A Fine-Structure Constant Can Be Explained Using the Electrochemical Method

We proposed an empirical equation for a fine-structure constant: . Then, . where mp and me are the rest mass of a proton and the rest mass of an electron, respectively. In this report, using the electrochemical method, we proposed an equivalent circuit. Then, we proposed a refined version of our own old empirical equations about the electromagnetic force and gravity. Regarding the factors of 9/2 and π, we used 3.132011447 and 4.488519503, respectively. The calculated values of Tc and G are 2.726312 K and 6.673778 × 10-11 (m3⋅kg-1⋅s-2).

Possible Relations of Cosmic Microwave Background with Gravity and Fine-Structure Constant

Gravity is the only force that cannot be explained by the Standard Model (SM), the current best theory describing all the known fundamental particles and their forces. Here we reveal that gravitational force can be precisely given by mass of objects and microwave background (CMB) radiation. Moreover, using the same strategy we reveal a relation by which CMB can also precisely define fine-structure constant α.

Empirical Equation for a Fine-Structure Constant with Very High Accuracy

We proposed several empirical equations about the electromagnetic force and gravity. The main three equations were connected mathematically. However, these equations have small errors of approximately 10-3. Therefore, we attempted to improve the accuracy. Regarding the factors of 9/2 and π, we used 4.48870 and 3.13189, respectively. Then, the errors become smaller than 10-5. However, we could not show any reasons for these compensations. We noticed the following equations. , . Then, we can explain the von Klitzing constant Rk=3.131777037×4.488855463×13.5×136.0113077. It is well known that the von Klitzing constant can be measured with very high accuracy. We examined this equation for the von Klitzing constant in detail. Then, we noticed that 136.0113 should be uniquely determined. The von Klitzing constant is highly related to the fine-structure constant. After the examination of the numerical connections, we can explain the value of 137.035999081 as a fine-structure constant with very high accuracy. Then, we attempt to explain this value from Wagner’s equation.

Comment to Guynn’s Fine-Structure Constant Approach

Sommerfeld’s fundamental fine-structure constant α once more gives reason to be amazed. This comment is a Chapter of a publication in preparation dealing mainly with golden ratio signature behind Preston Guynn’s famous matter/space approach. As a result we present a relation of α to the galactic velocity , mediated by the circle constant π, which points to an omnipresent importance of this constant and its intrinsic reciprocity pecularity: α ≈ π2|βg| respectively . The designation fine-structure constant should be replaced simply by Sommerfeld’s constant. We present golden mean-based approximations for α as well as for electron’s charge and mass and connect the word average value of interaction coupling constant αs(mz) with |βg|.

Calculation of the Fine-Structure Constant

The fine-structure constant α [1] is a constant in physics that plays a fundamental role in the electromagnetic interaction. It is a dimensionless constant, defined as: (1) being q the elementary charge, ε0 the vacuum permittivity, h the Planck constant and c the speed of light in vacuum. The value shown in (1) is according CODATA 2014 [2]. In this paper, it will be explained that the fine-structure constant is one of the roots of the following equation: (2) being e the mathematical constant e (the base of the natural logarithm). One of the solutions of this equation is: (3) This means that it is equal to the CODATA value in nine decimal digits (or the seven most significant ones if you prefer). And therefore, the difference between both values is: (4) This coincidence is higher in orders of magnitude than the commonly accepted necessary to validate a theory towards experimentation. As the cosine function is periodical, the Equation (2) has infinite roots and could seem the coincidence is just by chance. But as it will be shown in the paper, the separation among the different solutions is sufficiently high to disregard this possibility. It will also be shown that another elegant way to show Equation (2) is the following (being i the imaginary unit): (5) having of course the same root (3). The possible meaning of this other representation (5) will be explained.

Studying Cosmological Time Variability of the Fine-Structure Constant from the Analysis of Quasar Spectra

The article has been retracted due to the investigation of complaints received against it. The substantial portions of the text came from Le Duc Thong’s former article, 'New method of searching for cos-mological time variation of the fine-structure constant', which has also been retraced by Prog. Theor. Phys. because of plagiarism. The scientific community takes a very strong view on this matter and we treat all unethical behavior such as plagiarism seriously. This paper published in Vol.2 No.6 533-537, 2011, has been removed from this site.

Spatial and temporal variations of the fine-structure constant in the Finslerian universe

Recent observations show that the electromagnetic fine-structure constant, αe, may vary with space and time. In the framework of Finsler spacetime, we propose here an anisotropic cosmological model, in which both spatial and temporal variations of αe are allowed. Our model naturally leads to the dipole structure of αe, and predicts that the dipole amplitude increases with time. We fit our model to the most up-to-date measurements of αe from the quasar absorption lines. It is found that the dipole direction points towards（l, b） =（330.2°±7.3°,-13.0°±5.6°）in galactic coordinates, and the anisotropic parameter is b_0 =（0.47±0.09）×10^-5, which corresponds to a dipole amplitude（7.2±1.4）×10^-8 at redshift z = 0.015. This is consistent with the upper limit of the variation of αe measured in the Milky Way. We also fit our model to Union2.1 type Ia supernovae, and find that the preferred direction of Union2.1 is consistent with the dipole direction of αe.

Granular behaviour under bi-directional shear with constant vertical stress and constant volume

This paper aims to investigate the role of bi-directional shear in the mechanical behaviour of granular materials and macro-micro relations by conducting experiments and discrete element method(DEM)modelling.The bi-directional shear consists of a static shear consolidation and subsequent shear under constant vertical stress and constant volume conditions.A side wall node loading method is used to exert bi-directional shear of various angles.The results show that bi-directional shear can significantly influence the mechanical behaviour of granular materials.However,the relationship between bidirectional shear and mechanical responses relies on loading conditions,i.e.constant vertical stress or constant volume conditions.The stress states induced by static shear consolidation are affected by loading angles,which are enlarged by subsequent shear,consistent with the relationship between bidirectional shear and principal stresses.It provides evidence for the dissipation of stresses accompanying static liquefaction of granular materials.The presence of bi-directional principal stress rotation(PSR)is demonstrated,which evidences why the bi-directional shear of loading angles with components in two directions results in faster dissipations of stresses with static liquefaction.Contant volume shearing leads to cross-anisotropic stress and fabric at micro-contacts,but constant vertical stress shearing leads to complete anisotropic stress and fabric at micro-contacts.It explains the differentiating relationship between stress-strain responses and fabric anisotropy under these two conditions.Micromechanical signatures such as the slip state of micro-contacts and coordination number are also examined,providing further insights into understanding granular behaviour under bi-directional shear.

Cyclic shear behavior of en-echelon joints under constant normal stiffness conditions

To reveal the mechanism of shear failure of en-echelon joints under cyclic loading,such as during earthquakes,we conducted a series of cyclic shear tests of en-echelon joints under constant normal stiffness(CNS)conditions.We analyzed the evolution of shear stress,normal stress,stress path,dilatancy characteristics,and friction coefficient and revealed the failure mechanisms of en-echelon joints at different angles.The results show that the cyclic shear behavior of the en-echelon joints is closely related to the joint angle,with the shear strength at a positive angle exceeding that at a negative angle during shear cycles.As the number of cycles increases,the shear strength decreases rapidly,and the difference between the varying angles gradually decreases.Dilation occurs in the early shear cycles(1 and 2),while contraction is the main feature in later cycles(310).The friction coefficient decreases with the number of cycles and exhibits a more significant sensitivity to joint angles than shear cycles.The joint angle determines the asperities on the rupture surfaces and the block size,and thus determines the subsequent shear failure mode(block crushing and asperity degradation).At positive angles,block size is more greater and asperities on the rupture surface are smaller than at nonpositive angles.Therefore,the cyclic shear behavior is controlled by block crushing at positive angles and asperity degradation at negative angles.

Gedankenexperiment for Modified ZPE and Planck’s “Constant”, h, in the Beginning of Cosmological Expansion, Partly Due to NLED

We initially look at a non singular universe representation of entropy, based in part on what was brought up by Muller and Lousto. This is a gateway to bringing up information and computational steps (as defined by Seth Lloyd) as to what would be available initially due to a modified ZPE formalism. The ZPE formalism is modified as due to Matt Visser’s alternation of k (maximum) ~ 1/(Planck length), with a specific initial density giving rise to initial information content which may permit fixing the initial Planck’s constant, h, which is pivotal to the setting of physical law. The settings of these parameters depend upon NLED.

Elementary Fermions: Strings, Planck Constant, Preons and Hypergluons

Using real fields instead of complex ones, it is suggested here that the fermions are pairs of coupled strings with an internal tension. The interaction between the two coupled strings is due to an exchange mechanism which is proportional to Planck’s constant. This may be the result of two massless bosons (hypergluons) coupled by a preon (prequark) exchange. It also gives a physical explanation to the origin of the Planck constant, and origin of spin.

ESTIMATE ON THE BLOCH CONSTANT FOR CERTAIN HARMONIC MAPPINGS UNDER A DIFFERENTIAL OPERATOR

In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,using these results,we present better estimations for the Bloch constants of certain harmonic mappings L(f),where f is a K-quasiregular harmonic or open harmonic.Finally,we establish three versions of BlochLandau type theorem for biharmonic mappings of the form L(f).These results are sharp in some given cases and improve the related results of earlier authors.

The Extremal Universe Exact Solution from Einstein’s Field Equation Gives the Cosmological Constant Directly

Einstein’s field equation is a highly general equation consisting of sixteen equations. However, the equation itself provides limited information about the universe unless it is solved with different boundary conditions. Multiple solutions have been utilized to predict cosmic scales, and among them, the Friedmann-Lemaître-Robertson-Walker solution that is the back-bone of the development into today standard model of modern cosmology: The Λ-CDM model. However, this is naturally not the only solution to Einstein’s field equation. We will investigate the extremal solutions of the Reissner-Nordström, Kerr, and Kerr-Newman metrics. Interestingly, in their extremal cases, these solutions yield identical predictions for horizons and escape velocity. These solutions can be employed to formulate a new cosmological model that resembles the Friedmann equation. However, a significant distinction arises in the extremal universe solution, which does not necessitate the ad hoc insertion of the cosmological constant;instead, it emerges naturally from the derivation itself. To the best of our knowledge, all other solutions relying on the cosmological constant do so by initially ad hoc inserting it into Einstein’s field equation. This clarification unveils the true nature of the cosmological constant, suggesting that it serves as a correction factor for strong gravitational fields, accurately predicting real-world cosmological phenomena only within the extremal solutions of the discussed metrics, all derived strictly from Einstein’s field equation.

Enriched Constant Elements in the Boundary Element Method for Solving 2D Acoustic Problems at Higher Frequencies

The boundary element method(BEM)is a popular method for solving acoustic wave propagation problems,especially those in exterior domains,owing to its ease in handling radiation conditions at infinity.However,BEM models must meet the requirement of 6–10 elements per wavelength,using the conventional constant,linear,or quadratic elements.Therefore,a large storage size of memory and long solution time are often needed in solving higher-frequency problems.In this work,we propose two new types of enriched elements based on conventional constant boundary elements to improve the computational efficiency of the 2D acoustic BEM.The first one uses a plane wave expansion,which can be used to model scattering problems.The second one uses a special plane wave expansion,which can be used tomodel radiation problems.Five examples are investigated to showthe advantages of the enriched elements.Compared with the conventional constant elements,the new enriched elements can deliver results with the same accuracy and in less computational time.This improvement in the computational efficiency is more evident at higher frequencies(with the nondimensional wave numbers exceeding 100).The paper concludes with the potential of our proposed enriched elements and plans for their further improvement.

New Approach to Synchronize General Relativity and Quantum Mechanics with Constant “K”-Resulting Dark Matter as a New Fundamental Force Particle

Planck scale plays a vital role in describing fundamental forces. Space time describes strength of fundamental force. In this paper, Einstein’s general relativity equation has been described in terms of contraction and expansion forces of space time. According to this, the space time with Planck diameter is a flat space time. This is the only diameter of space time that can be used as signal transformation in special relativity. This space time diameter defines the fundamental force which belongs to that space time. In quantum mechanics, this space time diameter is only the quantum of space which belongs to that particular fundamental force. Einstein’s general relativity equation and Planck parameters of quantum mechanics have been written in terms of equations containing a constant “K”, thus found a new equation for transformation of general relativity space time in to quantum space time. In this process of synchronization, there is a possibility of a new fundamental force between electromagnetic and gravitational forces with Planck length as its space time diameter. It is proposed that dark matter is that fundamental force carrying particle. By grand unification equation with space-time diameter, we found a coupling constant as per standard model “αs” for that fundamental force is 1.08 × 10-23. Its energy calculated as 113 MeV. A group of experimental scientists reported the energy of dark matter particle as 17 MeV. Thorough review may advance science further.

Probing the electric double layer structure at nitrogen-doped graphite electrodes by constant-potential molecular dynamics simulations

Electric double layer(EDL)is a critical topic in electrochemistry and largely determines the working performance of lithium batteries.However,atomic insights into the EDL structures on heteroatom-modified graphite anodes and EDL evolution with electrode potential are very lacking.Herein,a constant-potential molecular dynamics(CPMD)method is proposed to probe the EDL structure under working conditions,taking N-doped graphite electrodes and carbonate electrolytes as an example.An interface model was developed,incorporating the electrode potential and atom electronegativities.As a result,an insightful atomic scenario for the EDL structure under varied electrode potentials has been established,which unveils the important role of doping sites in regulating both the EDL structures and the following electrochemical reactions at the atomic level.Specifically,the negatively charged N atoms repel the anions and adsorb Li~+at high and low potentials,respectively.Such preferential adsorption suggests that Ndoped graphite can promote Li~+desolvation and regulate the location of Li~+deposition.This CPMD method not only unveils the mysterious function of N-doping from the viewpoint of EDL at the atomic level but also applies to probe the interfacial structure on other complicated electrodes.

Predicting High Precision Hubble Constant Determinations Based on a New Theoretical Relationship between CMB Temperature and H0

Based on considerable progress made in understanding the Cosmic Microwave Background (CMB) temperature from a deep theoretical perspective, this paper demonstrates a useful and simple relationship between the CMB temperature and the Hubble constant. This allows us to predict the Hubble constant with much higher precision than before by using the CMB temperature. This is of great importance, since it will lead to much higher precision in various global parameters of the cosmos, such as the Hubble radius and the age of the universe. We have improved uncertainty in the Hubble constant all the way down to 66.8712 ± 0.0019 km/s/Mpc based on data from one of the most recent CMB studies. Previous studies based on other methods have rarely reported an uncertainty much less than approximately ±1 km/s/Mpc for the Hubble constant. Our deeper understanding of the CMB and its relation to H0seems to be opening a new era of high-precision cosmology, which may well be the key to solving the Hubble tension, as alluded to herein. Naturally, our results should also be scrutinized by other researchers over time, but we believe that, even at this stage, this deeper understanding of the CMB deserves attention from the research community.

Upsilon Constants and Their Usefulness in Planck Scale Quantum Cosmology

This paper introduces the two Upsilon constants to the reader. Their usefulness is described with respect to acting as coupling constants between the CMB temperature and the Hubble constant. In addition, this paper summarizes the current state of quantum cosmology with respect to the Flat Space Cosmology (FSC) model. Although the FSC quantum cosmology formulae were published in 2018, they are only rearrangements and substitutions of the other assumptions into the original FSC Hubble temperature formula. In a real sense, this temperature formula was the first quantum cosmology formula developed since Hawking’s black hole temperature formula. A recent development in the last month proves that the FSC Hubble temperature formula can be derived from the Stephan-Boltzmann law. Thus, this Hubble temperature formula effectively unites some quantum developments with the general relativity model inherent in FSC. More progress towards unification in the near-future is expected.

The Planck Constant and Its Relation to the Compton Frequency

The Planck constant is considered one of the most important universal constants of physics, and despite all we know much about it, the physical nature of it has not been fully understood. Further investigation and new perspectives on the Planck constant should therefore be of interest. We demonstrate that the Planck constant also can be directly linked to the Compton frequency of one, which again is divided by the Compton frequency in one kg. If this is right, it means also the Planck constant is linked to quantization of matter, not only energy. However, as we will show the frequency of one when expressed in relation to kg will be observational time dependent. This means the missing mass gap surprisingly both is equal to the Planck mass, which is larger than any known particle and also it is linked to a very small mass that again is equal to what has been suggested as the photon mass in the existing literature. This new view could be an important step forward in understanding the physical nature of the Planck constant as well as the mass gap and even the rest mass of a photon.

The Gravitational Constant as the Function of the Cosmic Scale

This paper uses the cosmic evolution picture constructed by the principal and associated fiber bundles and, with the help of gauge invariance, systematically proposes the γfactor theory that the Newton’s law of universal gravitation and the cosmological constant of Einstein’s equation must be corrected in the large-scale space-time structure of the universe. That is, it is found that the calculated value of Newton’s universal gravitation in space-time above the scale of galaxies must be multiplied by 1/γto be consistent with the measured value, and the cosmological constant of Einstein’s equation is no longer a constant but a function that increases with the increase of the scale of cosmic regions. Therefore, the cyclic hypothesis of cosmic evolution is proposed, and it is further found that the gravitational constant that people think is natural is not a constant but a function that changes with the scale of cosmic regions. Therefore, the reason for the dark matter and dark energy hypothesis may be that the gravitational constant is a variable. The existence of actual dark matter and dark energy may be just an illusory hypothesis, and their origin comes from the understanding that the gravitational constant is constant.