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General Relativity has had tremendous successes on both theoretical and experimental fronts for over a century by now. However, the theory contents are far from being exhausted. Only very recently, with gravitational wave detection from colliding black holes, have we started probing gravity behavior in the strongly non-linear regime. Even today, black hole studies keep revealing more and more paradoxes and bizarre results. In this paper, inspired by David Hilberts startling observation, we show that, contrary to the conventional wisdom, a freely falling test particle feels gravitational repulsion by a black hole as seen by an asymptotic observer. We dig deeper into this relativistic gravity surprising behavior and offer some explanations.
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In this work we consider some consequences of the Bohr-Sommerfeld-Hansson (Old or quasi-classical) quantum theory of the Newtonian gravity, i.e. of the gravitational atom. We prove that in this case (for gravitational central force and quantized angular momentum) centrifugal acceleration becomes formally-theoretically dependent (proportional to fourth degree) of the mass of gravitational electron rotating around gravitational nucleus for any quantum number (state). It seemingly leads toward a paradoxical breaking of the relativistic equivalence principle which contradicts to real experimental data. We demonstrate that this equivalence principle breaking does not really appear in the (quasi classical) quantum theory, but that it necessary appears only in a hypothetical extension of the quantum theory that needs a classical like interpretation of the Bohr-Sommerfeld angular momentum quantization postulate. It is, in some sense, similar to Bell-Aspect analysis that points out that a hypothetical deterministic extension of the quantum mechanics, in distinction to usual quantum mechanics, can reproduce experimental data if and only if it is non-local (superluminal) in contradiction with relativistic locality (luminality) principle.
Are Dark Matter and Dark Energy the result of uncalculated addition derivatives? The need to introduce dark matter dark and energy becomes unnecessary if we consider that, the phenomenon of dark matter and dark energy is a result of not computing the additional derivatives of the equation of motion. For this purpose, we use higher derivatives in the form of non-local variables, known as the Ostrogradsky formalism. As a mathematician, Ostrogradsky considered the dependence of the Lagrange function on acceleration and its higher derivatives with respect to time. This is the case that fully correspond with the real frame of reference, and that can be both inertial and non-inertial frames. The problem of dark matter and dark energy presented starting from basic observations to explain the different results in theory and experiment. The study of galactic motion, especially the rotation curves, showed that a large amount of dark matter can be found mainly in galactic halos. The search for dark matter and dark energy has not confirmed with the experimental discovery of it, so we use Ostrogradsky formalities to explain the effects described above, so that the need to introduce dark matter and dark energy disappears.
Turbulence is defined as an eddy-like state of fluid motion where the inertial-vortex forces of the eddies are larger than any other forces that tend to damp the eddies out. By this definition, turbulence always cascades from small scales where vorticity is created to larger scales where turbulence fossilizes. Fossil turbulence is any perturbation in a hydrophysical field produced by turbulence that persists after the fluid is no longer turbulent at the scale of the perturbation. Fossil turbulence patterns and fossil turbulence waves preserve and propagate energy and information about previous turbulence. Ignorance of fossil turbulence properties can be dangerous. Examples include the Osama bin Laden helicopter crash and the Air France 447 Airbus crash, both unfairly blamed on the pilots. Observations support the proposed definitions, and suggest even direct numerical simulations of turbulence require caution.
The so-called principle of relativity is able to fix a general coordinate transformation which differs from the standard Lorentzian form only by an unknown speed which cannot in principle be identified with the light speed. Based on a reanalysis of the Michelson-Morley experiment using this extended transformation we show that such unknown speed is analytically determined regardless of the Maxwell equations and conceptual issues related to synchronization procedures, time and causality definitions. Such a result demonstrates in a pedagogical manner that the constancy of the speed of light does not need to be assumed as a basic postulate of the special relativity theory since it can be directly deduced from an optical experiment in combination with the principle of relativity. The approach presented here provides a simple and insightful derivation of the Lorentz transformations appropriated for an introductory special relativity theory course.
In this work we consider an extraordinary quantum mechanical effect when, roughly speaking, the nucleus of an atom becomes (linearly) larger than the whole atom. Precisely, we consider Helium ion (in the ground state of the electron) moving translationally with the speed much smaller than speed of the electron rotation. This translation, effectively, changes neither the total momentum, nor the de Broglie wave length of the electron, nor the linear size of the atom corresponding to the diameter of the electron orbit. But, this translation implies a small nucleus momentum and nuclear de Broglie wavelength almost hundred times larger than the electron de Broglie wavelength. In the measurement of the nucleus wavelength using a diffraction apparatus with a characteristic length constant proportional to the proposed nucleus wavelength, according to standard quantum mechanical formalism, the nucleus behaves practically certainly as a wave. Then the unique, irreducible linear characteristic size for such a nucleus is de Broglie wavelength. Such a measurement effectively influences neither the electron dynamics nor linear size of the atom. This implies that, in such measurement, the size of the nucleus is in one dimension larger than the whole atom, i.e. electron orbital. All this corresponds metaphorically to the famous Leonardo fresco Last Supper where Jesus words coming from the nucleus, i.e. center of the composition, cause an expanding superposition or dramatic wave-like movement of the apostles.
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