GEODYNAMICS

The basic goal of this study (as the first step) is to collect the appropriate set of the fundamental astronomic-geodetics parameters for their further use to obtain the components of the density distributions for the terrestrial and outer planets of the Solar system (in the time interval of more than 10 years). The initial data were adopted from several steps of the general way of the exploration of the Solar system by iterations through different spacecraft. The mechanical and geometrical parameters of the planets allow finding the solution of the inverse gravitational problem (as the second stage) in the case of the continued Gaussian density distribution for the Moon, terrestrial planets (Mercury, Venus, Earth, Mars) and outer planets (Jupiter, Saturn, Uranus, Neptune). This law of Gaussian density distribution or normal density was chosen as a partial solution of the Adams-Williamson equation and the best approximation of the piecewise radial profile of the Earth, including the PREM model based on independent seismic velocities. Such conclusion already obtained for the Earth’s was used as hypothetic in view of the approximation problem for other planets of the Solar system where we believing to get the density from the inverse gravitational problem in the case of the Gaussian density distribution for other planets because seismic information, in that case, is almost absent. Therefore, if we can find a stable solution for the inverse gravitational problem and corresponding continue Gaussian density distribution approximated with good quality of planet’s density distribution we come in this way to a stable determination of the gravitational potential energy of the terrestrial and giant planets. Moreover to the planet’s normal low, the gravitational potential energy, Dirichlet’s integral, and other planets’ parameters were derived. It should be noted that this study is considered time-independent to avoid possible time changes in the gravitational fields of the planets.

INVESTIGATION OF THE ABSOLUTENESS OF TIME

In classical physics, time is considered absolute. It is believed that all processes, regardless of their complexity, do not affect the flow of time The theory of relativity determines that the flow of time for bodies depends both on the speed of movement of bodies and on the magnitude of the gravitational potential. It is believed that time in space orbit passes slower due to the high speed of the spacecraft, and faster due to the lower gravitational potential than on the surface of the Earth. Currently, the dependence of time on the magnitude of the gravitational potential and velocity (relativistic effect) is taken into account in global positioning systems. However, studying the relativistic effect, scientists have made a wrong interpretation of the difference between the clock frequency of an orbiting satellite and the clock frequency on the Earth's surface. All further studies to explain the relativistic effect were carried out according to a similar scenario, that is, only the difference in clock frequencies under conditions of different gravitational potentials was investigated. While conducting theoretical research, I found that the frequency of the signal changes along the way from the satellite to the receiver due to the influence of Earth's gravity. It was found that the readings of two high-precision clocks located at different heights will not differ after any period of time, that is, it is shown that the flow of time does not depend on the gravitational potential. It is proposed to conduct full-scale experiments, during which some high-precision clocks are sent aboard the space station, while others remain in the laboratory on the surface of the earth. It is expected that the readings of the satellite clock will be absolutely identical to the readings of the clock in the Earth laboratory.

Red shift of photon frequency in the gravitational field

It has been well known that there is a redshift of photon frequency due to the gravitational potential. Scott et al. [Can. J. Phys. 44 (1966) 1639, https://doi.org/10.1139/p66-137 ] pointed out that general relativity theory predicts the gravitational redshift. However, using the quantum mechanics theory related to the photon Hamiltonian and photon Schrodinger equation, we calculate the redshift due to the gravitational potential. The result is exactly the same as that from the general relativity theory.

Relativity of Energy

After proposing the Principle of Minimum Gravitational Potential, in a pursuit to find the explanation behind the correction to Newton's gravitational potential that accounts for Mercury's orbit, by finding all the higher-order corrections it is shown that the consequences of the existence of speed of light for gravity are not yet fully explored.

Effect of the Cubic Torus Topology on Cosmological Perturbations

We study the effect of the cubic torus topology of the Universe on scalar cosmological perturbations which define the gravitational potential. We obtain three alternative forms of the solution for both the gravitational potential produced by point-like masses, and the corresponding force. The first solution includes the expansion of delta-functions into Fourier series, exploiting periodic boundary conditions. The second one is composed of summed solutions of the Helmholtz equation for the original mass and its images. Each of these summed solutions is the Yukawa potential. In the third formula, we express the Yukawa potentials via Ewald sums. We show that for the present Universe, both the bare summation of Yukawa potentials and the Yukawa-Ewald sums require smaller numbers of terms to yield the numerical values of the potential and the force up to desired accuracy. Nevertheless, the Yukawa formula is yet preferable owing to its much simpler structure.

Black Holes as Markers of Dimensionality

Black hole temperature TBH = TP/2πd as a function of its Planck length real diameter multiplier d is derived from black hole surface gravity and Hawking temperature w.l.o.g. It is conjectured d = 1/2π describes primordial Big Bang singularity as in this case TBH = TP. A black hole interacts with the environment and observable black holes have uniquely defined Delaunay triangulations with a natural number of spherical triangles having Planck areas (bits), where a Planck triangle is active and has gravitational potential of -c2 if all its vertices have black hole gravitational potential of -c2/2 and is inactive otherwise. As temporary distribution of active triangles on an event horizon tends to maximize Shannon entropy a black hole is a fundamental, one-sided thermodynamic equilibrium limit for a dissipative structure. Black hole blackbody radiation, informational capacity fluctuations, and quantum statistics are discussed. On the basis of the latter, wavelength bounds for BE, MB, and FD statistics are derived as a function of the diameter multiplier d. It is shown that black holes feature wave-particle duality only if d ≤ 8π, which also sets the maximum diameter of a totally collapsible black hole. This outlines the program for research of other nature phenomena that emit perfect blackbody radiation, such as neutron stars and white dwarfs.

Tracker-assisted modelling: simultaneous validation of the conservation law of energy and the work-energy theorem

The video of a free-falling object was analysed in Tracker in order to extract the position and time data. On the basis of these data, the velocity, gravitational potential energy, kinetic energy, and the work done by gravity were obtained. These led to a rather simultaneous validation of the conservation law of energy and the work–energy theorem. The superimposed plots of the kinetic energy, gravitational potential energy, and the total energy as respective functions of time and position demonstrate energy conservation quite well. The same results were observed from the plots of the potential energy against the kinetic energy. On the other hand, the work–energy theorem has emerged from the plot of the total work-done against the change in kinetic energy. Because of the accessibility of the setup, the current work is seen as suitable for a home-based activity, during these times of the pandemic in particular in which online learning has remained to be the format in some countries. With the guidance of a teacher, online or face-to-face, students in their junior or senior high school—as well as for those who are enrolled in basic physics in college—will be able to benefit from this work.

Emergent gravity and the quantum

In this essay, we show that if one starts with a universe with some matter and a cosmological constant, then quantum mechanics naturally induces an attractive gravitational potential and an effective Newton’s coupling. Thus, gravity is an emergent phenomenon and what should be quantized are the fundamental degrees of freedom from which it emerges.