On conjugate complex time – II: equipotential effect of gravity retrodicts differential and predicts apparent anomalous rotation of the sun

Abstract

Equipotential effect of gravity (EEG), as opposed to radial interactions between bodies, is introduced here as the impact of a tangential potential. EEG causes frequency decrease that was observed in two specially devised and several indirect experiments. It depends on the distance that is measured along equipotential parts of trajectories and can explain an extraneous frequency decrease found in radio signals emitted by navigational positioning systems. It retrodicts the observed differential rotation of the sun without the assumed drag of the sun's photosphere as its cause, and predicts apparent anomalous rotation of the sun, for from the shifts in spectra taken from the sun's limb it should appear as if the sun rotates away faster than it does towards an observer on earth. The value predicted by it is over 10.56% excess over Einstein's value of deflection of light near the sun and agrees with the 10–15% excess estimated from the data that was obtained in numerous, quite independent experiments.

Introduction

The extraneous frequency decrease (FD) effect that affects radio signals emitted by navigational positioning systems [1], [2] (results of these experiments were briefly discussed in the accompanying paper) was also observed in a few other experiments. Two of the other experiments are especially suitable for comparisons, because one involves only the earth whereas the other is concerned with an influence of the sun. Radio signals triggered by earth-bound atomic clocks showed distance-dependent FD, but the distance was measured on the earth's surface that is along practically equipotential trajectory [3]. Also the light rays from Taurus A [4] that crossed the sun's gravitational field close to its `surface' revealed similar FD. The FD effects appeared in addition to the gravitational frequency shift (GFS) that is predicted by the general theory of relativity (GTR). Neither gravitational nor electromagnetic theories did predict such a FD effect [5], however. The unexpected FD was much larger than GFS and transverse Doppler effects combined [3]. Possible existence of a new, near surface effect of gravity was also suggested in [6]. My goal here is to show gravitational origin of the FD effect and my objective is to keep it simple.

The notion of an equipotential effect of gravity may sound like a contradiction in terms, since all we ever learned about potential, whether that of electromagnetic or gravitational field, always referred only to the radial effect that is measured along the gradient of the given field. Although Einstein realized the mathematical possibility of its existence, he disregarded the effect as too slight when measured on the earth's surface [7], [8]. He dismissed thus the tangential effect as a tiny deviation, rather than as a tangential component of a generalized vector potential (i.e., not from a theoretical standpoint). Probably he considered the tangential effect in terms of the Taylor series expansion, but he was quite correct indeed when it came to its magnitude. Even as a tiny second order effect, however, the existence of a tangential impact of gravity may change the way we understand gravity and relativity in particular.

Though tangential effect is suggested by the aforementioned experimental data, one may ask how could it be introduced without altering the former theories that just disregarded it? For by adding new potential, one could presumably change the previously obtained results which were based on the radial potential alone, unless the two potentials are separable so that the new potential does not always have to interfere with the old one. The reader can rest assured, however, for no reasoning that involved radial potentials must be changed by introduction of a nonradial one. First, the new effect applies mostly to near surface phenomena. Second, the usage of radial potential in quantum mechanics, as in the Schrödinger equation [9], for instance, requires separation of variables which is always possible [10] and quite simple when performed in spherical coordinates. The new effect does not really affect the way in which the radial potential is utilized in that equation. For purely radial phenomena nothing changes. The new effect will change only the tangential phenomena which we used to disregard anyway. Nonetheless, it will account for a few formerly unexplained experiments without forcing us to invalidate any theory.

The Laplace equation, however, from which the usual scalar radial potential was derived, seemingly also admits some solutions with not always vanishing nonradial components [11] which would correspond to some clearly equipotential effects. The notion of the tangential potential thus would not be mathematically contradictory. Though noncontradiction could imply existence in abstract mathematics, it may not necessarily be seen as such in physics. Therefore I want to demonstrate merely the theoretical possibility, rather than necessity of the tangential potential, as well as the experimental evidence that speaks in favor of its nonradial effects. In the sense the present paper is mainly a presentation of its experimental confirmation. This is the reason why this paper is purposely restricted and so tailored as to fit the familiar ground of classical physics. And to make our discussion here more concrete, a number of very simple though indicative examples shall be given. All I want to achieve here is to show that purely nonradial, equipotential effect of gravity can be derived from the law of energy conservation and the superposition principle alone.