THE PHYSICAL BASIS OF ‘RELATIVITY’ - Part II

Experiment to Verify that Light Moves having the Gravitational Field as the Local Reference and Discussion of Experimental Data.

Viraj P.L. Fernando,

Independent Researcher on Evolution and Philosophy of Physics

193, Kaldemulla Road, Moratuwa, Sri Lanka. [email protected]

Abstract:

The part I of this paper presented a novel Kinetic Theory of Relativity based upon action of energy by way of a thermodynamic analogy. The present part of the paper will discuss important experimental data relevant to this Kinetic Theory. The experiment will explain the result of Michelson’s experiment by way of demonstrating the reason why the velocity of light remains the same with respect to Earth’s orbital motion in all directions is because light moves having the Sun’s gravitational field as the local reference frame and not the frame of Earth’ orbital motion. In the course of explaining the reasons for the result of Michelson’s experiment, we also find an explanation for the aberration of starlight.

It will be shown that all presently known experiments are consistent with the theory presented in the original paper (Part I). Since the same principle of redundancy a fraction energy applies to all cases equally, the case of delay of disintegration of a fast moving muon, which is supposed to fall into the domain of the special theory, and the case of the precession of the perihelion of Mercury, which is supposed to fall into the domain of the general theory are solved identically. In each case the required result is obtained by the application of the methodology of ‘synthesis of antithetical equations’. Hence the dichotomy between special theory relativity and general theory of relativity gets transcended.

Einstein’s and Lorentz’ Explanations of the Result of Michelson’s Experiment.

Lorentz contended that one arm of the apparatus of Michelson’s experiment shortens in length. He also postulated that not only the distance but the time also adjusts reciprocally in a compensatory manner, so that the effect of the velocity of the reference frame to slow down the velocity of light gets hidden, and therefore the velocity of light appears to remain the same in all directions (6, p. 172 ). Einstein considered both arms equally long in every inertial system and attributed the contraction factor to relativity of simultaneity (7, p.195). But the fact is that neither Lorentz nor Einstein has explained the result of Michelson’s experiment satisfactorily, as it would become clear from the following statements of Reichenbach. "… we can speak of an explanation (of ….Michelson’s experiment ) by Einstein’s theory as little as we can speak of an explanation by Lorentz’s theory or by classical theory. ….. It would be mistaken to argue that Einstein’s theory gives an explanation of Michelson’s experiment, since it does not do so. (The result of) Michelson’s experiment is simply taken over as an axiom" (7, pp. 201-2). It must be noted that Reichenbach was no ordinary commentator on special relativity. He was a foremost authority on the subject by virtue of the fact that he has been the prime contributor in the development of special relativity to its ‘third and final stage’ if one were to analyse the evolution of the theory and categorise it into stages of development. First stage has been developed by Einstein at the level of On Electrodynamics of moving bodies. Second stage has been developed with Minkowski’s contribution of ‘World Geometry’. And third stage has been developed beginning with the contribution by Reichenbach who has introduced ‘sets of simultaneous events’ in place of Einstein’s ‘one and only one event simultaneous with a given event’ (8, p.135 ).

Reichenbach also states: "In order to explain the (Michelson’s) experiment, Lorentz made the assumption that one arm of the apparatus is contracted by the amount (1-v2/c 2)1/2 , when it moves relative to ether. Einstein on the other hand, considered both arms equally long in every inertial system and calculated the contraction factor (1-v2/c 2)1/2 , in an entirely different manner, as a consequence of relativity of simultaneity. The opinion has been expressed that the contraction of one arm of the apparatus is an ‘ad hoc hypothesis’ while Einstein’s hypothesis is a natural explanation that is a consequence of the relativity of simultaneity. Both explanations are wrong . The relativity of simultaneity has nothing to do with the contraction in Michelson’s experiment, and Einstein’s theory explains the experiment as little as does that of Lorentz" (7, pp.195-6).

Our contention is different from that of Einstein, in regard to why velocity of light remains the same in all directions with respect to the velocity of orbit of the Earth. Our contention is that, it is as a consequence of gravitational redshift occurring due to light moving with respect to the gravitational energy of Sun’s field of gravity at the position of Earth’s orbit, as the background energy. This needs further explanation. We have shown previously that transmission of energy takes place by the action of energy within a local system between upper and lower magnitude limits of its intensive property. And for it to form the local system, it acquires the magnitude of the intensive component of background energy as the magnitude of its lower limit. Gravitational energy is equal to gravitational potential (intensive property) times mass (extensive property) of the moving object. So when we say here that ‘light moves against the background of the gravitational energy’, what we mean is that for this transmission, the energy of the photon forms a local system by adapting the intensive component of the gravitational energy (i.e., gravitational potential) as the lower limit of its intensive component.

It will be noted that the velocity of orbit of the Earth v at any given position R from the Sun is determined by the gravitational potential GM/R of the Sun’s field at that position such that v = (GM/R) 1/2 . Simply put, the photon moves against the background of the gravitational field energy, and screens off the energy of Earth’s orbital motion by means of aberration (see below). Unlike the velocity of Earth’s orbital motion, which is a vector, the gravitational potential is a scalar and its effects do not vary according to the direction considered. Therefore, the result of Michelson’s experiment is simply a case of the gravitational potential at the position of Earth’s orbit being adapted by light as the lower limit of its intensive component and consequently this affecting the energy of the photon irrespective of the direction of its motion.

An Experiment to verify that Light Moves having the Gravitational Field as the Local Reference Frame in lieu of having Earth’s Orbital Frame for it.

The above contention can be verified in the following manner. Velocity of Earth’s orbital motion is the same irrespective of whether a point on the surface of the Earth is nearest to the Sun (noon) or farthest away from it (midnight). However, the gravitational potential of the Sun’s field of where the point is located differs between noon and midnight. A Pound and Rebka type of an experiment is proposed to be performed to measure redshifts at a given elevation. (Whether it is noon or midnight the redshift due to Earth’s gravitational field at a given elevation is the same and this can be eliminated). But if there is a redshift that varies between noon and midnight it will be found that it corresponds to the variation of the gravitational potential of the Sun’s field for the point between noon and midnight. And this redshift will be uniform for light incident from all directions at a given time proving that the Sun’s gravitational field is the local reference frame of the motion of light.

The experiment will also show that there is another redshift, which does not change between noon and midnight, and that has the mean value of the varying redshift due to the Sun’s gravitational field. This redshift will be due to Earth’s orbital motion, and the value of the redshift will vary depending on the direction of incidence of light with respect to the direction of orbit of the Earth. This result will confirm that in the motion of light, it excludes the energy of Earth’s orbital motion being considered as the local reference frame, and in preference it takes the Sun’s gravitational field energy for this. And we provide the explanation of how this exclusion is done by way of explaining Bradley aberration of starlight below.

Einstein’s theory accounts for stellar aberration in the following way. Viewed from an inertial frame, light will traverse a straight path from the star to a telescope. But Earth’s motion through that inertial frame will move the telescope a small amount during the time it takes the light to pass through the telescope, causing an apparent angular shift in the star’s position. This effect has an yearly periodicity since it is due to Earth’s motion through the inertial frame (9, p.6).

This explanation that light deviates upon entering the barrel of the telescope is not quite convincing. It tries to convey the idea that if a naked eye observation were to be done, then this aberrational effect will not be there. This can be checked in the following way. A taut thin wire is attached to a frame mounted on an adjustable stand and the star is observed with the naked eye along the wire and the inclination noted. At the same moment an observation is made through a telescope which is side by side. It must be checked whether there is a difference of the inclination that corresponds to Einsteinian claim of the deviation of light inside the barrel between the wire and the axis of the telescope. Our prediction is that there will be no difference in the inclinations.

Our contention is that this change occurs at the point of incidence, because the surface of incidence - the lens of the telescope - is a part of the orbiting Earth and the deviation occurs due to addition of velocities. But, then it leads to a paradox of how the velocities add and still the velocity of light remains at the value c.

It is to be noted that the angle of aberration α corresponds to a resultant velocity of (c 2+v 2)1/2 , where α = tan -1 v/c. There is no explanation of how the velocity of light still remains c, when the angle of incidence clearly indicates that it should be (c 2+v 2)1/2 . Our explanation is that intensive components of energy are additive. Accordingly ½ c 2 adds with ½ v2 to get ½ (c 2+v 2).. Since it is this resultant intensive component is the one that would determine the resultant velocity, the photon then compensates for this excessive level of intensive component of energy, by instantaneously producing an opposing intensive component of energy equal to ½ v 2. . This brings the velocity back to c.

(c 2 + v 2) – v2 = c 2

The above is a two-step process. In the first step the intensive component of the ‘object in motion’ gets literally added to the intensive component of the other. In contrast to this, if the frame of Earth’s orbital motion were the local reference frame for the motion of the photon, then a fraction of energy determined by the intensive component of the energy of the local reference frame has to get deducted, as we showed in part I of this paper. The fact that this does not happen, but the opposite happens in the first-step indicates that the frame of Earth’s orbital motion is not the local reference frame in the motion of light.

Bradley Aberration of Starlight and the Explanation of the Result of Michelson’s Experiment.

We contend that the motion of a photon consists of two components (vortex motion): a rotational or an oscillatory motion superimposed on the translational motion of velocity c. When starlight is incident in the direction of orbital motion, the effect of the orbital motion is screened off by transferring this effect to the rotational motion of the photon. Any transfer of energy to or from the rotational component increases or decreases the rotational velocity of the photon. Since, the translational velocity c is constant, an increase in rotational velocity decreases the wavelength and vice- versa . Therefore, according as whether the starlight is incident along the direction of orbital motion or opposite to it, there has to be a red or a blue shift. It is to be expected that when starlight is incident obliquely at an angle θ to the direction of Earth’s orbital motion, the red or blue shift should decline in proportion to the cosine of the angle of incidence, until these effects disappear completely when the light is incident from the perpendicular direction. We saw such a relationship in the experiment of the two charges, where the full effect of the local reference frame (namely the loss of a fraction of energy), was there when the line of centres of the two charges was in the direction of motion of the local reference frame, and this effect disappeared totally when the line of centres was perpendicular to the latter.

However, when there are two objects that move relative to the same local reference frame, there is a resultant motion between the two even when their motions are perpendicular. This resultant motion is apparent with no physical relationship between the energy of the moving objects so long as the two objects remain apart like two cars moving on two perpendicular roads. But if the two objects impact, there comes a real physical relationship of their energies. Similar to the energy relationship of the two colliding cars, the energy relationship between the incident photon and the front piece of the telescope (as a part of the orbiting Earth), becomes real at the moment of the impact. In this, the photon as well as the telescope as a part of the orbiting Earth, are in motion relative to the Sun ’s gravitational field as the common local reference frame, similar to the two cars moving relative to Earth as their common local reference frame. The velocity and the direction of the photon relative to the telescope is determined by their velocities relative to their common local reference frame. Therefore, a photon approaching the Earth vertically, acquires a velocity relative to the telescope of the value (c 2+v 2)1/2 , and a direction inclined at tan -1v/c to the vertical as the first step just before the impact. Then in the second step just before the impact, the photon neutralizes the excessive velocity by releasing a fraction of energy acting in the direction opposite to its motion relative to the telescope, the magnitude of whose intensive component being ½v 2. This way the velocity of the photon acquires the value c relative to the telescope, while still being incident from a direction inclined at tan -1v/c to the vertical.

This type of energy adjustments occurring just prior to the moment of impact was studied and established by Boscovich in 1747, in his research into collisions of pendulums. (Boscovich’s experiment is described in full in the book ‘Concepts of Force’ by Max Jammer). It is of utmost interest to note that Boscovich made his calculations in terms of squares of velocities, namely in terms of intensive components of kinetic energy. Therefore it will be seen that it is no coincidence that in Boscovich’s work and in our work, interactions of energy occur in terms of intensive components.

For the photon to release a fraction of energy and still maintain the velocity c, it means that a photon has to have two discrete components of energy, each equal to E i in its nascent state at the instant of its generation. We contend that one of these components is bound up with the translational motion at velocity c, and the other is the ‘stored up’ component, which is bound up with the rotational motion, and the wavelength is determined by this latter motion. Our contention is that in order to overcome constraints confronted in the course of translational motion, it (the translational component) borrows energy from the stored up component. It is the effects of these various borrowings that manifest as the various non-Doppler redshifts. For instance as a photon moves from a distant galaxy, it confronts constraints along its long passage. In overcoming these constraints it loses energy. After losing energy, it cannot maintain the same velocity c, unless the lost energy is replenished. This replenishment is done by the constant borrowing of energy from the stored up component. As more energy is transferred, the rotational motion of the photon slows down proportionately, and therefore the wavelength expands. This is how the cosmological redshift comes about.

In terms of the screening off process of Earth’s orbital motion in the phenomenon of aberration, in order to prevent it from duplicating the role of the local reference frame, which role is already played by the Sun’s gravitational field, we get a very natural explanation for the null result of Michelson-Morley experiment. It will be clear that there can be no difference between light coming from a star and light generated on Earth, in regard to the background energy against which light moves in a given location. Since light moves having its lower limit of the intensive component to be equal in magnitude to that of the gravitational potential of the Sun’s gravitational field in a given location, the locally generated light in Michelson-Morley experiment also would screen off the effect of Earth’s orbital motion, just like starlight does by way of Bradley aberration. This is why Earth’s orbital velocity cannot be detected in the measurements of velocity of light, whereas Earth’s rotational velocity which is much smaller in magnitude than its orbital velocity is detected in GPS measurements and Sagnac type experiments. It is of interest to note that even in M&M type experiments of very high degree of accuracy, effects of Earth’s rotational velocity has been detected (10, p.9).

However, this screening off process of Earth’s orbital motion would have to leave its tell- tale signs in the form of red and blue shifts depending on the direction of incidence of light relative to the direction of orbit of the Earth. In situations of (c + v cos θ ) where θ is the angle of incidence of light relative to the direction of Earth’s motion, the translational component will adjust its energy level to have its intensive component at ½c 2 by transferring a fraction of its energy to the rotational component. This will increase the rotational velocity and a blue shift will occur. In situations of (c – v cos θ ), the translational component will adjust its energy level to have its intensive component at ½c 2 by borrowing a fraction of its energy from the rotational component. This will decrease the rotational velocity and a red shift will occur. And these red and blue shifts should be experimentally verifiable.

The above predicted red and blue shifts are in regard to the component of Earth’s motion along the direction of incidenceof light. Aberration of light occurs due to the component of Earth’s motion perpendicular to the direction of incidence of light. Due to this component, the resultant velocity of incident light relative to Earth’s orbital motion tends to acquire the value (c 2+ v 2sin 2θ ) ½ . The resultant velocity has the highest value (c 2+v 2)1/2 when θ = 90 ° i.e., when light is incident perpendicular to the motion of the Earth. And the least value c, when θ = 0° , i.e., when light is incident along the direction of motion of the Earth. To compensate for this excessive velocity, the translational component borrows a fraction of energy whose intensive component is equal in value to ½ v 2sin 2θ from the rotational component of the photon. Therefore, it is predicted that there will be a redshift that fluctuates periodically whose value is related to ½v 2sin 2θ . (It may well be that instead of the translational component of the photon borrowing the fraction of energy from the rotational component and getting it to act in the opposite direction, it transfers a fraction of this magnitude to the rotational motion directly. In this case, there will be a periodically fluctuating blue shift instead of such a redshift).

Explanation of Relativistic Phenomena - An Inevitable Pattern in all Physical Processes in the Course of Action of Energy.

1. Delay in the Duration of Disintegration of a Fast Moving Muon.

Similar to the case of the two charges in motion in Lorentz’ experiment discussed above in the Part III of this paper, the external motion of the muon serves as the ‘motion of local reference frame’ with respect to its internal process. When a muon is in a laboratory on Earth, its local reference frame is at rest (i.e. by convention it is assumed that there is no external motion). And the internal energy is considered to be available for destined action in full. When the muon is in fast motion at velocity u, this is tantamount to the local reference frame of the internal process being in motion.

2 The action of internal energy E i now has to occur within the upper limit of intensive component at ½c and the lower limit of the intensive component at ½ u 2. The situation is identical to the case depicted in fig. 2 in part I of 2 2 this paper. Accordingly, a fraction of energy becomes redundant equal in magnitude to E i.u /c . So the energy 2 2 that remains available for the destined action is Ei(1-u /c ).

As we have shown from equations (9), (10) and (11) we contend that the time of disintegration of a muon is inversely proportional to the square root of the energy available for destined action.

Therefore, if the time of disintegration is t when the muon is in a laboratory on Earth and the internal energy 2 2 available for destined action is E i, then when the energy available for action is E i(1-u /c ) in the fast moving mode, the time of disintegration is t/(1-u2/c 2)1/2 .

In this example of the muons, there is no question of one and the same event being observed from two different reference systems as the special theory of relativity generally contends for the manifestation of relativistic effects. It is clearly not a case of the time of disintegration of one and the same muon being recorded to be different with respect to two reference systems as the theory generally contends. It is a case of two different disintegrations of two different muons in two different states of motion turning out to occur in two different durations.

2. Gravitational Redshift -Gravitational Field as the Local Reference Frame:

Heuristically, it is convenient to conceive the internal process of the system as an object in mechanical motion relative to its local frame of reference, and the external motion of the system as the mechanical motion acquired by the system by virtue of its common motion with the local reference frame. However, in real situations relativistic phenomena arise with any combination of energy forms constituting internal and external action. And most common would be the action of field energy assuming the role of the ‘external motion’. In these, the role of the ‘local reference frame’ would be played by the gravitational field or the electromagnetic field concerned at the point of action.

We can demonstrate how the role of the ‘local reference frame’ is played by the gravitational field of the point of emission of a photon in the case of gravitational redshift .

As we discussed already when we explained the result of Michelson ’s experiment, we contend that the motion of a photon consists of two components – rotational component which is superposed on the translational component and that the ensuing combined motion is trochoidal in form (vortex motion). Initially in the nascent state, each component has energy E i. The translational component tends to be invariant so that under most circumstances it maintains this component of motion at velocity c. All constraints are confronted by the energy of the rotational component and in doing so, this component loses fractions of it. Since the translational velocity of the trochoidal motion is constant, the wavelength of the photon is determined by its rotational velocity. If this velocity slows down, then the wavelength becomes longer (i.e. a redshift occurs). We contend that the rotational velocity of a photon is proportional to the square root of the energy remaining available for action, and by virtue of this, the wavelength is inversely proportional to the square root of this energy.

λ Initially the rotational component has the full complement of energy = E i and the corresponding wavelength is 0

λ ∝ 1/2 1/ 0 (Ei) ------(13)

2 The extensive property of the internal energy of the photon = 2E i/c (inertia of energy)

The upper limit of the intensive property of internal energy = ½c 2

The lower limit of the intensive property of internal energy is equal in magnitude to the intensive property of the gravitational field energy (i.e. the intensive component of external energy) = GM/R

2 The fraction of energy that becomes redundant to the system = 2E i/c x GM/R

The energy remaining available for action of rotational component of motion of the photon

2 2 = E i – 2E i.GM/Rc = E i(1- 2GM/Rc )

λ The wavelength after losing the fraction of energy = 1

λ ∝ 2 1/2 1/ 1 {Ei (1- 2GM/Rc )} ------(14)

By the synthesis of the two antithetical equations (45) and (46)

λ 2 1/2 0 = λ 1 (1- 2GM/Rc ) ------(15)

It would be of interest to note that Einstein’s explanation of the gravitational redshift is quite different. Upon noticing the term 2GM/R in the equation (15) is obtained empirically, and because 2GM/R is coincidentally equal to the square of the escape velocity from a point where the gravitational potential is GM/R, he has immediately arrived at the ad hoc conclusion that escape velocity is involved in the process and provides an ‘explanation’ in terms of escape velocity.

3. The Precession of the Perihelion of Mercury.

According to Newtonian theory, Mercury undergoes its clockwise Keplerian elliptic orbit due to the attraction of the Sun, and in addition, as Leverrier demonstrated, the total effect of the attraction of the rest of the planets is for Mercury’s elliptic orbit to be rotated in the counter clockwise direction. However, Leverrier’s prediction was found to be 43" per century short. And ever since, there have been many hypotheses to account for this discrepancy. Einstein-Schwarzchild hypothesis is yet another one of these.

Leverrier himself offered a hypothesis. He proposed that while the outer planets rotated Mercury’s orbit in the counter clockwise direction, there is a planet inner to Mercury, (which he named as ‘Vulcan’), which rotates Mercury’s orbit in the clockwise direction at the rate of 43" per century. By assigning the required mass and distance to this planet, he could contrive the result very accurately. In Einstein’s hypothesis, he has in fact borrowed Leverrier’s basic idea of a clockwise rotation happening. He has replaced the action of the mass of the inner planet Vulcan with the ‘action of the masses of the Universe’ to get the same desired effect. But the essential difference is that while Leverrier obtains his result from his rigorous solution directly, Einstein’s rigorous solution has to be substituted with an approximation to get the desired result.

To achieve the above end we do not have to go through a long and tedious, rigorous solution to obtain a term, and then jettison it and substitute it with another term to get at the required result. We, by logical thinking and by applying our consistent theoretical standpoint, derive the result directly in a very few simple steps.

Our solution is as follows:

The background energy on which the action of the rest of the planets rotates the orbit of Mercury is the total gravitational (potential + kinetic) energy of orbit of Mercury = 1.5 (GM sMm/R), where G = Gravitational Constant, M s = mass of the Sun, M m = Mass of Mercury, R = Radius of orbit of Mercury.

The magnitude of intensive property of background energy = 1.5 GM s /R

Let the internal energy of action of the planets rotating Mercury’s orbit be E i.

2 The magnitude of the extensive property of internal energy = 2E i/c .

2 The redundant fraction of energy of this motion of Mercury = 1.5 GM s/R x 2E i/c

We contend that the area of an orbit is proportional to the energy of that orbit.

π 2 ∝ R Ei ------(16)

Let the angle of precession of the perihelion of Mercury due to loss of the fraction of energy be θ per orbit. Then the area of the segment formed by this angle = 1/2R 2θ

2θ ∝ 2 1/2R 1.5 GM s/R x 2E i/c ------(17)

By the synthesis of the antithetical equations (16) and (17) we have,

θ π 2 = 6 GM s/Rc ------(18)

So we derive the equation (18) by the direct logic of our theory of a loss of a fraction of energy in the process of transmission, in comparison to Einstein’s theory in which, a different term is derived from the premises of the theory and then this is substituted by another term to arrive at the required equation.

The Methodology of Synthesis of Antithetical Equations.

It is to be noted that, although equation (10) clearly prompts a partial dependence of the velocity v’ of an object, on the velocity u of the local reference frame, this obvious pointer of a connection between the two has been willfully overlooked traditionally by giving an interpretation to it as a ‘relativistic effect’ arising due to ‘kinematic reasons’. This is because admission of such a connection leads to the enigma of having to put Galilean principle of relativity in jeopardy. So the traditional approach has been, to ‘save the principle’ by escaping from the enigma by means of providing the above kinematic interpretation, and thereby denial of any kinetic cause attributable to it. Rather than resorting to escapism from the enigma as above, the ‘bull can be taken by the horns’ so to speak, as follows.

This enigmatic situation gets removed once we recognise Galilean relativity as an essential principle in physics , which nevertheless belongs to the realm of the ideal similar to the Ideal Gas Equation. On this basis we adapt the consistent methodology of relating the expected theoretical result under ideal condition in which the principle holds as in equation (8) to an empirical result in which the principle is found to be violated as in equation (9). From this methodology of synthesis of antithetical equations , we arrive at equation (10). And it puts an absolute footing to what has traditionally been viewed as a ‘relativistic phenomenon’.

It is rather strange and ironic that Einstein missed applying the above methodology to this particular problem. This is because, in his view it is precisely the correct methodology to be adapted. To understand this in the context of the subject matter of this paper, it should be borne in mind that the Galilean transformation based on Galilean relativity is the ‘theoretical proposition’. However it is found from results of experiments that empirical data (in violation of the theoretical proposition) conform to Lorentz transformations instead. Einstein found such situations to be the rule in physics. He described this rule in the following manner. "In so far as propositions of mathematics refer to reality, they are not certain; and in so far as they are certain, they do not refer to reality" (1, p. 380). At another instance he has stated: "Let us now cast an eye over the development of the theoretical system, paying special attention to the relations between the content of the theory and the totality of empirical fact. We are concerned with the eternal antithesis between the two inseparable components of our knowledge, the empirical and the rational …." (1, p. 390).

Einstein states: "Science is the attempt to make the chaotic diversity of our sense experience correspond to a logically uniform system of thought. In this system single experiences must be correlated with the theoretic structure in such a way that the resulting co -ordination is unique and convincing"( 1, p.406). And Filmer Northrop’s elucidation of it is: "….the relation between the theoretic component and the empirical component in scientific knowledge is the relation of correlation. Analysis of scientific method shows that this relation is a two-termed relation . …. The recognition of the presence of this relation in scientific method is the key to understanding of Einstein’s conception of scientific method and scientific epistemology" (1, p.406). In the light of what Einstein has stated in regard to the essay containing the above passage Northrop wrote to accompany Einstein’s ‘Autobiographical Notes’: " I see in this critique a masterpiece of unbiased thinking and concise discussion, which nowhere permits itself to be diverted from the essential"(1, p.683), Northrop’s elucidation of Einstein’s above statement could be construed as one of latter’s own statements.

The scientific method we use consistently in regard to solution of every problem in this paper is exactly the above professed methodology of correlation the theoretical component and the empirical component, which we call ‘the synthesis of antithetical equations’. For instance in Part I, equation (8) expresses the theoretical component on the basis that Galilean principle of relativity holds true, and the equation (9) expresses the empirical component which is in violation of the above principle. By correlating these two antithetical equations we obtain the equation (10). We have used this same methodology consistently in this paper (Parts I to II), in finding solutions to all relativistic phenomena such as the precession of the perihelion of Mercury, gravitational redshift, delay of disintegration of a fast moving muon etc..

ACKNOWLEDGEMENTS: I owe greatly to Dr. Delbert Larson (former Professor of Physics UCLA) for all the critical and invaluable guidance provided, in spite of his busy schedule, in developing this theory and enabling me to bring it to this final form. I am also immensely thankful to Emeritus Prof. P.A. De Silva of the Dept. of Mechanical Engineering, University of Moratuwa, Sri Lanka for the academic and technical support provided, and to Prof. Siddhartha Chatterjee of University of Syracuse, N.Y. for the longstanding support provided.

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