Fine Structure Constant Research Articles

Theoretical and observational implications of Planck’s constant as a running fine structure constant

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.

Constraining fundamental constants with fast radio bursts: unveiling the role of energy scale

ABSTRACT 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.

About Dark Energy

We have considered the physical space filled by a quantum fluid made up of discrete elements organized into several coexisting phases. In this model, what we call “dark energy” appears as main phase of the Vacuum, we propose here that it is the phase associated with the fundamental level of this quantum fluid. After an examination of its main properties, we show that the refractive index of the real vacuum, which is consisting largely of dark energy and fossil radiation, has an “abnormal” value compared to it. We thus verify that the inverse of the fine structure constant associated with the dark energy is indeed the integer 137.

Quantum duality in electromagnetism and the fine structure constant

We describe the interplay between electric-magnetic duality and higher symmetry in Maxwell theory. When the fine structure constant is rational, the theory admits noninvertible symmetries which can be realized as composites of electric-magnetic duality and gauging a discrete subgroup of the one-form global symmetry. These noninvertible symmetries are approximate quantum invariances of the natural world which emerge in the infrared below the mass scale of charged particles. We construct these symmetries explicitly as topological defects and illustrate their action on local and extended operators. We also describe their action on boundary conditions and illustrate some consequences of the symmetry for Hilbert spaces of the theory defined in finite volume. Published by the American Physical Society 2024

Laser spectroscopy of triply charged 229Th isomer for a nuclear clock.

Thorium-229 (229Th) possesses an optical nuclear transition between the ground state (229gTh) and low-lying isomer (229mTh). A nuclear clock based on this nuclear-transition frequency is expected to surpass existing atomic clocks owing to its insusceptibility to surrounding fields1-5. In contrast to other charge states, triply charged 229Th (229Th3+) is the most suitable for highly accurate nuclear clocks because it has closed electronic transitions that enable laser cooling, laser-induced fluorescence detection and state preparation of ions1,6-8. Although laser spectroscopic studies of 229Th3+ in the nuclear ground state have been performed8, properties of 229mTh3+, including its nuclear decay lifetime that is essential to specify the intrinsic linewidth of the nuclear-clock transition, remain unknown. Here we report the trapping of 229mTh3+ continuously supplied by a 233U source and the determination of nuclear decay half-life of the isolated 229mTh3+ to be through nuclear-state-selective laser spectroscopy. Furthermore, by determining the hyperfine constants of 229mTh3+, we reduced the uncertainty of the sensitivity of the 229Th nuclear clock to variations in the fine-structure constant by a factor of four. These results offer key parameters for the 229Th3+ nuclear clock and its applications in the search for new physics.

Precision Measurement of the n=2 Triplet P J=1 to J=0 Fine Structure of Atomic Helium Using Frequency-Offset Separated Oscillatory Fields.

Increasing accuracy of the theory and experiment of the n=2 ^{3}P fine structure of helium has allowed for increasingly precise tests of quantum electrodynamics (QED), determinations of the fine-structure constant α, and limitations on possible beyond the standard model physics. Here we present a 2ppb measurement of the J=1 to J=0 interval. The measurement is performed using frequency-offset separated-oscillatory fields. Our result of 29 616 955 018(60)Hz represents a landmark for helium fine-structure measurements, and, for the first time, will allow for a 1-ppb determination of the fine-structure constant when QED theory for the interval is improved.

Optimizing the heat capacities of sphalerite phases as single system, or how nuclear physics can help physical chemistry

The correct mathematical description of heat capacities Cp in a wide range of temperatures is still unsolved problem. A fragmental description of some phases is like a vision of one part of a large mosaic picture. A single description of Cp or other property of a phase of any isostructural series does not allow one to see the integrity of the entire ensemble. We propose a special mathematical model to describe Cp in a wide temperature range for a whole large class of isostructural sphalerite phases. In the proposed model, it is believed that an ideal crystal does not have any foreign inclusions, defects, or dislocations. The group IV elements (Si, Ge, α-Sn and diamond-like Pb) were taken as the basis, with flerovium (114Fl) closing this group. There should be no other elements in this group according to the fine structure constant (α) (or the Sommerfeld constant). As a consequence, the limiting value of the heat capacities of phases with a sphalerite structure falls on the element 114 (114Fl) and has a value of Cp = 30.5 ± 0.3 J · mol-at−1 · K−1. This value was obtained as a maximal virtual point Cp of the last element (114Fl) of group IV and corresponds to Ln (Cp/R) = 1.30 ± 0.01 for the isotherms ln (Cp/R) vs Ln(N), where N is an atomic number of an element of group IV or the sum of the atomic numbers of AIIIBV or AIIBVI compounds per mole-atom. The common point of heat capacity attributable to flerovium is obtained from the linear equations Ср/R vs Ln(N) at low temperatures from 25 to 35K. For only pure elements of group IV (Si, Ge, α-Sn and diamond-like Pb), flerovium closes this group, and there are no other elements behind it, according to α. The maximum heat capacity of flerovium can be taken as 30.5 J·mol-at−1·K−1 with an accuracy of 1%. As the temperature decreases, this value slowly decreases (within 1%), and then, when it approaches 0 K, it drops sharply to 0 J·mol-at−1·K−1. To describe the set of the isostructural experimental data Cp(T) for diamond-like phases in solid state as a whole system, here we used a special multi-parameter family of functions. For each substance, the parameters are found by minimizing the discrepancy between the theoretical dependence Cp(T) and corresponding experimental data. The dependence of the heat capacities for elements of group IV (Si, Ge, α-Sn, diamond-like Pb, Fl) at fixed temperatures on Ln(N), where N is the atomic number or the demi sum of the atomic numbers of phases AIIBVI or AIIIBV. In this case, either a break point or an inflection point attributable to germanium is observed for parameter dependencies on Ln(N).

Characterization of the ESPRESSO line-spread function and improvement of the wavelength calibration accuracy

ABSTRACT 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.

Derivation of the Schrödinger equation from QED

The Schrödinger equation relates the emergent quantities of wavefunction and electric potential and is postulated as a principle of quantum physics or obtained heuristically. However, physical consistency requires that the Schrödinger equation is a low-energy dynamical condition we can derive from the foundations of quantum electrodynamics. Due to the small value of the electromagnetic coupling constant, we show that the electric potential accurately represents the contributions of intermediate low-energy photon exchanges. Then, from the total nonrelativistic energy relation, we see that the dominant term of the electron wavefunction is a superposition of plane waves that satisfies the Schrödinger equation. Our derivation shows that the Schrödinger equation is not an energy conservation relation because its middle term does not represent the electron kinetic energy as assumed. We analyze the physical content of the Schrödinger equation and verify our assessments by calculating and evaluating the physical quantities in the ground state of the hydrogen atom. Furthermore, we explain why nonrelativistic quantum dynamics differs from classical dynamics. Undergraduate students can follow the derivation because it involves fundamental physical concepts and mathematical expressions, and we explain every step.

Multiple soft-photon emission at next-to-leading power to all orders

This paper derives a next-to-leading power (NLP) soft theorem for multi-photon emission to all orders in the electromagnetic coupling constant, generalising the leading-power theorem of Yennie, Frautschi, and Suura. Working in the QED version of heavy-quark effective theory, multi-emission amplitudes are shown to reduce to single- and double-radiation contributions only. Single soft-photon emission, in turn, is described by the recent all-order extension of the Low-Burnett-Kroll theorem, where the tree-level formula is supplemented with a one-loop exact soft function. The same approach is used in this article to prove that the genuine double-emission contribution is tree-level exact. As a validation and a first non-trivial application of the multi-photon theorem, the real-real-virtual electron-line corrections to muon-electron scattering are calculated at NLP in the soft limit.

Cosmological variation of the proton-to-electron mass ratio constrained by strong gravitational fields

Exploring the cosmological variations of fundamental dimensionless constants, such as the fine-structure constant, [Formula: see text], the proton-to-electron mass ratio, [Formula: see text], 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 [Formula: see text] over extended time scales, [Formula: see text], incorporating the gravitational redshift [Formula: see text]. This finding represents a new tool for checking the parameters for Grand Unified Theories (GUTs).

Mathematical definition of the fine-structure constant: A clue for fundamental couplings in astrophysics

Astrophysical tests of the stability—or not—of fundamental couplings (e.g., can the numerical value ∼1/137 of the fine-structure constant α = e2/ℏc vary with astronomical time?) are a very active area of observational research. Using a specific α-free non-relativistic and nonlinear isotropic quantum model compatible with its quantum electrodynamics (QED) counterpart yields the 99% accurate solution α = 7.364 × 10−3 vs its experimental value 7.297 × 10−3. The ∼1% error is due to the deliberate use of mean-field Hartree approximation involving lowest-order QED in the calculations. The present theory has been checked by changing the geometry of the model. Moreover, it fits the mathematical solution of the original nonlinear integro-differential Hartree system by use of a rapidly convergent series of nonlinear eigenstates [G. Reinisch, Phys. Lett. A 498, 129347 (2024)]. These results strongly suggest the mathematical transcendental nature—e.g., like for π or e—of α’s numerical value of ∼1/137 and, hence, its astrophysical as well as its cosmological stability.

Towards the full Heisenberg-Euler effective action at large N

We study the Heisenberg-Euler effective action in constant electromagnetic fields F¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{F} $$\\end{document} for QED with N charged particle flavors of the same mass and charge e in the large N limit characterized by sending N → ∞ while keeping Ne2 ∼ eF¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ e\\overline{F} $$\\end{document} ∼ N0 fixed. This immediately implies that contributions that scale with inverse powers of N can be neglected and the resulting effective action scales linearly with N . Interestingly, due to the presence of one-particle reducible diagrams, even in this limit the Heisenberg-Euler effective action receives contributions of arbitrary loop order. In particular for the special cases of electric- and magnetic-like field configurations we construct an explicit expression for the associated effective Lagrangian that, upon extremization for two constant scalar coefficients, allows to evaluate its full, all-order result at arbitrarily large field strengths. We demonstrate that our manifestly nonperturbative expression correctly reproduces the known results for the Heisenberg-Euler effective action at large N , namely its all-loop strong field limit and its low-order perturbative expansion in powers of the fine-structure constant.

A Classical Interpretation of the Quantum Universe Extrapolated from the Fine Structure Constant

The Fine Structure Constant (FSC) model of the universe is a conceptual perspective based on a classical method for analyzing the Fine Structure Constant (α). A Python algorithm calculates prime number property sets where the sum of the elements equals the whole number values for αequal to 137 and 139. A hybrid coupling of these property sets produces a U{137/139}twin prime metaverse where α=137.036, an almost exact match to the observed value. The FSC Model projects that the Fractional Coupling Constant (α137= 0.036)is a more accurate measure of its relative electromagnetic (EM) strength. This same calculation is used to determine the Fractional Coupling Constants (αm) for the twin prime metaverses (U{2/3}, U{3/5}, U{5/7}through U{197/199}) to estimate their respective electromagnetic forces. The results suggest that this model mirrors our observable universe and offers an abstract landscape into the quantum nature of electromagnetic forces, including Baryonic Matter, Dark Matter, Dark Energy, and a possible variable speed of light.

Radiation of a short linear antenna above a topologically insulating half-space

The topological magnetoelectric effect is a unique macroscopic manifestation of quantum states of matter possessing topological order and it is described by axion electrodynamics. In three-dimensional topological insulators, for instance, the axion coupling is of the order of the fine structure constant, and hence, a perturbative analysis of the field equations is plenty justified. In this paper, we use Green’s function techniques to obtain time-dependent solutions to the axion field equations in the presence of a planar domain wall separating two media with different topological order. We apply our results to investigate the radiation of a short linear antenna near the domain wall.

A mass scale law connecting cosmophysics to microphysics

We introduce different mass scales corresponding to the Universe, fermion stars, mini boson stars, Planck black holes, the electron, the neutrino, and the cosmon. These mass scales are obtained by combining the maximum mass of fermion stars, boson stars and soliton stars set by quantum mechanics and general relativity with the Eddington relation connecting the mass me of the electron to the cosmological constant Λ. In this manner, we can express the mass of these objects in terms of the fundamental constants of physics G, c, ħ and Λ. By normalizing the mass Ma of these objects by the Planck mass MP, we find that Ma/MP∼χa/6, where χ∼ρP/ρΛ∼10120 is the “largest large number” in Nature (the ratio of the Planck density on the Einstein cosmological density) and a=3,2,1,0,−1,−2,−3 for the Universe, fermion stars, mini boson stars, Planck black holes, the electron, the neutrino, and the cosmon respectively. This formula suggests an interesting symmetrical mass scale law connecting cosmophysics (Universe, fermion stars, mini boson stars) to microphysics (electron, neutrino, cosmon). A generalization of this law including the earth mass and another neutrino mass scale is proposed. We highlight an accurate form of Eddington relation me≃α(Λħ4/G2)1/6 or Λ≃G2me6/α6ħ4=α−6(me/MP)6lP−2, where α=e2/ħc≃1/137 is the fine structure constant, and provide different heuristic derivations of this relation. We consider another relation Λ=Gc(mΛ∗)4/ħ3=(mΛ∗/MP)4lP−2, where mΛ∗=(Λħ3/Gc)1/4 is the neutrino mass. We relate these relations to the two expressions of the vacuum energy density given by Zeldovich in 1968. We suggest that the dark energy particle (cosmon) of mass mΛ=ħΛ/c could be a quantum of mass and entropy so that Λ=mΛ2c2/ħ2=(mΛ/MP)2lP−2. We relate the large number 10120 to the total number of degrees of freedom (or number of cosmons) in the universe. Finally, we give hints how to possibly solve the cosmological constant problem, the cosmic coincidence problem, and the large number coincidence problem.

Bleustein-Gulyaev waves in topological piezoelectric crystals

A topological insulator with piezoelectric properties is considered, and an action is proposed to find the equations of motion and the constitutive relations of the generalized coordinates of electrodynamic and elastic origin, paying special attention to the restructuring induced by the topological properties. The results are used to demonstrate that the electromechanical factor of the Bleustein-Gulyaev waves on the surface of a topological piezoelectric crystal of class C6v in contact with vacuum undergoes a second-order correction in the fine structure constant, associated with the topological properties.

Free electron laser prepared high-intensity metastable helium and helium-like ions

In the precision spectroscopy of few-electron atoms, the generation of high-intensity metastable helium atoms and helium-like ions is crucial for implementing experimental studies as well as a critical factor for improving the signal-to-noise ratio of experimental measurements. With the rapid development of free-electron laser (FEL) and technology, FEL wavelengths extend from hard X-rays to soft X-rays and even vacuum ultraviolet bands. Meanwhile, laser pulses with ultra-fast, ultra-intense and high repetition frequencies are realized, thus making it possible for FEL to prepare single-quantum state atoms/ions with high efficiency. In this work, we propose an experimental method for obtaining high-intensity single-quantum state helium atoms and helium-like ions by using FEL. The preparation efficiency can be calculated by solving the master equation of light-atom interaction. Considering the experimental parameters involved in this work, we predict that the efficiencies of preparing metastable 2<sup>3</sup>S He, Li<sup>+</sup> and Be<sup>2+</sup> are about 3%, 6% and 2%, respectively. Compared with the common preparation methods such as gas discharge and electron bombardment, a state-of-the-art laser excitation method can not only increase the preparation efficiency, but also reduce the effects of high-energy stray particles such as electrons, ions, and photons generated during discharge. Furthermore, combined with the laser preparation technique, the sophisticated ion confinement technique, which can ensure a long interaction time between the ions and laser, increases the efficiency of metastable Li<sup>+</sup> and Be<sup>2+</sup> by several orders of magnitude. Therefore, the preparation of high-intensity metastable helium and helium-like ions can improve the measurement accuracy of precision spectroscopy of atoms and ions. A new experimental method, based on FEL, to study the fine structure energy levels 2<sup>3</sup>P of helium, has the potential to obtain the results with an accuracy exceeding the sub-kHz level. Thus, the high-precision fine structure constants can be determined with the development of high-order quantum electrodynamics theory. In order to measure energy levels with higher accuracy, a new detection technique, which can reduce or even avoid more systematic effects, must be developed. For example, the quantum interference effect, which has been proposed in recent years, seriously affects the accuracy of fine-structure energy levels. If the interference phenomenon of spontaneous radiation between different excited states can be avoided in the detection process, the measurement accuracy will not be affected by this quantum interference effect. High-intensity metastable atoms or ions in chemical reaction dynamics studies also have better chances to investigate reaction mechanisms. In summary, the FEL preparation of high-intensity metastable helium atoms and helium-like ions proposed in this work will lay an important foundation for developing cold atom physics and chemical reaction dynamics.

A Spectroscopic Investigation of the Lowest Electronic States of the I+ 2 Cation as a Candidate for Detecting the Time Variation of Fundamental Constants

The four lowest Ω substates (X2Π3/2,g, X2Π1/2,g, A2Π3/2,u and A2Π1/2,u) of the I+ 2 cation have been studied by high-precision ab initio calculations in comparison with experimental high-resolution absorption spectra. The potential energy curves were calculated using the multi-reference configuration interaction (MRCI) method and Dirac method, respectively. Rovibrational levels of these electronic states were derived by solving the radial Schrödinger rovibrational equation. Molecular constants were obtained in fitting energy levels to a spectroscopic model. Using the fit spectroscopic constants and newly calculated transition dipole moment matrix elements, line strengths of vibronic bands in the A2Π3/2,u- X2Π3/2,g system, as well as Einstein A coefficients for 45 of these bands with ν′ = 11−19 and ν′′ = 1−5, have been derived. The Einstein A coefficients were used to compute radiative lifetimes of the ν′ = 11−19 vibrational levels of the A2Π3/2,u state. Enhancement factors for detecting the variation of the fine-structure constant (α) and the proton-to-electron mass ratio(µ) using transitions between nearly degenerate rovibronic levels of these low-lying states have been calculated.

Non-perturbative SQED beta function using the functional renormalization group approach and the NSVZ exact beta function

Abstract 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.