Physics, Volume 4, Issue 4 (December 2022) – 22 articles

The paper considers momentum operators on intrinsically curved manifolds. Given that momentum operators are Killing vector fields whose integral curves are geodesics, the corresponding manifold is flat or of the compact type with positive constant sectional curvature and dimensions equal to 1, 3, or 7. Explicit representations of momentum operators and the associated Casimir element are discussed for the 3-sphere $S^3$. It is verified that the structural constants of the underlying Lie algebra are proportional to 2 $\hslash /R$, where R is the curvature radius of $S^3$ and ℏ is the reduced Planck’s constant. This results in a countable energy and momentum spectrum of freely moving particles in $S^3$. The maximal resolution of the possible momenta is given by the de Broglie wave length, ${\lambda }_R=\pi R$, which is identical to the diameter of the manifold. The corresponding covariant position operators are defined in terms of geodesic normal coordinates, and the associated commutator relations of position and momentum are established. Full article

Observation of the onset of color transparency in baryons would provide a new means of studying the nuclear strong force and would be the first clear evidence of baryons transforming into a color-neutral point-like size in the nucleus as predicted by quantum chromodynamics. Recent C$(e,e^{\prime }p)$ results from electron-scattering did not observe the onset of color transparency (CT) in protons up to spacelike four-momentum transfers squared, $Q^2=14.2$ GeV${}^2$. The traditional methods of searching for CT in $(e,e^{\prime }p)$ scattering use heavy targets favoring kinematics with already initially reduced final state interactions (FSIs) such that any CT effect that further reduces FSIs will be small. The reasoning behind this choice is the difficulty in accounting for all FSIs. D$(e,e^{\prime }p)n$, on the other hand, has well-understood FSI contributions from double scattering with a known dependence on the kinematics and can show an increased sensitivity to hadrons in point-like configurations. Double scattering is the square of the re-scattering amplitude in which the knocked-out nucleon interacts with the spectator nucleon, a process that is suppressed in the presence of point-like configurations and is particularly well-studied for the deuteron. This suppression yields a quadratic sensitivity to CT effects and is strongly dependent on the choice of kinematics. Here, we describe a possible Jefferson National Accelerator Facility (JLab) electron-scattering experiment that utilizes these kinematics and explores the potential signal for the onset of CT with enhanced sensitivity as compared to recent experiments. Full article

The emergence of a minimal length at the Planck scale is consistent with modern developments in quantum gravity. This is taken into account by transforming the Heisenberg uncertainty principle into the generalized uncertainty principle. Here, the position-momentum commutator is modified accordingly. In this paper, majorization uncertainty relations within the generalized uncertainty principle are considered. Dealing with observables with continuous spectra, each of the axes of interest is divided into a set of non-intersecting bins. Such formulation is consistent with real experiments with a necessarily limited precision. On the other hand, the majorization approach is mainly indicative for high-resolution measurements with sufficiently small bins. Indeed, the effects of the uncertainty principle are brightly manifested just in this case. The current study aims to reveal how the generalized uncertainty principle affects the leading terms of the majorization bound for position and momentum measurements. Interrelations with entropic formulations of this principle are briefly discussed. Full article

In this paper, we investigate the modified symmetric teleparallel gravity or $f\left(Q\right)$ gravity, where Q is the nonmetricity, to study the evolutionary history of the universe by considering the functional form of $f\left(Q\right)=\alpha Q^n$, where $\alpha$ and n are constants. Here, we consider the parametrization form of the deceleration parameter as $q=q_0+q_{1}z/{(1+z)}^2$ (with the parameters $q_0$$(q$ at $z=0)$, $q_1$, and the redshift, z), which provides the desired property for a sign flip from a decelerating to an accelerating phase. We obtain the solution of the Hubble parameter by examining the mentioned parametric form of q, and then we impose the solution in Friedmann equations. Employing the Bayesian analysis for the Observational Hubble data (OHD), we estimated the constraints on the associated free parameters $(H_0,q_0,q_1)$ with $H_0$ the current Hubble parameter to determine if this model may challenge the $\mathrm{\Lambda }$CDM ($\mathrm{\Lambda }$ cold dark matter with the cosmological constant, $\mathrm{\Lambda }$) limitations. Furthermore, the constrained current value of the deceleration parameter $q_0=-0.{832}_{-0.091}^{+0.091}$ shows that the present universe is accelerating. We also investigate the evolutionary trajectory of the energy density, pressure, and EoS (equation-of-state) parameters to conclude the accelerating behavior of the universe. Finally, we try to demonstrate that the considered parametric form of the deceleration parameter is compatible with $f\left(Q\right)$ gravity. Full article

Exactly soluble models can serve as excellent tools to explore conceptual issues in non-perturbative quantum gravity. In perturbative approaches, it is only the two radiative modes of the linearized gravitational field that are quantized. The goal of this investigation is to probe the ‘Coulombic’ aspects of quantum geometry that are governed entirely by matter sources. Since there are no gravitational waves in three dimensions, 3-dimensional (3-d) gravity coupled to matter provides an ideal arena for this task. The analysis presented here reveals novel aspects of quantum gravity that bring out limitations of classical and semi-classical theories in unforeseen regimes: non-linearities of general relativity can magnify small quantum fluctuations in the matter sector to large effects in the gravitational sector. Finally, this analysis leads to thought experiments that bring out rather starkly why understanding of the nature of physical reality depends sensitively on the theoretical lens with which it is probed. As theories become richer, new scales emerge, triggering novel effects that could not be imagined before. The model provides a concise realization of this well-known chain. Full article

Entanglement has become a hot topic in nuclear and particle physics, although many physicists are not sure they know what it means. We maintain that an era of understanding and using quantum mechanics on a dramatically new basis has arrived. We review a viewpoint that treats the subject as being primarily descriptive and completely free of the intellectual straitjackets and mysticism argued over long ago. Quantum probability is an extension of classical probability, but with universal uses. Density matrices describe systems where entanglement or its absence is a classification tool. Most of these have been known for decades, but there is a new way of understanding them that is liberated from the narrow outlook of the early days. Full article

Nonuniform plasma across an imposed magnetic field, such as those present in the solar atmosphere, can support collective Alfvénic oscillations with a characteristic damping time. The damped transverse oscillations of coronal loops are an example of this process. In ideal magnetohydrodynamics (MHD), these transient collective motions are associated with quasi-modes resonant in the Alfvén continuum. Quasi-modes live in a non-principal Riemann sheet of the dispersion relation, and so they are not true ideal MHD eigenmodes. The present study considers the illustrative case of incompressible surface MHD waves propagating on a nonuniform interface between two uniform plasmas with a straight magnetic field parallel to the interface. It is explored how the ideal quasi-modes of this configuration change when the width of the nonuniform transition increases. It is found that interfaces with wide enough transitions are not able to support truly collective oscillations. A quasi-mode that can be related with a resonantly damped surface MHD wave can only be found in interfaces with sufficiently thin transitions. Full article

A non-minimally coupled cosmological scenario is considered in the context of $f(R,T)=f_1\left(R\right)+f_2\left(R\right)f_3\left(T\right)$ gravity (with R being the Ricci scalar and T the trace of the energy-momentum tensor) in the background of the flat Friedmann–Robertson–Walker (FRW) model. The field equations of this modified theory are solved using a time-dependent deceleration parameter for a dust. The behavior of the model is analyzed taking into account constraints from recent observed values the deceleration parameter. It is shown that the analyzed models can explain the transition from the decelerating phase to the accelerating one in the expansion of the universe, by staying true to the results of the observable universe. It is shown that the models are dominated by a quintessence-like cosmological dark fluid at the late universe. Full article

Particle physics is an exciting subject for high school students, and there have been various approaches on how to introduce the topic in the classroom. Feynman diagrams (FDs) are an often-used form of representation in particle physics and could play an important role in such an introduction. However, their potential educational value has not yet been investigated. To this end, we interviewed four experts in the field of particle physics education on the opportunities and challenges Feynman diagrams could pose for high school students. We analyzed their answers using a thematic analysis framework, categorizing them into five themes. The results of these interviews show that there are two challenges (FDs elicit and perpetuate inadequate conceptions about particle physics, and FDs can only be treated superficially in school) and three opportunities (FDs can link particle physics and other physics topics in high school education, FDs offer an opportunity for different particle physics topics to be taught, and FDs offer a connection to current research). The results of this expert interview study lead to several suggestions on how to design learning environments that incorporate Feynman diagrams. Full article

Motivated by the recent study about the extended uncertainty principle (EUP) black holes, we present in this study its extension called the generalized extended uncertainty principle (GEUP) black holes. In particular, we investigated the GEUP effects on astrophysical and quantum black holes. First, we derive the expression for the shadow radius to investigate its behavior as perceived by a static observer located near and far from the black hole. Constraints to the large fundamental length scale, $L_{*}$, up to two standard deviations level were also found using the Event Horizont Telescope (EHT) data: for black hole Sgr. A*, $L_{*}=5.716\times {10}^{10}$ m, while for M87* black hole, $L_{*}=3.264\times {10}^{13}$ m. Under the GEUP effect, the value of the shadow radius behaves the same way as in the Schwarzschild case due to a static observer, and the effect only emerges if the mass, M, of the black hole is around the order of magnitude of $L_{*}$ (or the Planck length, $l_{\mathrm{Pl}}$). In addition, the GEUP effect increases the shadow radius for astrophysical black holes, but the reverse happens for quantum black holes. We also explored GEUP effects to the weak and strong deflection angles as an alternative analysis. For both realms, a time-like particle gives a higher value for the weak deflection angle. Similar to the shadow, the deviation is seen when the values of $L_{*}$ and M are close. The strong deflection angle gives more sensitivity to GEUP deviation at smaller masses in the astrophysical scenario. However, the weak deflection angle is a better probe in the micro world. Full article

The goal of teaching quantum physics (QP) in high school is a problematic and highly turbulent area of divergent views, curricula studies, and claims. The innovative curricular approach of discipline-culture (DC) suggests a way of overcoming its significant difficulties. It suggests presenting QP as a fundamental theory structured in terms of the nucleus, body, and periphery. Applying this perspective in our study, we interviewed nine experts with respect to their view of how the nucleus of QP should be presented to high-school students. With the different viewpoints of the core essentials in hand, we compiled the nucleus of the QP. We also examined this subject using nine introductory university textbooks that might suit high school students and considered their coherence and suitability with regard to the specified nucleus. We found some confusion regarding the status of theoretical items: some fundamental principles, as perceived in the eyes of the experts, are presented as phenomena. Not only does this mismatch represent a special barrier for both the teachers and students to understand QP, it promotes an inadequate image of QP as well as a distorted view of the nature of science. Finally, we offer a framework for a DC-based QP curriculum free of the noted deficiencies. Full article

This international curricular review provides a structured overview of the particle physics content in 27 state, national, and international high-school physics curricula. The review was based on a coding manual that included 60 concepts that were identified as relevant for high-school particle physics education. Two types of curricula were reviewed, namely curricula with a dedicated particle physics chapter and curricula without a dedicated particle physics chapter. The results of the curricular review show that particle physics concepts are explicitly or implicitly present in all reviewed curricula. However, the number of particle physics concepts that are featured in a curriculum varies greatly across the reviewed curricula. We identified core particle physics concepts that can be found in most curricula. Here, elementary particles, fundamental interactions, and charges were identified as explicit particle physics concepts that are featured in more than half of the reviewed curricula either as content or context. Indeed, theoretical particle physics concepts are more prominent in high-school physics curricula than experimental particle physics concepts. Overall, this international curricular review provides the basis for future curricular development with respect to particle physics and suggests an increased inclusion of experimental particle physics concepts in high-school physics curricula. Full article

In an atom, the interaction of a bound electron with the vacuum fluctuations of the electromagnetic field leads to complex shifts in the energy levels of the electron, with the real part of the shift corresponding to a shift in the energy level and the imaginary part to the width of the energy level. The most celebrated radiative shift is the Lamb shift between the $2s_{1/2}$ and the $2p_{1/2}$ levels of the hydrogen atom. The measurement of this shift in 1947 by Willis Lamb Jr. proved that the prediction by Dirac theory that the energy levels were degenerate was incorrect. Hans Bethe’s non-relativistic calculation of the shift using second-order perturbation theory demonstrated the renormalization process required to deal with the divergences plaguing the existing theories and led to the understanding that it was essential for theory to include interactions with the zero-point quantum vacuum field. This was the birth of modern quantum electrodynamics (QED). Numerous calculations of the Lamb shift followed including relativistic and covariant calculations, all of which contain a nonrelativistic contribution equal to that computed by Bethe. The semi-quantitative models for the radiative shift of Welton and Power, which were developed in an effort to demonstrate physical mechanisms by which vacuum fluctuations lead to the shift, are also considered here. This paper describes a calculation of the shift using a group theoretical approach which gives the shift as an integral over frequency of a function, which is called the “spectral density of the shift.“ The energy shift computed by group theory is equivalent to that derived by Bethe yet, unlike in other calculations of the non-relativistic radiative shift, no sum over a complete set of states is required. The spectral density, which is obtained by a relatively simple computation, reveals how different frequencies of vacuum fluctuations contribute to the total energy shift. The analysis shows, for example, that half the radiative shift for the ground state 1S level in H comes from virtual photon energies below 9700 eV, and that the expressions of Power and Welton have the correct high-frequency behavior, but not the correct low-frequency behavior, although they do give approximately the correct value for the total shift. Full article

With quantum physics being a particularly difficult subject to teach because of its contextual distance from everyday life, the need for multiperspective teaching material arises. Quantum physics education aims at exploring these methods but often lacks physical models and haptic components. In this paper, we provide two analog models and corresponding teaching concepts that present analogies to quantum phenomena for implementation in secondary school and university classrooms: While the first model focuses on the polarization of single photons and the deduction of reasoning tools for elementary comprehension of quantum theory, the second model investigates analog Hardy experiments as an alternative to Bell’s theorem. We show how working with physical models to compare classical and quantum perspectives has proven helpful for novice learners to grasp the abstract nature of quantum experiments and discuss our findings as an addition to existing quantum physics teaching concepts. Full article

Quantum gravity theories rely on a minimal measurable length for their formulations, which clashes with the classical formulation of the uncertainty principle and with Lorentz invariance from general relativity. These incompatibilities led to the development of the generalized uncertainty principle (GUP) from string theories and its various modifications. GUP and covariant formulations of the uncertainty principle are discussed, together with implications for space–time quantization. Full article

For around five decades, physicists have been experimenting with single quanta such as single photons. Insofar as the practised ensemble reasoning has become obsolete for the interpretation of these experiments, the non-classical intrinsic probabilistic nature of quantum theory has gained increased importance. One of the most important exclusive features of quantum physics is the undeniable existence of the superposition of states, even for single quantum objects. One known example of this effect is entanglement. In this paper, two classically contradictory phenomena are combined to one single experiment. This experiment incontestably shows that a single photon incident on an optical beam splitter can either be reflected or transmitted. The almost complete absence of coincident clicks of two photodetectors demonstrates that these two output states are incompatible. However, when combining these states using two mirrors, we can observe interference patterns in the counting rate of the single photon detector. The only explanation for this is that the two incompatible output states are prepared and kept simultaneously—a typical consequence of a quantum superposition of states. (Semi-)classical physical concepts fail here, and a full quantum concept is predestined to explain the complementary experimental outcomes for the quantum optical “non-waves” called single photons. In this paper, we intend to demonstrate that a true quantum physical key experiment (“true” in the sense that it cannot be explained by any classical physical concept), when combined with full quantum reasoning (probability, superposition and interference), influences students’ readiness to use quantum elements for interpretation. Full article

Quantum technologies have outgrown mere fundamental research in laboratories over recent years, and will facilitate more and more potentially disruptive applications in a wide range of fields in the future. In foresight, qualification opportunities need to be implemented in order to train qualified specialists, referred to as the future quantum workforce, in various fields. Universities world-wide have launched qualification programmes for engineers focusing on quantum optics and photonics. In many of these programmes, students attend courses on quantum physics contextualized via quantum optics experiments with heralded photons, because: (1) their experimental and physical foundations may be directly leveraged to teaching a number of quantum technology applications, and (2) physics education research has provided empirical evidence, according to which such quantum optics-based approaches are conducive to learning about quantum concepts. While many teachers are confident about the effectiveness of their concepts, there is little empirical evidence due to the lack of content-area-specific research tools. We present a 16-item concept inventory to assess students’ conceptual understanding of quantum optics concepts in the context of experiments with heralded photons adopted from a test instrument published in the literature. We have administered this Quantum Optics Concept Inventory as a post-test to $N=216$ students after instruction on quantum optics as part of an undergraduate engineering course. We evaluated the instruments’ psychometric quality, both in terms of classical test theory, and using a Rasch scaling approach. The Quantum Optics Concept Inventory enables a reliable measure ($\alpha =0.74$), and the data gathered show a good fit to the Rasch model. The students’ scores suggest that fundamental quantum effects pose striking learning hurdles to the engineering students. In contrast, most of the students are able to cope with the experimental and technical foundations of quantum optics experiments with heralded photons and their underlying principles, such as the coincidence technique used for the preparation of single-photon states. These findings are in accordance with prior research, and hence, the Quantum Optics Concept Inventory may serve as a fruitful starting point for future empirical research with regard to the education of the future quantum workforce. Full article

In the de Sitter gauge theory (DGT), the fundamental variables are the de Sitter (dS) connection and the gravitational Higgs/Goldstone field ${\xi }^A$, where A is a 5 dimensional index. Previously, a model for DGT was analyzed, which generalizes the MacDowell–Mansouri gravity to have a variable cosmological constant, $\mathsf{\Lambda }=3/l^2$, where l is related to ${\xi }^A$ by ${\xi }^A{\xi }_A=l^2$. It was shown that the model sourced by a perfect fluid does not support a radiation epoch and the accelerated expansion of the parity invariant universe. In this paper, I consider a similar model, namely, the Stelle–West gravity, and couple it to a modified perfect fluid, such that the total Lagrangian 4-form is polynomial in the gravitational variables. The Lagrangian of the modified fluid has a nontrivial variational derivative with respect to l, and as a result, the problems encountered in the previous study no longer appear. Moreover, to explore the elegance of the general theory, as well as to write down the basic framework, I perform the Lagrange–Noether analysis for DGT sourced by a matter field, yielding the field equations and the identities with respect to the symmetries of the system. The resulted formula are dS covariant and do not rely on the existence of the metric field. Full article

Stimulated by the European project “QTEdu CSA”, within the flagship “Quantum Technologies”, a community of researchers active in the fields of quantum technologies and physics education has designed and implemented an extracurricular course on quantum physics concepts and quantum technologies applications for high school. The course, which featured eight interactive lectures, was organized online between March and May 2021 and attended by about 250 students from all over Italy. In this paper, we describe the main tenets and activities of the course. Moreover, we report on the effectiveness of the course on students’ knowledge of the basic concepts of quantum physics and students’ views about epistemic aspects and applications of quantum technologies. Results show that the designed activities were effective in improving students’ knowledge about fundamental aspects of quantum mechanics and familiarizing them with quantum technology applications. Full article

Studies of weak interaction in nuclei are important tools for testing different aspects of the fundamental symmetries of the Standard Model. Neutrinoless double beta decay offers an unique venue of investigating the possibility that neutrinos are Majorana fermions and that the lepton number conservation law is violated. Here, I use a shell model approach to calculate the nuclear matrix elements needed to extract the lepton-number-violating parameters of a few nuclei of experimental interest from the latest experimental lower limits of neutrinoless double beta decay half-lives. The analysis presented here could reveal valuable information regarding the dominant neutrinoless double beta decay mechanism if experimental half-life data become available for different isotopes. A complementary shell model analysis of the two-neutrino double beta decay nuclear matrix elements and half-lives is also presented. Full article

Prior research has shown that many secondary school students have a insufficient conceptual understanding of basic optics concepts even after formal instruction. In this paper, we empirically investigate whether a phenomenological approach might be a sensible alternative to traditional model-based instruction of introductory optics in early physics education. We report the results of a quasi-experimental field study to examine the effect of a phenomenological approach following the Erlangen teaching–learning sequence of introductory optics on $N=42$ eight graders’ acquisition of conceptual understanding related to (1) the process of vision, (2) refraction, and (3) image formation by converging lenses. We contrast the learning outcomes with those of $N=55$ control group students who participated in traditional model-based instruction. The results of this study indicate that the phenomenological approach is superior to traditional (model-based) instruction in promoting students’ conceptual understanding of basic optics concepts, in particular with regard to circumventing widespread learning difficulties related to image formation. Our results are further substantiated by a comparison of students’ situational interest in optics between both groups. This adds further arguments in favor of the use of phenomenological approaches when it comes to teaching basic optics concepts in classroom practice. Full article

The Barbero–Immirzi parameter, (γ), is introduced in loop quantum gravity (LQG), whose physical significance is still the biggest open question because of its profound traits. In some cases, it is real valued, while it is complex valued in other cases. This parameter emerges in the process of denoting a Lorentz connection with a non-compact group SO(3,1) in the form of a complex connection with values in a compact group of rotations, either SO(3) or SU(2). Initially, it appeared in the Ashtekar variables. Fernando Barbero proposed its possibility for inclusion within formalism. Its present value is fixed by counting micro states in loop quantum gravity and matching with the semi-classical black hole entropy computed by Stephen Hawking. This parameter is used to count the size of the quantum of area in Planck units. Until the discovery of the spectrum of the area operator in LQG, its significance remained unknown. However, its complete physical significance is yet to be explored. In the present paper, an introduction to the Barbero–Immirzi parameter in LQG, a timeline of this research area, and various proposals regarding its physical significance are given. Full article