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This article is a response to a comment made by Professor Liu regarding a previously published paper. The response addresses questions raised by Professor Liu and focuses on three key aspects of the validity of the paper. It explains the use of different contractions in the construction of the QED Hamiltonians and clarifies the commutation relations used in the calculations. The article also highlights that the formulation of the molecular orbital method described in the paper is independent of the ordering of the operators and can derive expressions for various perturbation theories. The response concludes by stating that alternative criteria for the QED Hamiltonians are not ruled out and could be explored in future research. [Extracted from the article]

Based on the thermal phase structure of pure SU(2) quantum Yang–Mills theory, we describe the electron at rest as an extended particle, a droplet of radius r 0 ∼ a 0 , where a 0 is the Bohr radius. This droplet is of vanishing pressure and traps a monopole within its bulk at a temperature of T c = 7.95 keV. The monopole is in the Bogomolny–Prasad–Sommerfield (BPS) limit. It is interpreted in an electric–magnetically dual way. Utilizing a spherical mirror-charge construction, we approximate the droplet's charge at a value of the electromagnetic fine-structure constant α of α − 1 ∼ 134 for soft external probes. It is shown that the droplet does not exhibit an electric dipole or quadrupole moment due to averages of its far-field electric potential over monopole positions. We also calculate the mixing angle θ W ∼ 30 ° , which belongs to deconfining phases of two SU(2) gauge theories of very distinct Yang–Mills scales ( Λ e = 3.6 keV and Λ CMB ∼ 10 − 4 eV). Here, the condition that the droplet's bulk thermodynamics is stable determines the value of θ W . The core radius of the monopole, whose inverse equals the droplet's mass in natural units, is about 1% of r 0 . [ABSTRACT FROM AUTHOR]

We study the fine structure constant dependence of the rates of some selected radiative capture reactions within the framework of so-called Halo Effective Field Theory in order to assess the adequacy of some assumptions made on the Coulomb penetrability. We find that this dependence deviates from that implied by a parameterization of the cross sections of this effect via a simple penetration factor. Some features of this fine-structure dependence are discussed, in particular its potential impact on the abundances of the light elements in primordial nucleosynthesis. [ABSTRACT FROM AUTHOR]

This work re-derives and discusses non-Lorentz invariant variable speed of light (VSL) theories in the context of cosmological problems. Following a thorough introduction to the subject, an explicit solution demonstrating a possible dependence of the speed of light on the cosmological scale factor is presented and analyzed. The parameters of the initial ansatz, c (t) = c 0 a n , are constrained by requiring the VSL formulation to be a solution to the flatness and horizon problems. The theoretical section is concluded with a derivation of the change of entropy in a VSL Universe. Even though such findings imply that the speed of light can vary only in non-flat spacetime, an adapted approach using the Generalized Second Law of Thermodynamics is shown to loosen this restriction. Further, in the experimental section, recent evidence for a temporally varying fine structure constant at ≈ 4 σ significance is presented as a potential test for the VSL hypothesis. Overall, this work introduces and evaluates many aspects of non-Lorentz invariant VSL theories whilst encouraging future research and serving as a largely self-sufficient comprehensive overview paper. [ABSTRACT FROM AUTHOR]

Understanding physical mechanisms relies on the accurate determination of fundamental constants, although inherent limitations in experimental techniques introduce uncertainties into these measurements. This paper explores the uncertainties associated with measuring the fine-structure constant (⁠|$\alpha$|⁠) and the proton-to-electron mass ratio (⁠|$\mu$|⁠) using observed fast radio bursts (FRBs). We select 50 localized FRBs to quantify the effects of varying this fundamental coupling on the relation between dispersion measure and redshift. By leveraging independent measurements of dispersion measures and redshifts of these FRBs, we constrain the uncertainties in |$\alpha$| and |$\mu$| approximately to |$\Delta \alpha /\alpha =1.99\times 10^{-5}$| and |$\Delta \mu /\mu =-1.00\times 10^{-5}$| within the standard |$\Lambda$| CDM cosmological framework. Remarkably, these constraints improve nearly an order-of-magnitude when considering a dynamical dark energy model. This investigation not only yields one of the most stringent constraints on |$\alpha$| and |$\mu$| to date but also emphasizes the criticality of accounting for the energy scale of the system when formulating constraints on fundamental parameters. [ABSTRACT FROM AUTHOR]

A Fourier-transform recording of protactinium in the infrared range is reanalysed with high precision in order to determine the hyperfine interaction constants A and B. Starting with a selection of best lines and least-squares fits of hyperfine structure intervals, large systems of linear equations compare experimental hyperfine peak wavenumbers with a theoretical representation. The theoretical representation is based on Ritz's combination principle and Casimir's formula according to the existing classification. Weighted least-squares fits allow a discrimination between unperturbed and perturbed data such as blended hyperfine structure components. For the first time, the wavenumbers of the hyperfine components of more than 600 lines are fitted using the characteristics of about 250 levels as parameters. When adding adjustable wavenumber-scale correction parameters, global consistency for the whole IR spectrum is obtained with local limits of about 0.3 × 10 - 3 cm - 1 . This demonstrates the high precision in both recording and analysis. The values of the fine structure energies are revised. Standard errors around 0.1 × 10 - 3 cm - 1 for the A constants and 10 - 3 cm - 1 for the B constants and the fine structure energies are achieved. Representative examples illustrate extensive results obtained for atomic protactinium. This high precision facilitates further search for new energy levels, and 20 new levels were presented. Foreword The data presented here are the results of a study carried out at the Laboratoire Aimé Cotton (LAC) at Paris-Orsay in the years 2003 and 2004, when I was there for a research stay. At this time, I worked together with Jean-François Wyart and Annie Ginibre on the re-examination of protactinium spectra that have been measured about 30 years earlier and that were available in the form of a printed list of peak wavenumbers and a printed paper chart of the intensity profile. The spectra had already been analysed, but there was still a lot of additional information that could be extracted from the spectra with time and effort. The review of the data, the selection of the data and the step-by-step optimization of the data set took a lot of time. When I returned to Berlin in 2004, we had made good progress, but in principle, it is like a bottomless pit. We continued together to optimize the data and tried to the finishing touches to it. At some point, we decided that we had reached a 'level of maturity' where the data could be published. We have discussed a lot about how detailed the text should be. This discussion has dragged on over the years and this project has repeatedly been lost in the stream of other everyday tasks. Every now and then there was a small attempt to return to this topic, but it quickly got lost in the daily hustle and bustle. In 2012, we presented the results at a conference. The death of both of them within two years hit me hard. I very much regret that this work was not published earlier. This special volume was the right motivation for me to finally publish this data. I no longer have access neither to the computer programs used at the time, which ran on large computer systems, nor to the original measurement data. I have not been able to find out what happened to the large quantity of paper (printed list of peak wavenumbers anda printed paper chart of spectra). But I have a bunch of input and output files of the calculations that have become a bit jumbled over the years, which contain a lot of information, as well as our unfinished manuscript. The resulting data contain important information for posterity – particularly since the element is radioactive and the experiments to collect laboratory data are unlikely to be repeated any time soon. I think it is worth publishing these data. High precision FT spectra of Pa: analysis of fine and hyperfine structure [ABSTRACT FROM AUTHOR]

The triplet contribution is computed to the 1 and 2 S 0 e 1 states of the He atom, to the 1 S 0 e 1 state of the Li+ and Be2+ ions, and to the X 1 Σ g + ground state of the H2 molecule by extensive use of double-group symmetry (equivalent to LS coupling for the atomic systems) during the course of the variational solution of the no-pair Dirac–Coulomb–Breit (DCB) wave equation. The no-pair DCB energies are converged within sub-parts-per-billion relative precision, using an explicitly correlated Gaussian basis optimized to the non-relativistic energies. The α fine-structure constant dependence of the triplet sector contribution to the variational energy is α4Eh at leading order, in agreement with the formal perturbation theory result available from the literature. [ABSTRACT FROM AUTHOR]

This paper explores how a reinterpretation of the generalized uncertainty principle as an effective variation of Planck's constant provides a physical explanation for a number of fundamental quantities and couplings. In this context, a running fine structure constant is naturally emergent and the cosmological constant problem is solved, yielding a novel connection between gravitation and quantum field theories. The model could potentially clarify the recent experimental observations by the DESI Collaboration that could imply a fading of dark energy over time. When applied to quantum systems and their characteristic length scales, a simple geometric relationship between energy and entropy is disclosed. Lastly, a mass–radius relation for both quantum and classical systems reveals a phase transition-like behavior similar to thermodynamical systems, which we speculate to be a consequence of topological defects in the universe. [ABSTRACT FROM AUTHOR]

The article presents a theoretical study of Oleinik resonances in the process of scattering a gamma quantum by an ultrarelativistic electron in the field of a strong electromagnetic wave with intensities up to  10 27 Wcm − 2 . The resonant kinematics for three possible resonant reaction channels in a strong external field have been studied in detail. It is shown that under resonant conditions, the scattering channels of the reaction effectively split into two first-order processes according to the fine structure constant, such as the external field-stimulated Compton effect. The annihilation channel of the reaction effectively decays into direct and reverse the external field-stimulated Breit–Wheeler processes. In the absence of interference from the reaction channels, a resonant differential cross-section was obtained in a strong external electromagnetic field. The cases when the energy of the initial electrons significantly exceeds the energy of the initial gamma quanta have been studied. At the same time, all particles (initial and final) fly in a narrow cone away from the direction of wave propagation. The conditions under which the energy of ultrarelativistic initial electrons is converted into the energy of a finite gamma quantum are studied. It is shown that the resonant differential cross-section of such a process significantly (by several orders of magnitude) exceeds the corresponding nonresonant cross-section. This theoretical study predicts a number of new physical effects that may explain the high-energy fluxes of gamma quanta produced near neutron stars and magnetars. [ABSTRACT FROM AUTHOR]

Yarman’s Approach, which serves as the basis of YARK gravitation theory (as abbreviated from “Yarman-Arık-Kholmetskii”), together with its recently developed extension QTG (Quantal Theory of Gravity), motivated us to question the suitability of Natural Units commonly used in Quantum Field Theory (QFT) and other areas of physics. That and the consensus of the General Conference on Weights and Measures (CGPM) towards the establishment of “New SI” inspired us to explore an appropriate way of normalizing the metric system in order to make the utmost theoretical speed limit of light c and the Planck Constant h unities, as well as universal constants, respectively. Our metrological approach herein reveals that the correction factor k introduced to the retired definition of vacuum permeability µ0 — as extracted from an indiscriminate Fine-Structure Constant α value — does not suffice to align the computed α with the latest experimental measurements of α. One may therefore require a rectified value for the elementary charge e along with the need to restore its uncertainty digits. All this is especially relevant within the context of the 20 May 2019 international decision to fix the Planck Constant to a definite value while letting the kilogram vary instead. One thus remarkably ends up with the necessity to either restore the uncertainty parts of the elementary charge in contrast to the SI redefinition, or to recalculate the correction factor k that latterly appears in vacuum permeability, or both. Another far-reaching option is the idea of restituting the uncertainties for the Planck Constant and/or lightspeed too when SI is normalized and then re-normalized without disturbing the meaningfulness of the related physical dimensions. [ABSTRACT FROM AUTHOR]

Achieving a truly accurate wavelength calibration of high-dispersion echelle spectrographs is a challenging task but crucially needed for certain science cases, e.g. to test for a possible variation of the fine-structure constant in quasar spectra. One of the spectrographs best suited for this mission is Very Large Telescope/Echelle SPectrograph for Rocky Exoplanets and Stable Spectroscopic Observation (ESPRESSO). Nevertheless, previous studies have identified significant discrepancies between the classical wavelength solutions and the one derived independently from the laser frequency comb. The dominant parts of these systematics were intra-order distortions, most-likely related to a deviation of the instrumental line-spread function from the assumed Gaussian shape. Here, we therefore present a study focused on a detailed modelling of the ESPRESSO instrumental line-spread function. We demonstrate that it is strongly asymmetric, non-Gaussian, different for the two slices and fibres, and varies significantly along the spectral orders. Incorporating the determined non-parametric model in the wavelength calibration process drastically improves the wavelength calibration accuracy, reducing the discrepancies between the two independent wavelength solutions from |$50\,\rm{m\,s^{-1}}$| to about |$10\, \rm{m\,s^{-1}}$|⁠. The most striking success is, however, that the different fibres and slices now provide fully consistent measurements with a scatter of just a couple m s−1. This demonstrates that the instrument-related systematics can be nearly eliminated over most of the spectral range by properly taking into account the complex shape of the instrumental line-spread function and paves the way for further optimizations of the wavelength calibration process. [ABSTRACT FROM AUTHOR]

Variational and perturbative relativistic energies are computed and compared for two-electron atoms and molecules with low nuclear charge numbers. In general, good agreement of the two approaches is observed. Remaining deviations can be attributed to higher-order relativistic, also called non-radiative quantum electrodynamics (QED), corrections of the perturbative approach that are automatically included in the variational solution of the no-pair Dirac–Coulomb–Breit (DCB) equation to all orders of the α fine-structure constant. The analysis of the polynomial α dependence of the DCB energy makes it possible to determine the leading-order relativistic correction to the non-relativistic energy to high precision without regularization. Contributions from the Breit–Pauli Hamiltonian, for which expectation values converge slowly due the singular terms, are implicitly included in the variational procedure. The α dependence of the no-pair DCB energy shows that the higher-order (α4Eh) non-radiative QED correction is 5% of the leading-order (α3Eh) non-radiative QED correction for Z = 2 (He), but it is 40% already for Z = 4 (Be2+), which indicates that resummation provided by the variational procedure is important already for intermediate nuclear charge numbers. [ABSTRACT FROM AUTHOR]

The electromagnetic-gravity optimization (EMGO) framework is a novel optimization technique that integrates the fine-structure constant and leverages electromagnetism and gravity principles to achieve efficient and robust optimization solutions. Through comprehensive performance evaluation and comparative analyses against state-of-the-art optimization techniques, EMGO demonstrates superior convergence speed and solution quality. Its unique balance between exploration and exploitation, enabled by the interplay of electromagnetic and gravity forces, makes it a powerful tool for finding optimal or near-optimal solutions in complex problem landscapes. The research contributes by introducing EMGO as a promising optimization approach with diverse applications in engineering, decision support systems, machine learning, data mining, and financial optimization. EMGO’s potential to revolutionize optimization methodologies, handle real-world problems effectively, and balance global exploration and local exploitation establishes its significance. Future research opportunities include exploring adaptive mechanisms, hybrid approaches, handling high-dimensional problems, and integrating machine learning techniques to enhance its capabilities further. EMGO gives a novel approach to optimization, and its efficacy, advantages, and potential for extensive adoption open new paths for advancing optimization in many scientific, engineering, and real-world domains.

Based on the thermal phase structure of pure SU(2) quantum Yang–Mills theory, we describe the electron at rest as an extended particle, a droplet of radius r0∼a0, where a0 is the Bohr radius. This droplet is of vanishing pressure and traps a monopole within its bulk at a temperature of Tc=7.95 keV. The monopole is in the Bogomolny–Prasad–Sommerfield (BPS) limit. It is interpreted in an electric–magnetically dual way. Utilizing a spherical mirror-charge construction, we approximate the droplet’s charge at a value of the electromagnetic fine-structure constant α of α−1∼134 for soft external probes. It is shown that the droplet does not exhibit an electric dipole or quadrupole moment due to averages of its far-field electric potential over monopole positions. We also calculate the mixing angle θW∼30°, which belongs to deconfining phases of two SU(2) gauge theories of very distinct Yang–Mills scales (Λe=3.6 keV and ΛCMB∼10−4 eV). Here, the condition that the droplet’s bulk thermodynamics is stable determines the value of θW. The core radius of the monopole, whose inverse equals the droplet’s mass in natural units, is about 1% of r0.

Searches for space–time variations of fundamental constants have entered an era of unprecedented precision. New, high-quality quasar spectra require increasingly refined analytical methods. In this paper, a continuation in a series to establish robust and unbiased methodologies, we explore how convergence criteria in non-linear least-squares optimization impact on quasar absorption system measurements of the fine structure constant α. Given previous claims for high-precision constraints, we critically examine the veracity of a so-called blinding approach, in which α is fixed at the terrestrial value during the model building process, releasing it as a free parameter only after the 'final' absorption system kinematic structure has been obtained. We show that this approach results in such small consecutive parameter steps during minimization that convergence is unlikely to be reached, even after as many as 1000 iterations. The fix is straightforward: α must be treated as a free parameter from the earliest possible stages of absorption system model building. The implication of the results presented here is that all previous measurements that have used initially fixed α should be reworked. [ABSTRACT FROM AUTHOR]

In this paper, we study the relationship between the Dirac–Fock model and the electron-positron Hartree–Fock model. We justify the Dirac–Fock model as a variational approximation of QED when the vacuum polarization is neglected and when the fine structure constant α is small and the velocity of light c is large. As a byproduct, we also prove, when α is small or c is large, the no-unfilled shells theory in the Dirac–Fock theory for atoms and molecules. The proof is based on some new properties of the Dirac–Fock model. [ABSTRACT FROM AUTHOR]

Recent observations of anomalous angular correlations of electron–positron pairs in several nuclear reactions have indicated the existence of a hypothetical neutral boson of rest mass ~17 MeV/c2, called the X17 particle. Similarly, one has interpreted an independent set of experiments on photon pair spectra around the invariant mass ~38 MeV/c2, by assuming the existence of the so-called E38 particle. In the present paper, we derive analytical mass formulas for the X17 particle and the E38 particle, on the basis of quantum electrodynamics. We shall use the exact solutions of the Dirac equation of the joint system of a charged particle and plane waves of the quantized electromagnetic radiation. When these solutions are applied to a proton, they lead to dressed radiation quanta with a rest mass of 17.0087 MeV/c2, which may be identified with the X17 vector bosons. A similar consideration, applied to the udd quarks of the neutron, yields dressed quanta, whose mass equals 37.9938 MeV/c2, corresponding to the E38 particle. These formulas, besides the Sommerfeld fine structure constant and the masses of the nucleons, do not contain any adjustable parameters. The present analysis also delivers the value 0.846299 fm for the proton radius. [ABSTRACT FROM AUTHOR]

Exploring the cosmological variations of fundamental dimensionless constants, such as the fine-structure constant, α , the proton-to-electron mass ratio, μ , and the gravitational constant, G, is essential for testing new phenomena beyond the standard cosmological models. This study focuses on investigating the potential variation of constants by analyzing strong gravitational fields associated with white dwarf stars. Utilizing the observed spectrum of G191-B2B, we present a new constraint on the cosmological variation of μ over extended time scales, Δ μ / μ = (0. 0 8 4 ± 1. 0 4 4) × 1 0 − 8 , incorporating the gravitational redshift z ≈ 5 × 1 0 − 5 . This finding represents a new tool for checking the parameters for Grand Unified Theories (GUTs). [ABSTRACT FROM AUTHOR]

[O  iii ] λλ4960,5008 doublet are often the strongest narrow emission lines in starburst galaxies and quasi-stellar objects (QSOs), and thus are a promising probe to possible variation of the fine-structure constant α over cosmic time. Previous such studies using QSOs optical spectra were limited to z < 1. In this work, we constructed a sample of 40 spectra of Ly α emitting galaxies (LAEs) and a sample of 46 spectra of QSOs at 1.09 < z < 3.73 using the VLT/X-Shooter near-infrared spectra publicly available. We measured the wavelength ratios of the two components of the spin-orbit doublet and accordingly calculated α(z) using two methods. Analysis on all of the 86 spectra yielded Δα/α = (− 3 ± 6) × 10−5 with respect to the laboratory α measurements, consistent with no variation over the explored time interval. If assuming a uniform variation rate, we obtained α−1dα/d t = (− 3 ± 6) × 10−15 yr−1 within the last 12 Gyr. Extensive tests indicate that α variation could be better constrained using starburst galaxies' spectra than using QSO spectra in future studies. [ABSTRACT FROM AUTHOR]

Fundamental constants are crucial for comprehending physical mechanisms, but their measurements contain uncertainties due to experimental limitations. We investigate the impact of system temperature on these uncertainties using nearby white dwarfs observed in the Gaia Early Data Release 3 (EDR3) survey. Using the structures of these white dwarfs, we show that the variation in system temperature can affect the accuracy of measurements for fundamental parameters such as the fine-structure constant and the proton-to-electron mass ratio. This exploration emphasizes the importance of considering the energy of a system while putting bounds on the values of fundamental constants. [ABSTRACT FROM AUTHOR]

The renormalization group equations of massive |$\mathcal {N}=1$| supersymmetric quantum electrodynamics are studied using the functional renormalization group approach. A non-perturbative form of the beta function has been computed via a derivative expansion of the effective action. In the local potential approximation, the functional form of the non-perturbative beta function is closely related to the form of the Novikov–Shifman–Vainshtein–Zakharov (NSVZ) exact beta function; this relationship is exact if an effective fine-structure constant is defined. The non-massive limit of the same is also analyzed. Furthermore, the calculation of the beta function has been improved by incorporating the influence of momentum modes on the propagation of the superfields in the non-perturbative running of the electric charge, applying a second-order truncation for the derivative expansion, which we use to find the momentum contributions to the β function. Again, we find the NSVZ relation for an effective fine-structure constant. It is with sadness that I say goodbye to my professor, Iván Schmidt Andrade, who left us during the course of this work. His passion for research and his special vision of physics work will remain with us. Thank you for everything. [ABSTRACT FROM AUTHOR]

The portal connecting the invisible and visible sectors is one of the most natural explanations of the dark world. However, the early-time dark matter production via the portal faces extremely stringent late-time constraints. To solve such tension, we construct the scalar-controlled kinetic mixing varying with the ultralight CP-even scalar's cosmological evolution. To realize this and eliminate the constant mixing, we couple the ultralight scalar within 10−33eV ≲ m0 ≪ eV with the heavy doubly charged messengers and impose the ℤ2 symmetry under the dark charge conjugation. Via the varying mixing, the keV – MeV dark photon dark matter is produced through the early-time freeze-in when the scalar is misaligned from the origin and free from the late-time exclusions when the scalar does the damped oscillation and dynamically sets the kinetic mixing. We also find that the scalar-photon coupling emerges from the underlying physics, which changes the cosmological history and provides the experimental targets based on the fine-structure constant variation and the equivalence principle violation. To ensure the scalar naturalness, we discretely re-establish the broken shift symmetry by embedding the minimal model into the ℤN-protected model. When N ~ 10, the scalar's mass quantum correction can be suppressed much below 10−33eV. [ABSTRACT FROM AUTHOR]

Axions provide a solution to the strong CP problem and are excellent dark matter candidates. The presence of additional sources of CP violation, for example to account for the matter/antimatter asymmetry of the universe, can lead to CP-violating interactions between axions and Standard Model fields. In case axions form a coherent dark matter background, this leads to time-oscillating fundamental constants such as the fine-structure constant and particle masses. In this work we compare the sensitivity of various searches for CP-odd axion interactions. These include fifth-force experiments, searches for time-oscillating constants induced by axion dark matter, and direct limits from electric dipole moment experiments. We show that searches for oscillating constants can outperform fifth-force experiments in the regime of small axion masses, but, in general, do not reach the sensitivity of electric dipole moment experiments. [ABSTRACT FROM AUTHOR]

Bounds on the cosmological variation of the fine structure constant α inferred from Oklo neutron capture data are sometimes taken cum grano salis. It is possible to quantify uncertainties related to the treatment of excitation, deformation and the Coulomb interaction. On the basis of this analysis, it is concluded that Oklo data imply the relative change in α over the last 1.9 billion years is < 0.01 ppm (95% CL). Accommodation of this constraint represents a challenge to dark energy models that predict that fundamental constants do change. [ABSTRACT FROM AUTHOR]

This document is an erratum for a published paper titled "Computation of the masses of the elementary particles." The author has identified two errors in the original paper and provides corrections for them. The corrections involve replacing equations, code tables, and graph figures. The corrected results are qualitatively the same as the original paper, but not quantitatively. The author suggests that using high-performance computing and refining the integrations may result in predicted particle masses closer to the measured values. The erratum includes tables, code listings, and graphs to support the corrections. [Extracted from the article]

This paper uses a limited scope to present an explanation of how quantum jumps prevent quantum mechanics from being a fundamental theory, and this paper explains how Einstein's theory that radiation conveys inertia between the emitting and absorbing bodies plays a critical role in the presented explanation. [ABSTRACT FROM AUTHOR]

Experiments confirmed Einstein's proposal that gravitational fields bend light. We propose that in order to understand the mechanism of the red shift of light, the intimate connection between gravity and light must first be made apparent. The structure/behavior of the internal workings of photons, including gravity photons, gps, which make up space, points to another mechanism that is both simple and intuitive. Our approach is to establish the steps that lead to our proposed connection between gravity and light. [ABSTRACT FROM AUTHOR]

The Lamb shift, one of the most fundamental interactions in atomic physics, arises from the interaction of H atoms with the electromagnetic fluctuations of the quantum vacuum. The energy shift has been computed in a variety of ways. The energy shift, as Feynman, Power, and Milonni demonstrated, equals the change in the vacuum energy in the volume containing the H atoms due to the change in the index of refraction arising from the presence of the H atoms. Using this result and a group theoretical calculation of the contribution to the Lamb shift from each frequency of the vacuum fluctuations, in this paper we obtain an expression for the region of the vacuum energy for each frequency ω around the H atom due to the Lamb shift. This same field plays an essential role in the van der Waals force. We show the ground state atom is surrounded by a region of positive vacuum energy that extends well beyond the atom for low frequencies. This region can be described as a steady state cloud of vacuum fluctuations. For energies E = ℏ ω less than 1 eV, where ℏ is the reduced Planck constant and ω is frequency, the radius of the positive energy region is shown to be approximately 14.4/E Å. For a vacuum fluctuation of wavelength, λ , the radius is (α / 2 π) λ , where α is the fine-structure constant. Thus, for long wavelengths, the region has macroscopic dimensions. The energy–time uncertainty relation predicts a maximum possible radius that is larger than the radius based on the radiative shift calculations by a factor of 1 / 4 α . [ABSTRACT FROM AUTHOR]

The article explores the relationship between fundamental physical constants and the characteristics of biological processes. It suggests that there is a specific range of values for these constants that are conducive to life processes, particularly those related to motion and flow within cells. It discusses how variations in fundamental constants, such as Planck's constant (ℏ) and the electron charge (e), can impact viscosity and diffusion in biological systems.

A method for obtaining an exhaustive set of multiplicative equations of relationship between the elements of an arbitrary set of the tested physical constants Cj in the form of their products in integer powers mj ranging from –N to N is proposed and used (calculations were performed for N = 2 and 4). A formal application of the proposed procedure reveals the minimum quanta of charge, mass, time, and distance and also a number of the relations describing the most general physical laws. It is shown that it is possible to construct a system of fundamental physical constants le, te, ee, me, α, and β (α is the fine-structure constant) with the simplest (m, s, kg, C) and zero dimensions to describe electromagnetic and gravitational interactions, as well as with the addition of Boltzmann's constant (k), to describe the laws of thermal radiation. Planck's constant (h), the speed of light in vacuum (c), electric (ε0), magnetic (μ0) and gravitational (G) constants are expressed through the revealed minimum quanta of length, time, charge, mass, and dimensionless constants. [ABSTRACT FROM AUTHOR]

Electric charges and masses of elementary fermions of the Standard Model and fundamental physical constants (speed of light in vacuum, Planck constant, gravitational constant, vacuum permittivity, electron charge) are related through a simple equation. This new relation links 10 of the free parameters of the Standard Model—the masses of the three charged leptons and six quarks, and the electromagnetic coupling—in a compact formula, leaving strong constraints for allowing further elementary charged fermions beyond the Standard Model’s physics. The formula is not derived by theoretical calculations, but it is based on the empirically measured values of the electric charges and proper masses of the known elementary fermions.

In bound states in the continuum (BIC) the mass of a composite particle is greater than the total mass of its constituents. The BIC state is investigated in a system of two charged particles a and b with different masses ( m b ≫ m a ), using the ladder Bethe–Salpeter equation. We demonstrate that there are two momentum space regions for the positive binding energy, in which the electromagnetic interaction between the particles is strongly enhanced, and the effective coupling constant turns out to be equal to α m b ∕ m a , where α is the fine structure constant. The interaction resonance confines the constituents in the BIC state with the positive binding energy, which is of the order of the mass of the lighter particle from this pair. [ABSTRACT FROM AUTHOR]

The high resolution spectrograph ESPRESSO on the VLT allows measurements of fundamental constants at unprecedented precision and hence enables tests for space–time variations predicted by some theories. In a series of recent papers, we developed optimal analysis procedures that expose and eliminate the subjectivity and bias in previous quasar absorption system measurements. In this paper, we analyse the ESPRESSO spectrum of the absorption system at zabs  = 1.15 towards the quasar HE 0515-4414. Our goal here is not to provide a new unbiased measurement of Δα/α in this system (that will be done separately). Rather, it is to carefully examine the impact of blinding procedures applied in many previous measurements of the fine structure constant in quasar absorption systems. To do this, we emulate previous procedures, using supercomputer Monte Carlo AI calculations to generate a large number of independently constructed models of the absorption complex. Each model is obtained using ai-vpfit , with Δα/α fixed until a 'final' model for the absorption system is obtained, at which point Δα/α is then released as a free parameter for one final optimization. The results show that the value of Δα/α obtained in this way is systematically biased towards the initially fixed value i.e. this process produces measurements that are unrelated to the true value of Δα/α. The implication is straightforward: to avoid bias, all future measurements must include Δα/α as a free parameter from the beginning of the modelling process. [ABSTRACT FROM AUTHOR]

The Survey for Distant Solar Twins aims to find stars very similar to the Sun at distances of 1– |$4\, {\rm kpc}$|⁠ , several times more distant than any currently known solar twins and analogues. The goal is to identify the best stars with which to test whether the fine-structure constant, α, varies with dark matter density in our Galaxy. Here, we use epic , our line-by-line differential technique, to measure the stellar parameters – effective temperature T eff, surface gravity log  g , and metallicity [Fe/H] – from moderate-resolution (R ≲ 32 000) spectra of 877 solar twin and analogue candidates (547 at 1– |$4\, {\rm kpc}$|⁠) observed with the High Efficiency and Resolution Multi-Element Spectrograph (HERMES) on the Anglo-Australian Telescope. These are consistent with expectations for T eff and log  g from photometry, and for [Fe/H] from the Besançon stellar population model. epic provides small enough uncertainties (⁠|$\sim 90\, {\rm K}$|⁠ , |$0.08\, {\rm dex}$|⁠ , and |$0.05\, {\rm dex}$|⁠ , respectively), even at the low signal-to-noise ratios available (⁠|${\rm S/N}\gtrsim$| 25 per pixel), to identify 299 new solar analogues (⁠|$\ge 90~{{\ \rm per\ cent}}$| confidence) and 20 solar twins (≥50 per cent confidence), 206 and 12 of which are at 1– |$4\, {\rm kpc}$|⁠. By extending epic to measure line broadening and lithium abundance from HERMES spectra, and with ages derived from isochrone fitting with our stellar parameters, we identify 174 solar analogues at 1– |$4\, {\rm kpc}$| that are relatively inactive, slowly rotating, and with no evidence of spectroscopic binarity. These are the preferred targets for follow-up spectroscopy to measure α. [ABSTRACT FROM AUTHOR]

The Generalized Uncertainty Principle (GUP) has been discussed in the thick braneworld scenario. By considering Rydberg atoms in this background, we show that the spacetime geometry affects Maxwell equations inducing an effective dielectric constant on the space. In its turn, the corrected Coulomb potential by the gravitational interaction yields a deviation on the 3-dimensional Bohr radius. Then, we compute the corrections on the fine structure constant owing to the GUP in higher-dimensional spacetime. We also found constraints for the deformation parameter β and D-dimensional Planck length l D by comparing the predicted deviations with the recent empirical data of the fine structure constant. We compute the intermediate length scale, which in principle may be larger than the Planck length scale. It is conjectured that below such scale Quantum Gravity effects should take place. [ABSTRACT FROM AUTHOR]

In a previous paper, it was explained that the absorption and emission process (AE-process) of Bohr's model of the hydrogen atom must involve an electric charge (i.e., electron) transiting between atomic energy levels instead of quantum jumping; otherwise, there is no way to use the AE-process to predict the fine structure constant. In this paper, it is shown that (1) a complete oscillation of the atomic electron (i.e., an electric charge) and of the induced magnetic field must occur for Bohr's hydrogen atom to emit electromagnetic radiation, and (2) an atomic electron (i.e., electric charge) of Bohr's hydrogen atom can transit between energy levels without the atom emitting electromagnetic radiation. [ABSTRACT FROM AUTHOR]

Accounting for isospin-breaking corrections is critical for achieving subpercent precision in lattice computations of hadronic observables. A way to include QED and strong-isospin-breaking corrections in lattice QCD calculations is to impose C⋆ boundary conditions in space. Here, we demonstrate the computation of a selection of meson and baryon masses on two QCD and five QCD+QED gauge ensembles in this setup, which preserves locality, gauge and translational invariance all through the calculation. The generation of the gauge ensembles is performed for two volumes, and three different values of the renormalized fine-structure constant at the U-symmetric point, corresponding to the SU(3)-symmetric QCD in the two ensembles where the electromagnetic coupling is turned off. We also present our tuning strategy and, to the extent possible, a cost analysis of the simulations with C⋆ boundary conditions. [ABSTRACT FROM AUTHOR]

We present principles of Measurement Quantization (MQ) and approaches to measurement that support the discreteness of measure. Several claims are addressed. Notably, that measure is discrete with respect to the internal frame, non-discrete with respect to the system frame and that length is contracted due to the discreteness of measure. We address the relation of angular measure to momentum, the physical significance of count bounds and that the fundamental measures — more precise expressions for Planck's units — are an emergent property of the internal frame. Quantum experiments by Shwartz, et. al and CODATA provide physical support. We predict and derive values for elementary charge and the gravitational, Hubble, reduced Planck, electric, magnetic, Coulomb, and fine structure constants. We then correlate gravity with electromagnetism (unification). We present expressions for galactic rotation, dark matter, dark energy, and accelerating expansion. MQ advances over Loop Quantum Gravity with two frames, the difference which leads to the physical constants and the laws of nature. We correlate the quantum and cosmological, describing an inflation free quantum epoch, why it ceases and expansion. Therein are solutions to the horizon problem and homogenous, isotropic properties of the universe. Predictions include length contraction unrelated to special or general relativity (SR/GR), 13-digit measures of the gravitational constant, the Planck momentum, and universal mass accretion. A calculation of CMB age, quantity, present-day density and temperature provides additional support. Also offered, discrete solutions to the size and age of the universe, ground state orbital, SR, GR, and equivalence. [ABSTRACT FROM AUTHOR]

Explanations are proposed for several light behaviors using classical mechanics. The Planck-Einstein relation is the starting point. A careful inspection reveals that this relationship has two dynamic interacting entities. One is a free (moving) photon, fp, represented by its angular frequency, x. The other is a proposed, resting, independent, electromagnetic field denoted by the reduced Planck constant S, which is the product of energy and period. Consistent with these entities are several proposals supported by well-established equations. They include the presence of a hidden factor that allows for the photon's internal dynamics, a more precise description of the electromagnetic interactions of gravity with light, the mechanism behind Fraunhofer diffraction, the role of gravity in the fine structure constant, the role of gravity in the refraction of light and its implications for relativity, and the mechanism of Fermat's principle. [ABSTRACT FROM AUTHOR]

Sun-like stars are a new probe of variations in the fine-structure constant, α , via the solar twins approach: velocity separations of close pairs of absorption lines are compared between stars with very similar stellar parameters, i.e. effective temperature, metallicity, and surface gravity within 100 K, 0.1 dex, and 0.2 dex of the Sun's values. Here, we assess possible systematic errors in this approach by analysing ≳10 000 archival exposures from the High-Accuracy Radial Velocity Planetary Searcher (HARPS) of 130 stars covering a much broader range of stellar parameters. We find that each transition pair's separation shows broad, low-order variations with stellar parameters that can be accurately modelled, leaving only a small residual, intrinsic star-to-star scatter of 0–33 m s−1 (average ≈7 m s−1, ≈1 × 10−4 Å at 5000 Å). This limits the precision available from a single pair in a single star. We consider potential systematic errors from a range of instrumental and astrophysical sources (e.g. wavelength calibration, charge transfer inefficiency, stellar magnetic activity, line blending) and conclude that variations in elemental abundances, isotope ratios, and stellar rotational velocities may explain this star-to-star scatter. Finally, we find that the solar twins approach can be extended to solar analogues – within 300 K, 0.3 dex, and 0.4 dex of the Sun's parameters – without significant additional systematic errors, allowing a much larger number of stars to be used as probes of variation in α , including at much larger distances. [ABSTRACT FROM AUTHOR]

The rich absorption spectra of Sun-like stars are enticing probes for variations in the fine-structure constant, α, which gauges the strength of electromagnetism. While individual line wavelengths are sensitive to α, they are also sensitive to physical processes in the stellar atmospheres, which has precluded their use so far. Here we demonstrate a new differential approach using solar twins: velocity separations between close pairs of transitions are compared across stars with very similar physical properties, strongly suppressing astrophysical and instrumental systematic errors. We utilize 423 archival exposures of 18 solar twins from the High-Accuracy Radial velocity Planetary Searcher (HARPS), in which calibration errors can be reduced to ≲3 m s−1. For stars with ≈10 high-signal-to-noise ratio spectra (≥200 per pixel), velocity separations between pairs are measured with ≈10 m s−1 statistical precision. A companion paper assesses a range of systematic error sources using 130 stars, with a greater range of stellar parameters, providing accurate corrections for astrophysical effects and a residual, intrinsic star-to-star scatter of 0–13 m s−1. Within these uncertainties, we find no evidence for velocity separation differences in 17 transition pairs between solar twins. In a second companion paper, this is found to limit local (≲50 pc) variations in α to ≈50 parts per billion, ∼2 orders of magnitude less than other Galactic constraints. [ABSTRACT FROM AUTHOR]

The muonic 2P-2S Lamb shift in muon-electron atoms and ions of helium, lithium, beryllium, and boron with the electron in the ground state was calculated by the perturbation theory using the fine structure constant and the electron-muon mass ratio. The corrections of first- and second-orders of perturbation theory on the Coulomb interaction and nucleus recoil were taken into account. The obtained analytical results were validated numerically using calculations within the variational method. [ABSTRACT FROM AUTHOR]

We explore the possibility of solving the dark energy and the coincidence problems by postulating the massless sector of closed strings. This sector constitutes the gravitational multiplet of string theory and, when applied to four-dimensional cosmology, predicts that the expansion of an open Universe defined in string frame is readily accelerating. We confront the prediction with the late-time cosmological data of Type Ia supernovae and quasar absorption spectrum, which probe the evolutions of the Hubble parameter and possibly the fine-structure constant. We report that these observations are in admirable agreement with the prediction without any dark sector or coincidence problem. We estimate the Hubble constant, H 0 ≃ 71.2 ± 0.2 km / s / Mpc. [ABSTRACT FROM AUTHOR]

We identify two metastable excited states in Sm 10 + highly charged ion as candidates for high accuracy optical clocks. Several atomic properties relevant to optical clock development are calculated using relativistic many-body methods. This includes energy levels, transition amplitudes, lifetimes, scalar polarizabilities, black body radiation shift, and the sensitivity to the fine structure constant variation. We found that the clock transitions are not sensitive to perturbation, e.g., relative black body radiation shifts are ∼ 1 0 − 19 . The enhancement factor for the α variation is ∼ 0.8 for one clock transition and ∼ 16 for another. • Studying the possibility of using metastable states in the Sm 10 + ion for optical clocks. • Calculation of atomic properties relevant to the development of optical clocks. • Demonstrating a small value of the black body radiation shift, ∼ 1 0 − 19 . • Finding a large enhancement factor for the fine-structure constant variation, ∼ 16. [ABSTRACT FROM AUTHOR]

Dr. Jorge S. Diaz's JK^0 YouTube channel features videos on the physics of explosions, shockwaves, and early atomic and quantum physics. His content includes detailed explanations of topics like the Stern-Gerlach experiment and the Franck-Hertz experiment, suitable for undergraduate physics majors. Diaz's engaging storytelling style and richly illustrated presentations make his channel a valuable resource for students interested in quantum mechanics history and related mathematical concepts. [Extracted from the article]

The fundamental physical constants are at the root of physics theories, but no theoretical framework provides their experimental values. In addition, they are assumed to be independent of each other. Here, we present two valuable dimensionless numbers based on vacuum properties and fundamental constants. The value of these dimensionless numbers provokes questioning, since they are of order 101. In particular, they mean that it is possible to build a velocity and a parameter homogeneous to the Planck constant of the same order as the speed of light and the Planck constant respectively, only based on five well-known physical parameters. These formulas are very unlikely to be two coincidences and suggest that the parameters involved depend on each other. They also seem to indicate that light is a material wave and quantum mechanics is a deterministic theory. A link between these numbers and the fine-structure constant is also established. [ABSTRACT FROM AUTHOR]

The recent Fermilab muon g - 2 result and the same for electron due to fine-structure constant measurement through 133 Cs matter-wave interferometry are probed in relation to MSSM with non-holomorphic (NH) trilinear soft SUSY breaking terms, referred to as NHSSM. Supersymmetric contributions to charged lepton (g - 2) l can be enhanced via the new trilinear terms involving a wrong Higgs coupling with left and right-handed scalars. Bino-slepton loop is used to enhance the SUSY contribution to g - 2 where wino mass stays at 1.5 TeV and the left and right slepton mass parameters for the first two generations are considered to be the same. Unlike many MSSM-based analyses completed before, the model does not require a light electroweakino, or light sleptons, or unequal left and right slepton masses, or a very large higgsino mass parameter. In absence of popular UV complete models, we treat the NH terms at par with MSSM soft terms, in a model independent framework of Minimal Effective Supersymmetry. The first part of the analysis involves the study of (g - 2) μ constraint along with the limits from Higgs mass, B-physics, collider data, direct detection of dark matter (DM), while focusing on a higgsino DM which is underabundant in nature. We then impose the constraint from electron g - 2 where a large Yukawa threshold correction (an outcome of NHSSM) and opposite signs of trilinear NH coefficients associated with μ and e fields are used to satisfy the dual limits of Δ a μ and Δ a e (where the latter comes with negative sign). Varying Yukawa threshold corrections further provide the necessary flavor-dependent enhancement of Δ a e / m e 2 compared to that of Δ a μ / m μ 2 . A larger Yukawa threshold correction through A e ′ for y e also takes away the direct proportionality of a e with respect to tan β . With a finite intercept, a e becomes only an increasing function of tan β . We identified the available parameter space in the two cases while also satisfying the ATLAS data from slepton pair production searches in the plane of slepton mass parameter and the mass of the lightest neutralino. [ABSTRACT FROM AUTHOR]

Within the framework of the recently proposed Taylor–Lagrange regularization procedure, we reanalyze the calculation of radiative corrections in quantum electrodynamics (QED) at next to leading order. Starting from a well-defined local bare Lagrangian, the use of this regularization procedure enables us to manipulate fully finite elementary amplitudes in the ultra-violet (UV) as well as infrared (IR) regimes, in physical D = 4 space–time dimensions and for physical massless photons, as required by gauge invariance. We can thus separately calculate the electromagnetic form factors of the electron and the cross-section for real photon emission, each quantity being finite in these physical conditions. We then discuss the renormalization group (RG) equations within this regularization procedure. Thanks to the taming of IR divergencies, the RG equation associated to the (physical) effective charge exhibits an UV stable fixed point at α ∗ = 0 , showing an asymptotic freedom-type behavior. We finally consider the case of two mass scales, one low and one heavy, paying particular attention to the natural decoupling properties between heavy and light degrees of freedom. As a direct consequence, the fine structure constant should be zero in the limit of massless electrons. [ABSTRACT FROM AUTHOR]

Recently, the CDF Collaboration has announced a new precise measurement of the W-boson mass MW that deviates from the Standard Model (SM) prediction by 7σ. The discrepancy in MW is about ΔW ≃ 70 MeV and is probably caused by a beyond the SM physics. Within a certain scenario of extension of the SM, we obtain the relation ΔW ≃ 3 α 8 π MW ≃ 70 MeV, where α is the electromagnetic fine structure constant. The main conjecture is the appearance of longitudinal components of the W-bosons as the Goldstone bosons of a spontaneously broken additional SU(2) global symmetry at distances much smaller than the electroweak symmetry breaking scale rEWSB. We argue that within this scenario, the masses of charged Higgs scalars can obtain an electromagnetic radiative contribution which enhances the observed value of MW± with respect to the usual SM prediction. Our relation for ΔW follows from the known one-loop result for the corresponding effective Coleman–Weinberg potential in combination with the Weinberg sum rules. [ABSTRACT FROM AUTHOR]