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Optica!

Ben T. Ito

August 11, 2015

'''This paper will analyze the wave theory of light.

§ 1. Introduction

The ancient Greeks believed the eye sent out feelers that emanated from the eye and felt the object being observed. All of the ancient Greek writings, includes that which involved democracy and law, were translated from Arabic since the Romans attempted to destroy everything that the Greeks wrote. In the 7th century AD Middle East, Iraqi scholars studying the ancient Greek writings resulted in the advent of the light ray theory that was a monumental achievement, in the history of light. al-Kindi (b. 801 AD) introduced the theory of vision, where light rays, interacting with the eye, formed vision. al-Haytham (b. 965) enhanced al-Kindi's light ray theory, by dissecting the eye and analyzing the anatomy of the eye, resulting in the invention of the two lens celestial magnifier that Sirian scholar al-Shatir (b. 1304) used to form the theory that planets revolved around the sun. Copernicus (1474) used al-Shatir's diagrams and calculations to describe planets revolving around the sun. Galileo (1610) discovered the rings of Saturn, and supported al Shartir theory which, at the time, was highly controversial; consequently, Galileo was punished with a life sentence, of home incarceration, for his outspoken support of al Shartir theory.

Huygens (1690) describes the propagation, and transmission-reflection effects of light, using light waves formed by the motion of an Ethereal matter where the particles of the ether formed a hardness that produced a springiness that is used to form light waves which propagate through the optical ether, composed of matter (solid, liquid or gas). Fresnel's (1819) describes diffraction using Huygens' principle where interfering light-waves produced by the vibration of an elastic fluid forms the intensity of the diffraction pattern. Maxwell (1864) depicted polarization using transverse light waves, formed by the motion, of an elastic medium yet the propagation, diffraction and polarization effects of light form in vacuum, that is void of an optical ether, composed of matter. Michelson (1881) tests for the existence of Fresnel's optical ether (Michelson, p. 120), composed of matter, but the result was negative. Lorentz (1899) reversed the negative result of Michelson's experiment (Lorentz, § 9) to justify the existence of Fresnel's ether. In Einstein's paper, "Relativity: Special and General Theory" (1917), Einstein reverse the negative result of Michelson-Morley experiment to justify the existence of Fresnel's ether (Einstein5, § 15) but light propagating in vacuum is definitive and irreversible experimental proof Fresnel's ether does not physically exist. Einstein (1910) describes an electromagnetic ether (Einstein4, § 1) but the electromagnetic field of Einstein's electromagnetic ether originates from Faraday's induction experiment that is not luminous.

"More artificial theories have been tried out, assuming that the real truth lies somewhere between these two limiting cases: that the ether is only partially carried by the moving bodies. But they all failed! Every attempt to explain the electromagnetic phenomena in moving CS with the help of the motion of the ether, motion through the ether, or both these motions, proved unsuccessful. Thus arose one of the most dramatic situations in the history of science. All assumptions concerning ether led nowhere! The experimental verdict was always negative. Looking back over the development of physics we see that the ether, soon after its birth, became the "enfant terrible" of the family of physical substances. First, the construction of a simple mechanical picture of the ether proved to be impossible and was discarded. This caused, to a great extent, the breakdown of the mechanical point of view. Second, we had to give up hope that through the presence of the ether-sea one CS would be distinguished and lead to the recognition of absolute, and not only relative, motion. This would have been the only way, besides carrying the waves, in which ether could mark and justify its existence. All our attempts to make ether real failed. It revealed neither its mechanical construction nor absolute motion." (Weaver, p. 145-6).

Maxwell's (1864) electromagnetic theory of light, based on Faraday induction experiment, was introduced, since induction forms in vacuum but induction is not luminous; consequently, Poynting (1884) supports Maxwell's theory by deriving an electromagnetic energy equation of light (Poynting, p. 358) but Poynting's current wire is also not luminous. Maxwell and Poynting describe the varying capacitor induction effect that is the transition between Faraday's induction effect and Hertz's radio waves. Hertz's (1887) supports Maxwell by structurally uniting light with induction, using a spark gap experiment, that emits light and the radio induction effect, but Hertz's spark gap also emits electrons yet induction is not ionization effect. Planck (1901) attempts to structurally unite light with induction using the blackbody radiation effect but Planck's blackbody also emits electrons. In Einstein's (1905) electrodynamics, Einstein alters the dimensions of Maxwell's equations to justify Maxwell's theory but manipulating the coordinate system of Maxwell's equations does not change the fact that Maxwell's equations are derived using Faraday induction experiment that is not luminous. The analysis of the wave theory of light begins with Huygens' principle.

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§ 2. Huygens

In Huygens' paper, "Treatise on Light" (1690), Huygens' describes light using spherical waves based on a sound wave analogy.

"We know that by means of the air, which is an invisible and impalpable body, Sound spreads around the spot where it has been produced, by a movement which is passed on successively from one part of the air to another; and that the spreading of this movement, taking place equally rapidly on all sides, ought to form spherical surfaces ever enlarging and which strike our ears. Now there is no doubt at all that light also comes from the luminous body to our eyes by some movement impressed on the matter which is between the two; since, as we have already seen, it cannot be by the transport of a body which passes from one to the other. If, in addition, light takes time for its passage—which we are now going to examine—it will follow that this movement, impressed on the intervening matter, is successive; and consequently it spreads, as Sound does, by spherical surfaces and waves" (Huygens, p. 5).

"It is true that we are here supposing a strange velocity that would be a hundred thousand times greater than that of Sound. For Sound, according to what I have observed, travels about 180 Toises in the time of one Second, or in about one beat of the pulse. But this supposition ought not to seem to be an impossibility; since it is not a question of the transport of a body with so great a speed, but of a successive movement which is passed on from some bodies to others. I have then made no difficulty, in meditating on these things, in supposing that the emanation of light is accomplished with time, seeing that in this way all its phenomena can be explained, and that in following the contrary opinion everything is incomprehensible. For it has always seemed tome that even Mr. Des Cartes, whose aim has been to treat all the subjects of Physics intelligibly, and who assuredly has succeeded in this better than any one before him, has said nothing that is not full of difficulties, or even inconceivable, in dealing with Light and its properties." (Huygens, p. 7).

"the velocity of Light is more than six hundred thousand times greater than that of Sound. This, however, is quite another thing from being instantaneous, since there is all the difference between a finite thing and an infinite. Now the successive movement of Light being confirmed in this way, it follows, as I have said, that it spreads by spherical waves, like the movement of Sound." (Huygens, p. 10).

Huygens' spherical waves are formed by the motion of an optical ether, composed of matter, yet light propagates in vacuum that is void of matter which contradicts the existence of Huygens' spherical waves. A wave is a mechanical entity that is formed by the motion of a medium, composed of matter (solid, liquid or gas). A force that acts upon the medium produces waves. Air is the medium that forms sound waves. A force disturbs the air molecules forming sound waves but sound waves cannot propagate in vacuum since vacuum is void of air molecules that is the medium that forms propagating sound waves yet Huygens is using a sound wave analogy to represent the propagation of light. The most important characteristic of sound is not applicable to light since light propagates in vacuum that is void of matter which is experimental proof Huygens' sound wave analogy is physically invalid.

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Huygens is describing the formation of light waves produced by the motion of an Ethereal matter.

"Now if one examines what this matter may be in which the movement coming from the luminous body is propagated, which I call Ethereal matter" (Huygens, p. 11).

"But the extreme velocity of Light, and other properties which it has, cannot admit of such a propagation of motion, and I am about to show here the way in which I conceive it must occur. For this, it is needful to explain the property which hard bodies must possess to transmit movement from one to another." (Huygens, p. 13).

"But it is still certain that this progression of motion is not instantaneous, but successive, and therefore must take time. For if the movement, or the disposition to movement, if you will have it so, did not pass successively through all these spheres, they would all acquire the movement at the same time, and hence would all advance together; which does not happen. For the last one leaves the whole row and acquires the speed of the one which was pushed. Moreover there are experiments which demonstrate that all the bodies which we reckon of the hardest kind, such as quenched steel, glass, and agate, act as springs and bend somehow, not only when extended as rods but also when they are in the form of spheres or of other shapes." (Huygens, p. 13).

"Now in applying this kind of movement to that which produces Light there is nothing to hinder us from estimating the particles of the ether to be of a substance as nearly approaching to perfect hardness and possessing a springiness as prompt as we choose. It is not necessary to examine here the causes of this hardness, or of that springiness, the consideration of which would lead us too far from our subject. I will say, however, in passing that we may conceive that the particles of the ether" (Huygens, p. 14).

"But though we shall ignore the true cause of springiness we still see that there are many bodies which possess this property; and thus there is nothing strange in supposing that it exists also in little invisible bodies like the particles of the Ether. Also if one wishes to seek for any other way in which the movement of Light is successively communicated, one will find none which agrees better, with uniform progression, as seems to be necessary, than the property of springiness; because if this movement should grow slower in proportion as it is shared over a greater quantity of matter, in moving away from the source of the light, it could not conserve this great velocity over great distances. But by supposing springiness in the ethereal matter, its particles will have the property of equally rapid restitution whether they are pushed strongly or feebly; and thus the propagation of Light will always go on with an equal velocity." (Huygens, p. 15).

Huygens describes the Ethereal matter with ether spheres that hardness produces a springiness which transfers light energy through the optical ether, forming light waves yet light propagates through a glass vacuum tube that is void of matter which is experimental proof the propagation of light does not involve an optical ether, composed of matter. Huygens is clearly describing an optical ether that is composed of matter which is important since Fresnel's diffraction mechanism is based on Huygens principle and Michelson's experiment is based on Fresnel's ether.

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Huygens states optical ether, composed of matter, penetrates glass and exists in vacuum.

"This may be proved by shutting up a sounding body in a glass vessel from which the air is withdrawn by the machine which Mr. Boyle has given us, and with which he has performed so many beautiful experiments. But in doing this of which I speak, care must be taken to place the sounding body on cotton or on feathers, in such a way that it cannot communicate its tremors either to the glass vessel which encloses it, or to the machine; a precaution which has hitherto been neglected. For then after having exhausted all the air one hears no Sound from the metal, though it is struck. One sees here not only that our air, which does not penetrate through glass, is the matter by which Sound spreads; but also that it is not the same air but another kind of matter in which Light spreads; since if the air is removed from the vessel the Light does not cease to traverse it as before. And this last point is demonstrated even more clearly by the celebrated experiment of Torricelli, in which the tube of glass from which the quicksilver has withdrawn itself, remaining void of air, transmits Light just the same as when air is in it. For this proves that a matter different from air exists in this tube, and that this matter must have penetrated the glass or the quicksilver, either one or the other, though they are both impenetrable to the air. And when, in the same experiment, one makes the vacuum after putting a little water above the quicksilver, one concludes equally that the said matter passes through glass or water, or through both." (Huygens, p. 11 & 12).

Huygens' optical ether, composed of matter, propagating through glass would produces a hole, in the glass, or shatter the glass which would eliminate the vacuum yet light propagates through a glass vacuum tube without eliminating the vacuum which is experimental proof Huygens' ether does not exist in vacuum. Maxwell's uses a similar argument to justify the existence of the ether in vacuum.

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Huygens represents the propagation of light with partial waves (fig 1).

"There is the further consideration in the emanation of these waves, that each particle of matter in which a wave spreads, ought not to communicate its motion only to the next particle which is in the straight line drawn from the luminous point, but that it also imparts some of it necessarily to all the others which touch it and which oppose themselves to its movement. So it arises that around each particle there is made a wave of which that particle is the centre. Thus if DCF is a wave emanating from the luminous point A, which is its centre, the particle B, one of those comprised within the sphere DCF, will have made its particular or partial wave KCL, which will touch the wave DCF at C at the same moment that the principal wave emanating from the point A has arrived at DCF; and it is clear that it will be only the region C of the wave KCL which will touch the wave DCF, to wit, that which is in the straight line drawn through AB. Similarly the other particles of the sphere DCF, such as bb, dd, etc., will each make its own wave. But each of these waves can be infinitely feeble only as compared with the wave DCF, to the composition of which all the others contribute by the part of their surface which is most distant from the centre A." (Huygens, p. 19).

Huygens' expanding partial waves KCL originate from points b, b, b, along the wave HI. The far points C, C, C, of the partial waves KCL, are used to construct the wave DCF which represents Huygens' wave propagation mechanism of light. The sun, a light bulb or candle flame are physical light source that emit light energy. Huygens' wave HI is arbitrary creating energy (partial waves), away from the light source, which violates energy conservation. In addition, only the far points C, C, C, of the partial waves, are used to construct the wave DCF. The structure of a partial waves between K and C, and between C and L, are destroyed after the wave DCF is constructed which violates energy conservation. An enormous amount of energy (partial waves) is created then destroyed in Huygens' wave propagation mechanism of light.

Huygens describes the transmission and reflection effects of light (fig 2 & 3) using spherical waves generated by the transmission and reflection surface.

If one considers further the other pieces H of the wave AC, it appears that they will not only have reached the surface AB by straight lines HK parallel to CB, but that in addition they will have generated in the transparent air, from the centres K, K, K, particular spherical waves, represented here by circumferences the semi-diameters of which are equal to KM, that is to say to the continuations of HK as far as the line BG parallel to AC. (Huygens, p. 24).

Huygens' spherical waves originate from points K, K, K, along the transmission and reflection surface AB. The far points of the expanding spherical waves are used to construct the transmission and reflection waves NB. The sun, a candle flame or a light bulb are light sources that emit light energy. The generation of spherical waves, by the transmission and reflection surface, represents the surface AB as a light source that is arbitrarily creating energy (spherical waves) that violates energy conservation. In addition, the spherical waves, that are used to construct the transmission and reflection waves have varying circumferences when the transmission and reflection waves are constructed which would form inconsistent amplitudes along the transmission and reflection wave fronts.

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§ 3. Fresnel's Transmission and Reflection Equations

Fresnel's transmission and reflection equations of light are derived using light waves (Hecht, p. 111) that interaction, at the surface interface (fig 4), is represented with,

Io cos(k1x - wt) j + Ro cos(k1x - wt) j = To cos(- k2x + wt) j......................1

Using t = 0 and x = 0, equation 1 forms (Hecht, p. 113), (Klein, p. 570),

Io + Ro = To...........................................................2

The following equation (Hecht, p. 114),

n1Io - n1Ro = n2To.................................................3

and equation 2 are used to derive Fresnel's transmission and reflection equations,

t = 2n1 / (n1 + n2).................................................4

r = (n2 - n1) / (n1 + n2).........................................5

To test Fresnel's derivation, equation 3 is represented with an air (n1 = 1) and glass (n2 = 1.5) surface interface which forms,

Io - Ro = 1.5To.................................................6

The transmission and reflection equations (equ 4 & 5) are derived, using equations 2 and 3, but equation 3 forms equation 6 which conflicts the equation 2. The quantum mechanics step potential method derivation of the transmission and reflection equations produces the same result (Eisberg, p. 211), (McGervey, p. 102).

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§ 4. Fresnel's Diffraction Equation

In Fresnel's paper, "Memorie su la Diffraction de la Lumiere" (1819), Fresnel describes light waves formed by the vibration of the elastic fluid (optical ether).

"21. If we call λ the length of a light-wave, that is to say, the distance between two points in the ether where vibrations of the same kind are occurring at the same time" (Fresnel, § 21).

"Admitting that light consists in vibrations of the ether similar to sound-waves, we can easily account for the inflection of rays of light at sensible distances from the diffraction body." (Fresnel, § 33).

"APPLICATIONS OF HUYGENS'S PRINCIPLE TO THE PHENOMENA OF DIFFRACTION

43. Having determined the resultant of any number of trains of light-waves. I shall now show how by the aid of these interference formulae and by the principle of Huygens alone it is possible to explain, and even to compute, all the phenomena of diffraction. This principle, which I consider as a rigorous deduction from the basal hypothesis, may be expressed thus: The vibrations at each point in the wave-front may be considered as the sum of the elementary motions which at any one instant are sent to that point from all parts of this same wave in any one of its pervious* positions, each of these parts acting independently the one of the other. It follows from the principle of the superposition of small motions that the vibrations produced at any point in an elastic fluid" (Fresnel, § 43).

Fresnel's diffraction effect of light is based on interfering light waves formed by the motion of an elastic fluid yet diffraction forms in vacuum that is void of matter which proves Fresnel's interference mechanism of invalid. In addition, Fresnel's diffraction mechanism is based on Huygens' principle that describes light waves formed by the motion of an ether, composed of matter, which is extremely important since Michelson's experiment is based on Fresnel's ether and Einstein's relativity is based on Michelson's experiment.

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Fresnel describes diffraction using interfering light waves that resultant amplitudes are used to form the intensity and dark fringes of the diffraction pattern (fig 5).

"In order to compute the total effect, I refer these partial resultants to the wave emitted by the point M on the straight line CP, and to another wave displaced a quarter of a wave-length with reference to the preceding. This is the process already employed (p. 101) in the general solution of the interference problem. We shall consider only a section of the wave made by the plane perpendicular to the edge of the screen, and shall indicate by dz an element, nn', of the primary wave, and by z its distance from the point M. These, as I have shown, suffice to determine the position and the relative intensities of the bright and dark bands." (Fresnel, § 53).

Fresnel's wave AMI forms expanding secondary waves, at the diffraction object. The expanding spherical waves propagate to the diffraction screen and interfere. The sun, a candle flame or a light bulb are light sources that emit light energy. The formation of expanding secondary waves, from points along the wave AMI, represents the arbitrary creation of energy, away from the light source, which violates energy conservation.

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Fresnel derives a diffraction intensity equation by summating the interfereing light waves' amplitudes, at the diffraction screen, using a line integral.

"Hence the intensity of the vibration at P resulting from all these small disturbances is

{ [ ʃ dz cos (π z2 (a + b) / abλ) ]2 + [ ʃ dz sin (π z2 (a + b) / abλ)]2 }1/2 "..................................7

(Fresnel, § 53). Fresnel is using a line integral to summate the interfering light waves' amplitudes, at the diffraction screen, but a line integral (ʃ dz) represents the length of the wave AMI using the interval of dz yet Fresnel is using the line integral to summate the interfering light waves amplitudes, at the diffraction screen, which is mathematically invalid and proves Fresnel's derivation of the diffraction intensity equation of light is invalid.

During the diffraction effect, as to time increases, the crests and nodes, of the propagating light waves, propagate in the forward direction. At a point P on the diffraction screen, as time increases, the propagating light waves' amplitudes oscillate, forming a resultant amplitude of zero, which would eliminate the interference effect which proves Fresnel's derivation of the diffraction intensity equation of light (equ 7) is physically invalid. In addition, Fresnel's light waves' amplitudes form the intensity (energy) of the diffraction pattern that represent a light energy that is dependent on the wave amplitude which conflicts with Lenard's photoelectric effect that proves light is composed of particles that energy is dependent on only the frequency.

A small circular aperture forms a diffraction pattern (fig 5); the diffraction pattern is formed by the constructive and destructive interference of the light waves' amplitudes. The destructive interference of Fresnel's light waves' amplitudes would result in a measureable reduction in the total light intensity of the diffraction pattern since the destroyed light waves amplitudes (intensities) do not contribute to the total light intensity of the diffraction pattern. Experimentally, in the small circular aperture diffraction effect (fig 5), 10% of the diffraction pattern is composed of dark areas which would result in a 10% reduction of the total light intensity of the diffraction pattern yet experimentally, the total light intensity that enters the aperture (dt = 1s) equals the total light intensity of the diffraction pattern (dt = 1s) which proves the aperture diffraction effect of light is not formed by Fresnel's wave interference mechanism.

§ 5. Maxwell

In Maxwell's paper, "Dynamical Theory of the Electromagnetic Field" (1864), Maxwell's describes an electromagnetic theory of light based on Ampere and Faraday induction experiments.

"ON ELECTROMAGNETIC INDUCTION" (Maxwell, Part II).

"If, therefore, the phenomena described by Faraday in the Ninth Series of his Experimental Researches were the only known facts about electric currents, the laws of Ampere relating to the attraction of conductors carrying currents as well as those of Faraday about the mutual induction of currents, might be deduced by mechanical reasoning." (Maxwell, Part II).

"ELECTROMAGNETIC THEORY OF LIGHT" (Maxwell, Part VI).

"We then examine electromagnetic phenomena, seeking for their explanation in the properties of the field which surrounds the electrified or magnetic bodies." (Maxwell, Part VI).

Maxwell's electromagnetic theory of light is based on Faraday (1835) induction experiment but induction is not luminous; consequently, Poynting (1884) supports Maxwell's theory by deriving an electromagnetic energy equation of light but Poynting's current wire, that forms Poynting electric and magnetic fields, is also not luminous. Hertz's (1887) attempts to structurally unite light with induction, using a spark gap experiment, that emits light and the radio induction effect, but Hertz's spark gap emits electrons yet induction is not an ionization effect which is experimental proof light is not an electromagnetic phenomenon. Planck (1901) and Einstein (1905) uses the blackbody radiation effect (Planck, Part I), (Einstein, § 4), that emits light and the radio induction effect, to structurally unite light with induction, in the derivation of Planck's energy element (hv) and Einstein's energy quanta (Rβv/N), but the blackbody emits electrons yet induction is not an ionization effect which proves Planck and Einstein unification of Maxwell's electromagnetic field with light is physically invalid.

"Maxwell's electrodynamics proceeds in the same unusual way already analyzed in studying his electrostatics. Under the influence of hypotheses which remain vague and undefined in his mind, Maxwell sketches a theory which he never completes, he does not even bother to remove contradictions from it; then he starts changing this theory, he imposes on it essential modifications which he does not notify to his reader; the latter tries in vain to fix the fugitive and intangible thought of the author; just when he thinks he has got it, even the parts of the doctrine dealing with the best studied phenomena are seen to vanish. And yet this strange and disconcerting method led Maxwell to the electromagnetic theory of light!" (Duhem, 1902).

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Maxwell's electric current is formed within a dielectric of a varying capacitor.

"PART V. — THEORY OF CONDENSERS.

Capacity of a Condenser.

(83) The simplest form of condenser consists of a uniform layer of insulating matter bounded by two conducting surfaces, and its capacity is measured by the quantity of electricity on either surface when the difference of potentials is unity.

Let S be the area of either surface, a the thickness of the dielectric, and k its coefficient of electric elasticity; then on one side of the condenser the potential is Y1 and on the other side Y1 + 1, and within its substance" (Maxwell, Part V).

"(85) When the dielectric of which the condenser is formed is not a perfect insulator, the phenomena of conduction are combined with those of electric displacement. The condenser, when left charged, gradually loses its charge, and in some cases, after being discharged completely, it gradually acquires a new charge of the same sign as the original charge, and this finally disappears. These phenomena have been described by Professor Faraday (Experimental Researches, Series XI.) and by Mr. F. Jenkin (Report of Committee of Board of Trade on Submarine Cables), and may be classed under the name of "Electric Absorption." (Maxwell, Part V).

Maxwell's electric current is formed the varying capacitor induction effect yet the varying capacitor effect occurs in vacuum that is void of matter which is experimental proof Maxwell's electric current does not physically exist.

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Maxwell's electric current is formed by the displacement of the molecules of the dielectric.

"In a dielectric under the action of electromotive force, we may conceive that the electricity in each molecule is so displaced that one side is rendered positively and the other negatively electrical, but that the electricity remains entirely connected with the molecule, and does not pass from one molecule to another. The effect of this action on the whole dielectric mass is to produce a general displacement of electricity in a certain direction. This displacement does not amount to a current, because when it has attained to a certain value it remains constant, but it is the commencement of a current, and its variations constitute currents in the positive or the negative direction according as the displacement is increasing or decreasing. In the interior of the dielectric there is no indication of electrification, because the electrification of the surface of any molecule is neutralized by the opposite electrification of the surface of the molecules in contact with it; but at the bounding surface of the dielectric, where the electrification is not neutralized, we find the phenomena which indicate positive or negative electrification.

The relation between the electromotive force and the amount of electric displacement it produces depends on the nature of the dielectric, the same electromotive force producing generally a greater electric displacement in solid dielectrics, such as glass or sulphur, than in air." (Maxwell, Part I).

Maxwell states the motion of the dielectric, such as glass, sulphur or air, forms the electric current displacement yet the varying capacitor induction effect forms in vacuum that is void of matter (solid, liquid or gas) which is experimental proof Maxwell's electric current does not physically exist yet Maxwell's varying capacitor induction effect is the transition between Faraday's induction experiment and Hertz's radio radio waves.

Maxwell's equations are derived using Ampere and Faraday induction experiments and Maxwell's electric current.

"Equations of Magnetic Force.

uα' = dH/dy - dG/dz............................................8

uβ' = dF/dz - dH/dx.............................................9

uλ' = dG/dx - dF/dy.............................................10

Equations of Currents...

dλ/dy - dβ/dz = 4πp'............................................11

dα/dz - dλ/dx = 4πq'............................................12

dβ/dx - dα/dy = 4πr'............................................13

We may call these the Equations of Currents." (Maxwell, part III).

Maxwell's equations are derived using Faraday induction experiment that is not luminous. In addition, Maxwell's electric current is formed by the motion of the molecules of a dielectric yet light propagates in vacuum that is void of matter which is experimental proof Maxwell's electric current does not physically exist. The varying capacitor induction effect is formed by a surface current that varying magnetic effect induces a surface current on the adjacent plate. In addition, Maxwell's electric current violates Ampere's law that only represents an external magnetic field.

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Maxwell states the optical aether, composed of matter, exists within Geissler's glass vacuum tube.

"It may be filled with any kind of matter, or we may endeavour to render it empty of all gross matter, as in the case of Geissler’s tubes and other so called vacua. There is always, however, enough of matter left to receive and transmit the undulations of light" (Maxwell, Intro).

Maxwell states that the ether exists within a glass vacuum tube but matter propagating through glass would produces a hole, in the glass, or shatter the glass which would eliminate the vacuum yet light propagates through a glass vacuum tube which proves the propagation of light does not involve an ether or light waves.

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Maxwell represents polarization using transverse waves formed by the motion of the elastic medium.

"(91) At the commencement of this paper we made use of the optical hypothesis of an elastic medium through which the vibrations of light are propagated" (Maxwell, part VI).

"the disturbance at any point is transverse to the direction of propagation, and such waves may have all the properties of polarized light." (Maxwell, part VI).

Polarized light propagates in vacuum that is void of an elastic medium (ether) which contradicts the existence of Maxwell's transverse light waves that are used to represent polarization. In addition, a transverse wave is a surface wave that cannot form within a volume since a disturbance within a volume produces a spherical wave that produces a longitudinal wave.

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Maxwell derives a wave propagation equation of light using Maxwell's equations.

"(93) If we combine the equations of Magnetic Force (B) with those of Electric Currents (C)....

Absolute Values of the Electromotive and Magnetic Forces called into play in the Propagation of Light.

(108) If the equation of propagation of light is

F = A cos [(2π/λ)(z - Vt)]"...................................................14

(Maxwell, Part VI). A wave is a mechanical entity formed by the motion of a medium, composed of matter (solid, liquid or gas). Maxwell's electric and magnetic forces vibrate an ether forming propagating light waves represented with equation 14 but light propagates through a glass vacuum tube that is void of matter which is experimental proof Maxwell's propagating light waves, represented with equation 14, do not physically exist.

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§ 6. Maxwell's Structure of Light

Maxwell's electromagnetic transverse wave equations of light are derived using Maxwell's equations,

∇x E = - dB/dt........∇ x B = 1/c (dE/dt).....................................15a,b

Maxwell's curl equations (equ 15a,b) are expanded and the following differential components are used to form (Jenkins, p. 410),

dEy /dz = 1/c (dBx /dt)..............dBx /dz = 1/c (dEy /dt)...................16a,b

Differentiating equation 16a, with the respect to d/dz, and equation 16b with respect to d/dt then equating the result produces,

dEy /d"z = 1/c2 (d"Ey /d"t).............................................................17

The electric transverse wave equation of light is derived using equation 17. The magnetic transverse wave equation is derived using a similar method,

Ey = Eo cos(kz - wt) ĵ ....................................................................18

Bx = Bo cos(kz -wt) î .....................................................................19

To test the derivation, the electric and magnetic transverse wave equations of light (equ 18 & 19) are used in equation 16a,

d/dz[Eo cos(kz - wt)] ĵ = - (1/c) d/dt[Bo cos(kz - wt)] î.....................20

Equation 20 produces,

Eo ĵ = Bo î''' ......................................................................................21

The derivation of the electromagnetic transverse wave equations of light, using Maxwell's equations, produces superimposing electromagnetic fields, represented with equation 21, since Maxwell's equations represent a spherical wave that forms a longitudinal wave.

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In an alternative method, the electromagnetic transverse wave equations of light are derived using Maxwell's equations using the gradient method,

∇ x E = - dB/dt..............∇ x B = 1/c (dE/dt)...................22a,b

Applying a curl operator to Maxwell's electric curl equation (equ 22a) forms,

∇ x (∇ x E) = - 1/c (d"E/d"t)...................................................23

A gradient identity (Klein, p. 523),

∇ x (∇ x E) = E(∇ · E) - ∇2 E........................................24

and ∇ · E = 0 are used to form,

∇ x (∇ x E) = ∇2 E...........................................................25

Equating equations 23 and 25 (Hobson, p. 23),

d"E/d"t - c2 ∇2 E = 0.......................................................26

A similar equation is derived for the magnetic field,

d"B/d"t - c2 ∇2 B = 0........................................................27

Using equation 26 and 27, the electromagnetic wave equations of light are derived,

E = Eo ei(kr - wt) r.......................................................28

B = Bo ei(kr - wt) r........................................................29

The second order gradient (∇2), of equations 26 and 27, forms electromagnetic longitudinal wave of equations (equ 28 & 29) that conflicts with Maxwell's transverse waves.

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§ 7. Einstein Electrodynamics

In Einstein's paper, "On the Electrodynamics of Moving Bodies" (1905), Einstein states the luminiferous ether is superfluous.

"The introduction of a “luminiferous ether” will prove to be superfluous inasmuch as the view here to be developed will not require an “absolutely stationary space” provided with special properties, nor assign a velocity-vector to a point of the empty space in which electromagnetic processes take place." (Einstein, Intro).

"the electrodynamic foundation of Lorentz's theory of the electrodynamics of moving bodies agrees with the principle of relativity." (Einstein, § 9).

"On the other hand, all coordinate systems moving relatively were to be regarded as in motion with respect to the æther. To this motion against the æther ("æther-drift") were attributed more complicated laws which were supposed to hold relative to. Strictly speaking, such an æther-drift ought also to be assumed relative to the earth, and for a long time the efforts of physicists were devoted to attempts to detect the existence of an æther-drift at the earth's surface....Although the estimated difference between these two times is exceedingly small, Michelson and Morley performed an experiment involving interference in which this difference should have been clearly detectable. But the experiment gave a negative result — a fact very perplexing to physicists. Lorentz and FitzGerald rescued the theory from this difficulty by assuming that the motion of the body relative to the æther produces a contraction of the body in the direction of motion, the amount of contraction being just sufficient to compensate for the difference in time mentioned above." (Einstein5 § 16).

Einstein states the ether is superfluous but in section 9 Einstein state relativity agrees with Lorentz's electrodynamic theory yet Lorentz represents the aether with Maxwell's equations and reverses the negative result of Michelson's experiment to justify the existence of the ether. Furthermore, in Einstein's paper "Relativity: Special and General Theory" (1917), Einstein uses the reversal of Michelson-Morley experiment to justifying the existence of Fresnel's ether, composed of matter (Michelson-Morley, p. 334), (Fresnel, § 43), (Huygens, p. 14) which contradicts Einstein's statement that the luminiferous ether is superfluous.

..................................................................................................................

Einstein alters the coordinate system of Maxwell's equations to justify light propagating in vacuum (empty space).

"§ 6. Transformation of the Maxwell-Hertz equations for empty space. On the nature of the electromotive forces that arise upon motion in a magnetic field.

Let the Maxwell-Hertz equations for empty space be valid for the system at rest K, so that we have

dX/dt = dN/dy - dM/dz.................................................30

dY/dt = dL/dz - dN/dx..................................................31

dZ/dt = dM/dx - dL/dy..................................................32

.......................................................................................

dL/dt = dY/dz - dZ/dy...................................................33

dM/dt = dZ/dx - dX/dz..................................................34

dN/dt = dX/dy - dY/dx...................................................35

where (X,Y,Z) denotes the vector of the electric force, and (L,M,N) that of the magnetic force." Einstein2, § 6).

β = 1/(1 - v2/c2)1/2...................................................................36

Applying equation 36 to the coordinate system of Maxwell's equations,

"X' = X............................ L' = L..................................37a,b

Y' = β[Y - (v/c)N]............. M'= β[M + (v/c)Z]....................38a,b

Z' = β[Z + (v/c)M],.............N' = β[N - (v/c)Y]"..................39a,b

(Einstein2, § 6). Altering the coordinates system of Maxwell's equations does not change the fact that vacuum is void of an optical ether, composed of matter, nor does changing the coordinate system alter the fact that Maxwell's equations are derived using Ampere and Faraday induction experiments that are not luminous. In addition, the electromagnetic transverse wave equations of light cannot be derived using Maxwell's equation which proves Einstein's electrodynamics theory of light is physically invalid.

§ 8. Einstein's Inertial Energy

In Einstein's paper, "Does the Inertia of a Body depend upon its Energy Content?" (1905), Einstein describes the reduction of the mass of an electron, that emits an electromagnetic photon.

"There I based myself upon the Maxwell-Hertz equations for empty space along with Maxwell's expression for the electromagnetic energy" (Einstein3, p. 639).

"Let this body simultaneously emit plane waves of light of energy L/2" (Einstein3, p. 640).

"The kinetic energy of the body with respect to (ξ,η,ς) decreases as a result of the emission of light..... If a body releases the energy L in the form of radiation, its mass decreases by L/V2." (Einstein2, p. 641).

Einstein describes the reduction of the electron mass by L/V2 when a photon is emitted where L is the energy of the emitted electromagnetic photon but Planck describes the blackbody surface electrons' varying kinetic energies (Planck, Part I, § 3) where Planck's blackbody surface electrons vibrate a diathermic medium (ether) that motion forms electromagnetic photons (Planck, Part 1, § 7); consequently, Planck needs the ether. The energy equation E = mc2 is used to justify the electromagnetic ether but E = mc2 represent the massless inertial energy of an electromagnetic photon that cannot be used to represent the ether, composed of matter. In addition, Einstein uses the aberration of light to justify massless electromagnetic field forming light waves but the formation of a light wave requires two opposite motions which would eliminate the aberration effect of light.

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§ 9. Conclusion

Maxwell's electromagnetic theory of light, based on Faraday induction experiment, is introduced since induction forms in vacuum but induction is not luminous; consequently, Poynting (1884) supports Maxwell's theory by deriving an EM energy equation of light but Poynting's current wire is also not luminous. Hertz's (1887) attempts to support Maxwell by structurally uniting light with induction, using a spark gap experiment, that emits light and the radio induction effect, but Hertz's spark gap emits electrons yet induction is not an ionization effect. In addition, Planck (1901) uses the blackbody radiation effect to support Maxwell's theory but Planck's blackbody also emits electrons. The emission of light is always accompanied by the emission of electrons yet Faraday induction experiment is not ionization effect which proves light is not an electromagnetic induction phenomenon.

Lorentz is justifying the existence of Fresnel's ether, composed of matter, by reversing the negative result of Michelson's experiment yet light propagating in vacuum proves Fresnel's ether does not physically exist. In Einstein's (1905) electrodynamics, Einstein alters the dimensions of Maxwell's equations to justify light propagating in vacuum but manipulating the coordinate system of Maxwell's equations does not change the fact that vacuum is void of matter, nor does Einstein's coordinate system transformation change the fact that Maxwell's equations are derived using Faraday induction experiment that is not luminous. Einstein describes an electromagnetic ether (Einstein4, § 1) but the electromagnetic field of Einstein's electromagnetic ether originates from Faraday induction effect that is not lumninous. Also, in Einstein's paper, "Relativity: Special and General Theory" (1917), Einstein is reversing the negative result of Michelson-Morley experiment to justify the existence of Fresnel's ether, composed of matter, that does not physically exist (vacuum).

Quantum mechanics3, quantum electrodynamics4, string theory5, and particle physics6, (boson) are supporting Maxwell's theory by using the gauge transformation of Maxwell's equations but representing Maxwell's equations with a potential does not change the fact that Maxwell's equations are derived using Faraday induction experiment that is not luminous. Quantumn mechanics is based on Planck's quantization of Maxwell's electromagnetic field but Planck's blackbody emits electrons yet induction is not an ionization effect. Davisson–Germer (1927) electron scattering experiment is used to justify wave interference but the destructive interference of an electron matter wave to form the non-electron fringes of the electron scattering pattern, violates energy conservation. Furthermore, electron probability waves are used to justify wave interference but an electron's position probability cannot form a negative value required in representing wave interference. In gravitational physics, Webber (1970) experimentally detected gravity waves that have the frequency of sound (1662 Hz) (Webber Intro) yet the vacuum of celestial space does not transmit sound waves. Wheeler's (1973) describes electromagnetic gravity waves (Misner, p. 961) that Thorne states propagates at the velocity of light (Hawking, p. 338). The gravity inteferometer of the European pulsar timing array (EPTA) detected electromagnetic gravity waves of frequencies of approximately v = 10-8 Hz which forms a wavelength of λ = 1013 miles that proves the complete failure of modern theoretical physics based on the wave theory of light. I predict that the aperture diffraction effect is formed by photons, that are redirected, by the aperture, to only the intensity areas of the diffraction pattern without involving an ether, light waves, wave interference, electromagnetic fields or Maxwell's equations.