Fundamental Constants Of Nature Research Articles

Non-parametric reconstruction of the fine structure constant with galaxy clusters

Testing possible variations in fundamental constants of nature is a crucial endeavor in observational cosmology. This paper investigates potential cosmological variations in the fine structure constant (α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}) through a non-parametric approach, using galaxy cluster observations as the primary cosmological probe. We employ two methodologies based on galaxy cluster gas mass fraction measurements derived from X-ray and Sunyaev–Zeldovich observations, along with luminosity distances from type Ia supernovae. We also explore how different values of the Hubble constant (H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document}) impact the variation of α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} across cosmic history. When using the Planck satellite’s H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document} observations, a constant α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} is ruled out at approximately the 3σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma $$\\end{document} confidence level for z≲0.5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z \\lesssim 0.5$$\\end{document}. Conversely, employing local estimates of H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document} restores agreement with a constant α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}.

The cosmological constant and energy quantization in hydrogen atom in light of a doubly special relativity with a minimum speed

We show the existence of an invariant minimum speed in space–time as a new fundamental constant of nature by forming the basis of a doubly special relativity so-called Symmetrical Special Relativity (SSR). Such an observer-independent minimum speed emerges from the Dirac’s Large Number Hypothesis (LNH), which leads us to build SSR-theory. This allows us to understand that the hydrogen atom represents the most stable bound state in the universe as being a fundamental structure in space–time with two speed limits, i.e., the speed of light c and a minimum speed V. So the symmetry in space–time given by an invariant minimum speed, which has origin in the electrical and gravitational bound states in hydrogen atom is able to provide a deeper understanding of the proton-electron mass ratio. We investigate how the minimum speed plays a fundamental role in the quantization of energy in hydrogen atom. The minimum speed V is related to a preferred background frame (ultra-referential SV) represented by the surface of a dark cone forbidden to the world line of any particle. It is related to the vacuum energy that leads to the cosmological constant. An investigation of SSR is done and a hypothetical experiment of Bose–Einstein condensation is proposed to detect the minimum speed as a possible Lorentz violation at very low energies.

Fundamental Constants of Nature: Building Blocks of Metrology

Fundamental Constants of Nature: Building Blocks of Metrology

Universal lower bound on orbital periods

It is proved, using the curved line element of a spherically symmetric charged object in general relativity and the Schwinger discharge mechanism of quantum field theory, that the orbital periods T_{infty } of test particles around central compact objects as measured by flat-space asymptotic observers are fundamentally bounded from below. The lower bound on orbital periods becomes universal (independent of the mass M of the central compact object) in the dimensionless ME_{text {c}}gg 1 regime, in which case it can be expressed in terms of the electric charge e and the proper mass m_{e} of the lightest charged particle in nature: T_{infty }>{{2pi ehbar }over {sqrt{G}c^2 m^2_{e}}} (here E_{text {c}}=m^2_{e}/ehbar is the critical electric field for pair production). The explicit dependence of the bound on the fundamental constants of nature {G,c,hbar } suggests that it may reflect a fundamental physical property of the elusive quantum theory of gravity.

On the Philosophical Significance of the Reform of the International System of Units (SI): A Double-Adjustment Account of Scientific Enquiry

Abstract The philosophical significance attached to the construction of systems of units has traditionally been confined to the notion of convention, while their adoption was considered to be the exclusive province of the history and sociology of science. Against this tradition, a close articulation between history, philosophy, and sociology of science is needed in order to analyse the recent reform of the International system of units (SI). In the new SI, units are redefined on the basis of certain fundamental constants of nature, established by physical theories, whose values are fixed without uncertainty. The purpose of this article is to show that the redefinition of SI units, far from being a convention, involves a holistic reconstruction of our concepts of quantities from accepted theoretical laws. Fixing the values of the defining constants stabilizes these laws within the framework of physics through a twofold adjustment procedure that ensures both a semantic coordination between theory and world and an intersubjective coordination between human agents required by social activities. This double adjustment implies a treatment of uncertainties that results in closely entwining the pursuit of truth as correspondence and truth as coherence which turn out to be complementary, thus highlighting the anthropological underpinnings of scientific realism.

Vacuum energy density measured from cosmological data

Within the ΛCDM cosmological model, the absolute value of Einstein's cosmological constant Λ, sometimes expressed as the gravitating mass-energy density ρ Λ of the physical vacuum, is a fundamental constant of nature, whose accurate measurement plays a central role in testing some proposed theories of quantum gravity. Several combinations of currently public cosmological data and an assumed flat ΛCDM cosmological model are used here to make a joint Bayesian inference on the combination of conventional parameters ΩΛ h 2 that corresponds to the absolute physical density ρ Λ. In physical units, we obtain ρ Λ = (60.3 ± 1.3)× 10-31 g/cm3, the most accurate constraint to date, with an absolute calibration of cosmological measurements based on CMB temperature. Significantly different values are obtained with calibrations that use a local distance scale, mainly connected to systematic differences in the value of the Hubble constant. It is suggested that future comprehensive cosmological parameter studies assuming the ΛCDM model include constraints on the vacuum density.

Electron Mass Is Specified by Five Fundamental Constants, <i>a</i>, <i>ħ</i>, <i>G</i>, Λ, and Ω<sub>Λ</sub>, from Quantum Mechanics and General Relativity

Electron mass has been considered a fundamental constant of nature that cannot be calculated from other constants such as Planck’s constant ħ and gravitational constant G. In contrast, holographic analysis takes account of the finite amount of information available to describe the universe and specifies electron mass to six significant figures in terms of five fundamental constants: fine structure constant a, ħ , G, cosmological constant Λ, and vacuum fraction ΩΛ of critical density. A holographic analysis accounts for charge conservation, mass quantization, and baryon/antibaryon ratio. A holographic analysis relates electromagnetism and gravitation, specifies electron Compton wavelength in terms of Planck length and cosmological event horizon radius, and has implications for charged Standard Model fermion masses, minimum stellar mass at redshift z, and use of continuum mathematics in a discontinuous universe.

Robust laboratory limits on a cosmological spatial gradient in the electromagnetic fine-structure constant from accelerometer experiments

Quasar absorption spectral data indicate the presence of a spatial gradient in the electromagnetic fine-structure constant $\ensuremath{\alpha}$ on cosmological length scales. We point out that experiments with accelerometers, including torsion pendula and atom interferometers, can be used as sensitive probes of cosmological spatial gradients in the fundamental constants of nature, which give rise to equivalence-principle-violating forces on test masses. Using laboratory data from the E\"ot-Wash experiment, we constrain spatial gradients in $\ensuremath{\alpha}$ along any direction to be $|\mathbf{\ensuremath{\nabla}}\ensuremath{\alpha}/\ensuremath{\alpha}|<6.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}{(\text{Glyr})}^{\ensuremath{-}1}$ at $95%$ confidence level. Our result represents an order of magnitude improvement over laboratory bounds from clock-based searches for a spatial gradient in $\ensuremath{\alpha}$ directed along the observed cosmological $\ensuremath{\alpha}$-dipole axis. Improvements to accelerometer experiments in the foreseeable future are expected to provide sufficient sensitivity to test the cosmological $\ensuremath{\alpha}$ dipole seen in astrophysical data.

Probing fast oscillating scalar dark matter with atoms and molecules

Light scalar dark matter (DM) with scalar couplings to matter is expected within several scenarios to induce variations in the fundamental constants of nature. Such variations can be searched for, among other ways, via atomic spectroscopy. Sensitive atomic observables arise primarily due to possible changes in the fine-structure constant or the electron mass. Most of the searches to date have focused on slow variations of the constants (i.e. modulation frequencies <1 Hz). In a recent experiment (2019 Phys. Rev. Lett. 123 141102) called weekend relaxion-search laboratory (WReSL), we reported on a direct search for rapid variations in the radio-frequency band. Such a search is particularly motivated within a class of relaxion DM models. We discuss the WReSL experiment, report on progress toward improved measurements of rapid fundamental constant variations, and discuss the planned extension of the work to molecules, in which rapid variations of the nuclear mass can be sensitively searched for.

Majorana bosonic quasiparticles from twisted photons in free space

The speed of light in vacuum, $c$, is a fundamental constant of nature. Photons belonging to a structured beam of finite transverse size, generated by a spatial light modulator, have been observed to travel with a group velocity, $v_g$, which is smaller than $c$ also when propagating in vacuum [1-3]. This is an effect that depends on the geometry of the beam. From quantum mechanical considerations, these photons must in any case propagate at the speed of light. This paradox can be resolved by taking into account a projection effect. What was measured in these experiments as group velocity was in fact its projection onto the beam propagation axis [4]. This depends on the divergence of the beams used in these experiments. We have found that for hypergeometric beams carrying orbital angular momentum (OAM), generated by sources with equal aperture [5-8], $v_g$ obeys an OAM/velocity relationship similar to that proposed by Majorana between spin and mass for bosonic and fermionic relativistic particles. This relationship, depending on the geometrical properties of the beam, can pave the way for an alternative estimation of OAM or to implement a time buffer in optical communications.

A Cosmological View for the Time - Variation of the Fundamental Constants of Nature

Time variation of constants of nature is still a question of debate among astronomers, physicists, geologists, and palaeontologists. But are the fundamental physical constants really varying in space or time and how changing these parameters may occur?. Paul Dirac was interested in this question in the large number hypothesis (LNH). He arrived by coincidence at the revolutionary hypothesis that the gravitational constant G should be varied inversely with the cosmic time t. LNH sparked off many ideas and arguments about the possibility of time or space variations of the fundamental constants of nature. In this work, we review details and arguments regarding the time and space variation of dimensional and dimensionless constants based on a detailed comparison for the recorded literature over about one and a half-century.

Position Dependent Planck’s Constant in a Frequency-Conserving Schrödinger Equation

There is controversial evidence that Planck’s constant shows unexpected variations with altitude above the earth due to Kentosh and Mohageg, and yearly systematic changes with the orbit of the earth about the sun due to Hutchin. Many others have postulated that the fundamental constants of nature are not constant, either in locally flat reference frames, or on larger scales. This work is a mathematical study examining the impact of a position dependent Planck’s constant in the Schrödinger equation. With no modifications to the equation, the Hamiltonian becomes a non-Hermitian radial frequency operator. The frequency operator does not conserve normalization, time evolution is no longer unitary, and frequency eigenvalues can be complex. The wavefunction must continually be normalized at each time in order that operators commuting with the frequency operator produce constants of the motion. To eliminate these problems, the frequency operator is replaced with a symmetrizing anti-commutator so that it is once again Hermitian. It is found that particles statistically avoid regions of higher Planck’s constant in the absence of an external potential. Frequency is conserved, and the total frequency equals “kinetic frequency” plus “potential frequency”. No straightforward connection to classical mechanics is found, that is, the Ehrenfest’s theorems are more complicated, and the usual quantities related by them can be complex or imaginary. Energy is conserved only locally with small gradients in Planck’s constant. Two Lagrangian densities are investigated to determine whether they result in a classical field equation of motion resembling the frequency-conserving Schrödinger equation. The first Largrangian is the “energy squared” form, the second is a “frequency squared” form. Neither reproduces the target equation, and it is concluded that the frequency-conserving Schrödinger equation may defy deduction from field theory.

Entropy bounds and nonlinear electrodynamics

Bekenstein's inequality sets a bound on the entropy of a charged macroscopic body. Such a bound is understood as a universal relation between physical quantities and fundamental constants of nature that should be valid for any physical system. We reanalyze the steps that lead to this entropy bound considering a charged object in conformity to Born-Infeld electrodynamics and show that the bound depends of the underlying theory used to describe the physical system. Our result shows that the nonlinear contribution to the electrostatic self-energy causes a raise in the entropy bound. As an intermediate step to obtain this result, we exhibit a general way to calculate the form of the electric field for a given nonlinear electrodynamics in Schwarzschild spacetime.

Scalar Dark Matter in the Radio-Frequency Band: Atomic-Spectroscopy Search Results.

Among the prominent candidates for dark matter are bosonic fields with small scalar couplings to the standard-model particles. Several techniques are employed to search for such couplings, and the current best constraints are derived from tests of gravity or atomic probes. In experiments employing atoms, observables would arise from expected dark-matter-induced oscillations in the fundamental constants of nature. These studies are primarily sensitive to underlying particle masses below 10^{-14} eV. We present a method to search for fast oscillations of fundamental constants using atomic spectroscopy in cesium vapor. We demonstrate sensitivity to scalar interactions of dark matter associated with a particle mass in the range 8×10^{-11} to 4×10^{-7} eV. In this range our experiment yields constraints on such interactions, which within the framework of an astronomical-size dark matter structure are comparable with, or better than, those provided by experiments probing deviations from the law of gravity.

Measuring gravitational constant using a planetary system constructed with levitated superconducting test masses

Newton’s gravitational constant G is the least known fundamental constant of nature, partly because the gravity signal produced in the laboratory is extremely weak and difficult to measure accurately. There also seem to be unknown systematics in many G measurements. Since Cavendish made the first measurement of G with a torsion balance over two hundred years ago, torsion balances have been used in many G experiments, but uncorrected anelasticity of torsion fibers make the results questionable. We present a new method of G measurement by using a superconducting gravity gradiometer constructed with levitated test masses, which is free from the irregularities of mechanical suspension. The detector is rotated to null the gravity field from the source mass by centrifugal acceleration, forming an artificial planetary system. We show that this experiment can potentially measure G with accuracy better than 10 ppm.

Measurements of the gravitational constant using two independent methods.

The Newtonian gravitational constant, G, is one of the most fundamental constants of nature, but we still do not have an accurate value for it. Despite two centuries of experimental effort, the value of G remains the least precisely known of the fundamental constants. A discrepancy of up to 0.05 per cent in recent determinations of G suggests that there may be undiscovered systematic errors in the various existing methods. One way toresolve this issue is to measure G usinga number of methods that are unlikely to involve the same systematic effects. Here we report two independent determinations of G using torsion pendulum experiments with the time-of-swing method and the angular-acceleration-feedback method. We obtain G values of 6.674184 × 10-11 and 6.674484 × 10-11 cubic metres per kilogram per second squared, with relative standard uncertainties of 11.64 and 11.61 parts per million, respectively. These values have the smallest uncertainties reported until now, and both agree with the latest recommended value within two standard deviations.

Concept study of measuring gravitational constant using superconducting gravity gradiometer

Newton’s gravitational constant G is the least known fundamental constant of nature. Since Cavendish made the first measurement of G with a torsion balance over two hundred years ago, the best results of G have been obtained by using torsion balances. However, the uncorrected anelasticity of torsion fibers makes the results questionable. We present a new method of G measurement by using a superconducting gravity gradiometer constructed with levitated test masses, which is free from the irregularities of mechanical suspension. The superconducting gravity gradiometer is rotated to generate a centrifugal acceleration that nulls the gravity field of the source mass, forming an artificial planetary system. This experiment has a potential accuracy of G better than 10 ppm.

Quantum of temperature necessary for the thermal electron excitation in a one–dimensional metal

An analysis of the electron specific heat of a quasi one dimensional free electron system leads to conclusion that some minimal quantum of temperature should be applied to the system in order to promote the excitation of an electron present on the Fermi level The value of the minimal excitation temperature depends on the length of the one dimensional potential box containing the electrons the quantum state of the electron and the actual temperature of the system as well as the fundamental constants of nature

Big bang nucleosynthesis with stable Be8 and the primordial lithium problem

A change in the fundamental constants of nature or plasma effects in the early universe could stabilize $^8$Be against decay into two $^4$He nuclei. Coc et al. examined this effect on big bang nucleosynthesis as a function of $B_8$, the mass difference between two $^4$He nuclei and a single $^8$Be nucleus, and found no effects for $B_8 \le 100$ keV. Here we examine stable $^8$Be with larger $B_8$ and also allow for a variation in the rate for $^4$He + $^4$He $\longrightarrow$ $^8$Be to determine the threshold for interesting effects. We find no change to standard big bang nucleosynthesis for $B_8 < 1$ MeV. For $B_8 \gtrsim 1$ MeV and a sufficiently large reaction rate, a significant fraction of $^4$He is burned into $^8$Be, which fissions back into $^4$He when $B_8$ assumes its present-day value, leaving the primordial $^4$He abundance unchanged. However, this sequestration of $^4$He results in a decrease in the primordial $^7$Li abundance. Primordial abundances of $^7$Li consistent with observationally-inferred values can be obtained for reaction rates similar to those calculated for the present-day (unbound $^8$Be) case. Even for the largest binding energies and largest reaction rates examined here, only a small fraction of $^8$Be is burned into heavier elements, consistent with earlier studies. There is no change in the predicted deuterium abundance for any model we examined.

Boltzmann and Planck constants remeasured

NIST has announced more accurate measurements of the Boltzmann and Planck constants. The new values will contribute to an international effort to move away from defining basic units using physical objects and instead, starting in 2019, derive them from seven fundamental constants of nature. The kelvin, for example, is currently defined by measuring the triple point of water in a sealed glass cell. Going forward, metrologists want to define the kelvin in terms of the Boltzmann constant, which NIST researchers determined to be 1.3806410 × 10–23 J/K by measuring the degree of random motion of electrons in a resistor (Metrologia 2017, DOI: 10.1088/1681-7575/aa7b3f). Meanwhile, the kilogram is currently defined as the mass of a plum-sized cylinder of platinum-iridium alloy. Instead, metrologists want to define the kilogram in terms of the Planck constant. NIST scientists have now measured that constant’s value as 6.626069934 × 10–34 kg·m2/second by using a Kibble balance,