An Interesting Mathematical Relation between the Proton Mass, the Proton Radius, the Fine Structure Constant, the Compton Wavelength and the Hagedorn Temperature

In this short note we present a possible connection between the proton radius and the proton mass using the fine structure constant. The Hagedorn temperature is related to the energy levels assumed to be required to free the quarks from the proton, where hadronic matter is unstable. We also speculate that there could be a connection between the Hagedorn temperature and the Planck temperature through the fine structure constant. Regarding whether or not there is something to this (or if it is purely a coincidence), we will leave to others and future research to explore. However, we think these possible relationships are worth further investigation.

Mass Constituents of a Flat Lattice Multiverse: Conclusion from Similarity between Two Universal Numbers, the Rocksalt-Type 2<i>D</i>Madelung Constant and the Golden Mean

In fairly good agreement with the consensus range of dark energy to matter this ratio of the critical density is suggested to be connected with the golden mean &phi;=0.6180339887, yielding for dark energy to matter mass fractions .?Assuming the baryonic matter to be only 4.432%, the ratio of matter to baryonic matter would be , and further the ratio of dark matter to baryonic one . If one subtracts from the dark matter a contribution of antimatter with the same mass of baryonic matter, according to the antigravity theories of Villata respectively Hajdukovic, the remaining mass ratio would yield . Replacing the “Madelung” constant α of Villata’s “lattice universe” by &phi;, one reaches again 1 + &phi;as the ratio of the repulsive mass contribution to the attractive one. Assuming instead of a 3D lattice a flat 2D one of rocksalt type, the numerical similarity between the Madelung constant and φ&minus;1 could not be just coincidence. The proposed scaling of the cosmological mass fractions with the square of the most irrational universal number &phi;may indicate that the chaotic cosmological processes have reached a quite stable equilibrium. This may be confirmed by another, but similar representation of the mass constituents by the Archimedes’ constant &pi;, giving for respectively for the dark components . However, the intimate connection of φ with its reciprocal may ignite the discussion whether our universe is intertwined with another universe or even part of a multiverse with the dark constituents contributed from there.

Electron Mass Is Specified by Five Fundamental Constants, α, ħ, G, Λ, and ΩΛ, 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 α, 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.

Highly Accurate Relations between the Fine Structure Constant and Particle Masses, with Application to Its Cosmological Measurement

Highly accurate algebraic relations between the fine structure constant a and a wide range of particle masses are given, ranging from Δa/a = (2.1 ±0.1)×10-7 to Δa/a = (-2.7 ±0.3 ±0.6)×10-8, and with a very large standard deviation, ranging to Δa/a = -5.5×10-9. The analysis is based on empirical relations that exist among some particle masses, and also on several theoretical assumptions, of which the most significant is that the electromagnetic contribution to the electron’s mass is finite, and given by f ameb, where f is a dimensionless parameter that is shown to be equal to 1.032409810 (63), and where meb is the electron’s “bare mass.” The relations for a and f are homogeneous degree zero in the particle masses. The relations for f in terms of particle masses are found by trial and error. A quadratic equation is given relating a to f and me/mp. This equation is used in the application to cosmological measurements of a, and , where it is shown that, to a few percent accuracy, δa/a ≈ -δμ/μ. This relation can serve to test the validity of measurements of a and μ.

Mass of the Universe from Quarks: A Plausible Solution to the Cosmological Constant Problem

A framework to estimate the mass of the universe from quarks is presented, taking spacetime into account. This is a link currently missing in our understanding of physics/science. The focus on mass-energy balance is aimed at finding a solution to the Cosmological Constant (CC) problem by attempting to quantize space-time and linking the vacuum energy density at the beginning of the universe and the current energy density. The CC problem is the famous disagreement of approximately 120 orders of magnitude between the theoretical energy density at the Planck scale and the indirectly measured cosmological energy density. Same framework is also used to determine the mass of the proton and neutron from first principles. The only input is the up quark (u-quark) mass, or precisely, the 1st generation quarks. The method assumes that the u-quark is twice as massive as the down-quark (d-quark). The gap equation is the starting point, introduced in its simplest form. The main idea is to assume that all the particles and fields in the unit universe are divided into quarks and everything else. Everything else means all fields and forces present in the universe. It is assumed that everything else can be “quark-quantized”;that is, assume that they can be quantized into similar sizeable u-quarks and/or it’s associated interactions and relations. The result is surprisingly almost as measured and known values. The proton structure and mass composition are also analysed, showing that it likely has more than 3 quarks and more than 3 valence quarks. It is also possible to estimate the percentage of dark matter, dark energy, ordinary matter, and anti-matter. Finally, the cosmological constant problem or puzzle is resolved by connecting the vacuum energy density of Quantum Field Theory (5.1E+96 kg/m3) and the energy density of General Relativity (1.04E−26 kg/m3). Upon maturation, this framework can serve as a bridging platform between Quantum Field Theory and General Relativity. Other aspects of natures’ field theories can be successfully ported to the platform. It also increases the chances of solving some of the unanswered questions in physics.

The Fundamental Relationship between Harmonic Quark Masses and Reduced Max Planck Constant

O. A. Teplov developed an approach to describe the meson quark model by establishing a mathematical quark series (harmonic quark series). With respect to the physical mesons, he made some basic hypotheses of his own and used the well-known theory of harmonic oscillation to construct a numerical mass series that obeys a rigid multiplicative pattern and allows the physical meson masses to be calculated accurately. We have found that his numerical quark series, i.e., their masses, has a fundamental relation to the reduced Max Planck constant &#295;and report on it in the present paper. This discovery is obviously a theoretical contribution to the correctness of Teplov’s harmonic quark model approach and at the same time a confirmation of the importance of this simple and powerful research work.

The Mystery behind the Fine Structure Constant Contracted Radius Ratio Divided by the Mass Ratio? A Possible Atomist Interpretation

This paper examines various alternatives for what the fine structure constant might represent. In particular, we look at an alternative where the fine structure constant represents the radius ratio divided by the mass ratio of the electron, versus the proton as newly suggested by Koshy [1], but derived and interpreted here based on Haug atomism (see [2]). This ratio is remarkably close to the fine structure constant, and it is a dimensionless number. We also examine alternatives including the proton mass divided by the Higgs mass, which appears to be another possible candidate for what the fine structure constant might represent.

Numerical Solution of MHD Convection and Mass Transfer Flow of Viscous Incompressible Fluid about an Inclined Plate with Hall Current and Constant Heat Flux

The present numerically study investigates the influence of the Hall current and constant heat flux on the Magneto hydrodynamic (MHD) natural convection boundary layer viscous incompressible fluid flow in the manifestation of transverse magnetic field near an inclined vertical permeable flat plate. It is assumed that the induced magnetic field is negligible compared with the imposed magnetic field. The governing boundary layer equations have been transferred into non-similar model by implementing similarity approaches. The physical dimensionless parameter has been set up into the model as Prandtl number, Eckert number, Magnetic parameter, Schmidt number, local Grashof number and local modified Grashof number. The numerical method of Nactsheim-Swigert shooting iteration technique together with Runge-Kutta six order iteration scheme has been used to solve the system of governing non-similar equations. The physical effects of the various parameters on dimensionless primary velocity profile, secondary velocity profile, and temperature and concentration profile are discussed graphically. Moreover, the local skin friction coefficient, the local Nusselt number and Sherwood number are shown in tabular form for various values of the parameters.

Galactic Route to the Strong Coupling Constant αs(mz) and Its Implication on the Mass Constituents of the Universe

Some fundamental physical quantities need an alternative description. We derive the word average value of interaction coupling constant αs(mz) from the observed maximum galactic rotation velocity by the simple relation , where is the velocity, at which the difference between galactic rotation velocity and Thomas precession is equal, and α is Sommerfeld’s constant. The result is in excellent agreement with the value of αs = 0.1170 ± 0.0019, recently measured and verified via QCE analysis by CERN researchers. One can formulate a reciprocity relation, connecting αs with the circle constant: . It is the merit of Preston Guynn to derive the Milky Way maximum value of the galactic rotation velocity βg, pointing to its “extremely important role in all physics”. The mass (energy) constituents of the Universe follow a golden mean hierarchy and can simply be related to the maximum of Guynn’s difference velocity respectively to αs(mz), therewith excellently confirming Bouchet’s WMAP data analysis. We conclude once more that the golden mean concept is the leading one of nature.

Effects of thermodynamics parameters on mass transfer of volatile pollutants at air-water interface

A transient three-dimensional coupling model based on the compressible volume of fluid （VOF） method was developed to simulate the transport of volatile pollutants at the air-water interface. VOF is a numerical technique for locating and tracking the free surface of water flow. The relationships between Henry＇s constant, thermodynamics parameters, and the enlarged topological index were proposed for nonstandard conditions. A series of experiments and numerical simulations were performed to study the transport of benzene and carbinol. The simulation results agreed with the experimental results. Temperature had no effect on mass transfer of pollutants with low transfer free energy and high Henry＇s constant. The temporal and spatial distribution of pollutants with high transfer free energy and low Henry＇s constant was affected by temperature. The total enthalpy and total transfer free energy increased significantly with temperature, with significant fluctuations at low temperatures. The total enthalpy and total transfer free energy increased steadily without fluctuation at high temperatures.

Calculation of the Masses of All Fundamental Elementary Particles with an Accuracy of Approx. 1%

The masses of a l l fundamental elementary particles (those with a lifetime > 10-24 sec) can be calculated with an inaccuracy of approx. 1% using the equation m/melectron = N/2α where α is the coupling constant of quantum electrodynamics (also known as fine structure constant) (= 1/137.036), and N is an integer variable. This is the by far most accurate and most comprehensive approach to calculate the particle masses.

Using Kiefer Density Matrix for Time Flow Analysis and How This Links to a Proof of Production of Planck Mass BHs during Inflation and Their Resulting Breakup, Leading to a DE Candidate

We are using the book “Towards Quantum Gravity” with an article by Claus Kiefer as to a quantum gravity interpretation of the density matrix in the early universe. The density matrix we are using is a one loop approximation, with inflaton value and potential terms, like V (phi) using the Padmanabhan values one can expect if the scale factor is a ~a (Initial) times t ^ gamma. In doing so, we identify two time steps and presume a very small initial time step candidates initial time values which are from a polynomial for time values. A gravity wave analysis concludes our article with inflaton decay, which is finally linked to BHs. And then finally we show using work done by Hawking, et al. how this may give us Planck Sized Black Holes, in the onset of Inflation, with resulting consequences so outlined. A vastly simplified proof of BH masses of Planck mass is presented which ties in directly with issues of the mass of the inflaton initially generated by the 2nd derivative of the effective potential V (phi) at a time t ~4 times Planck time. And we include at the close questions as to DE, and data sets which may give credence to speculation as to different time flow rates at the start and then the conclusion later on, of expansion of our universe. The DE would be created by the breakup of the black holes due to a mechanism brought up by Dr. Freeze in 2012, and we also are using the future works section 8 to define the contours of our DE model which builds upon quite directly the sequence of material from pages 1 to 9 which are cited as to making connection between early universe conditions and the ideas of primordial DE models.

EXTRACTION KINETICS OF RARE EARTH（Ⅰ） A Constant Interfacial Cell with Laminar Flow

A technique was developed to study mass trans fer process and inter facial reaction in two phases system. This constant inter facial cell with a laminar flow was made into a cubic structure. The two fluids were continuously recycled and mixed. The concentration of each liquid could be monitored by two different methods. This kind of structure made both flows near the inter face flow parallel to the inter face. The inter face was smooth and steady. The mass trans fer rate could be judged by the linear velocity of the flows. The technique can be used for the analyses of the control step in both phases near the inter face in a diffusion control process. A preliminary hydrodynamics and mass trans fer study on the cell was presented, which ensures the distinguishing between a diffusion and a chemical reaction control process. A simplified mass transfer equation,N =0.5303D 1 /2* (Ci- Cb)* (V / B) 1/2, was achieved.

Research on Constant-Speed Rapeseed Drying Mechanism

This paper presents research on constantspeed rapeseed drying mechanism and the mathematical model established for constant speed drying period.

The Relation between Thermodynamics and Gravitational Constant (<i>G</i>)

Although many centuries have elapsed since Newton set forth his gravitational law, physics has been unable so far to create an exact theoretical value for the universal gravitational constant (G). Through a simple thought experience (i.e. it may not be possible to perform it), it can be concluded a mathematical formula which links three different physical sciences with each other: mechanics, electromagnetism and thermodynamics in a simple form, it is possible to find an exact value for the gravitational constant using this form. In fact, the importance of this research is that it also tells us more information about the electromagnetic and gravitomagnetic origin of masses, the negative and positive masses (i.e. matter and dark matter), and the smallest possible distance in the universe, which equals 1.0252 × 10-56 m.

An Electron Model Based on the Fine Structure Constant

In previous publications, the author has proposed a model of the electron’s internal structure, wherein a positively-charged negative mass outer shell and a negatively-charged positive mass central core are proposed to resolve the electron’s charge and mass inconsistencies. That model is modified in this document by assuming the electron’s radius is exactly equal to the classical electron radius. The attributes of the internal components of the electron’s structure have been recalculated accordingly. The shape of the electron is also predicted, and found to be slightly aspherical on the order of an oblate ellipsoid. This shape is attributed to centrifugal force and compliant outer shell material. It is interesting to note that all of the electron’s attributes, both external and internal, with the exception of mass and angular moment, are functions of the fine structure constant a, and can be calculated from just three additional constants: electron mass, Planck’s constant, and speed of light. In particular, the ratios of the outer shell charge and mass to the electron charge and mass, respectively, are 3/2a. The ratios of the central core charge and mass to the electron charge and mass, respectively, are 1-(3/2a). Attributes of the electron are compared with those of the muon. Charge and spin angular momentum are the same, while mass, magnetic moment, and radius appear to be related by the fine structure constant. The mass of the electron outer shell is nearly equal to the mass of the muon. The muon internal structure can be modeled exactly the same as for the electron, with exactly the same attribute relationships.

On the Quantization of One-Dimensional Conservative Systems with Variable mass

The Hamiltonian associated to the mass variable system is constructed from first principles through finding a constant of motion of the system. A comparison is made of the classical motion of a body with its mass position depending in the (x,v) space and (x,p) space which are defined by the constant of motion and the Hamiltonian, for a particular model of mass variation. As one could expected, these motion looks different on these spaces. The quantization of the harmonic oscillator with this mass variation is done, and a comparison is made by using the usual Hamiltonian approach with the proposed quantization of the constant of motion approach. This comparison is done at first order in perturbation theory, and one sees a difference between both approaches which can, in principle, be measured.

Unity Formulas for the Coupling Constants and the Dimensionless Physical Constants

In this paper in an elegant way will be presented the unity formulas for the coupling constants and the dimensionless physical constants. We reached the conclusion of the simple unification of the fundamental interactions. We will find the formulas for the Gravitational constant. It will be presented that the gravitational fine-structure constant is a simple analogy between atomic physics and cosmology. We will find the expression that connects the gravitational fine-structure constant with the four coupling constants. Perhaps the gravitational fine-structure constant is the coupling constant for the fifth force. Also will be presented the simple unification of atomic physics and cosmology. We will find the formulas for the cosmological constant and we will propose a possible solution for the cosmological parameters. Perhaps the shape of the universe is Poincare dodecahedral space. This article will be followed by the energy wave theory and the fractal space-time theory.

One Dimensional Conservative System with Quadratic Dissipation and Position Depending Mass

Forl a 1-D conservative system with a position depending mass within a dissipative medium, its effect on the body is to exert a force depending on the squared of its velocity, a constant of motion, Lagrangian, generalized linear momentum, and Hamiltonian are obtained. We apply these new results to the harmonic oscillator and pendulum under the characteristics mentioned about, obtaining their constant of motion, Lagrangian and Hamiltonian for the case when the body is increasing its mass.

Reciprocity Relation between the Mass Constituents of the Universe and Hardy’s Quantum Entanglement Probability

In this short contribution, a reciprocity relation between mass constituents of the universe was explained governed by Hardy’s maximum entanglement probability of φ5 = 0.09017. While well explainable through a set-theoretical argumentation, the relation may also be a consequence of a coupling factor attributed to the normed dimensions of the universe. Also, very simple expressions for the mass amounts were obtained, when replacing the Golden Mean φ by the Archimedes’ constant π. A brief statement was devoted to the similarity between the E-Infinity Theory of El Naschie and the Information Relativity Theory of Suleiman. In addition, superconductivity was also linked with Hardy’s entanglement probability.