Uniform Scaling: Relativistic Energy-Momentum Relationships

A number of the most often cited results of relativity theory deal with the relationships between energy, momentum and inertial mass. The history of how Einstein and Planck came to these conclusions is reviewed. It is pointed out that considerations of how the speed of light is affected by the motion of the Earth played a determining role in these developments. After the Michelson-Morley null-interference result became available, Voigt introduced a new space-time transformation by amending the classical Galilean transformation so that the speed of light in free space has the same value of c regardless of the state of motion of both the light source and the observer. This led to the Lorentz transformation which has been the cornerstone of relativity theory for the past century. A thought experiment is presented which proves, however, that there are many situations for which the measured speed of light is NOT equal to c. Furthermore, it is pointed out that the rate of an inertial clock cannot change spontaneously, which result is perfectly compatible with Newton’s First Law of Kinetics (Law of Inertia). This result contradicts the space-time mixing characteristic of the Lorentz transformation and leads to the conclusion that events which are spontaneous for one inertial frame will also be so for every other one. The uniform scaling procedure is a generalization of this result for all other physical properties than elapsed times. Its application shows that the commonly accepted relationships between energy and momentum are only special cases in which it is assumed that the observer is stationary in the rest frame in which force has been applied to cause the object’s acceleration

Discretization and degeometrization: A new relational quantum physics and an alternate path to quantum gravity

A novel quantum mechanical framework in discrete space and time leads to the derivation of the relativistic energy equation and a potential path toward quantum gravity. A unique approach to geometry is also derived where pregeometric points containing intrinsic compactified geometries generate a topologically 4D cosmos with a local dynamical 3D geometry. An interpretation of the quantum mechanics wavefunction is considered as longitudinal density waves traveling through dynamical pregeometric points. Similarly, general relativity can be described as density variations of the pregeometric points caused by matter-energy distribution. A primordial quantum (Higgs) field emerging at the big bang that generates all the other quantum fields is considered. A four-dimensional structure of black holes, and dark matter and energy are discussed.

THEORETICAL STUDYING EXCITED STATES SPECTRUM OF THE YTTERBIUM WITHIN THE OPTIMIZED RELATIVISTIC MANY-BODY PERTURBATION THEORY

Theoretical studying spectrum of the excited states for the ytterbium atom is carried out within the relativistic many-body perturbation theory with ab initio zeroth approximation and generalized relativistic energy approach. The zeroth approximation of the relativistic perturbation theory is provided by the optimized Dirac-Kohn-Sham ones. Optimization has been fulfilled by means of introduction of the parameter to the Kohn-Sham exchange potentials and further minimization of the gauge-non-invariant contributions into radiation width of atomic levels with using relativistic orbital set, generated by the corresponding zeroth approximation Hamiltonian. The obtained theoretical data on energies E and widths W of the ytterbium excited states are compared with alternative theoretical results (the Dirac-Fock, relativistic Hartree-Fock, perturbation theories) and available experimental data. Analysis shows that the theoretical and experimental values ​​of energies are in good agreement with each other, however, the values ​​of widths differ significantly. In our opinion, this fact is explained by insufficiently accurate estimates of the radial integrals, the use of unoptimized bases, and some other approximations of the calculation.

RELATIVISTIC CALCULATION OF WAVELENGTHS AND E1 OSCILLATOR STRENGTHS IN Li-LIKE MULTICHARGED IONS AND GAUGE INVARIANCE PRINCIPLE

The spectral wavelengths and oscillator strengths for 1s22s (2S1/2) → 1s23p (2P1/2) transitions in the Li-like multicharged ions with the nuclear charge Z=28,30 are calculated on the basis of the combined relativistic energy approach and relativistic many-body perturbation theory with the zeroth order optimized Dirac-Kohn-Sham one-particle approximation and gauge invariance principle performance. The comparison of the obtained results with available theoretical and experimental (compilated) data is performed. The important point is linked with an accurate accounting for the complex exchange-correlation (polarization) effect contributions and using the optimized one-quasiparticle representation in the relativistic many-body perturbation theory zeroth order that significantly provides a physically reasonable agreement between theory and precise experiment.

RELATIVISTIC CALCULATION OF THE RADIATIVE TRANSITION PROBABILITIES AND LIFETIMES OF EXCITED STATES FOR THE RUBIDIUM ATOM IN A BLACK-BODY RADIATION FIELD

We present the results of relativistic calculation of the radiative transition probabilities and excited states lifetimes for a heavy Rydberg atomic systems in a black-body (thermal) radiation field on example of the rubidium. As theoretical approach we apply the combined generalized relativistic energy approach and relativistic many-body perturbation theory with ab initio Dirac zeroth approximation. There are obtained the calculational data for the radiative transition probabilities and excited states lifetimes, in particular, the rubidium atom in the Rydberg states with principal quantum number n=10-100. It is carried out the comparison of obtained theoretical data on the effective lifetime for the group of Rydberg nS states of the rubidium atom at a temperature of T = 300K with experimental data as well as data of alternative theoretical calculation based on the improved quasiclassical model. It is shown that the accuracy of the theoretical data on the radiative transition probabilities and excited states lifetimes is provided by a correctness of the corresponding relativistic wave functions and accounting for the exchange-correlation effects.

CASCADE OF AUGER TRANSITIONS IN SPECTRUM OF XENON: THEORETICAL DATA

The energy parameters of the Auger transitions for the xenon atomic system are calculated within the combined relativistic energy approach and relativistic many-body perturbation theory with the zeroth order density functional approximation. The results are compared with reported experimental data as well as with those obtained by semiempirical method. The important point is linked with an accurate accounting for the complex exchange-correlation (polarization) effect contributions and using the optimized one-quasiparticle representation in the relativistic many-body perturbation theory zeroth order that significantly provides a physically reasonable agreement between theory and experiment.

RELATIVISTIC ENERGY APPROACH AND MANY-BODY PERTURBATION THEORY TO COMPUTING ELECTRON-COLLISION CROSS-SECTIONS OF COMPLEX MULTIELECTRON IONS

An advanced relativistic energy approach combined with a relativistic many-body perturbation theory with ab initio zeroth approximation is used to calculate the electron-collision excitation cross-sections for complex multielectron systems. The relativistic many-body perturbation theory is used alongside the gauge-invariant scheme to generate an optimal Dirac-Kohn-Sham- Debye-Hückel one-electron representation. The results of relativistic calculation (taking into account the exchange and correlation corrections) of the electron collision cross-sections of excitation for the neon-like ion of the krypton are presented and compared with alternative results calculation on the basis of the R-matrix method in the Breit-Pauli approximation, in the relativistic distorted wave approximation and R- matrix method in combination with Dirac-Fock approximation

NEW RELATIVISTIC APPROACH TO COMPUTING SPECTRAL PARAMETERS OF MULTICHARGED IONS IN PLASMAS

It is presented a new relativistic approach to computing the spectral parameters of multicharged ions in plasmas for different values of the plasmas screening (Debye) parameter (respectively, electron density, temperature). The approach used is based on the generalized relativistic energy approach combined with the optimized relativistic many-body perturbation theory (RMBPT) with the Dirac-Debye shielding model as zeroth approximation, adapted for application to study the spectral parameters of ions in plasmas. An electronic Hamiltonian for N-electron ion in plasmas is added by the Yukawa-type electron-electron and nuclear interaction potential. The special exchange potential as well as the electron density with dependence upon the temperature are used.

Stochastic gravity and turbulence

We study the ensemble average of the thermal expectation value of an energy momentum tensor in the presence of a random external metric. In a holographic setup this quantity can be read off of the near boundary behavior of the metric in a stochastic theory of gravity. By numerically solving the associated Einstein equations and mapping the result to the dual boundary theory, we find that the non relativistic energy power spectrum exhibits a power law behavior as expected by the theory of Kolmogorov and Kraichnan.