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Absolute Velocities:

The Detailed Predictions of the Emission Theory of Light

                                                       

 

A.     A.  Faraj

 

email: a_a_faraj@hotmail.com

 

 

Abstract

 

 

In this exposition, the predictions of the Emission Theory of light, concerning absolute velocities of isolated systems, have been worked out and discussed in detail. In addition, the related aspects of this theory have been reviewed and investigated at length. The aim is to facilitate the task of possible experimental testing, in the future, and to dispel long-standing and appalling misconceptions surrounding this important subject.

 

 

Keywords:   Doppler effect; light aberration; relative velocity; absolute space; superluminality

 

 

 

Introduction

 

 

            Absolute velocity can be defined as the common uniform linear velocity of the various components of a physical system, relative to absolute space. Absolute space, in turn, can be defined as the immobile three-dimensional physical void that exists independent of material bodies.

 

In spite of all the claims to the contrary, absolute space is one of the most intuitive and self-evident concepts ever encountered. Rational beings that lack a clear perception of absolute space, simply, do not exist. In fact, if all the obscurities of matter vanished, and the notion of matter were as simple and clear-cut as the notion of absolute space, there would have been no need, in that case, for physics at all.

 

Since Newton’s time, it has been recognized that measuring rotational and non-uniform velocities of isolated systems, on the basis of Galilean kinematics, presents no great difficulty.

By contrast, the determination of uniform linear velocities, with respect to absolute space, is fraught with all sorts of difficulties.  The main stumbling blocks are, undoubtedly, the immense blind spots induced by theoretical prejudices and historical controversies.

 

Right from the start, the Copernicans set out to destroy the Ptolemaic astronomy. However, they encountered a startling but otherwise erroneous objection, namely, "a moving Earth flings non-attached bodies away into space"!

Galileo responded to this major objection of the Ptolemaists by expounding, in great detail, the kinematics of relative velocities.

 

As it is often the case with great truths, in the end, dogmatism prevails. Some of Galileo's successors have, actually, gone too far in this direction to assert the absolute impossibility of finding out uniform linear motions relative to absolute space under any conceivable circumstances. This is despite the fact that such determination, is not only possible; but it's, also, an immediate and straightforward consequence of Galilean and Newtonian Relativity.

 

The widely publicized failure of the Wave Theory’s prediction, regarding velocities relative to the Ether, has made this dogmatism even stronger. So much so, that the supposed impossibility of measuring absolute velocities has become a fundamental principle of physics, i.e. the Relativity Principle.  And eventually, A. Einstein has chosen this principle to be one of the two pillars of his Special Theory. Ironically, even here, absolute velocities, ‘beautifully unexpected’, show up as a consequence of this Relativity-Principle-based theory.

 

Nonetheless, there are more daunting aspects of this notorious problem than mere collective prejudices and conventional blind spots. Here, we shall discuss, primarily, only those aspects related to the Emission Theory of light.

 

First and foremost, wrestling with the kinematical Principle of Relativity can be very unpleasant experience, and it is not recommend for the faint-hearted! Like a whirlpool, it draws you deeper and deeper into an incredible abstract world where infinity is the limit and where the most brilliant breakthroughs are made and destroyed in matter of minutes.

The Relativity Principle, in this respect, is quite unique among other principles of physics. Try, for instance, to disprove Newton’s First Law; and you won’t go far in that direction, before your attempt at disproof is crushed under a heavy load of internal contradictions. That is not the case with the much weaker Relativity Principle where a successful disproof always appears to be just over the horizon.

Furthermore, the theory under discussion does not invalidate the Relativity Principle. It, merely, restricts the scope of its application.

 

As it will be demonstrated in this discussion, the common linear velocity of an isolated system in uniform motion with respect to absolute space, can be determined, on the basis of the current theory, if and only if two or more of its parts are in relative motion with respect to each other. And accordingly, the Principle of Relativity must be recast, on the basis of this theory, as follows:

 

[A] It is impossible, within the framework of the Emission Theory, to determine the common uniform linear velocity of an isolated system whose components are at rest with respect to each other. 

   

[B] It is impossible, within the framework of the Emission Theory, to determine the common uniform linear velocity of an isolated system whose components have only relative-velocity vectors along the line of the common-velocity vector of that system.

 

In addition, the minuteness of the predicted magnitudes of observable effects of comparatively low absolute velocities, based upon this theory, can be, depressingly, Einsteinian. For example, the observable variations, as predicted by the most generalized form of the Emission Theory, concerning two bodies with absolute velocity of (300 kms-1 ) and relative velocity of (30 kms-1), are no greater than (30 ms-1). The predicted magnitudes of observable effects are, of course, more significant and much easier to measure, if the given absolute velocities are about or greater than (1,000 kms-1).

 

 The Emission Theory, whose predictions are the main topic of this paper, is itself an obscure and less known theory. And it’s essential, therefore, to begin this exposition with a brief discussion of the relevant aspects of this theory.

 

 

 

1. General Remarks

 

 

            The synonymous terms "emission theory", "ballistic theory", and " corpuscular theory" of light have been used in the published literature to refer to a collection of closely related theories based firmly on Galilean and Newtonian kinematics.

To avoid redundancy, the term 'emission theory’ will be used consistently throughout this discussion to denote the most generalized version of those theories.

 

The published work on the Emission Theory is substantial and it goes as far back as Newton’s ‘Opticks’ in the 17th century.  Consequently, no attempt at the survey of such extensive literature is made here. And only references, to it, will be specified when appropriate.

 

Although the Emission Theory has its roots in studies of optical and electromagnetic phenomena, its revolutionary nature is more conspicuous in the field of astronomy. It, literally, turns the science of astronomy on its head. Not a single bit of modern astronomy can remain unchanged, if the speed of light is taken to be variable in the Galilean sense and in accord with the generalized version of the Emission Theory. Thus, if ever there is a second Copernican revolution in astronomy, it will most likely be based on the Emission Theory or something very close to it. That is because right from the beginning, astronomy has been built entirely upon the assumption of constant speed of light.  Just place the old Assumption of ‘Earth at rest’ beside the current Postulate of ‘constant light speed’; and it should be obvious at once what the overthrow of the latter assumption means for the future of modern astronomy.

 

In its current stage of development, astronomy has become increasingly cluttered with useless kludges and artificial hypotheses to such a degree that the Ptolemaic astronomy, in comparison, looks like a paragon of science and rational thinking itself. And so a second revolution may not be out of the question. But again, the tenacity of the astronomers is proverbial. And so it should come as no surprise, if they still have enough inertia left in them to keep astronomy on its status-quo trajectory for the next 1,500 years.

 

By then, however, the idea of developing general consensus around one single theory could become obsolete. Such a development has occurred already in the field of politics, which at present is far more advanced than any other field in this regard. Likewise, it may well be found necessary, in the long run, that the optimal arrangement and the best mechanism for advancement, in the field of astronomy and science in general, is to have two or more opposing schools take control of shared resources in a periodic and organized fashion. That is, of course, still a long way off, perhaps 1,500 years or more! For the time being, let’s examine next the fundamentals of the Emission Theory of light, and hope that this theory is destined to rule over physics someday.

 

 

 

2.  Change of Velocities upon Reflection

 

 

The Stewart-Thomson Law:

 

            In the reference frame of the laboratory, light is always reflected from a moving reflecting surface with the resultant velocity of its relative velocity with respect to the reflecting surface and the velocity of the reflecting surface relative to the laboratory, [Ref. #1].

 

This important law is a generalization of the law of reflection. And it plays an important role in the treatment of optical phenomena on the basis of the Emission Theory. In its precise mathematical form, the Stewart-Thomson law can be derived and formulated by treating reflection of light as a special case of elastic collision and applying the conservation laws of linear momentum and kinetic energy, for moving bodies, to the incident light and the reflecting surface.

 

The quantitative treatment of this subject can be significantly simplified by assuming that the ratio between the mass of the incident light and the mass of the reflecting surface is infinitesimally small and practically equal to zero. And therefore, the recoil caused by the incident light on the reflecting surface can be neglected without affecting the exactness and precision of the quantitative treatment.

 

Consider the simple case of a plane mirror approaching or receding from a stationary light source along the normal to its reflecting surface with a uniform linear velocity, v.  If the angle of incidence with the normal, i, is measured counterclockwise with respect to the velocity vector of the mirror, then the magnitude of the relative velocity of the incident light, c', can be computed by applying the law of cosines:

 

 c'   =   [ c2  +  v2  +  2vccosi ]1/2                                                                       [2.1].

 

Where c is the Maxwellian speed of light in vacuum.

The direction of this relative velocity, i', can be obtained by applying the law of sines to the above arrangement:

 

sini'   =   [c/c' ]sini                                                                                           [2.2].

 

The angle i’ is the true angle of incidence as measured in the reference frame of a moving mirror.

 

From the law of reflection, the angle of reflection for reflected light, in the reference frame of a moving mirror, must be equal to the direction of the relative velocity of the incident light, i', and as a result:

 

 

cosi'   =  [ 1  -  sin2i' ]1/2   =   [ 1  -  c2/c'2 sin2i ]1/2  = (ccosi  + v)  / c’                      [2.3].

 

 

And by applying the law of cosines once more to compute the speed of the reflected light in the reference frame of the laboratory, we obtain c'':

 

c''   =   [ c'2  +  v2  +  2vc'cosi' ]1/2                                                                         [2.4].

 

 

By combining equations  [2.1], [2.3], & [2.4], we obtain for the general case:

 

 

c'' = c[1  + 4v2/c2  + (4v/c)cosi]1/2                                                                           [2.5].

 

 

The direction of this relative velocity, i, can be obtained by applying the law of sines once more:

 

sini”   =   [c’/c” ]sini’ =    [c/c” ]sini  = sini / [1  + 4v2/c2  + (4v/c)cosi]1/2                  [2.6].

 

The angle i is the true angle of reflection as measured in the reference frame of the laboratory.

 

 

 When a mirror approaches directly a light source along the normal to its reflecting surface, Equation #[2.5] is reduced to:

 

 

c''   =   c  + 2v                                                                                                        [2.7].

 

 

And when it recedes from the source along the same line, we obtain:

 

                     

 c''   =   c  -  2v                                                                                                       [2.8].

                                                                                            

 

If one insists on taking account of the vanishingly small recoil of an approaching or receding mirror under the effect of incident light, the following exact equations of linear elastic collision should be used for both cases:

 

 

c''  =  c[(mm – mc)/(mc + mm)]  +  v[2mm/(mc + mm)]                                                  [2.9],       

 

c''  =  c[(mm – mc)/(mc + mm)]  -  v[2mm/(mc + mm)]                                                   [2.10].       

 

 Where mc and mm   are the mass of the incident light and the mass of the mirror, respectively.

 

Equation #[2.5] can be generalized further, through the rotation of the normal to the surface of the plane mirror by an angle, j, around the velocity vector of the mirror and applying the laws of cosines and sines in each case.

 

One important case is when j = 90o.

 

Consider the case of a plane mirror approaching or receding from a stationary light source along its reflecting surface, i.e. j = 90o, with a uniform linear velocity v.  If the angle of incidence with the normal, i, is measured counterclockwise with respect to the velocity vector of the mirror, then the angle between the velocity vector of the incident light and the velocity vector of the mirror is (q = 90o – i) when (j = 90o) & the mirror is approaching the source; and (q = 90o + i) when (j = 90o) & the mirror is receding from the source.

 

We, now, compute the resultant of (c & v) in the case of approach:

 

c'   =   [ c2  +  v2  +  2vccosq ]1/2   =  [ c2  +  v2  +  2vcsini ]1/2                                        [2.11].

 

 The direction of c’, in the reference frame of the approaching mirror, is q:

 

sinq   =   (c/c' )sinq  =  (c/c' )cosi                                                                            [2.12].

 

Using q, we obtain the angle q’’ between the velocity vector of the reflected light and that of the mirror:

 

q” = 180o - q                                                                                                            [2.13].

 

Then we use (c’ & q) to obtain the velocity of the reflected light c” with respect to the reference frame of the laboratory:

 

c”  =  [ c’2  +  v2  +  2vc’cosq” ]1/2                                                                              [2.14].

 

From equations [2.12] & [2.13], we calculate cosq:

 

 cosq” = - cosq  = -[(csini + v)/c’]                                                                             [2.15].

 

Inserting the values of (c’ & cosq“) in Equation #[2.14], we obtain c”:

 

c”  = c                                                                                                                     [2.16].

 

Where c” is the speed of the reflected light relative to the reference frame of the laboratory.

 

By applying the law of sines, we obtain the direction i’ of c” with respect to the velocity vector of the mirror:

 

sini’  =  (c’/c”)sinq                                                                                               [2.17].

 

By using equations [2.12], [2.16], & [2.17], we obtain:

 

sini’  = cosi                                                                                                            [2.18].

 

To obtain the angle of reflection i with respect to the normal to the mirror surface, we use the relation (i” = i’ - 90o) & Equation #[2.18]:

 

sini”  = sin(i’ – 90o) = cosi’ = sini                                                                            [2.19].

 

Where i” is the angle of reflection as measured in the reference frame of the laboratory.

 

Thus, in the case of (approach & j = 90o), we have (c” = c & sini” = sini), which are the same values as in the case of reflection from a stationary mirror.

 

Finally, to calculate the resultant of (c & v) in the case of a receding mirror whose (j = 90o), we use the relation (q = 90o + i):

 

c'   =   [ c2  +  v2  +  2vccosq ]1/2   =  [ c2  +  v2  -  2vcsini ]1/2                                      [2.20].

 

 The direction of c’, in the reference frame of the receding mirror, is q:

 

sinq   =   (c/c' )sinq  =  (c/c' )cosi                                                                          [2.21].

 

Accordingly, cosq’ = -[(csini - v)/c’].

 

By the use of q, we obtain the angle q’’ between the velocity vector of the reflected light and that of the mirror:

 

q” = 180o - q                                                                                                          [2.22].

 

Then we use (c’ & q) to obtain the velocity of the reflected light c” with respect to the reference frame of the laboratory:

 

c”  =  [ c’2  +  v2  +  2vc’cosq” ]1/2                                                                              [2.23].

 

From equations [2.21] & [2.22], we calculate cosq:

 

 cosq” = - cosq  = (csini - v)/c’                                                                                [2.24].

 

Inserting the values of (c’ & cosq) in Equation #[2.23], we obtain c”:

 

c”  = c                                                                                                                     [2.25].

 

Using the law of sines, we obtain the direction I’ of c” with respect to the velocity vector of the mirror:

 

sini’  =  (c’/c” )sinq “= (c’/c” )sinq                                                                          [2.26].

 

By using equations [2.21], [2.25], & [2.26], we obtain:

 

sini’  = cosi                                                                                                             [2.27].

 

To obtain the angle of reflection i with respect to the normal to the mirror surface, we use the relation (i” = i’ - 90o) & Equation #[2.27]:

 

sini”  = cosi’ = sini                                                                                                  [2.28].

 

 

Hence, in the case of (recession & j = 90o), we have (c” = c & sini” = sini), which are the same results as in the case of reflection from a stationary mirror.

 

Therefore, we conclude that in the case of a plane mirror approaching or receding from a stationary light source along its reflecting surface (i.e. j = 90o) with a uniform linear velocity v, the speed of the reflected light is always equal to the speed of the incident light (c’’ = c) regardless of its angle of incidence; and its direction is governed by the law of reflection (sini” = sini) as in the stationary case.

 

As it is clear from Equations #[2.7]  &  #[2.8], the speed of reflected light, each time, is increased by twice the speed of a directly approaching mirror, and decreased by twice the speed of a directly receding mirror. The process can be repeated indefinitely. This, in fact, is one of the most astonishing predictions of the theory under discussion. In principle, at least, it implies no less than the complete control over speed of light by increasing or decreasing it to any desirable level through the use of multiple reflection from moving mirrors in the reference frame of the laboratory. Because of the high speed of light, the desired results can be achieved by the use of this mechanism, even in the case of slowly moving mirrors, in a fraction of a second. Consider, for example, a mirror moving directly with velocity of (100 ms-1) towards a stationary mirror 20 m away. By making multiple passes, through this optical loop, light can reach a superluminal speed of 2c in less than 0.2 of a second.

 

In practice, however, for superluminal speeds over 2c, Doppler effect presents a serious problem. As it will be shown later in this discussion, each time the speed of the reflected light is doubled, its frequency is doubled as well due to Doppler effect on light whose speed is boosted to a superluminal level by the use of multiple reflection from approaching mirrors. In practical terms, this Doppler shift to higher frequencies means that every part of the visible light will be shifted to the ultra-violet region of the spectrum; by the time its superluminal speed is close to 3c.

 

Ordinary mirrors are inefficient ultra-violet reflectors; and so the process of speed boosting through the use of multiple reflections from those mirrors must fail for speeds greater than 2c. Is there a way out of this Doppler-boosting problem?

 

Despite their horrific miasma of “Tunneling”, “Exiting-before-entering”, and similar theoretical nonsense, experimenters of the so-called 'Photonic Revolution’ have, in the last decade or so, amassed an impressive array of experiments, techniques, and data on superluminality, through the use of anomalous dispersion in carefully-prepared materials. 

Their finding, in itself, is undoubtedly one of the most striking discoveries in experimental physics in recent years, and most certainly bound to sweep away, in due time, long-held false beliefs and errors in this field. See, for instance, [Ref. #9].

 

Nonetheless, neither anomalous dispersion, nor photonic crystals, nor specially prepared refractive media, have any potential use within the context of the Doppler-boosting problem encountered here. Refractive indices, simply, cannot be used to boost speed of light outside their artificially prepared media. That is because light, upon exiting the prepared medium, very simply, restores its standard Maxwellian speed in vacuum.

 

It’s possible, however, that the superluminal speeds of light, in those experiments, are caused by multiple reflections from moving layers of atoms inside the artificial media. If that is indeed the case, then upon exit, light can retain its superluminal speeds in vacuum. But this possibility, of course, does not solve the Doppler-boosting problem.                        

 

In a nutshell, multiple reflection from approaching mirrors is the only technically feasible method for achieving long-range superluminal speeds of light in free space. But Doppler boosting to higher frequencies and the unavoidable absorption of light by the materials of mirrors, impose severe limitations on the practicality of this method.

 

Suppose, for a moment, that a perfect mirror capable of reflecting electromagnetic radiation of any frequency repeatedly and with 100% efficiency is practically feasible.

Can the superluminal speeds of light produced by that mirror be used in long-range communications?

If such a perfect mirror can be found, and if the Emission Theory is correct and universally applicable, then the answer to the above question is, absolutely and unequivocally, ‘yes’.

Not only that, but one also can be absolutely sure that advanced civilizations, across the cosmos, are talking to each other over our heads. But thanks to the Einsteinian slumber of our physics, we, Homo sapiens, are completely oblivious of their communications!

So let's hope that, someday, our Homo sapiens shall live up to their illustrious name! And let us try to figure out how superluminal signaling can be achieved in practice.

 

Given a perfect mirror, it's quite possible to start with the radio portion of the spectrum; and to code your message using standard methods in radio communications.

After that, you can use the perfect mirror to boost the speed of the coded radiation to the desirable superluminal level.

To minimize the effect of the Inverse Square Law on the coded radiation, maser and laser techniques have to be used. However, to maximize the chances of reception, the Inverse Square Law must be allowed to work as required, during travel time, to make the cross section of the carrying beam large enough to encompass the entire targeted area by the time of its arrival. In brief, your tasks as a sender, in superluminal telecommunications, are to code, boost, collimate, and send.                       

 

Receivers of superluminal signals must, in turn, be equipped with a perfect mirror, as well, to be able to tune in. The mirror, here, is used to convert the received superluminal radiation to its original Maxwellian form, which can be fed to a regular radio receiver to decode the sender's message in a standard fashion.

 

It should be mentioned, in this context, that a team of the Italian Council of Research reported, recently, achieving superluminal speeds in air by bouncing a microwave beam off a mirror, [Ref. #6]. From the viewpoint taken in this section, their experiment is very interesting, although it is not clear from their report how exactly and how efficiently a microwave mirror works.

 

 

 

3.  The Characteristics of the Corpuscular Photon

 

 

            The concept of the Corpuscular Photon is an integral part of the Emission Theory of light. In the published literature, the Corpuscular Photon is defined in two different ways:

 

[A] The Corpuscular Photon is defined as one single corpuscle whose mass is in direct proportion with frequency across the electromagnetic spectrum. This concept of the Corpuscular Photon is extremely rigid and inadequate in dealing with the wave aspects of light. For this reason, it is often used as a 'straw-man' argument against the Emission Theory.  How on Earth, its opponents ask, can it account correctly for interference and diffraction phenomena?  However, this old objection sounds increasingly hollow after the discovery of similar phenomena related to electrons and other subatomic particles. Nevertheless, the inadequacy of the 'One-Corpuscle Photon’ is obvious. And its fundamental flaws cannot be weeded out by merely pointing out more serious flaws in the concept of the Conventional Wave Photon.

 

[B] The Corpuscular Photon can, also, be defined as a group of corpuscles whose number and spatial separation (wavelength) vary in direct proportion with frequency across the electromagnetic spectrum. The total number of corpuscles, in a photon, is determined only by its frequency and the duration of its pulse during the time of emission. Its energy and momentum, in turn, depend solely on the number and the speed of its corpuscles. For a non-polarized photon, the linear trajectories of its corpuscles form randomly its cross section. Thus, it should be clear that a corpuscular photon whose cross section consists of only one single geometrical point, though appealing, is a fictional idealization that cannot be realized in actual situations.

 

The Corpuscular Photon, when defined in terms of distinct groups of corpuscles on the basis of their frequencies, is a versatile and powerful concept. It, literally, transforms the Emission Theory from a weak and timid hypothesis to a revolutionary tool of the first order. It, no longer, suffices for the critics of this theory to throw on it Poisson's ‘Bright Spot’, de Setter's ‘Circular Orbits’, and similar obsolete objections to score a point. The table has, really, been turned on them. And this is how:

 

(1) The notion of distinct groups of corpuscles allows the theory, under discussion, to account for interference, diffraction, polarization, and related phenomena, in a natural and satisfactory manner, and to dispose of the old objections, along with the Wave-Particle Duality, at once.

 

(2) Since subatomic particles emit photons, and since photons consist of corpuscles, it follows as a natural consequence of this theory that the subatomic particles themselves are structured aggregates of corpuscles. The idea of particles composed of aggregates of corpuscles, analogous to aggregates of stars in galaxies, has the potential of restoring order to the current chaotic state, opening new avenues for probing deeper into the nature of matter, and revolutionizing the stagnant field of elementary particles.

 

(3) The concept of corpuscular photons enables the Emission Theory to include precise formulae for the Doppler effect, the Fresnel Convection, and the Law of Aberration derived on a basis more solid and intuitive than that of any other theory in this field.

 

(4) This concept of photons, in conjunction with the Stewart-Thomson Law, enables the Emission Theory to explain clearly and correctly the Michelson-Morley Experiment and related experiments, giving it a decisive edge over a variety of unrealistic kludges such as the notorious Lorentz-Fitzgerald Contraction Hypothesis.

 

(5) Redefining the photons in terms of distinct groups of corpuscles leads to the inclusion of the J. G. Fox  Re-radiation’ hypothesis as a special case, and disposing, at the same time, of its undesirable consequences, [Ref. #4].  Notwithstanding its success in the special case, the application of the Re-radiation hypothesis, generally, has the misfortune of making no prediction at all. That is because the re-radiation mechanism, as used by Fox in his Extended Ritz Theory, leads to de-facto constant speed of light, banishes superluminality, and renders the application of the Galilean Transformations to electromagnetic phenomena useless. See  [Ref. #7], and, [Ref. #8]. Furthermore, except in the special case, where the refractive medium absorbs and re-emits the incident light with different frequencies, the Re-radiation hypothesis is in contradiction with the conservation laws of energy and momentum. Where does the truncated portion of the initial energy and momentum go? The Re-radiation hypothesis gives no answer. It’s true that the Conventional theories, in the field, have violated these same laws at more basic levels. But that is no excuse for committing another clear violation of them. In brief, the Re-radiation mechanism must be restricted and its unwarranted generalization has to be abandoned, in order to apply the Galilean Equations in a productive and self-consistent manner.

 

(6) The definition of photons, as independent groups of corpuscles, enables the Emission Theory to give a clear and natural explanation of the Cosmological Red-shift of distant galaxies and to do away with the hypothesis of ‘Expanding Universe’ along with its bizarre and absurd consequences. By merely taking accelerations of the light source into account, one can easily obtain the exact formula of the Hubble Law as a natural consequence of this theory. And as a bonus, the ‘Big Bang’ can more readily be consigned to the dustbin of history along with its monstrous offspring.

 

(7) This is the most controversial part of the Emission Theory.

The exact quantitative details of this topic have been elaborated elsewhere.

See [Ref. #1]. Here, it suffices to restate the main problem in more general terms. Without doubt, the empirical classification of stars on the basis of their luminosity, size, and spectral type, is the most concrete part of modern astronomy. In addition, it's the foundation upon which Stellar Evolution; one of the most attractive theories in astrophysics has been built. The Emission Theory does not contradict outright the Theory of Stellar Evolution. It, simply, creates, on purely kinematical grounds, an exact replica of its foundation. It's easy to see that systematic and continuous variations in the velocity of a light source, lead to systematic and continuous variations in the velocity of its radiation output. These variations in the velocity of the output, inevitably, lead to changes in the spectrum and the radiant flux of the source, which vary linearly with distance. Thus, it's possible to produce the entire phenomena included in stellar classification by merely using a 'hypothetical sun' and varying its orbital configurations at various distances from the observer. Take, for instance, the spectacular phenomenon of Supernova Explosion.  As spectacular as it is, the Supernova Phenomenon is the easiest to duplicate using nothing more than our 'hypothetical sun'. Increasing its velocity by an extremely tiny but continuous amount, which the far half of its orbit around some distant galaxy can do, our 'hypothetical sun' can pour its output of radiation, during one hundred million years, in just only few days, and fools naive Einsteinian observers that they have just witnessed a stellar explosion on a gigantic scale!  In the same way, the variability of speed of light can make out of our 'hypothetical sun' every star of every size and spectral type in the Hertzprung-Russel Diagram. And it can replicate every star in the Variable Stars' Catalogue. In short, the observational basis of modern astronomy has been undercut. And serious doubts have been cast upon its dynamical reality. This, of course, does not mean that all the stars are identical to the sun, nor their classification is physically baseless. All what the above considerations imply is that if speed of light is variable in accord with the Emission Theory, then a thick cocoon of mirages and optical illusions must be removed first, before the real dynamical phenomena underneath can be unveiled. Then, and only then, a true understanding of the physical universe can follow the observation.

 

 

4.  The Doppler Effect

 

 

            As discussed earlier, the Corpuscular Photon of the Emission Theory is composed of a finite number of corpuscles whose primary source emits them one after the other at regular intervals of time. This definition makes the task of deriving the exact formulas of the Doppler Principle straightforward and simple. Compare the following easy steps with the convoluted methods of deducing the Doppler Equations on the basis of the One-Corpuscle Emission Theory or on the basis of Einstein Theory:

 

[1] The Case of Direct Approach:

 

Consider the simple case of a light source approaching directly with velocity vs an observer at rest in the reference frame of the laboratory.  Let the period of the emitted corpuscles of a photon be T as measured in the inertial frame of their source, and T’ as measured in the reference frame of the laboratory.

Since the frequency f, by definition, is the reciprocal of the period T, we obtain:

 

f  = 1/T                                                                                                   [4.1],

 

f’  = 1/T’                                                                                                 [4.2].

 

Where f and f’ are the frequencies in the inertial frame of the source and the reference frame of the laboratory, respectively.

Since the source is approaching directly, then the velocity of its light c’, relative to the laboratory:

 

c’  = c  +   vs                                                                                           [4.3].

 

Where c is the velocity of light in the inertial frame of the source.

Next, we use T, vs, and c’ to compute T’:

 

T’  =  [T(c  +  vs ) - T vs ] /  (c  +  vs )   =  Tc / (c  +  vs )                             [4.4].

 

From Equations # [4.2] and # [4.4], we obtain the Doppler formula for this special case:

 

f’  = 1/T’  =  f[1  +  vs/c]                                                                           [4.5].

 

If the observer approaches with velocity vo a stationary source of light, we obtain:

 

T’  =  (Tc  -  T’ vo )/ c   =  Tc/(c  +   vo )                                                    [4.6],

 

f’  = 1/T’  =  f[1  +  vo /c]                                                                          [4.7].

 

Where f’ is the frequency in the inertial frame of the observer.

 

[2] The Case of Direct Recession:

 

Repeating the above steps, we obtain for a source receding directly from an observer at rest:

 

f’  =   f[1 -  vs /c]                                                                                     [4.8].

 

 

And we obtain for an observer receding directly from a source of light at rest:

 

 f’  =   f[1 -  vo /c]                                                                                     [4.9].

 

 

[3] The General Case:

 

In order to obtain the Doppler formula in the general case, let the angle i, between the line of sight and the velocity vector of the source vs, be measured counter-clockwise.

Let the angle j that the velocity vector of the observer vo makes with the line of sight be measured clockwise and corrected for Light Aberration. Since the line of sight is the direction of the resultant velocity of light c' from a moving source, we obtain:

 

c'  =  c[1  -  (vs2/c2)sin2i]1/2  +  vscosi                                                         [4.10].

 

For light emitted with period T and frequency f in the inertial frame of the source, we compute the period as measured by the observer:

 

T'  =  [Tc'  - Tvscosi  - T'vocosj] / c'  = T(c' -vscosi) / (c'  + vocosj)             [4.11].

 

By taking the reciprocal of T', we obtain the general formula for Doppler effect in the reference frame of moving observer:

 

f'  =  f[1  +  {(vs /c)cosi  +  (vo/c)cosj} / {1  - (vs2/c2)sin2i}1/2]                         [4.12].

 

 

            Let's now compare the Doppler formulas for the first two simple cases of direct approach and direct recession, according to the Emission Theory, with the Doppler formulas for the same two cases according to Maxwell's Theory and Einstein's Special Relativity, respectively. 

 

[A] Maxwell’s Theory:

 

1.  For a source approaching directly an observer at rest, the theory gives:

 

f'   =  f[1  +  vs/(c  -  vs)]                                                                            [4.13].

 

By comparing this equation with Equation #[4.5], we find that the Doppler shift of approaching sources i.e., (f' - f)/f, as computed on Maxwell's Theory, is always greater than that of the Emission Theory by a factor of  [1 - vs/c]-1.

 

2.  For an observer approaching directly a stationary source of light, the Maxwell Doppler formula is:

f'   =  f[1  +  vo/c]                                                                                     [4.14].

By comparing this equation with Equation #[4.7], we conclude that the Doppler effect in this case is the same as calculated on both theories.

 

3.  For a source receding directly from an observer at rest, Maxwell’s Theory gives:

 

f'   =  f[1  -  vs/(c  +  vs)]                                                                            [4.15].

 

By comparing this equation with Equation #[4.8], we find that the Doppler shift of receding sources, as calculated on Maxwell's Theory, is always less than that deduced from the Emission Theory by a factor of  [1 + vs/c]-1.

 

4.  For an observer receding directly from a stationary source of light, the Maxwell Doppler formula is:

 

f'   =  f[1  -  vo/c]                                                                                        [4.16].

 

By comparing this equation with Equation #[4.9], we conclude that the Doppler effect, in this case, is the same as calculated on both theories.

 

[B] Einstein’s Special Theory:

 

This theory has two different sets of equations for computing Doppler effect:

 

[1According to Einstein:

 

Special Relativity, as expounded in Einstein’s 1905 paper, takes the Maxwellian Doppler formulas for the moving observer, and divides them by the factor {1 – v2/c2 }1/2, where  v stands for vs , vo , or both.  And then, it uses these new formulas in all the four simple cases above:

 

f'   =  f[(c + vs ) / (c  -  vs)]1/2                   (for directly approaching source)        [4.17],

 

f'   =  f[(c + vo ) / (c  -  vo)]1/2                  (for directly approaching observer)      [4.18],

 

f'   =  f[(c - vs )/(c +  vs)]1/2                     (for directly receding source)              [4.19],

 

f'   =  f[(c - vo ) / (c  +  vo)]1/2                  (for directly receding observer)           [4.20].

 

f'   =  f[{1 - (v/c)cosf} / {1 – v2/c2 }1/2]     (for the general case)                         [4.21].

 

Where v stands for vs, vo, or both, and f stands for i, j, or both, [Ref. #3].

 

 

[2According to Ives & Stilwell:

 

Special Relativity, according to Ives & Stilwell, takes the Maxwellian Doppler formulas for the moving source, and multiplies them by the factor  {1 – v2/c2 }1/2, where  v stands for vs , vo , or both.  Then, it uses these new formulas in all the simple cases above and gives in the general case:

 

f'   =  f[{1 – v2/c2 }1/2    /  {1 - (v/c)cosf}]                                                            [4.22].

 

Where f stands for i, j, or both [Ref. #5].

 

The Einstein and the Ives-Stilwell general formulae give the same numerical results at f = 0o and f = 180o; but they make contradictory predictions at f = 90o with regard to the transverse Doppler effect.

Now by comparing the above equations with those of the Emission Theory, we obtain:

f'E/f'R  =  [1 - vs 2/c2]1/2                                                                                     [4.23]

Where f'E  & f 'R are the observed frequencies as predicted by the Emission Theory and Einstein's Relativity, respectively.

Therefore, we conclude that in all cases of approach, Einstein’s Theory predicts Doppler shift i.e. (f'-f)/f greater than the one predicted by the Emission Theory. And in all cases of recession, it predicts Doppler shift less than that predicted by the Emission Theory. Thus, from the perspective of the Emission Theory, Einstein’s Special Relativity makes the correct Maxwell formulas of the moving observer erroneous by a factor of {1 – v2/c2}-1/2, but, at the same time, it restores the symmetry and reduces the error in the case of the moving source by using the same formulas for both the source and the observer.

 

 

 

 

5.  The Law of Aberration

 

 

            Within the framework of the Emission Theory, Light Aberration is defined as the angle between the true position of the source, at the time of emission, and the direction of the resultant relative velocity of the velocity of the incident light, from that source, and the velocity of the observer, at the time of reception.

Thus, if the direction of the resultant relative velocity of the incident light and the observer is j, and the true position of the source, at emit time, is j', then the Light Aberration b is the difference between j' and j:

 

b   =   j'  -  j  = Dj                                                                                                 [5.1].

 

Notice that the angle j' can be computed, but can never be observed in the inertial frame of a moving observer.

Two forms of the Law of Light Aberration will be discussed here:

 

[1] The Standard Form of the Law of Light Aberration:

 

Let's consider, first, the simple case of a stationary source of light and an observer moving with uniform linear velocity vo. By applying the law of sines to this case, we obtain the well-known form of Bradley's Law of Aberration:

 

sinDj   =   (vo/c)sinj                                                                                              [5.2].

 

Where c is the speed of light with respect to the reference frame in which its source is at rest.

For small values of Dj:

 

Dj   »   (vo/c)sinj                                                                                                    [5.3].

 

Within the context of wave theories of light, the phenomenon of Light Aberration is decidedly asymmetrical. That is because the shift, in the true position of the source, caused by the motion of the observer, and the shift, in the same position, caused by the motion of the source, are not equal. And as a result, the symmetry of relative motions is shattered. See [Ref. #2].

By comparison, on the basis of ballistic theories of light, the shift caused by the Light Aberration is exactly equal to the shift caused by the Light Travel Time introduced by a source moving with the same speed as that of the observer but in the opposite direction. Consequently, the symmetry of relative velocities is retained. This conclusion can be illustrated by comparing, for example, Maxwell's Theory with the Emission Theory, in this regard.

Take, for instance, the case of j = 90o.

Let v be the velocity of the observer, with respect to a source of light at rest.

Using Equation #[5.2], we obtain the shift of Light Aberration Djo, on both theories:

 

sinDjo   =   v/c                                                                                                     [5.4].

 

Now let v be the velocity of the source with respect to an observer at rest.

Light, emitted by the source at Emit Time, takes time t to reach the stationary observer at receive time. By then, the source has moved, at right angle to the line of sight, a distance vt.  From the right triangle of ct and vt, we obtain, on Maxwell's Theory, the Light-Travel-Time shift Djs:

 

tanDjs  =  vt/ct  =  v/c                                                                                          [5.5].

 

From trigonometry:

 

sinDjs  =  tanDjs /[1  +  tan2Djs]1/2  = [1  +  cot2Djs]-1/2                                                [5.6].

 

Combining Equation #[5.5] and Equation #[5.6], we get:

 

sinDjs  =  [v/c] / [1 + v2/c2]1/2                                                                                   [5.7].

 

By comparing Djo in Equation #[5.4] with Djs in Equation #[5.7], we conclude that the shift of Light Aberration is always greater than the shift of Light Travel Time, as both calculated on the basis of Maxwell's Theory.

 

Let's turn next to the Emission Theory of light. According to this theory, light, emitted by a moving source, moves along the line of sight with the combined velocity c'. Since the source, in the case under discussion, is moving at right angle to the line of sight, then

i = 90o.  Using this value of i in Equation #[4.10], we obtain:

 

c'  =  c[1  -  v2/c2]1/2                                                                                                [5.8].

 

From the right triangle of c't and vt, we obtain, on the basis of the Emission Theory, the Light-Travel-Time shift Djs:

 

tanDjs  =  v/c'                                                                                                         [5.9].

 

From the equations #[5.6], #[5.8], & #[5.9], we obtain:

 

sinDjs   =   v/c                                                                                                        [5.10].

 

Therefore, by comparing this equation with Equation #[5.4], we conclude that the shift of Light Aberration is always equal to the shift of Light Travel Time, as both computed on the basis of the Emission Theory of light.

 

[2] The General Form of the Law of Aberration:

 

Now, we consider the case in which both the source and the observer are in motion.

Let the velocity vector of the source  vs make an angle i with the line of sight.

And let the velocity vector of the observer vo make an angle j with the line of sight. Let c' denote the combined velocity of the velocity of light c and the velocity of its source  vs:

 

c'  =  c[1  -  (v2/c2)sin2i]1/2  +  vscosi                                                                           [5.11].

 

Applying the law of sines to the above case, we obtain:

 

sinDj  =  (v/c')sinj                                                                                                    [5.12].

 

From Equations #[5.11] and #[5.12], we obtain the general form of the Law of Aberration:

 

sinDj  =  vosinj / { c[1  -  (vs2/c2)sin2i]1/2  + vscosi}                                                       [5.13].

 

Where Dj is the shift of Light Aberration.

 

Finally, it should be pointed out that the shift, in the source position due to Light Aberration, represents only an instance of apparent rotation. And so the source image, at receive time, remains as it was at emit time. No aspect of the image at emit time is hidden, and no new aspect of the source is revealed at receive time, by this apparent shift, in the source position, due to Light Aberration. More importantly, the rotation of the line of sight, in the forward direction, by an angle Dj, does not affect the angle i that the velocity vector of the source makes with the line of sight. In other words, the angle i, in Equation #[5.13], is invariant under the process of Light Aberration.

 

 

6.  Velocities Relative to Absolute Space

 

 

            Having discussed the essentials of the Emission Theory, we can, now, proceed to examine its predictions with regard to uniform motions relative to absolute space. It should be mentioned at the outset that, from the standpoint of kinematics, the space motion of any physical body can have potentially an infinite number of components in an infinite number of directions. But, at any instant, those components can only have one instantaneous resultant in only one direction.

 

The term 'absolute velocity' will be used throughout this discussion to refer to the instantaneous resultant of the various velocity components of a moving object with respect to immobile space.

 

The Doppler Principle, the Law of Aberration, and the Concept of Relative Motion, are the only required input for determining absolute velocities through the use of the Emission Theory of light. The basic method of inference, used here, is to calculate the Doppler shift and the Bradley shift for a given value of relative velocity of two or more objects on the assumption of common absolute velocity equal to zero, and to compare the final results with the results obtained by assuming non-zero common velocity relative to absolute space. In its broad aspects, this procedure is analogous to the methods used in dynamics to infer rotation relative to absolute space from the effects of the Coriolis force and related phenomena. As stated at the start of this discussion, in order to deduce the values of absolute velocities from the given quantities, the absolute value of the given relative velocity of, at least, two parts of the moving system, must be greater than zero.  In other words, if all the components of the system in question are at rest relative to each other, then the absolute velocity of that system cannot be determined on the basis of the Emission Theory. Any type of relative velocity can be used for this purpose. Here, we shall discuss the two important cases of uniform translational motion and uniform circular motion.

 

[A] The Case of Uniform Translational Motion:

 

Let an isolated system consist of two independent bodies in uniform linear motion relative to each other. And let the inertial frame of one of these two bodies be the reference frame in which the observer is at rest. In the context of the theory under discussion, this system can only be in one of three distinct states: 

 

(1) The Observer at Rest:

 

Let the common absolute velocity of the system be vA, and vA  = 0.

Let the second body of the system be the light source, and let its velocity vs make an angle i with the line of sight. Since the observer is at rest, we set vo and j to zero in Equation #[4.12]:

 

f'  =  f[1 + {(vs/c)cosi}/{1 - (vs2/c2)sin2i}1/2]                                               [6.1].

 

Where f' is the observed frequency in the inertial frame of the observer.

Equation #[6.1] is the Doppler equation, in the special case of moving source and observer at rest, for a system whose absolute velocity is nil, i.e.  vA  =  0.

 

Now let’s assume that the absolute value of the above system’s absolute velocity is greater than zero, i.e. vA  ¹  0.  Let the vector  vA  be parallel to the vector of the relative velocity of the source  vs, in order to make the calculations simple. 

And hence, vo  = vA   & vs  = vA + vs, where vo  is  the velocity of the observer, vs  is the vector sum of the absolute velocity of the system and the velocity of the source relative to the observer.  Inserting the values of vo and  vs’ in Equation #[4.12], we obtain:

 

f'  =  f[1 + {(vA/c)cosj + ((vA + vs )/c)cosi } / {1 - ((vA + vs )2/c2)sin2i}1/2]       [6.2].

 

Since vA, by definition, is the common velocity of the source and the observer, and by the above configuration j + i = 180o, the terms ‘(vA/c)cosj’ and  ‘(vA/c)cosi’ in Equation #[6.2], therefore, cancel each other out.  Rewriting this equation, we obtain:

 

 f'  =  f[1 + {( vs/c)cosi } / {1 - ((vA + vs )2/c2)sin2i}1/2]                                  [6.3].

 

Where f' is the observed frequency in the inertial frame of the observer.

Equation #[6.3] is the Doppler equation, in the special case of moving source and observer at rest, for a system whose absolute velocity is vA  ¹  0.

 

Let z  =  Df’/f.  And compute zo from Equation #[6.1] and zA from Equation #[6.3], and then divide zA by zo: 

 

zA/zo = {1 - (vs2/c2)sin2i}1/2 / {1 - ((vA + vs )2/c2)sin2i}1/2                                 [6.4].

 

Therefore, we conclude that the Doppler shift of a moving source as measured in a system moving with a non-zero linear absolute velocity is greater than the Doppler shift of the same local motion as measured in a system at rest with respect to absolute space. Consequently, the ratio between the observed Doppler shift zA and the Doppler shift expected theoretically zo for a system at absolute rest, can be always used, in principle, to determine the absolute velocity of an isolated system with respect to absolute space, from inside that system, and without any reference to anything else in the universe.

 

 

(2) The Source at Rest:

 

Let vA  = 0, and the velocity of the observer vo make an angle j with the apparent position of the source. Since the source is at rest, we set vs and i to zero in Equation #[5.13]:

 

sinDj  =  ( vo/c)sinj                                                                                   [6.5].

 

Where Dj is the shift of Light Aberration.

From Equation #[6.5], we obtain the true position of the source j0, where j0’ = j + Dj, and then we insert j0 instead of j in Equation #[4.12]:

 

f'  =  f[1 + (vo/c)cos j0]                                                                              [6.6].

 

Where f' is the observed frequency in the inertial frame of the observer.

Equation #[6.6] is the Doppler equation, in the special case of moving observer and source at rest, for a system whose absolute velocity is nil, i.e.  vA  =  0.

 

Now let’s assume that the absolute value of the above system’s absolute velocity is greater than zero, i.e. vA  ¹  0.   Let the vector vA be parallel to the vector of the relative velocity of the observer vo, in order to simplify the calculations. 

And hence,  vo' =  vA  +  vo  and   vs  =  vA,  where vs  is  the velocity of the source, and vo  is the vector sum of the absolute velocity of the system and the velocity of the observer relative to the source.  Inserting the values of  vs  and   vo’ in Equation #[5.13], we obtain the shift of Light Aberration Dj:

 

sinDj  =  [( vA + vo)/c']sinj                                                                        [6.7].

 

Where c’ = c {1 - (vA2/c2)sin2i}1/2  +  vA cosi.

 

And then we use jA = j + Dj in Equation #[4.12] to obtain f':

 

f'  =  f[1 + {( vA + vo)cosjA + vAcosi } / c{1 - (vA2/c2)sin2i}1/2]                       [6.8].

 

Since vA, by definition, is the common velocity of the source and the observer, and by assumption jA + i = 180o, the terms ‘vAcosjA  & ‘vAcosi’ in Equation #[6.8], therefore, cancel each other out.  Rewriting this equation, we obtain:

 

 f'  =  f[1 + ( vo/c)cosjA } / {1 - (vA2/c2)sin2i}1/2]                                           [6.9].

 

Where f' is the observed frequency in the inertial frame of the observer.

Equation #[6.9] is the Doppler equation, in the special case of moving observer and source at rest, for a system whose absolute velocity is vA  ¹  0.

 

Let z  =  Df’/f.  And compute zo from Equation #[6.6] and zA from Equation #[6.9], and then divide zA by zo: 

 

zA/zo = [cos jA’ / cos j0] / [1 - (vA2/c2)sin2i] 1/2                                            [6.10.

 

Therefore, we conclude that the Doppler shift of a moving observer as measured in a system moving with a non-zero linear absolute velocity is greater than the Doppler shift of the same relative motion as measured in a system at rest with respect to absolute space.

 

Let us, now, compare the shift of Light Aberration in Equation #[6.5] to that in Equation #[6.7]. For an observer and light source moving with a common absolute velocity vA, the shift of Light Aberration is exactly cancelled out by the shift of the Secular Parallax. To demonstrate that is indeed the case, let the line joining the source and the observer make a right angle with the vector of their common velocity vA, so that j = i = 90o.   

Light emitted by the source, at Emit Time, takes time t to reach the observer, at Receive Time. During that time, the observer has moved a distance vAt parallel to that of the source image.  From the right triangle vAt and c’t, we obtain:

 

 sinDj  =   vA / c'                                                                                     [6.11].

 

Where Dj is the angle of the Secular Parallax. This angle is exactly equal to the angle of Light Aberration as calculated from Equation #[5.13], but in the opposite direction. Light Aberration, therefore, takes this shifted image of the source, in the backward direction, and shifts it by an equal amount, in the forward direction, to coincide exactly with the true position of the source at Receive Time. Thus the two effects of the velocity component vA cancel each other out, and we obtain from

Equation #[6.7]:

 

sinDj  =  (vo/c')sinj                                                                                  [6.12].

 

Let Dj0 = sinDj for Equation #[6.5], and DjA = sinDj for Equation #[6.12], and divide DjA by Dj0: 

 

DjA/Dj0  =  c/c’                                                                                         [6.13].

 

Where c’ = c {1 - (vA2/c2)sin2i}1/2   +  vA cosi.

 

Therefore, we conclude that the shift of Light Aberration as measured in a system moving with a non-zero linear absolute velocity is greater for (j £ 90o) and less for (j > 90o) than the shift of Light Aberration for the same relative motion as measured in a system at absolute rest with respect to absolute space..

 

It should be pointed out that, unlike the Light-Aberration shift, the Parallax shift represents a true rotation of the source image with respect to the observer. Accordingly, it changes the viewing angle and the angle ‘i’ that the velocity vector of the source ‘vs’ makes with the line of sight. Since the Parallax shifts the source image to the opposite direction to that of the observer motion, then   i’  = i - Dj, where Dj is the Parallax shift. The angle i’ is observable in the inertial frame of the observer.  It’s, simply, the angle that the observer measures and refers to as the angle i in the previous equations. However, if the angle i is given or deduced from dynamic considerations, for example, then the angle i’ must be used instead of the angle i in all the cases in which the Parallax shift is involved.

 

 

(3) The Source and the Observer in Motion:

 

Let vA  = 0, vo ¹ 0, and vs ¹ 0 and let vo & vs make, respectively, angles j & i with the line of sight. Inserting these values in Equation #[5.13]:

 

sinDj  =  vo/c’)sinj                                                                                      [6.14].

 

Where c’ = c{1 - vs 2/c2sin2i}1/2  +  vs cosi.

From Equation #[6.14], we obtain the true position of the source j0, where j0’ = j + Dj, and then we use j0 instead of j in Equation #[4.12]:

 

f'  =  f[1 +{ vocos j0’ + vscosi }/ c{(1 -  vs 2/c2)sin2i}1/2 ]                                    [6.15].

 

Where f' is the observed frequency in the inertial frame of the observer.

 

Next, let’s assume that the absolute value of the above system’s absolute velocity is greater than zero, i.e. vA  ¹  0.   Let the vector vA be parallel to the vectors vo & vs in order to simplify the calculations. And let vo' = vA  + vo and   vs  = vA + vs.   Inserting the values of vs and vo’ in Equation #[5.13], we obtain the shift of Light Aberration Dj:

 

sinDj  =  [( vA + vo)/c'']sinj                                                                           [6.16].

 

Where  c’’ =  c{1 - (vA + vs )2/c2)sin2i}1/2   +  (vA + vs )cosi.

 

Since vA is the common velocity of both the source and the observer, the shift of its Light Aberration cancels out in the above equation by the shift caused by the Parallax and we rewrite Equation #[6.16]:

 

sinDj  = ( vo/c’’)sinj                                                                                     [6.17].

 

And then we insert jA’ = j + Dj in Equation #[4.12] to obtain f':

 

f'  =  f[1 + {( vA + vo)cosjA+(vA + vs)cosi} / c{1 - (vA + vs )2/c2)sin2i}1/2]               [6.18].

 

Since vA, by definition, is the common velocity of the source and the observer, and by our assumption jA  + i = 180o, the terms ‘vAcos jA’ &  vAcosi’ in Equation #[6.18], therefore, cancel each other out.  Rewriting this equation, we obtain:

 

 f'  =  f[1 + {vocosjA + vscosi} / c{1 - (vA + vs )2/c2)sin2i}1/2]                                  [6.19].

  

Where f' is the observed frequency in the inertial frame of the observer.

Let z  =  Df’/f.  And compute zo from Equation #[6.15] and zA from Equation #[6.19]. Let (b0 = vocos j0’ + vscosi) & (bA = vocosjA’ + vscosi), and then divide zA by zo: 

 

zA/zo =  {bA / b0} {[1 - (vs2/c2)sin2i] / [1 – ((vA + vs  )2/c2)sin2i]}1/2                               [6.20].

 

 

Therefore, we conclude that the Doppler shift as measured in a system moving with a linear absolute velocity is greater than the Doppler shift of the same relative motion as measured in a system at rest with respect to absolute space.

 

Let us, now, compare the shift of Light Aberration in Equation #[6.14] to that in Equation #[6.17]. Let   b0 = sinDj for Equation #[6.14], and bA  = sinDj for Equation #[6.17], and divide bA by b0: 

 

bA/ b0  =  c’/c’’                                                                                                 [6.21].

 

Therefore, we conclude that the shift of Light Aberration as measured in a system moving with a non-zero linear absolute velocity is greater for (j £ 90o) and less for (j > 90o) than the shift of Light Aberration for the same relative motion as measured in a system at absolute rest.

 

[B] The Case of Uniform Circular Motion:

 

We have now to consider the important special case of uniform circular motion. The magnitude of the tangential velocity, in this case, is constant, but its direction is changing continually around the circular orbit. Let an isolated system consist of two independent bodies revolving clockwise in uniform circular motion relative to each other. And let the inertial frame of one of these two bodies be the reference frame in which the observer is at rest. In the context of the theory under discussion, this system can only be in one of the following states: 

 

(1) The Source in Motion:

 

Let the common absolute velocity of the system be vA, and vA  = 0, and let the light source revolve clockwise with a linear velocity vs, around the observer. Because the source is moving in a circular trajectory, its velocity vector vs always forms an angle of 90o with the observer’s line of sight. And hence, according to the Emission Theory, no Doppler shift, caused by this motion, can be observed in the inertial frame of the observer.

 

Now let’s assume that the absolute value of the above system’s absolute velocity vA is greater than zero, and vA & vs are in the same plane. Since the observer is, now, moving with the common velocity of the system,  vo  =  vA.   Let vs’ denote the vector sum of vA  & vs, and a denote the angle between these two vectors. The effect of the Parallax, caused by the observer motion, is to rotate the line of sight counter-clockwise by an angle of Dj. Accordingly, each angle, made with the line of sight by the velocity vectors of the source, is decreased by an angle Dj, when the source is revolving in the direction of vA, and increased by the same amount, when the source is revolving in the opposite direction. And thus, the angle a remains constant. By contrast, the effect of the Light Aberration, which is also caused by the observer motion, is to rotate the line of sight clockwise by an angle Dj to its initial position. But because this rotation is not real, it does not affect the vectors rotated by the Parallax. The Parallax shift of the source velocity components leads to a corresponding Doppler shift in the light of the source received by the observer. To calculate this change in the observed frequency, vs’, c’, and Dj must be determined. 

From the law of cosines:

 

vs  =  [vA2   +  vs2  +  2vAvscosa]1/2                                                              [6.22].

 

From the given geometry above:

 

cosa   =  sinj                                                                                             [6.23].

 

Where j is the direction of the observer velocity vector.

 

Substituting j for a in Equation #[6.22]:

 

vs  =  [vA2  +  vs2  +  2vAvssinj]1/2                                                                  [6.24].

 

The direction of vs’ is the angle i.  Both i and j are observable and can be used to compute the velocity of light c’ in the inertial frame of the observer:

 

c’  =  c[1- (vs2/c2)sin2i]1/2  +  vs’cosi                                                              [6.25]. 

 

Where (vs’) is calculated from Equation # [6.24].

Since both effects are equal in magnitude, Light Aberration can be used to determine the Parallax shift of the velocity components of the source, Dj, using Equation #[5.13]:

 

sinDj  =  (vA/c')sinj                                                                                     [6.26].

 

Where c' is determined by Equation #[6.25].

 

Because vA is the common velocity of the system, the direction of the source velocity component vA, and the direction of the observer velocity component vA, always, form an angle of 180o with each other. As a result, the Doppler shift of the two components cancels out and cannot be observed in the inertial frame of the observer. Therefore, only the source velocity component vs can produce an observable Doppler shift with respect to the observer frame of reference. As implied by the definition of uniform circular motion, the vector vs, always, makes an angle of 90o with the line of sight in the inertial frame of the observer. But because of the Parallax, this angle is decreased by Dj, when the source is revolving in the direction of the vector vA, and increased by the same amount, when the source is revolving in the opposite direction. To compute the Doppler shift of this component, z, we take its radial projection with respect to the observer, and divide it by the velocity term (c[1-(vs'2/c2)sin2i]1/2) of light received from the revolving source:

 

z =  Df/f  =  [vssinDj] /  [c{1-(vs'2/c2)sin2i}1/2]                                                   [6.27].

 

Where (Dj) is computed from Equation #[6.26].

 

Hence, for a source revolving clockwise, the maximum Doppler blue shift, as measured by an observer at the centre of the orbit, is at j = 90o, and the maximum Doppler red shift is at j = 270o. And the Doppler shift is equal to zero at j = 0o and j = 180o.  For small values of vA and vs, the Doppler shift, computed from the above equation, can be irritatingly Einsteinian. For example, for vA = 300 kms-1 & vs = 30 kms-1, Equation #[6.27] gives a maximum Doppler shift, on both sides of the circular orbit, of only ±30 ms-1. The Doppler shift, however, can be higher for higher vA and vs.

 

Therefore, we conclude that in an isolated system moving with a linear absolute velocity vA ¹ 0, a source of light in a uniform circular motion around an observer at rest shows regular variations in its Doppler shift as measured by the same observer, and that the observer can use those measured variations to deduce the magnitude and the direction of the uniform linear velocity of an isolated system relative to absolute space.

 

(2) The Observer in Motion:

 

Let the common absolute velocity of the system vA  = 0, and let the observer revolve clockwise with a tangential velocity vo around the light source. Because the observer is moving in a circular trajectory, the velocity vector vo always forms an angle of 90o with the line of sight. And hence, according to the Emission Theory, no Doppler shift, caused by this motion, can be observed in the inertial frame of the observer.

 

Now let’s assume that the absolute value of the above system’s absolute velocity vA is greater than zero, and vA  & vs are in the same plane. Since the source is, now, moving with the common velocity of the system, vs  = vA.   Let vo’ denote the vector sum of vA & vo, and a denote the angle between these two vectors. The effect of the Parallax, caused by the observer motion, is to rotate the line of sight counter-clockwise by an angle of Dj. Accordingly, each angle, made to the line of sight by the velocity vectors of the observer, is increased, with respect to the source image, by an angle Dj, when the observer is revolving in the direction of vA, and decreased by the same amount, when the observer is revolving in the opposite direction. And hence, the angle a remains constant. By contrast, the effect of the Light Aberration, which is also caused by the observer motion, is to rotate the line of sight clockwise by an angle Dj to its initial position. But because this rotation is illusory, it does not affect the vectors rotated by the Parallax. The Parallactic shift of the observer velocity components leads to a corresponding Doppler shift in the light of the source received by the observer. To calculate this change in the observed frequency, vo’, c’, and Dj must be computed. 

From the law of cosines:

 

vs’ =  [vA2   +  vo2  +  2vAvocosa]1/2                                                                  [6.28].

 

From the given geometry above:

 

cosa  =  sini                                                                                                 [6.29].

 

Where i is the direction of the source velocity vector vA.

Substituting i for a in Equation #[6.28]:       

 

vo’ =  [vA2  +  vo2  +  2vAvosini]1/2                                                                     [6.30].

 

The direction of vA of the source is the angle i and the direction of  vo’ of the observer  is j.  Both i and j are observable and, therefore, the angle i can be used to compute the velocity of light c’ in the inertial frame of the observer:

 

c’  =  c[1- (vA2/c2)sin2i]1/2  +  vAcosi                                                                  [6.31]. 

 

Since both effects are equal in magnitude, Light Aberration can be used to determine the Parallax shift of the velocity components of the source, Dj, using Equation #[5.13]:

 

sinDj   =  (vo’/c')sinj                                                                                       [6.32].

 

Where vo is calculated from Equation #[6.30] and c’ from Equation #[6.31].

 

Because vA is the common velocity of the system, the direction of the source velocity component vA, and the direction of the observer velocity component vA always form an angle of 180o with each other. As a result, the Doppler effect of the two components cancels out and cannot be observed in the inertial frame of the observer. Therefore, only the observer velocity component vo can produce an observable Doppler shift with respect to the observer frame of reference. As implied by the definition of uniform circular motion, the vector vo always makes an angle of 90o with the line of sight in the inertial frame of the observer. But because of the Parallax, this angle is increased by Dj, when the observer is revolving in the direction of the vector vA, and decreased by the same amount, when the observer is revolving in the opposite direction. To compute the Doppler shift of this component, z, we take its radial projection with respect to the source image, and divide it by the velocity term (c[1-(vA2/c2)sin2i]1/2) of light received from the source by the revolving observer:

 

z  =  Df/f  =  [vosinDj] /  [c{1-(vA2/c2)sin2i}1/2]                                                      [6.33].

 

Where (Dj) is computed from Equation #[6.32].

Thus, for an observer revolving clockwise around a source at the centre of the orbit, the maximum Doppler red shift, as measured by the same observer, is at i = 90o, and the maximum Doppler blue shift is at i = 270o. And the Doppler shift is equal to zero at i = 0o and i = 180o.

 

Therefore, we conclude that in an isolated system moving with a linear absolute velocity vA ¹ 0, an observer’s uniform circular motion around a source of light at rest shows regular variations in its Doppler shift as measured by the same observer, and that the observer can use those observed variations to determine the magnitude and the direction of the uniform linear velocity of an isolated system relative to absolute space.

 

 

(3) The Source and the Observer in Motion:

 

Let the common absolute velocity of an isolated system vA  = 0, and let the source and the observer revolve clockwise with tangential velocities vs and vo respectively around a common centre. Because both are moving in a circular trajectory, each of their velocity vectors vs and vo always forms angle of 90o with the line of sight. And hence, according to the Emission Theory, no Doppler shift, caused by this motion, can be observed in the inertial frame of the observer.

 

Now let’s assume that the absolute value of the above system’s absolute velocity vA is greater than zero, and vA , vo, &  vs  are in the same plane. Both the source and the observer are, now, moving with the common velocity of the system vA.  Let vs denote the vector sum of vs and vA, and as denote the angle between these two vectors.  And let vo’ denote the vector sum of vA  & vo, and ao denote the angle between these two vectors.

The effect of the Parallax, caused by the observer motion, is to rotate the line of sight counter-clockwise by an angle of Dj. Consequently, each angle, made to the line of sight by the velocity vectors of both the source and the observer, is increased, as measured in the inertial frame of the observer, by an angle Dj, when the observer is revolving in the direction of vA, and decreased by the same amount, when the observer is revolving in the opposite direction. And hence, as and ao remain constant. By contrast, the effect of Light Aberration, which is also caused by the observer motion, is to rotate the line of sight clockwise by an angle Dj to its initial position. But because this rotation is only apparent, it does not affect the velocity vectors rotated by the Parallax. The Parallactic shift of the velocity components of the source and the observer leads to a corresponding Doppler shift in the light of the source received by the observer. To calculate this change in the observed frequency, vo’, vs’, c’, and Dj must be computed. 

From the law of cosines:

 

vo  =  [vA2   +  vo2  +  2vAvocosao]1/2                                                                    [6.34].

 

Where vo’ is the resultant velocity of the observer.

 

vs  =  [vA2   +  vs2  +  2vAvscosas]1/2                                                                     [6.35].

 

Where vs’ is the resultant velocity of the source.

The direction of the vector vs is the angle i, and the direction of  vo’ of the observer  is j.  Both i and j are observable and, therefore, the angle i can be used to compute the velocity of light c’ in the inertial frame of the observer:

 

c’  =  c[1- (vs2/c2)sin2i]1/2  + vs’cosi                                                                       [6.36].

 

Where (vs’) is computed from Equation #[6.35].

Since both effects are equal in magnitude, Light Aberration can be used to determine the Parallax shift of the velocity components of the source, Dj, using Equation #[5.13]:

 

sinDj   =  (vo’/c')sinj                                                                                            [6.37].

 

Where vo is calculated from Equation #[6.34] and c’ from Equation #[6.36].

Because vA is the common velocity of the system, the direction of the source velocity component vA, and the direction of the observer velocity component vA, always, form an angle of 180o with each other. As a result, the Doppler effect of the two components cancels out and cannot be observed in the inertial frame of the observer. Therefore, only the velocity components vo and vs can produce an observable Doppler shift with respect to the observer frame of reference. As implied by the definition of uniform circular motion, both vectors,  vo and  vs,  always, make an angle of 90o with the line of sight in the inertial frame of the observer. But because of the Parallax, this angle is increased by Dj, when the observer is revolving in the direction of the vector vA, and decreased by the same amount, when the observer is revolving in the opposite direction. To compute the Doppler shift of these two components, z, we take their radial projections with respect to the source image, as measured in the inertial frame of the observer, and then divide the two by the velocity term "c[1-( vs2 /c2)sin2i]1/2" of light received from the source by the revolving observer:

 

z  =  Df/f  =  [(vo  +  vs )sinDj] /  [c{1-(vs2/c2)sin2i}1/2]                                             [6.38].

 

Where (Dj) is computed from Equation #[6.37].

 

Therefore, for an observer and source revolving clockwise around a common centre, the maximum Doppler red shift, as measured in the reference frame of the observer, is at ao = 0o, and the maximum Doppler blue shift is at ao = 180o. And the Doppler shift is equal to zero at ao =90o and ao = 270o.

 

By considering, in the three cases above, a system whose two components are in uniform circular motion with respect to each other, we conclude that a system, moving with linear absolute velocity vA ¹ 0, produces a Doppler shift that can be measured in the inertial frame of the observer. The Doppler shift, produced in this manner, varies differently from that caused by the motion of the system’s components in elliptical trajectories and vA = 0.  And consequently, it can be always used, in principle, to determine the absolute velocity of an isolated system with respect to absolute space, from within and without any reference to anything else outside that system.

 

 

7. Concluding Remarks

 

 

            No doubt, the Emission Theory of light, in terms of its explanatory and predictive power, is far more productive than and superior to any other theory in this field.  The relative ease with which one deduces its logical consequences is immensely refreshing. Especially, if you recall the agony of deriving the meager and often logically untenable results of Einstein’s Relativity and its Siamese twin, the Quantum Theory.

 

One may argue that if the theory under discussion comes under severe criticism for a century or so, it will, eventually, become as complex and sterile as these two theories.

It may turn out that way, but if and only if it’s wrong from the outset. That is because in science, as in politics, if you start with the wrong assumptions, you will, eventually, in due time, take refuge, without even noticing it, in vagueness, complexity, and false distinction. 

 

The problem of false starts is even more severe almost to the point of incurability in the field of physics. Because in physics, no matter how wrong your start point is, if you work hard enough, and if you don’t lose sight of the experimental results, you will in the end have a set of mathematical equations that can describe and save the phenomena, at hand, reasonably well. The only penalty, for being qualitatively wrong, in this regard, is to be quantitatively complicated. And since complexity per se does not prove that a hypothesis is wrong, there is no such thing that can be, even remotely, called  decisive evidence’ or a ‘knockout’ in physics.

 

It’s true that experimenters, in particular, love to think otherwise. But with a bit of ingenuity and hard work on the part of the theorist, even the most sophisticated experiment can be turned on its head and used to support the theory in question. And so whenever you hear a historian or some naïve onlooker talking about such and such a ‘knockout’ experiment, or such and such an ‘ill-fated’ theory, you can be absolutely sure that, either the proponents of that theory have been unfairly marginalized, or they haven’t worked hard enough to modify their theory and meet the challenge.

 

Therefore, the correctness or falsity of any physical theory hinges entirely on its qualitative part. Is it true?  Is it physically feasible? Is it logically consistent?  These are the bothersome questions, which the proponents of erroneous theories wish to eradicate and bury forever, and always end up in having their theories and hypotheses buried by them instead.

 

It should be borne in mind, however, that the most enduring legacy of any scientific endeavor is its collection of facts and observational data. Theories and hypotheses don’t matter in the long run. Thus, if the use of some false hypothesis can add new facts to those collections, then so be it. Only if the fallacious hypothesis starts to be an obstacle in the way of progress and agent of stagnation and darkness, then it must be bombarded with criticism continuously until its proponents relent and get out of the way of new approaches and new methods in the investigation of the natural world.

 

At present, it’s glaringly obvious that the notorious pair (The Relativity & the Quantum) have outlived their usefulness and begun to corrupt the hard science of physics. Their twisted and absurd interpretations of reality are insulting to rational thinking and reason. It’s, therefore, the duty of every thinking individual alive to try to free physics of their shackles and to have their dogmatists boxed up and tamed for good.  

 

 

 

 

References

 

 

 

1.  Cyrenika, A.A., “Principles of Emission Theory”:

http://redshift.vif.com/JournalFiles/Pre2001/V07NO1PDF/V07N1CYR.pdf

 

2. Dogra, R., “Apparent Lack of Symmetry in Stellar Aberration and Euclidean Space Time”: http://www.rajandogra.freeservers.com/

 

3. Einstein, A., “On the Electrodynamics of Moving Bodies“: http://www.fourmilab.ch/etexts/einstein/specrel/www/

 

4.  Fox, J.G., “Evidence Against Emission Theories, Am. J. of Phys, 33, 1, (1965).

 

5. Ives, H., et al, (1938). J. Opt. Soc. Am., 28, 215-226

 

6.  Weiss, P.,  Light Pulses Flout Sacrosanct Speed Limit”: http://www.sciencenews.org/articles/20000610/fob7.asp

 

7.  Waldron, R.A., (1980). Speculations in Science & Technology, 3, 4, 385-408.

 

8.  Waldron, R.A., (1979). Speculations in Science & Technology, 2, 3, 303-312.

 

9. Wang, L.J., et al, “Gain-Assisted Superluminal Light Propagation”: http://www.nature.com/cgi-taf/DynaPage.taf?file=/nature/journal/v406/n6793/full/406277a0_fs.html

  

 

 

Related Papers

  

[1] Restricted Relativity: http://www.wbabin.net/physics/faraj3.htm

[2Fake Physics - A Dialogue: http://www.wbabin.net/physics/faraj.htm

[3] Remarks on Davidson's Apeiron Article: http://www.wbabin.net/physics/faraj2.htm

[4] Superluminal Light: http://www.wbabin.net/science/faraj8.htm