the Foundations of Quantum Mechanics

Our aim in this paper is to take quite seriously Heinz Post’s claim that the non-individuality and the indiscernibility of quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry conditions. Using a different mathematical framework, namely, quasi-set theory, we avoid working within a label-tensor-product-vector-space-formalism, to use Redhead and Teller’s words, and get a more intuitive way of dealing with the formalism of quantum mechanics, although the underlying logic should be modified. We build a vector space with inner product, the Q-space, using the non-classical part of quasi-set theory, to deal with indistinguishable elements. Vectors in Q-space refer only to occupation numbers and permutation operators act as the identity operator on them, reflecting in the formalism the fact of unobservability of permutations. Thus, this paper can be regarded as a tentative to follow and enlarge Heinsenberg’s suggestion that new phenomena require the formation of a new “closed” (that is, axiomatic) theory, coping also with the physical theory’s underlying logic and mathematics. G. Domenech is a fellow of the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina. D. Krause is a fellow of the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil.     

Superstrings and the Foundations of Quantum Mechanics

It is put forward that modern elementary particle physics cannot be completely unified with the laws of gravity and general relativity without addressing the question of the ontological interpretation of quantum mechanics itself. The position of superstring theory in this general question is emphasized: superstrings may well form exactly the right mathematical system that can explain how quantum mechanics can be linked to a deterministic picture of our world. Deterministic interpretations of quantum mechanics are usually categorically rejected, because of Bell’s powerful observations, and indeed these apply here also, but we do emphasize that the models we arrive at are super-deterministic, which is exactly the case where Bell expressed his doubts. Strong correlations at space-like separations could explain the apparent contradictions.     

On the generator of Lorentz boost

Traditionally, the theory related to the spatial angular momentum has been studied completely, while the investigation in the generator of Lorentz boost is inadequate. This paper shows that the generator of Lorentz boost has a nontrivial physical significance: it endows a charged system with an electric moment, and has an important significance for the electrical manipulations of electron spin in spintronics. An alternative treatment and interpretation for the traditional Darwin term and spin--orbit coupling are given.