In this paper, the local inertial coordinate system is calculated through coordinate transformations from laboratory coordinate system. We derived the same free falling equations as those in General Relativity. However, the definitions of second and higher order covariant derivatives are different. Our results are different from the classic view of the principle of equivalence, and suggest that all the laws of physics in gravitational field can be given by doing coordinate transformations from local inertial coordinate system to lab coordinate system.
It is well known that simultaneity within an inertial frame is defined in relativity theory by a convention or definition. This definition leads to different simultaneities across inertial frames and the well known principle of relativity of simultaneity. The lack of a universal present implies the existence of past, present and future as a collection of events on a four dimensional manifold or continuum wherein three dimensions are space like and one dimension is time like. However, such a continuum precludes the possibility of evolution of future from the present as all events exist forever …
J. C. Maxwell, B. Riemann and H. Poincar$\acute{e}$ have proposed the idea that all microscopic particles are sink flows in a fluidic aether. Following this research program, a previous theory of gravitation based on a mechanical model of vacuum and a sink flow model of particles is generalized by methods of special relativistic continuum mechanics. In inertial coordinate systems, we construct a tensorial potential which satisfies the wave equations. Inspired by the equations of motion of a test particle, a definition of a metric tensor of a Riemannian spacetime is introduced. Applying Fock's …
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 …
The principle of equivalence postulating that an acceleration is indistinguishable from gravity by any experiment, is valid within families of particles having the same passive gravitational to inertial mass ratio $m_p/m_i$. Presently experimental observations indicate that we live in a universe with one single family for which $m_p/m_i=1$, but if we consider the imaginary case of a universe with several particle families having different $m_p/m_i$, the principle of equivalence would still apply to each one of them. On the basis of this generalized formulation of the equivalence principle, whi…
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…
