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We present general relativistic correction terms appearing in Newton's gravity to the second-order perturbations of cosmological fluids. In our previous work we have shown that to the second-order perturbations, the density and velocity…
The classical motion of spinning particles can be described without employing Grassmann variables or Clifford algebras, but simply by generalizing the usual spinless theory. We only assume the invariance with respect to the Poincare' group;…
A new formulation is presented for a variational calculation of $N$-body systems on a correlated Gaussian basis with arbitrary angular momenta. The rotational motion of the system is described with a single spherical harmonic of the total…
We show that gravitational solitons naturally carry gauge charges beyond those of any local quantum field. The effect of these charged excitations is to break a non-invertible symmetry to its maximal group-like sub-symmetry. Taking these…
Using the logarithmic superfluid model of physical vacuum, one can formulate a quantum theory, which successfully recovers Einstein's theory of relativity in low-momenta limit, but otherwise has different foundations and predictions. We…
Conventional non-Abelian SO(4) gauge theory is able to describe gravity provided the gauge field possesses a specific polarized vacuum state in which the instantons have a preferred orientation. Their orientation plays the role of the order…
Whereas nonrelativistic mechanics always connects the total momentum of a system to the motion of the center of mass, relativistic systems, such as interacting electromagnetic charges, can have internal linear momentum in the absence of…
The causality and stability of a relativistic hydrodynamic theory is shown to require a consensus between, either (i) newer degrees of freedom apart from the fundamental fluid fields, or (ii) a general hydrodynamic frame other than the…
We justify the Hamilton least action principle for the Maxwell-Lorentz equations with Abraham's rotating extended electron. The main novelty in the proof is application of the variational Poincare equations on the Lie group SO(3). The…
Recently there have emerged an assortment of theorems relating to the 'absoluteness of emerged events,' and these results have sometimes been used to argue that quantum mechanics may involve some kind of metaphysically radical…
This article reports the modeling of inertial rotational Brownian motion as an Ornstein-Uhlenbeck process evolving on the cotangent bundle of the rotation group, SO(3). The benefit of this approach and the use of a different…
Under certain conditions usually fulfilled in classical mechanics, the principle of conservation of linear momentum and Newton's third law are equivalent. However, the demonstration of this fact is usually incomplete in textbooks. We shall…
Planck's formula and General Relativity indicate that potential energy influences spacetime. Using Einstein's Equivalence Principle and an extension of his Chock Hypothesis, an explicit description of this influence is derived. We present a…
A description of neutrino oscillation phenomena is presented which is based on relativistic quantum mechanics and includes both entangled state and source dependent aspects, unlike both of the conventional approaches which use either equal…
Newton's Theorem of Revolving Orbits derives the force that is necessary to explain a particular precession that leaves the shape of an orbit unchanged. Newton showed that for an orbiting body that is already subject to any central force,…
Aspects of the full theory of loop quantum gravity can be studied in a simpler context by reducing to symmetric models like cosmological ones. This leads to several applications where loop effects play a significant role when one is…
Recent general-relativistic extensions of Newtonian rotation laws for self-gravitating stationary fluids allow one to rederive, in the first post-Newtonian approximation, the well known geometric dragging of frames, and two new weak-field…
In this paper we give a review of the most general approach to description of reference frames, the monad formalism. This approach is explicitly general covariant at each step, permitting to use abstract representation of tensor quantities;…
We develop a formulation of particle mechanics in which the functional relation between force and kinetic energy is derived directly from local conservation mechanical energy $E$, rather than postulated through Newton's second law or a…
A charged particle initially at rest in an external magnetic field starts to rotate when the magnetic field is switched off. This is a variant of the Feynman disc paradox, where the conservation of angular momentum is seemingly violated.…