scholarly journals EXTENDED PLANCK SCALE

2003 ◽  
Vol 18 (15) ◽  
pp. 1037-1042 ◽  
Author(s):  
F. I. COOPERSTOCK ◽  
V. FARAONI
Keyword(s):  
Z Boson ◽  
Mass Spectra ◽  
Planck Scale ◽  
Structure Constant ◽  
High Energy ◽  
Fine Structure Constant ◽  
High Energy Radiation ◽  
Planck Mass ◽  
Null Surface

Traditional derivations of the Planck mass ignore the role of charge and spin in general relativity. From the Kerr–Newman null surface and horizon radii, quantized charge and spin dependence are introduced in an extended Planck scale of mass. Spectra emerge with selection rules dependent upon the choice of Kerr–Newman radius to link with the Compton wavelength. The appearance of the fine structure constant suggests the possibility of a variation in time of the extended Planck mass, which may be much larger than the variation in the traditional one. There is a suggestion of a connection with the α value governing high-energy radiation in Z-boson production and decay.

scholarly journals THE NEW PLANCK SCALE: QUANTIZED SPIN AND CHARGE COUPLED TO GRAVITY

2003 ◽  
Vol 12 (09) ◽  
pp. 1657-1661 ◽  
Author(s):  
F. I. COOPERSTOCK ◽  
V. FARAONI
Keyword(s):  
Z Boson ◽  
Planck Scale ◽  
Structure Constant ◽  
High Energy ◽  
Fine Structure Constant ◽  
Gravitational Radius ◽  
High Energy Radiation ◽  
Null Surface ◽  
Quantum Domain ◽  
The Universe

In the standard approach to defining a Planck scale where gravity is brought into the quantum domain, the Schwarzschild gravitational radius is set equal to the Compton wavelength. However, ignored thereby are the charge and spin, the fundamental quantized aspects of matter. The gravitational and null-surface radii of the Kerr–Newman metric are used to introduce spin and charge into a new extended Planck scale. The fine structure constant appears in the extended Planck mass and the recent discovery of the α variation with the evolution of the universe adds further significance. An extended Planck charge and Planck spin are derived. There is an intriguing suggestion of a connection with the α value governing high-energy radiation in Z-boson production and decay.

scholarly journals Variation of the fundamental constants over the cosmological time: veracity of Dirac’s intriguing hypothesis

2016 ◽  
Vol 94 (1) ◽  
pp. 89-94 ◽  
Author(s):  
Cláudio Nassif ◽  
A.C. Amaro de Faria
Keyword(s):  
Fine Structure ◽  
Early Universe ◽  
Early Period ◽  
Planck Scale ◽  
Structure Constant ◽  
Energy Scale ◽  
Fine Structure Constant ◽  
Cosmological Time ◽  
Age Of The Universe ◽  
The Universe

We investigate how the universal constants, including the fine structure constant, have varied since the early universe close to the Planck energy scale (EP ∼ 1019 GeV) and, thus, how they have evolved over the cosmological time related to the temperature of the expanding universe. According to a previous paper (Nassif and Amaro de Faria, Jr. Phys. Rev. D, 86, 027703 (2012). doi:10.1103/PhysRevD.86.027703), we have shown that the speed of light was much higher close to the Planck scale. In the present work, we will go further, first by showing that both the Planck constant and the electron charge were also too large in the early universe. However, we conclude that the fine structure constant (α ≅ 1/137) has remained invariant with the age and temperature of the universe, which is in agreement with laboratory tests and some observational data. Furthermore, we will obtain the divergence of the electron (or proton) mass and also the gravitational constant (G) at the Planck scale. Thus, we will be able to verify the veracity of Dirac’s belief about the existence of “coincidences” between dimensionless ratios of subatomic and cosmological quantities, leading to a variation of G with time, that is, the ratio of the electrostatic to gravitational forces between an electron and a proton (∼1041) is roughly equal to the age of the universe divided by an elementary time constant, so that the strength of gravity, as determined by G, must vary inversely with time in the approximation of lower temperature or for times very far from the early period, to compensate for the time-variation of the Hubble parameter (H ∼ t−1). In short, we will show the validity of Dirac’s hypothesis only for times very far from the early period or T ≪ TP (∼1032 K).

scholarly journals The annihilation of fast positrons by electrons in the K-shell

1934 ◽  
Vol 146 (859) ◽  
pp. 723-736 ◽  
Keyword(s):  
Kinetic Energy ◽  
Cosmic Radiation ◽  
Nuclear Charge ◽  
Structure Constant ◽  
Photoelectric Effect ◽  
High Energy ◽  
Negative Energy ◽  
Fine Structure Constant ◽  
Quantum Process ◽  
High Energies

The probability of the simultaneous of a positron and an electron, with the emission of two quanta of radiation, has been calculated by Dirac and several other authors. From considerations of energy and momentum it follows that an electron and positron can only annihilate one another with the emission of one quantum of radiation in the presence of a third body. An electron bound in an atom could, therefore, annihilate a positron, represented by a hole on the Dirac theory, by jumping into a state of negative energy which happens to be free, the nucleus taking up the extra momentum. The process is now mathematically analogous to the photoelectric transitions to states of negative energy in the sense that the matrix elements concerned are the same, and we might expect that the effect would be most important for the electrons in the K-shell. Fermi and Uhlenbeck have calculated the process approximately, for the condition where the kinetic energy of the positron is of the order of magnitude of the ionization energy of the K-shell. The result they obtained was very small compared with the two quantum process, which is to be explained by the fact that for these small energies, the positron does not get near the nucleus. In view of the fact that positrons of energies of the order 100 mc 2 occur in considerable quantities in the showers produced by cosmic radiation, and that the primary cosmic radiation itself may consist, in part, of positrons, it becomes of interest to calculate the cross-section for the annihilation of positrons of high energy by electrons in the K-shell, and their absorption in matter, and also to compare this process with the two quantum process for high energies. In the photoelectric effect for hard γ -rays, the electron the electron leaves the atom in states of different angular momentum (described by the azimuthal quantum number l ), and the terms which give the largest contribution are roughly those for which l is of the order of the energy of the γ -ray in terms of mc 2 . For high energies, therefore, a calculation by the method of Hulme, in which the last step is carried out numerically, is out of the question, and we must find some approximate method of effecting a summation. We shall use an adaptation of Sauter's method, in which we shall treat as small the product of the fine structure constant and the nuclear charge. This method may be expected to give a good approximation for small nuclear charge. Our method has the further restriction that it is valid only when the kinetic energy of the positron is not small compared with mc 2 .

scholarly journals PHASE TRANSITION COUPLINGS IN U(1) and SU(N) REGULARIZED GAUGE THEORIES

2001 ◽  
Vol 16 (24) ◽  
pp. 3989-4009 ◽  
Author(s):  
L. V. LAPERASHVILI ◽  
D. A. RYZHIKH ◽  
H. B. NIELSEN
Keyword(s):  
Phase Transition ◽  
Effective Potential ◽  
Gauge Theories ◽  
Planck Scale ◽  
Structure Constant ◽  
Coupling Constants ◽  
Fine Structure Constant ◽  
Multiple Point ◽  
Yang Mills ◽  
Loop Approximation

Using a two-loop approximation for β functions, we have considered the corresponding renormalization group improved effective potential in the dual Abelian Higgs model (DAHM) of scalar monopoles and calculated the phase transition (critical) couplings in U(1) and SU (N) regularized gauge theories. In contrast to our previous result α crit ≈0.17, obtained in the one-loop approximation with the DAHM effective potential (see Ref. 20), the critical value of the electric fine structure constant in the two-loop approximation, calculated in the present paper, is equal to α crit ≈0.208 and coincides with the lattice result for compact QED10: [Formula: see text]. Following the 't Hooft's idea of the "Abelization" of monopole vacuum in the Yang–Mills theories, we have obtained an estimation of the SU (N) triple point coupling constants, which is [Formula: see text]. This relation was used for the description of the Planck scale values of the inverse running constants [Formula: see text] (i= 1, 2, 3 correspond to U(1), SU(2) and SU(3) groups), according to the ideas of the multiple point model.16

scholarly journals VLT and E-ELT spectrographs & fundamental-constants

2009 ◽  
Vol 5 (H15) ◽  
pp. 326-326
Author(s):  
Paolo Molaro
Keyword(s):  
Fine Structure ◽  
Equivalence Principle ◽  
Structure Constant ◽  
Rate Of Change ◽  
Fine Structure Constant ◽  
Doppler Velocity ◽  
Fundamental Constants ◽  
Velocity Shift ◽  
Theoretical Predictions

The fundamental dimensionless physical constants cannot be predicted by theory but can only be measured experimentally. And so it is of their possible variation where there are several theoretical predictions but unfortunately with little theoretical guidance on the expected rate of change. The role of fundamental constants in the representation of nature as well as the implications of their variability for the Equivalence Principle and cosmology have been highlighted in many contributions at this conference (cfr K. Olive and J.P Uzan, these proceedings). Measuring the variability of the fine structure constant α or the electron-to-proton ratio μ by means of absorption lines implies the measurement of a tiny variation of the position of one or a few lines with regard to other lines which are taken as reference. For the fine structure constant the relation between its change and the doppler velocity shift is:

scholarly journals Period Doubling Phenomenon as the Origin of Electron Properties

2020 ◽  
Author(s):  
Ari Lehto
Keyword(s):  
Electric Charge ◽  
Magnetic Moment ◽  
Degrees Of Freedom ◽  
Periodic Structures ◽  
Planck Scale ◽  
Structure Constant ◽  
Period Doubling ◽  
Fine Structure Constant ◽  
Coulomb Energy ◽  
Rest Energy

It is proposed that the electrons have an intrinsic periodic property, which determines particle’s rest energy, electric charge, and magnetic moment. Numerical analysis shows that the correct periods are generated by a precise period doubling cascade starting at the Planck scale. Periods corresponding to the values of the intrinsic physical properties of the electron and positron belong to a subset of stable periods. The periodic structures of the rest energy and magnetic moment consist of three internal degrees of freedom, whereas the Coulomb energy of the electric charge consists of four. The number of period doublings for the elementary charge determines the value of the fine structure constant alpha.

scholarly journals Dark matter, dark energy and the time evolution of masses in the universe

2014 ◽  
Vol 29 (21) ◽  
pp. 1444016 ◽  
Author(s):  
Joan Solà
Keyword(s):  
Dark Energy ◽  
Vacuum Energy ◽  
Planck Scale ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
Vacuum Energy Density ◽  
Electron Mass ◽  
Static Vacuum ◽  
The Masses ◽  
The Universe

The traditional "explanation" for the observed acceleration of the universe is the existence of a positive cosmological constant. However, this can hardly be a truly convincing explanation, as an expanding universe is not expected to have a static vacuum energy density. So, it must be an approximation. This reminds us of the so-called fundamental "constants" of nature. Recent and past measurements of the fine structure constant and of the proton–electron mass ratio suggest that basic quantities of the standard model, such as the QCD scale parameter, Λ QCD , might not be conserved in the course of the cosmological evolution. The masses of the nucleons and of the atomic nuclei would be time-evolving. This can be consistent with General Relativity provided the vacuum energy itself is a dynamical quantity. Another framework realizing this possibility is QHD (Quantum Haplodynamics), a fundamental theory of bound states. If one assumes that its running couplings unify at the Planck scale and that such scale changes slowly with cosmic time, the masses of the nucleons and of the DM particles, including the cosmological term, will evolve with time. This could explain the dark energy of the universe.

scholarly journals ON THE VARIABLE FINE STRUCTURE CONSTANT, STRINGS AND MAXIMAL-ACCELERATION PHASE SPACE RELATIVITY

2003 ◽  
Vol 18 (29) ◽  
pp. 5445-5473 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
Fine Structure ◽  
Phase Space ◽  
Physical Model ◽  
Planck Scale ◽  
Structure Constant ◽  
Relativity Theory ◽  
Fine Structure Constant ◽  
Full Detail ◽  
Acceleration Phase ◽  
Maximal Acceleration

We present a new physical model that links the maximum speed of light with the minimal Planck scale into a maximal-acceleration relativity principle in the space–time tangent bundle and in phase spaces (cotangent bundle). The maximal proper-acceleration bound is a = c2/Λ in full agreement with the old predictions of Caianiello, the Finslerian geometry point of view of Brandt and more recent results in the literature. The group transformation laws of this maximal-acceleration phase space relativity theory under velocity and acceleration boosts are analyzed in full detail. For pure acceleration boosts it is shown why the minimal Planck-areas (maximal string tension) are universal invariant quantities in any frame of reference. Inspired by the maximal-acceleration corrections to the Lamb shifts of one-electron atoms by Lambiase, Papini and Scarpetta, we derive the exact integral equation that governs the renormalization-group-like scaling dependence of the fractional change of the fine structure constant as a function of the cosmological redshift factor and a cutoff scale Lc, where the maximal acceleration relativistic effects are dominant. A particular physical model exists dominated entirely by the vacuum energy, when the cutoff scale is the Planck scale, with ΩΛ = 1. The cosmological implications of this extreme case scenario are studied.

scholarly journals The Role of Low-Energy Electron Interactions in cis-Pt(CO)2Br2 Fragmentation

2021 ◽  
Vol 22 (16) ◽  
pp. 8984
Author(s):  
Maicol Cipriani ◽  
Styrmir Svavarsson ◽  
Filipe Ferreira da Silva ◽  
Hang Lu ◽  
Lisa McElwee-White ◽  
...  
Keyword(s):  
Coordination Compound ◽  
Electron Attachment ◽  
High Energy ◽  
Low Energy ◽  
Carbonyl Complexes ◽  
Secondary Electrons ◽  
High Energy Radiation ◽  
Low Energy Electrons ◽  
In Cis

Platinum coordination complexes have found wide applications as chemotherapeutic anticancer drugs in synchronous combination with radiation (chemoradiation) as well as precursors in focused electron beam induced deposition (FEBID) for nano-scale fabrication. In both applications, low-energy electrons (LEE) play an important role with regard to the fragmentation pathways. In the former case, the high-energy radiation applied creates an abundance of reactive photo- and secondary electrons that determine the reaction paths of the respective radiation sensitizers. In the latter case, low-energy secondary electrons determine the deposition chemistry. In this contribution, we present a combined experimental and theoretical study on the role of LEE interactions in the fragmentation of the Pt(II) coordination compound cis-PtBr2(CO)2. We discuss our results in conjunction with the widely used cancer therapeutic Pt(II) coordination compound cis-Pt(NH3)2Cl2 (cisplatin) and the carbonyl analog Pt(CO)2Cl2, and we show that efficient CO loss through dissociative electron attachment dominates the reactivity of these carbonyl complexes with low-energy electrons, while halogen loss through DEA dominates the reactivity of cis-Pt(NH3)2Cl2.

scholarly journals The Theoretical Value of the Hubble Constant Ho and Unification of the Fundamental Forces of Nature

2021 ◽  
Vol 3 (4) ◽  
pp. 17-24
Author(s):  
Paul Cadelina Rivera
Keyword(s):  
Fine Structure ◽  
Structure Constant ◽  
Hubble Constant ◽  
High Energy ◽  
Theoretical Explanation ◽  
Fine Structure Constant ◽  
Fundamental Relation ◽  
Gravitational Fields ◽  
Cosmological Observations ◽  
Fundamental Forces

The Hubble constant Ho represents the speed of expansion of the universe and various cosmological observations and modeling methods were utilized by astronomers for a century to pin down its exact value. Determining Ho from cosmological observations is a long and tedious process requiring highly accurate datasets. To circumvent this need, a simple theoretical approach is introduced in this study which uses the concept of gravitational weakening and seismic-induced recession. As tremors occur among celestial objects, their gravitational fields would also change. This resulted in a fundamental relation of Ho and the computed rate of recession that gives a theoretical value for Ho=69.921 Km/s/Mpc. Using the newly discovered seismic-induced gravitational weakening and time dilation, it is possible that various astrophysical methods using different measurement methods would converge to this theoretical Ho value when cosmological distances and time delay measurements are corrected with the simple formulas we derived. The new model assumes that, as quakes occur in celestial objects, luminosity-induced acceleration and high-energy collision of protons and electrons may produce a massive number of neutrinos, quarks and other subatomic particles. Furthermore, the fine structure constant was found to be inversely proportional to Ho-squared and that the fine-structure constant obtained in this study gives a new physical interpretation of α. New relations for the speed of light, orbital velocity, gravitational force and the Hubble constant were further derived from the new recession constant using approximate relations for the Newtonian and electric force constant. This resulted in a modified gravitational law that is both repulsive and attractive and a theoretical explanation of the phenomenon of light-induced gravitation analogous to the electromagnetic force where photon is the force-carrier. Finally, the fundamental forces of gravitation, electromagnetism and strong nuclear force are now unified.

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