Studying the properties of light, and using the same technique as before [ 01 ], leads to the conclusion that light (radiation in general) might use the N's for propagation. Assuming this as a model, leads, in a simple and easy to follow manner, to the following results:

[04] Light in the presence of gravity.

Light in water moves at about three-quarter of the velocity in air, but in air again, it continues at the original velocity. This indicates that light does not behave as, and is not, a simple projectile from A to B but that there is some interchange with space that controls velocity.*
It seems that moving between and through the water molecules (temporarily) checks the velocity. The only substance present between -and inside- the molecules, are the N's.

Assume that the properties of the N's determine the velocity. Comparing the ratio of the lengths light travels -in the same time- in water and in vacuum produces a ratio for that effect, expressed as a ratio of the respective lengths.

[04-01]Take l_w, and c_w in water and l and c in vacuum so, that we have:

[04-02]The strength is proportional to:

[04-03]Division gives:

The effect of gravity on the velocity follows from the horizontal lengths l_R and l_x on distances R and R_x ( R_x = R - delta-R ) measured from the centre of M. The lengths so, that light passes in equal time. The ratios are:
[04-04]

[04-05]For gravity we have:

[04-06]Which gives:

[04-07]Resulting in:

[04-08]From this follows:

The general formula must satisfy the following conditions:

[04-09]Indicating for the velocity of light at R, the expression:

The figure [04-10] shows, that at a distance of .88 meter (100r), from a concentrated earth mass, the velocity is already 99% of its maximum. It approaches the maximum velocity asymptotically, making it nearly constant. For the earth, r is only 8.8 mm. This means that the graph shows a distance of about 18-cm from that centre. At the surface, the distance is more than 700.000.000 times r, and showing this to scale gives, in this figure, only a straight line for c.

The various differences in velocity are:

The 1264 m/s reduction in velocity near the sun is large enough to cause a noticeable change in direction and provides 'proof' for the idea of 'curved' space.

The velocity of light is not a constant and the c in the gamma-factor is a variable. For Mercury the effect is very small and can be ignored, for the binary PSR 1913+16 it causes the decaying of the semi-major axis by 3.5 meter per year. The calculations become more complicated, but understanding "what is going on" is clear.

The shift

The local strength of gravity determines the velocity of the emitted light. Thereafter the velocity adjusts everywhere to the local strength. Light emitted at the bottom, of e.g. the Harvard tower, has a velocity that is different from that emitted, by the same source, at the top.

The velocity is slightly greater at the top. This increase, by the same energy, means that the wavelength, the distance between successive photons, has increased.
The velocity, over a relatively small distance, can be considered uniformly accelerated.

That allows the ratio, increase in wavelength to wavelength, to be calculated. The result is 2.44 × 10^-15. This converts to 2.63 millimeters per hour (for the Mossbauer crystal), the velocity found in the Harvard experiment.

The velocity measured in this experiment also determines the difference in the light velocity. That difference, 5.26 mm per hour is extremely small, but a difference it is, and it provides confirmation for the dependence of the light velocity on the strength of gravity.

Calculating the shift

Light emitted at B (Bottom) and received at T (Top) has a velocity that differs from that when emitted.

[05-01]The light velocity at B is:

[05-02]A small change in R gives for the change in velocity:

This change causes a decrease (or increase) in the wavelength of the light. This increase, for a red shift, is not constant, but zero at R_B and proportional to delta-c at (R_B + delta-R.) The acceleration can, over that 'small' distance, be considered uniform, giving an average velocity:
[05-03]

[05-04]And further:

[05-05]The wavelength has lengthened to:

[05-06]And the proportional change at R_T is:

[05-07]At the Harvard experiment = 22.5 m giving:

[05-08]And the measured average velocity:

= c . 2.44 x 10^-15 = 0.732 x 10^-6 m / s = 2.63 mm / hr

In agreement with the experiment and indicating that the light velocity increased by about 5 mm / hr !

In the above diagram, Star is the true position of the star, Star' the direction as observed from earth. Earth' is the mirror position of the earth on the assumed curved part of the light path, i is the angle of incidence. The reduction in velocity is bending light. The light does not approach the sun diametrically, but under an angle, and this causes an asymmetric 'resistance' that also changes continually.

The reduced velocity increases again during the journey to the earth and so forms a, practically, symmetrical path. The effective radius, for the change in velocity, changes from the distance of the sun to earth, to the radius of the sun as a minimum. The tangent T-T' is the direction of the light at this point.

The direction of the light changes as dictated by the refraction index. Behaviour as described by Snell, but without the clear cut boundary between substances and with a continually changing index. Working this out gives an angle of 1.74 seconds, in agreement with observations.

The curve of the path the light takes to the earth is far from symmetrical, however, before reaching earth' it is follows a near straight line. The calculation of the angle is not effected by this assumption. It is worth noting that the angle is only four-millionth of a radian. To show such an angle in a sketch is impossible. The triangle formed with this angle would lie within a line, 0.1 millimeter thick and 25 meters long! This means all sketches and diagrams are grossly distorted.

It appears that this bending of light near the sun is no more than the well-known Fraunhofer diffraction, bending of light near sharp edges, but on a different scale. It has nothing to do with light that, as shown with the famous energy formula, has mass, and is attracted to the sun by gravitation. Light is repelled by gravity. Light decreases its velocity when 'falling', to zero near a black hole!

Calculating the angle

The velocity of the light, coming from the star, changes from a maximum- to a reduced velocity near the sun, and increases then again to a -near- maximum on its way to the earth. Near maximum: the difference with the maximum is, for the purpose of calculating the angle of bending, negligible.

[06-02]The change in the light velocity:

[06-03]Near the sun:

c = 3 x 10⁸ x 2935 / 6.965 x 10⁸ = 1264 m/s

The dependence, of the light velocity on gravity, gives, near the sun, a maximum index N of:
[06-04]

Snell's law, for a stratified medium, ignores the different layers, and the ratio between the sine (in) and the sine (out) is determined by the ratio of the velocity (in) to the final velocity (out).

This is usually demonstrated for distinct, parallel, layers, not for a continuously changing medium. If infinitesimal layers are assumed, then they are wedge shaped, and not parallel. The change in direction, at each instant, is still determined by the ratio of the velocities only, but the angles are measured from continually changing reference lines.

The complete mathematical treatment of this ostensible simple problem is, with the current theory of gravity, rather difficult and cumbersome. A much simpler approach is possible by making use of the very small angles. This can be done without noticeable loss of accuracy in the final outcome.

Light approaching the sun diametrically looses velocity, but does not change direction. Light approaching under an angle does both, until its path is tangential, when it does neither. This suggests that, if we consider the light velocity c_a to be the (vector) sum of the two components, c_t and c_r, the tangential and the radial velocity respectively, it is the radial velocity only that determines delta-c_r, the change in direction.

This is shown in Diagram I, it is to be noted that the angles u' and u" are so small that they can be ignored in the 'radius' R_a = R / cos a. The change in direction delta-u' is cumulative, and the sum is equal to i, the angle of incidence, when the angle a equals 0°.

[06-06]The expression for the velocity related to the angle a is:

[06-07]The radial and tangential components are respectively:

This is shown in Diagram II, again with the angles exaggerated to make it possible to show what is going on. From this diagram it is possible to see how simple it really is, all that is required is an understanding of the nature of the physics.

[06-09]The angle of incidence follows from:

The angle as seen from the earth is twice that, so that we have for the final angle ß:
[06-10]

Which is the observed value.

07 Fizeau's (1851) experiment

The strength of the gravitational field changes according to the inverse square law. For light in water there is an effective field strength, indicated by a radius R equal to 4 r in c_w = c ( 1 - r / R ) , giving a velocity in water of (3 / 4) . c.

For moving water, there is an increase (or decrease) in the -encountered- strength of that field, the strength has to be multiplied with the factors ( c_w -v ) / c_w for opposing, and ( c_w + v ) / c_w for coinciding velocities.

The signaling velocity is equal to the velocity of light in water. This means that, for the velocity, the 'radius' R has to be multiplied by the square root of one of these factors. For the opposing velocities the velocity of light c_wvis then:
[07-01]

The velocity of light, for small values of v / c_w, in moving water is:
[07-02]

The velocity of the light changes with halve the velocity of that substance as a first approximation (two terms only). A 'dragging-coefficient' of 1/2 instead of Fresnel's 7/16 for water. It indicates that it is only the velocity of the medium that matters.

With k the dragging coefficient, and using Fizeau's result, the proportional shift d in the wavelength l is:
[07-03]

With Fizeau's data ( from A.I.Miller 1981 on AE's srt ):
[07-04]

Compared with the result of the Fizeau experiment an improved result; the difference with Fresnel is about 15 % !

08 The Experiment

This famous experiment was to measure the difference in the velocity of light due to the orbital motion of the earth through the ether. The experiment showed no difference, or rather, less than expected, and the conclusion was, in conflict with the current theories, that the orbital velocity of the earth did not effect the velocity of light, and therefore there was no ether-wind and no ether.

To accept that result, without changing the existing theories, several solutions were suggested. One, by Fitz-Gerald, said --seriously-- the difference is there, but measuring it is impossible. Lengths contract and precisely so that the difference disappears. Empirical formulae supported that idea.

Showed ... no difference. The experiments, however,did show a difference, but less than the expected difference*. This deliberate misstatement of the result, that M & M obtained a null result, is still used to deny the possible existence of an ether, whatever the form or whatever properties it may have.

The ether wind, as expected, was not found, it was at best an ether-breeze. But breeze nor wind was acceptable to the followers of the relativity theories, and the result was, and is, published as a null result. As an amateur with limited access to the relevant information I became only recently aware of all this. Not everything about the ether is now clear and unambiguous, except that there is an ether, an ether to be studied, not to be ignored.

The explanation with the N's is simple; there are two main vectors on all N's:

[ a ] The force of gravitation from the sun.
[ b ] The force from the earth's inertia.

Light and all other forms of earth sourced electro-magnetic energy carries, on release from their respective sources, these two vectors [a and b] in addition to their normal source related energy. This makes light behave relative to the earth and not relative to the Newton-field.

10 Starlight aberration

Starlight, not carrying those two forces [a and b], moves therefore relative to this field and shows the earth's velocity relative to that field. Starlight aberration, (which is better called telescope aberration) supports clearly this Newton field.

Remarks

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