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.

Gravitational “Doppler Boosting / De-boosting” Effect within the Framework of General Relativity

The “Doppler boosting / de-boosting” relativistic effect increases / decreases the apparent luminosity of approaching / receding sources of radiation. This effect was analyzed in detail within the Special Relativity framework and was confirmed in many astronomical observations. It is however not clear if “Doppler boosting / de-boosting” exists in the framework of General Relativity as well, and if it exists, which equations describe it. The “Einstein’s elevator” and Einstein’s “Equivalence principle” allow to obtain the formula for “Doppler boosting / de-boosting” for a uniform gravitational field within the vicinity of the emitter/receiver. Under these simplified conditions, the ratio ℳ between apparent (L) and intrinsic (Lo) luminosity can be conveniently represented using source’s spectral index α and gravitational redshift z as ℳ(z, α) ≡ L/Lo=(z+1)^(α-3). This is the first step towards the complete set of equations that describe the gravitational "Doppler boosting / de-boosting" effect within the General Relativity framework including radial gravitational field and arbitrary values of distance h between emitter and receiver.

Shouldn’t Doppler 'De-boosting' be accounted for in calculations of intrinsic luminosity of Standard Candles?

"Doppler boosting / de-boosting" is a well-known relativistic effect that alters the apparent luminosity of approaching/receding radiation sources. "Doppler boosting" alters the apparent luminosity of approaching light sources to appear brighter, while "Doppler de-boosting" alters the apparent luminosity of receding light sources to appear fainter. While "Doppler boosting / de-boosting" has been successfully accounted for and observed in relativistic jets of AGN, double white dwarfs, in search of exoplanets and stars in binary systems it was ignored in the establishment of Standard Candles for cosmological distances. A Standard Candle adjustment appears necessary for "Doppler de-boosting" for high Z, otherwise we would incorrectly assume that Standard Candles appear dimmer, not because of "Doppler de-boosting" but because of the excessive distance, which would affect the entire Standard Candles ladder at cosmological distances. The ratio between apparent (L) and intrinsic (Lo) luminosities as a function of redshift Z and spectral index α is given by the formula ℳ(Z) = L/Lo=(Z+1)^(α-3) and for Type Ia supernova as ℳ(Z) = L/Lo=(Z+1)^(-2). These formulas are obtained within the framework of Special Relativity and may require adjustments within the General Relativity framework.

Relativistic quantum bouncing particles in a homogeneous gravitational field

In this paper, we study the relativistic effect on the wave functions for a bouncing particle in a gravitational field. Motivated by the equivalence principle, we investigate the Klein–Gordon and Dirac equations in Rindler coordinates with the boundary conditions mimicking a uniformly accelerated mirror in Minkowski space. In the nonrelativistic limit, all these models in the comoving frame reduce to the familiar eigenvalue problem for the Schrödinger equation with a fixed floor in a linear gravitational potential, as expected. We find that the transition frequency between two energy levels of a bouncing Dirac particle is greater than the counterpart of a Klein–Gordon particle, while both are greater than their nonrelativistic limit. The different corrections to eigen-energies of particles of different nature are associated with the different behaviors of their wave functions around the mirror boundary.

"Doppler De-boosting" and the Observation of "Standard Candles" in Cosmology

“Doppler boosting” is a well-known relativistic effect that alters the apparent luminosity of approaching radiation sources. “Doppler de-boosting” is the same relativistic effect observed but for receding light sources (e.g. relativistic jets of AGN and GRB). “Doppler boosting” alters the apparent luminosity of approaching light sources to appear brighter, while “Doppler de-boosting” alters the apparent luminosity of receding light sources to appear fainter. While “Doppler de-boosting” has been successfully accounted for and observed in relativistic jets of AGN, it was ignored in the establishment of Standard candles for cosmological distances. A Standard Candle adjustment of Z>0.1 is necessary for “Doppler de-boosting”, otherwise we would incorrectly assume that Standard Candles appear dimmer, not because of “Doppler de-boosting” but because of the excessive distance, which would affect the entire Standard Candles ladder at cosmological distances. The ratio between apparent (L) and intrinsic (Lo) luminosities as a function of the redshift Z and spectral index α is given by the formula ℳ(Z) = L/Lo=(Z+1)α -3 and for Type Ia supernova appears as ℳ(Z) = L/Lo=(Z+1)-2. “Doppler de-boosting” may also explain the anomalously low luminosity of objects with a high Z without the introduction of an accelerated expansion of the Universe and Dark Energy.

“Doppler de-boosting” and the observation of “Standard candles” in cosmology

“Doppler boosting” is a well-known relativistic effect that alters the apparent luminosity of approaching radiation sources. “Doppler de-boosting” is the name of relativistic effect observed for receding light sources (e.g. relativistic jets of active galactic nuclei and gamma-ray bursts). “Doppler boosting” changes the apparent luminosity of approaching light sources to appear brighter, while “Doppler de-boosting” causes the apparent luminosity of receding light sources to appear fainter. While “Doppler de-boosting” has been successfully accounted for and observed in relativistic jets of AGN, it was ignored in the establishment of Standard candles for cosmological distances. A Standard candle adjustment of an Z>0.1 is necessary for “Doppler de-boosting”, otherwise we would incorrectly assume that Standard Candles appear dimmer not because of “Doppler de-boosting” but because of the excessive distance, which would affect the entire Standard Candles ladder at cosmological distances. The ratio between apparent (L) and intrinsic (Lo) luminosities as a function of the redshift Z and spectral index α is given by the formula ℳ(Z) = L/Lo=(Z+1)α -3 and for Type Ia supernova appears as ℳ(Z) = L/Lo=(Z+1)-2. “Doppler de-boosting” may also explain the anomalously low luminosity of objects with a high Z without the introduction of an accelerated expansion of the Universe and Dark Energy.

PREPRINT. “Doppler de-boosting” and the observation of “Standard candles” in cosmology.

PREPRINT. “Doppler boosting” is a well-known relativistic effect that alters the apparent luminosity of approaching radiation sources. “Doppler de-boosting” is the term of the same relativistic effect observed for receding light sources (e.g.relativistic jets of active galactic nuclei and gamma-ray bursts). “Doppler boosting” alters the apparent luminosity of approaching light sources to appear brighter, while “Doppler de-boosting” alters the apparent luminosity of receding light sources to appear fainter. While “Doppler de-boosting” has been successfully accounted for and observed in relativistic jets of AGN, it was ignored in the establishment of Standard candles for cosmological distances. A Standard candle adjustment of Z>0.1 is necessary for “Doppler de-boosting”, otherwise we would incorrectly assume that Standard Candles appear dimmer, not because of “Doppler de-boosting” but because of the excessive distance, which would affect the entire Standard Candles ladder at cosmological distances. The ratio between apparent (L) and intrinsic (Lo) luminosities as a function of the redshift Z and spectral index α is given by the formula ℳ(Z) =L/Lo=(Z+1)^(α-3) and for Type Ia supernova appears as ℳ(Z)=L/Lo=(Z+1)^(-2). “Doppler de-boosting” may also explain the anomalously low luminosity of objects with a high Z without the introduction of an accelerated expansion of the Universe and Dark Energy.

On the reformulation of the Thomas–Fermi model to make it compatible with the Planck-scale

Thomas–Fermi model is considered here to make it cogent to capture the Planck-scale effect with the use of a generalization of uncertainty relation. Here generalization contains both linear and quadratic terms of momentum. We first reformulate the Thomas–Fermi model for the non-relativistic case. We have shown that it can also be reformulated for taking into account the relativistic effect. We study the dialectic screening for both the non-relativistic and relativistic cases and find out the Fermi length for both the cases explicitly.