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We define passive gravitational mass operator of a hydrogen atom in the post-Newtonian approximation of general relativity and show that it does not commute with energy operator, taken in the absence of gravitational field. Nevertheless,…

We describe "small bodies" in a non-metric gravity theory previously studied by this author. The main dynamical field of the theory is a certain triple of two-forms rather than the metric, with only the spacetime conformal structure, not…

Based on the model of a "soft" cellular space and deterministic quantum mechanics developed previously, the scattering of a free moving particle by structural units of the space -- superparticles -- is studied herein. The process of energy…

We consider the angle in mathematics and arrive at a conclusion that there are two concepts on the issue. One is a descriptive geometrical one, while the other is from functional analysis. They are somewhat different, allow for different…

We derive an expression for effective gravitational mass for any closed spacelike 2-surface. This effective gravitational energy is defined directly through the geometrical quantity of the freely falling 2-surface and thus is well adapted…

Any complete theory of physical reality must allow for the ubiquitous phenomenon of subjective experience at some level, or risk being conceptually incoherent. However, as long as the ontological status of subjectivity itself remains…

I analyze the meaning of mass in Newtonian mechanics. First, I explain the notion of primitive ontology, which was originally introduced in the philosophy of quantum mechanics. Then I examine the two common interpretations of mass: mass as…

After a short review on the use of time in various branches of physics, I suggest to change the interpretation of time, from a duration to a cut. A reassessment of terminology is also required to avoid meaning traps. I also address the…

This writing: a) Draws attention to the intricacies inherent to the pursuit of a universal seizure definition even when powerful, well understood signal analysis methods are utilized to this end; b) Identifies this aim as a multi-objective…

Courses in mathematical methods for physics students are not known for including too much in the way of mathematical rigour and, in some ways, understandably so. However, the conditions under which some quite commonly used mathematical…

The existence of static, self-gravitating elastic bodies in the non-linear theory of elasticity is established. Equilibrium configurations of self-gravitating elastic bodies close to the reference configuration have been constructed in [6]…

The idea of viewing gravitation as a many body phenomenon is put forward here. Physical arguments supporting this idea are briefly reviewed. The basic mathematical object of the new gravitational mechanics is a matrix of operators. Striking…

The concept of time is discussed in the context of the canonical formulation of the gravitational field. Using a hypersurface orthogonal foliation, the arbitrariness of the lapse function is eliminated and the shift vector vanishes,…

Mass is an important concept in classical mechanics, which regards a particle as a corpuscular object. But according to wave-particle duality, we know a free particle can behave like a wave. Is there a wave property that corresponds to the…

The classical concept of "mass density" is not fundamental to the quantum theory of matter. Therefore, mass density cannot be the source of gravitation. Here, we treat electromagnetic energy, momentum, and stress as its source. The…

The definitions of gravitational work as well as work done by the total external force on a massive probe particle moving in generic spacetime backgrounds are proposed. These definitions are given in the form of scalar integrals and thus,…

It is shown that, contrary to what is normally expected, it is possible to have angular momentum effects on the geometry of space time at the laboratory scale, much bigger than the purely Newtonian effects. This is due to the fact that the…

In this paper, we argue that there are foundational dilemmas in theoretical physics related to the concept of reality and the nature of mathematics in physics. Physical theory is treated as a conceptual organism which develops under the…

We shall review conformal gravity as a gauge natural theory and discuss the consequences of Weyl covariance on the definition of physical states.

It is shown that a gravitational compression of a spherical body results in an infinite growth of the energy of a body as its radius comes close to $GM/c^2$. This gives rise to a negative defect of mass and, due to an instability, to an…