- - -

THE UNIFIED THEORY OF RELATIVITY - Viraj Fernando

ABSTRACT

The reason why we have entitled this paper as 'the Unified Theory of Relativity' is because we explain the phenomena occurring in vector fields as well as gravitational fields under the same 'Universal Formal Principle' that energy has inertia, and when energy is in motion, the inertia of energy causes a resistance in the form of a drag against the background field, leading to the manifestation of various 'relativistic phenomena'. In this paper we derive the general formula for E = Mc2(Γ-1) for kinetic energy, by way of a geometrical theorem and show how it tends to 1/2Mv2 at low velocities. We demonstrate by derivation that the physical basis of Lorentz transformation is the fact that energy has inertia, and that when energy is in motion this inertia develops a resistance to the background space. In our theory, the constancy of the velocity of light is no more a postulate as in Einstein's theory. We demonstrate with facts confirmable by experiments, that there is a physical mechanism of self-adjustment between spin and linear momenta of an energy transmission in order to move at the constant translational velocity c. We also show how the gravitational redshift, the cosmological redshift and the aberration of starlight are manifestations of this mechanism of self-adjustment between spin and linear momenta. On the basis of the same 'universal formal principle': of possession of inertia by energy, and that when energy is in motion, this inertia develops a resistance to the background field, we show how an energy transmission deflects the direction of its transmission in gravitational fields. Unlike in Einstein's theory (where two equations are involved) we not only predict the advancement of the perihelion of planets and the bending of a ray of light under one and the same equation, but we also obtain a result of very high accuracy for the bending of a ray of light by a deflection of 1.313" as against 1.74" in Einstein's theory which has an error of over 20%. This will be the decisive test between the two theories.

INTRODUCTION

This paper finds explanations for all relativistic phenomena under a unified theory based on first principles originating from some of the concepts of Einstein, Maxwell and Newton which have not received the due attention in modern physics. This approach is in contrast to Einstein's constructive approach where the special theory or the general theory are required discriminately to explain these same phenomena depending on whether they occur in vector fields or gravitational fields. We have in our approach provided new dynamic explanations and predictions for some of the phenomena for which theory of relativity has been able to provide only kinematic explanations or none at all (e.g. aberration of starlight). And for some phenomena, we have also provided more accurate predictions, where the theory of relativity has been able to predict results only partially (e.g. bending of a ray of light, gravitational redshift). How we have arrived at this new approach is as follows.

Upon careful scrutiny of Einstein's 'Autobiographical Notes', the essays by other physicists, and Einstein's responses to these essays in the same book (1), it becomes clear that Einstein himself has considered his constructive theories to be tentative. Einstein goes so far as to say that there is a "right way and we are capable of finding it" implying that the way by which he has developed the theory is not the right way. Filmer Northrop points to this position taken up by Einstein and indicates that this is an unequivocal admittance by Einstein that his basic tenet of spatio-temporal relatedness in nature on which theory of relativity is constructed is a mere mental construct (1, p.398). In response Einstein endorses Northrop's view: "I see in this critique a masterpiece of unbiased thinking and concise discussion which nowhere permits it to be diverted from the essential" (1, p. 683). This situation necessitates us to review some of Einstein's ideas in his formative period and to consider whether his theory could be reformulated.

In reviewing Einstein's ideas in the early period, we find that as a corollary to the very first paper on special theory of relativity, and in the same volume of Annalen der Physik Vol 17, 1905, Einstein has written an accompanying paper on Inertia of Energy (2, p.69). In the same year (in Vol 18), he has written the rigorous derivation of the expression for inertia of energy, and then again he has written yet another paper on the same subject in 1906 (1, p. 524). All these show how much of importance Einstein has ascribed to the concept of inertia of energy originally, at the formative stages of his theory. It appears that Einstein has had a hunch that inertia of energy is the physical basis of relativistic phenomena, but his pre-occupation with the novel concepts of relativity of simultaneity and the spatio-temporal relatedness which he mistakenly thought to hold the key to unravelling of the mystery of Lorentz transformations, has obscured the simple path to the explanation of relativistic phenomena in terms of inertia of energy.

Einstein therefore has proved the 'law of inertia of energy' relativistcally (1, p.524), when in fact he should have proved the converse, that relativistic phenomena arise from the existence of inertia of energy.

It appears that it was while Einstein was still grappling to incorporate inertia of energy into the theory, that Minkowski has made the fatal formulation of the theory in terms of "world geometry" in 1908. It is worth noting that Einstein had at first rejected Minkowski's proposals. According to Arnold Sommerfeld: "When.. Minkowski built up the special theory of relativity into his 'world geometry' Einstein said on one occasion: 'Since the mathematicians have invaded the theory of relativity, I don't understand it myself anymore'. But soon after, at the time of the conception of the general theory of relativity, he readily acknowledged the indispensability of the four dimensional scheme of Minkowski" (1, p.102). We see here Einstein making a decision to abandon his preferred path of physics, and adopting mathematical physics instead, under youthful haste and expediency of developing his theory to embrace all phenomena around the year 1912. (In contrast to Einstein's approach, in the present paper we develop the theory on the premise that the inertia of energy is the physical basis of relativistic phenomena).

It is not only that Einstein has indicated that there is a "right way" as against the detour he has taken in terms of mathematical physics, but he has even ventured to point out the type of theory this "right way" would lead to. Although Einstein developed his relativity theory as a 'constructive theory', it becomes clear that he was convinced of the superiority of 'theories of principle', of the type of classical thermodynamics from the following statement. 'It (thermodynamics) is the only physical theory of universal content concerning which I am convinced that, it will never be overthrown...'(1, p.33). Therefore, contrasting the provisional nature of his theory in the present constructive form, and implying the necessity to write it as a theory of principle, he wrote, "there is, in my opinion, a right way, and that we are quite capable of finding it ....." (1, p. 398).
Einstein also wrote: .... 'The longer and the more despairingly I tried, the more I came to the conviction that only the discovery of a universal formal principle could lead to 3
assured results. The example I saw before me was thermodynamics. The general principle was there given in the theorem: the laws of nature are such that it is impossible to construct a perpetuum mobile' (1, p.53).

In thermodynamics, the impossibility of construction of a perpetuum mobile was demonstrated by Sadi Carnot, by showing that even in an ideal engine, where all the radiative, frictional etc., heat losses have been eliminated, there would still be a fraction of heat that will defect without being converted to work. Due to this defection of the fraction of heat, the construction of a perpetuum mobile becomes impossible. The greater the ambient temperature relative to the temperature of the source, greater the defective fraction of heat and lesser the heat available for the conversion to work. It was found that if the data were extrapolated so that the ambient temperature is reduced to absolute zero, then this fraction that defects disappears altogether, and the total heat produced would be available for conversion to work completely. There is a striking similarity between this and the implications of Maxwell's equations. The momentum available to move a charge appears to defect a fraction of it, depending on the velocity of the proper reference frame, and consequently work is performed only partially, when that reference frame is in motion. When the data are extrapolated so that the velocity of the proper reference frame is zero, the total momentum becomes completely available for work. Therefore, this was found to be analogical to the impossibility of construction of the perpetuum mobile in thermodynamics. However, a study of the pattern of changes of co-ordinates in a motion of a particle revealed that it follows a more complicated form - Lorentz transformation. Einstein therefore wrote intuitively, (i.e. without demonstrating how this analogy works), stating that: "The universal principle of the special theory of relativity is contained in the postulate: the laws of physics are invariant with respect to the Lorentz-transformations. .... This is a restricting principle for natural laws, comparable to the restricting principle of the non-existence of the perpetuum mobile which underlies thermodynamics" (1, p.57). We demonstrate how this analogy works in Appendix II.

Towards the end of his career Einstein came to the conclusion that there is a "total field". "Our problem is that of finding the field equations for the total field"(1, p. 89). In this paper in deriving the equation E = Mc2(Γ -1) for the quantity of kinetic energy required to set a body in motion, we prove that the momentum necessary for the motion of matter emanates from the "total field".

Maxwell realised that there are errors and omissions in the Newtonian conceptual framework and to address this problem he set out to develop his programme. "....the determination of the quantity of energy which enters or leaves a material system during the passage of the system from its standard state to any other definite state" (3, p. 74). Maxwell has insisted that in the implementation of this programme, the changes of configuration and motion, and the energy that enters or leaves a system, must be considered in extreme generality (3, p. 122). We believe that our theory is a synthesis of the conceptions of Newton and Maxwell together with some of Einstein's ideas in his formative stages which he abandoned in preference to Minkowski postulates.

Considering all the above factors, we believe that Einstein himself would have arrived at the simple theory we are presenting in this paper, had he not made the fatal error under expedient circumstances of following the path of mathematical physics chartered out by Minkowski.

(Download the whole paper here)

Email the author

See also:

WHERE DR. EINSTEIN WENT WRONG
Finding the Virtual Velocity of Light, Solving the Mystery of the Failed Michelson-Morley Experiment