Jaroslav Hynecek

Remarks on the Equivalence of Inertial and Gravitational Masses and on the Accuracy of Einstein's Theory of Gravity

This paper investigates the accuracy of Einstein’s theory of gravity by studying the gravitational field near a spherically symmetric non-rotating massive body. The well-known Schwarzschild metric, which describes the space-time in the vicinity of such bodies, according to Einstein’s theory of gravity, is compared with the new metric that is derived from first principles and without the use of Einstein’s field equation. The basis for the derivation of the new metric is the new mass equivalence principle derived as a consequence of thought experiments and a slightly modified Newton’s gravitational law written with the proper time and proper distance. The new theory of static gravity is therefore a scalar metric theory. The new metric predictions are evaluated and compared for accuracy with observations and with the predictions of the perihelion advance and the gravitational red shift of the Schwarzschild metric. It is found that an excellent agreement is obtained between the theory and observations and significant differences from the predictions of Schwarzschild metric are observed only in the vicinity of the Schwarzschild radius. The new metric has no problems related to the “black hole” geometry, has no coordinate pathologies, does not have the event horizon, and does not have the now famous singularity in the center of the black hole.

Resolution of the Ehrenfest paradox, Sagnac effect, and the Michelson–Morley experiment

In this article the resolution of the famous Ehrenfest paradox [1] is presented. The paradox relates to a spinning disk and the Special Relativity Theory (SRT) applied to it. The paradox resolution is based on the proposition that the paradox results from an incorrect application of SRT to a system that is not in an inertial motion. The centrifugal and centripetal forces resulting from the rotation are always present and need to be accounted for. Using the authors previously derived metric for the axially symmetric space-time the effect of centrifugal and centripetal forces can be correctly included. When this is done no paradox is obtained and it is shown that the spinning disk appears to have flat space-time geometry. This finding also provides the correct interpretation of the null result of Michelson-Morley experiment, the correct explanation of the Fizeau experiments, and a simple and consistent explanation of the Sagnac effect. The theoretical descriptions of all these experiments should, therefore, always include the effect of the centrifugal force of Earths rotation. The measured data from other experiments conducted on rotating systems are explained by the inertial mass increase as correctly described by SRT.

Relativistic pendulum and the weak equivalence principle

This paper derives equations for the relativistic proper period of oscillations of a pendulum driven by the electrical forces and for a pendulum driven by the gravitational forces. The derivations are based on the Einstein’s Special Relativity Theory and in particular on the Lorentz coordinate transformation, which has been experimentally verified many times and which is a well-recognized principle for all the modern physics. Since the pendulum proper period of oscillations is an absolute inertial motion invariant the derived formulas may be used to study the motion dependence of the inertial and gravitational masses. It is found that the well-publicized equivalence between these two masses, which is assumed independent of any inertial motion, cannot be sustained and a new mass equivalence principle must be considered where the equivalence of these two masses holds only at rest. INTRODUCTION The pendulum is an ages proven device that has attracted attention of many researchers in the past for its simplicity of operation, its accuracy to measure time, and for its ability to study the gravitational or electrical fields. One can only wonder why it was not studied in modern times in more detail, since it offers some clues for resolving the “mystery” of the inertial and gravitational mass equivalence, the so called Einstein’s week equivalence principle . Recently an interesting article was published [2] where the author derived relativistic equations of motion for the pendulum starting from a simple relativistic Lagrangian and the formula for the relativistic conservation of energy. This paper will also focus its attention of the relativistic equations of motion of the simple pendula, one that is driven by electrical forces, and the second one that is driven by gravitational forces and will compare how these pendula behave when they undergo an inertial motion relative to the laboratory coordinate system. The key idea of this work is to derive formulas for the proper period of oscillations of the particular pendulum in terms of the pendulum physical parameters such as the mass of the bob, the length of the pendulum string, and the remaining parameters of the experimental setup. Since the proper period of oscillations is an inertial motion invariant, the derived formulas must thus also be inertial motion invariants and * jhynecek@netscape.net 4/4/2006