-
=============================

Theorem I - Kinetic Energy = Mc
2
( v
-1)



Theorem III The Physical Basis of the Lorentz Transformation
Inertia of Energy Resistance to Motion of the Background Space - Action of Field Momentum



Theorem IX The Deflection of the Direction of Energy Transmissions in
Gravitational Fields
Advancement of the Perihelion of Mercury Bending of a Ray of Light in a Gravitational Field
3GM/Rc
2

= sin
2
(1- sin
2
)
-1/2
; sin
= (3GM/Rc
2
)
1/2

= 2. = 41.162 = 1.313

Theorem XII The Physical Basis of the Constancy of the Velocity of Light

The Cosmological Redshift The Aberration of Starlight
=
0
[1 (Ht/c)
2
]
1/2
1
/ 2
= u
(c-u)/c


1
THE UNIFIED THEORY OF RELATIVITY -
Viraj Fernando

THE 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 = Mc
2
(
-1) for kinetic energy, by way of a
geometrical theorem and show how it tends to 1/2Mv
2
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 Einsteins 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 Einsteins 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 Einsteins theory which has an error of over 20%. This will be the decisive test
between the two theories.

THE 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 Einsteins 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 Einsteins Autobiographical Notes, the essays by other
physicists, and Einsteins 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
2
response Einstein endorses Northrops 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 Einsteins ideas
in his formative period and to consider whether his theory could be reformulated.

In reviewing Einsteins 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
Minkowskis 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 dont 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 Einsteins 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,