The Society for the Diffusion of Knowledge P.O. Box 964, Kaunakakai, HI 96748

    "The discovery of the aberration of light in 1725, due to James Bradley (1693 - 1762) is one of the most important in the whole domain of astronomy; and in pure physics it has provoked a succession of investigations culminating in the theory of relativity. It was entirely unexpected, and it was only by extraordinary perseverance and perspicuity that Bradley was able to explain it in 1729.
     The discovery arose in the course of an attempt to discover whether the stars had appreciable parallaxes". (The Encyclopedia Britannica, Vol. 1, 1937, p. 42.)
     Throughout this investigative period, which actually commenced as early 1674, and lasted well into the first quarter of the twentieth century, a vast category of mechanism and effects had been examined, ranging from atmospheric refraction, nutation, parallax, and of course luminiferous ether and respective ether drag and irrotation, with numerous researchers involved: Jean Picard, J. Flamsteed, R. Hook, Samuel Molyneux, George Graham, James Pond, Roemer, Rutherford, Arago, Fresnel, Fizeau, Airy, Boscovitch, Michelson, Moreley, Sir George Stokes, Planck, Lorentz, J. Larmor, Fitzgerald, D.C. Miller, and Whittaker.
     In the evaluation of parallax, consistent variation occur in the observed position of stars, caused by nutation, discovered by Bradley, earth parallax, solar parallax, earth mass anomalies and galactic motion. The displacement of a star due to aberration was always found at right angles to that due to parallax.
    Once light was emitted by a star at a given angle relative to the observer, it should not change. For example, if the star and observer are traveling on parallel paths, with the star some distance ahead of the observer such that the beam of light in question is directed backwards towards the observer at a fixed angle, the observer should observe its approach at the same angle. Instead though, astronomers discovered that the approaching beam of light changes to a shallower angle than its original emission angle; logically impossible under the constraints of geometrically stable Newtonian space, but not under fluid like Descartian space.
     Within the rational constraints at the time, theoreticians had little choice but to evaluate these observations in light of Descartian space; thus leading to the necessity of luminiferous ether.
     But over the course of time, no well defined ether mechanism ever came to the forefront without problems.  Almost in every case, postulated ethers required some sort of fluid compression, which Max Planck debunked on the basis, that the range in density necessary in the explanation of its fluid compression would exceed that of the most dense neutron stars. This, coupled with the necessity that these potentially dense ethers must be able to pass between the particles of matter, seemed incomprehensible.
     Part of the problem was the natural expectancy that ontological arguments should abide to known material behavior, particularly in the case of ether, to that of fluids, leaving theoreticians with inexplicable problems associated with fluid dynamics, especially those concerning the earth's drag through ether. It should have been apparent to all researchers at the time, based upon much earlier implication of Newton's inertial studies, that space itself, rather than some sort of mystical fluid within space, possessed its own set of inexplicable behaviors.
     Rather than seeking an inherent mechanism of space which might explain the deflection of light, classical theoreticians eventually gave up, thus prematurely paving the way for a non ontological, mathematical premise, namely, relativity.
     Relativity is a set of mathematical expression providing a close fit to mensurable natural behavior, though not explaining natural behavior; being that is superficial. For example, manifolds and a space-time continuum are not real, but merely abstract objects within this abstract mathematical system, no more real than the monads proposed by Liebniz.
     Unfortunately, relativity provided a stumbling block to fundamental theoretical progress, in the same way that Hubble law had done, because of  limited interpretation.
     Had the theoreticians at the time, just before the turn of the twentieth century, continued to explore other possible and logical mechanisms, they would have discovered one which would accurately predict the aberration of starlight to within less than .02 seconds of arc!
     Several important facts were known at this time, besides the verification of the aberration of starlight. Light was known to have the constant velocity c. A fluid like ether provided no explanation. Empty space could not suffice. Light moved as a wave through a medium.
      From this point in the ratiocination of classical physics, if it had happened; most likely around the conclusion of ether wind experiments around 1890, it would only require a small step to the evaluation of a system of surfaces as the medium for the propagation of light; surfaces being the only possible forms which could allow this to happen.
     Given then a field of surfaces, light may be equated to what is a simple wave which may propagate through this field without any kind of impedance. Just like our apparent reality, you can consider this field as three-dimensional.
     As light moves in a rectilinear passage, it will encounter surfaces which are oriented in all manner of direction. Each time a simple wave encounters a surface, it has a fifty-fifty chance of reacting to that surface, providing the surface is situated orthogonal to the photon's direction; the more canted, the less of a chance of reaction. Each reaction forces the simple wave to take off on an orthogonal tack; hence the photon follows a microscopically zig-zagged course through the field, as it encounters surfaces oriented in all manner of direction. Any surfaces encountered by the photon, if too steeply canted in the direction of motion, will generally not interact with the photon.
     Essentially what happens, is that any ponderable mass moving through space, sweeps the field ahead into it; causing field compression in proximity to the mass, while at the same time, the field leaving the proximity of any mass, accelerates behind and away from the mass, regaining normal density within approximately ten radii behind it.
     If one were to measure the field density, both a great distance ahead and behind the moving mass, its density would be normal; directly ahead and behind the mass, it would be lower than normal; and very close to the mass, both ahead and behind it, and within the mass, it would be higher than normal. It is within this region, scientists tried to measure the change in the speed of light relative to the observer, in their attempt to measure the ether wind. Unfortunately, they did not think it possible for the ether (field) to slow down so greatly, more than 1/10 the orbital speed of the earth, because of this advanced compression of the field; all experiments at the time attempting to measure this variance, around 1883+/- 40 years, being far too insensitive.
     Actually, some ether wind experiments performed well into the twentieth century, did show some positive results, but were discounted by the scientific establishment; especially upon the subsequent introduction and acceptance of relativity.
    Thus in hypothesis, which you are about to encounter, starlight moving through a surface field would not be subject to laminar shearing, as in fluid flow, though the field itself would have gradients of motion. In extreme simplification, where one might imagine surfaces arranged both orthogonal to the earth's velocity and parallel to the earth's velocity, starlight approaching directly from the side would only interact with the latter, but not those surfaces orthogonal to the earth's velocity, though it would be the former interacting with the earth's passage, thus contributing to this gradient of motion of which I speak.

     Starlight approaching the earth from the side, would undergo the following deflective process. As the photons move through the field, they will encounter successive gradients of field motion, much like a small boat moving through faster moving water as it crosses a river. In the case of the boat, its resultant speed increases as the vector sum of its forward progress and the side wards motion caused by the flowing water. But in the case of the photons, they cannot be affected by any side ward moment since there is no mechanism which might cause this moment, thus their resultant scalar magnitude of motion remains unchanged, despite a change in direction of this same vector. Putting it another way, a boat can be pushed sideways by water, but a field comprising surfaces cannot push photons laterally, though their speed is measured against the field, resulting in a change of direction without a change in speed.
    Treating the field as consisting of a gradient of variable motion decreasing in magnitude to a minimal residual value (V_r ) at the earth's surface, as well as inside the earth, light will follow a curved path consistent to the aberration of starlight which reaches a maximum of 20.47 seconds of arc; what is called the constant of aberration. Since this ratiocination ideally should be taking place in mankind's history, we can assume light to travel at a constant speed (c); considered to be true prior to Einstein's work. In the corresponding illustration, a triangle is formed between the constant leg c, representing to the speed of light, and another leg (DV_k) corresponding to the difference in the speed of the field, in the time it takes light to move between successive gradients of the field as it approaches earth. The symbol D (delta), represents  a change in value. Angles o_k and o_k+1 represent the angle of the approach of light corresponding to gradients d_k and d_k+1. Both angles are measured from reference lines which are always parallel to the original vector directionDV_k.
     The leg DV_k is always parallel to the orbital motion of the earth, represented by vector V_e and directed opposite V_e.

     By the Law of Sines,

(I)    c / sin o_k = DV_k / sin (o_k+1 - o_k).

Since, DV_k = V_k+1 - V_k , and Do_k = o_k+1 - o_k,

giving, c / sin o_k =DV_k / sin Do_k.

This may be restated in general form corresponding to any d_k layer:

c / sin o = DV / sin Do.

Re-arranging terms:

(II) sin Do / sin o = DV / c.

For very small values of o,

sin Do / sin o = DV / Do / o,

equation II becomes:

(III) Do / o = DV / c.

Because field layers may be treated as discrete variations of a motion gradient, Equation III may be written as a differential, giving,

Do / o = dV / c .

Integrating and solving for o,

(IV)    o = e _v/c between the limits L₁ and L₂, where o represents the total angular change (aberration) of light propagating from L₁ and L₂, where V represents the motion of the field at any given distance between L₁ and L₂.
    Whether one considers the field at rest or moving relative to the earth does not matter, since all motion is relative. In this evaluation, the observer is considered at rest, as is the earth, and the field passing by; at great distances away, the field moving with the exact opposite motion of the earth in orbit around the sun (V_E), where V_E is about 18.5 miles per second). The sun is also moving much more rapidly around the galaxy, but this motion is not considered. Inside the earth, the field passes by with a small residual motion (V_R) at about 1/10th its orbital motion, or even less.
     With this in mind, a purely abstract relationship may be expressed for the motion of the field (V) at any distance from the earth's center (d), where:

(V)  V = V_R / A_d + V_E - V_E / Bd,

where A and B serve as constants, where d is the distance from the earth's center, and where V_R and V_E are variable parameters already explained.
     Since starlight comes from immense distance, the value for d may be considered infinite, yielding,

V_MAX = V_E.

Conversely, the nearest approach of starlight would be at the earth's surface, which in reference to celestial distances is pragmatically the same as the earth's center, in which case d would be zero, giving:

V_MIN = V_R.

     Such simplification as this is not essential in the evaluation of expression V, however, in doing so, little loss of significance or accuracy is suffered.
     Substituting these limiting parameters into Equation IV gives the following:

(VI)   o = e_VE/c - e_VR/c,
      where e is the natural number e = 2.71828....

     In this expression, o represents the angle of stellar aberration, V_E and V_R respectively represent the maximum velocity between the mean velocity of the field and the earth, and the residual velocity of the field within the earth.
     Evaluating this expression, where,

      V_E = 2.98 x 10⁴ (meters per second)
      V_R = 30 (meters per second)
      c = 2.997 x 10⁸ (meters per second)

yields: o = .000099335 ^r, or, 20.48934".

     Unlike vector addition typical in the analysis of basic fluid flow conditions, such as a boat crossing a stream or a sailboat in the wind, there is no addition of vectors; logically not permitted because the resultant vector must remain constant and equivalent to the speed of light. Remarkably, despite this variance from conventional mathematics, the sum of all vector change approaches the constant of aberration.