Current approaches to the problem of inertia attempt to explain the inertial properties of matter by expressing the inertial mass appearing in Newton's second law of motion in terms of some other more fundamental interaction. One increasingly popular approach explains inertial and gravitational forces as drag forces arising due to quantum vacuum zero-point phenomena. General relativity, however, suggests that gravitational and inertial forces are manifestations of space-time geometry. Based on this, the present analysis demonstrates that inertia and zero-point forces are ultimately relativistic in origin. Additionally, it is argued that body forces induced on matter through zero-point interactions are resistive forces acting in addition to inertia.
In this paper the analogues of the Lorentz transformations for non-inertial reference frames have been obtained. A common case when the movement speed of one coordinate frame in relation to another one can have time derivatives of higher orders. The obtained transformations conserve invariance of the space-time interval, and in the particular case of inertial frames become the well-known Lorentz transformations. It is shown that the transition from classical mechanics to the theory of relativity is analogous to the consideration of the vibrating system described by the equation of the sine-Gor…
We reformulate Classical Mechanics as a timeless relativistic theory. Readers are introduced to a new class of reference systems, the binate frames, where physical events are identified with four position-coordinates -- no clocks are used. The binate frames are inertial and adaptable to relative motions. Analyses that use binate frames are valid at all energy levels. When desirable to do so, the results are easily expressed as in special relativity, in terms of space and time coordinates of inertial observers. Given the importance of mass-and-spring systems to theoretical physics, we analyzed …
Interpretation of relativistic, transverse, and longitudinal mass using the Lorentz transformation of reference time: Explanation of time dilation via spherical light clock
An important methodological problem of theoretical mechanics related to inertia is discussed. Analysis Inertia is performed in four-dimensional Minkowski space-time based on the law of conservation of energy-momentum. This approach allows us to combine the laws of conservation of momentum and angular momentum into a single law and separate the forces of inertia that actually exist in nature from the imaginary forces introduced to simplify calculations or arising from the transition from one frame of reference to another. From the energy-momentum tensor, in a non-relativistic approximation, the…
Wide binary stars are within the low-acceleration regime in which galactic rotation curves deviate from Newtonian or general relativistic predictions. It has recently been observed that their rotation rates are similarly anomalous in a way that dark matter cannot explain, since it must be smooth on these small scales to fit galaxy rotation curves. Here, it is shown that Newtonian/GR models cannot predict these wide binaries since dark matter cannot be applied. It is also shown that MoND cannot predict these systems. However, a model which assumes that inertia is due to Unruh radiation made inh…
Riemann's principle "force equals geometry" provided the basis for Einstein's General Relativity - the geometric theory of gravitation. In this paper, we follow this principle to derive the dynamics for any static, conservative force. The geometry of spacetime of a moving object is described by a metric obtained from the potential of the force field acting on it. We introduce a generalization of Newton's First Law - the \emph{Generalized Principle of Inertia} stating that: \emph{An inanimate object moves inertially, that is, with constant velocity, in \emph{its own} spacetime whose geometry is…
The paper discusses, first, distinctions between gravitational and inertial masses (considered as isotopic field-charge (IFC)siblings of the gravitational field), and the ways, how they modify physical theories, including GTR. It shows that their equivalence does not mean identity. Introduction of qualitatively different mass terms modifies (among others) the gravitational equation. That leads to apparently losing its symmetry. In order to keep the symmetry of the stress-energy tensor, then, the paper identifies a symmetry group by the help of the tau algebra, which is isomorphic with the SU(2…
