n***@gmail.com
2017-05-26 00:44:07 UTC
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Optica!
Ben T. Ito
May 19, 2017
This paper will analyze the wave theory of light.
§ 1. Introduction
Huygens (1690) describes the propagation of light using light waves formed by the motion of an Ethereal matter (Huygens, p. 11). Bradley's (1725) stellar aberration is used to justify the existence of Huygens' ether but aberration does not alter the fact that light propagates through a glass vacuum tube that is void of matter. Also, the change in the position of Bradley's star is determined using two times that Bradley is viewing a specific star but the time measurement uncertainty of a 1725 pendulum clock is 60 seconds for 24 hours which produces a position uncertainty of the measurement of the position of Bradley star that is larger than the position change of Bradley's star which proves Bradley's stellar aberration is physically invalid. Fresnel (1819) established the wave theory of light by representing diffraction using interfering light-waves created by the vibration of an elastic fluid (Fresnel, 43) despite the fact that diffraction forms in vacuum that is void of matter which contradicts Fresnel's diffraction mechanism that is the foundation of the wave theory of light. Maxwell's (1864) electromagnetic theory of light based on Faraday induction effect was introduced since induction forms in vacuum but Faraday's induction effect is not luminous. Maxwell's theory is based on the assumption that since light and the radio induction effect propagate at the same velocity that light has an electromagnetic field structure but the velocity of light does not change the fact that Maxwell's theory is based on Faraday's induction effect that is not luminous. Poynting (1884) supports Maxwell's theory by deriving an electromagnetic energy equation (Poynting, p. 358) but Poynting's current wire is not luminous. Hertz (1887) attempts to structurally unite light with induction using a spark gap experiment that produces light and the radio induction effect but Hertz's spark gap emits electrons yet Faraday's induction effect is also not an ionization effect. The generation of light by a light source is always accompanied by the emission of electrons yet Maxwell's electromagnetic theory of light is based on Faraday's induction effect that is not an ionization effect which proves light is not an electromagnetic phenomenon. In addition, Lenard (1899-1902) proves light is composed of particles which conflicts with the continuity of Maxwell's electromagnetic field. Planck (1901) addresses Lenard's photoelectric effect by deriving an energy element (hγ) that represents the energy of an electromagnetic photon but Maxwell's expanding electromagnetic field cannot maintain a particle structure of a propagating electromagnetic photon. In Einstein's (1905) electrodynamics (special relativity), Einstein supports Maxwell's electromagnetic theory of light using Maxwell's equations but Maxwell's equations are derived using Faraday's induction experiment that is not luminous nor is induction an ionization or particle effect. Furthermore, Einstein's translation velocity varies form 463 m/s to 30,463 m/s for the time interval from 6:00 pm to 12:00 am yet special relativity is based on a constant value of the translational velocity. In Einstein's paper "Does the Inertia of a Body Depend Upon its Energy Content?" (1905), Einstein uses the inertial mass (L/V2) to structurally unify Maxwell's electromagnetic field with matter to structurally unify Maxwell's electromagnetic field with Fresnel's ether, composed of matter but Einstein's inertial mass (m = L/V2) is massless since L represents the energy of a massless electromagnetic photon. Einstein (1910) describes an electromagnetic ether but Maxwell's electromagnetic field originates from Faraday's induction effect that is not luminous; also, Maxwell's massless electromagnetic field that is propagating at the velocity of light conflicts with Fresnel's stationary ether composed of matter.
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§ 2. Fresnel
In Fresnel's paper, "Memorie su la Diffraction de la Lumiere" (1819), Fresnel describes diffraction using interfering light waves formed by the vibration of the elastic fluid (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 is describing diffraction using interfering light waves formed by the motion of an elastic fluid (ether) but diffraction forms in vacuum that is void of matter which contradicts Fresnel's diffraction mechanism.
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Fresnel describes diffraction using secondary waves that are formed by the wave AMI (fig 6).
"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 and interfering secondary waves when the bottom of the wave AMI touches the diffraction object. The expanding secondary light waves propagate to the diffraction screen and interfere forming the diffraction pattern but the creation of secondary waves (energy) away from the light source by the wave AMI is representing the wave AMI as a light source that is arbitrarily generating secondary waves which violates energy conservation.
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Fresnel derives a diffraction intensity equation by summating the interfering light waves' amplitudes, at the diffraction screen, using a line integral (equ 1).
"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 "..................................1
(Fresnel, 53). Fresnel is using a line integral to summate (equ 1) the interfering light waves' amplitudes at the diffraction screen (fig 2) but a line integral can only be used to represent the length of the wave AMI. In addition, the limits of Fresnel's line integral represents the length of the wave AMI yet in Fresnel's derivation, the wave amplitudes at a point P on the diffraction screen are summate yet the point P on the diffraction screen is not within the limits of the line integral which proves Fresnel's derivation is mathematically invalid. In addition, during the diffraction effect of light, the crests and nodes of Fresnel's propagating light waves propagate in the forward direction. At the diffraction screen point P, the propagating light waves' amplitudes would oscillate forming an average resultant amplitude of zero that would eliminate the diffraction pattern. Fresnel omits the time element from the derivation since propagating light waves eliminate the diffraction pattern but one of the most important physical characteristic of light is omitted from Fresnel's derivation since propagating light waves eliminate the intensity of the diffraction pattern.
The wave theory of light is based on light waves that energy is dependent on the magnitude of the wave amplitude. The bigger the wave amplitude the larger in intensity (energy) of the light wave. Fresnel is using the interfering light waves' amplitudes, at a point P, on the diffraction screen to represent the intensity (energy) of the diffraction effect which depicts 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 (Lenard, Intro). The varying intensity of a light ray is used to justify that the energy of a light wave is dependent on the wave amplitude but in Fresnel's derivation the interfering light waves are interacting at a point P on the diffraction screen which represents a light particle energy that is dependent on only the frequency which proves Fresnel's diffraction mechanism is physically invalid.
The formation of the small rectangular aperture diffraction pattern (fig 3) is represented using wave interference but the destructive interference of the light waves' amplitudes (energy) used to form the dark fringes of the diffraction pattern represents the destruction of energy which violates energy conservation; furthermore, the destruction of the light waves' amplitudes (intensity) would result in a reduction in the total light intensity of the diffraction pattern since the destroyed light waves' amplitudes do not contribute to the total light intensity of the diffraction pattern yet more than 80% of the small rectangular aperture diffraction pattern is composed of dark areas which would result in at least a 60% reduction in the total light intensity of the diffraction pattern yet experimentally, the total light intensity that enters a small rectangular aperture (dt = 1s) is equal to the total light intensity of the diffraction pattern.
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§ 3. Maxwell
In Maxwell's paper, "Dynamical Theory of the Electromagnetic Field" (1864), Maxwell states the ether 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 and heat, and it is because the transmission of these radiations is not greatly altered when transparent bodies of measurable density are substituted for the so-called vacuum, that we are obliged to admit that the undulations are those of an ethereal substance, and not of the gross matter, the presence of which merely modifies in some way the motion of the ether." (Maxwell, Intro).
Fresnel's wave theory of light is based on light waves formed by the vibration of an ether, composed of matter, but light propagates through a glass vacuum tube that is void of matter which contradicts Fresnel's wave theory of light. When confronted with the problem of how the ether, composed of matter, exists in the glass vacuum tube, Maxwell uses hyperbole to justify the ether, composed of matter, existing in vacuum forming light waves.
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Maxwell's equations are derived using Faraday's induction effect.
"PART III. - GENERAL EQUATIONS OF THE ELECTROMAGNETIC FIELD." (Maxwell, Part III).
"the total electromagnetic momentum of the circuit, or the number of lines of magnetic force which pass through it, the variations of which measure the total electromotive force in the circuit. This electromagnetic momentum is the same thing to which Professor Faraday has applied the name of the Electrotonic State. If the circuit be the boundary of the elementary area dydz." (Maxwell, Part III).
"Equations of Magnetic Force.
uα = dH/dy - dG/dz............................................2
uβ = dF/dz - dH/dx.............................................3
uλ = dG/dx - dF/dy.............................................4
Equations of Currents...
dλ/dy - dβ/dz = 4πp'............................................5
dα/dz - dλ/dx = 4πq'............................................6
dβ/dx - dα/dy = 4πr'............................................7
We may call these the Equations of Currents." (Maxwell, Part III).
Maxwell's equations are derived using Faraday's induction effect produced by the magnetic flux (α, β, λ) and internal conduction wire electric field (F, G, H) that forms Faraday's induction current in a wire loop.
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Maxwell's electromagnetic theory of light is based on Maxwell's equations.
"ELECTROMAGNETIC THEORY OF LIGHT" (Maxwell, Part VI).
"(93) If we combine the equations of Magnetic Force (B) with those of Electric Force (B) with those of Electric Current" (Maxwell, Part VI).
Maxwell's electromagnetic theory of light based on Faraday's induction effect was introduced since induction forms in vacuum but Faraday's induction effect is not luminous. Maxwell uses the velocity of light to justify the structural unification of light with induction but the velocity of light does not change the fact that Faraday's induction effect is not luminous. Poynting (1884) supports Maxwell's theory by deriving an electromagnetic energy equation using a current wire but Poynting's current wire is not luminous. Hertz (1887) attempts to structurally unite light with induction but Hertz's spark gap emits electrons yet Faraday's induction effect is also not an ionization effect. The production of the light is always accompanied by the emission of electrons yet induction is not an ionization effect which proves light is not an electromagnetic phenomenon. In addition, Lenard proves light is composed of particles which conflicts with the continuity of Maxwell's electromagnetic field since as a light ray propagates, the optic particles that compose a light ray form spaces between optic particles that distances between optic particles increase due to the dispersion of a light. Furthermore, the radio induction effect (radio waves) produces an intensity that is dependent on the inverse of the fifth order of the distance I = K/r5 yet the dispersion of a laser beam is less than the inverse of the second order of the distance I = K/r2. Experimentally, a 2.3 W laser beam with a diameter of one inch after propagating to the moon forms a diameter of four miles yet a one meter diameter 1000 W radio signal that originates from the surface of the earth forms a width of more than one million miles after propagating to the moon which is experimental proof light is not an electromagnetic phenomenon.
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§ 4. Michelson
In Michelson's paper, "The Relative Motion of the Earth and the Lumiferous Ether" (1881), Michelson tests for the effects of the ether wind formed by the earth's motion through Fresnel's ether, composed of matter.
"The undulatory theory of light assumes the existence of a medium called the ether, whose vibrations produce the phenomena of heat and light, and which is supposed to fill all space. According to Fresnel, the ether, which is enclosed in optical media, partakes of the motion of these media, to an extent depending on their indices of refraction. For air, this motion would be but a small fraction of that of the air itself and will be neglected." (Michelson, p. 120).
"Assuming then that the ether is at rest, the earth moving through it, the time required for light to pass from one point to another on the earth's surface, would depend on the direction in which it travels." (Michelson, p. 120).
"The interpretation of these results is that there is no displacement of the interference bands. The result of the hypothesis of a stationary ether is thus shown to be incorrect, and the necessary conclusion follows that the hypothesis is erroneous." (Michelson, p. 128).
Michelson is testing for the existence of Fresnel's optical ether, composed of matter, using an ether wind produced by the earth's daily and yearly rotational motions through Fresnel's stationary ether, composed of matter. At a point on the surface of the earth, the earth's daily and yearly motions interaction with Fresnel's stationary ether form an ether wind that is directed tangent to the earth's surface. An ach lamp is used to form two light rays using a beam splitter. One light ray propagates parallel to the direction of the ether wind and the second ray propagates perpendicular to the ether wind. According to Michelson, only the velocity of the ray that is propagating parallel to the ether wind is affected by the ether wind. Both light rays are recombined to form an interference effect but rotating Michelson's experimental apparatus, at certain angles, both light rays velocities would be altered by the ether wind which would result in the shift of the interference effect but after the rotation of the interferometer no change in the interference effect is observed which represents the negative result of Michelson's experiment. The velocity of light (3 x 108 m/s) is four order of magnitude greater than the maximum velocity of the ether wind (Vmax = 30,463 m/s); consequently, the ether wind cannot produce the shift of the interference effect which proves Michelson's ether experiment has no scientific value. Furthermore, Michelson's experiment is based on a constant magnitude of the ether wind but the magnitude of the ether wind varies as time increases. At 6:00 pm, the magnitude of the earth's tangential velocity vector formed by the earth daily and yearly motions that forms the ether wind is 463 m/s (fig 7), and, the magnitude of the ether wind increases to 5,077 m/s at 7:00 pm. At midnight, the earth' tangential velocity vector equals 30,463 m/s; consequently, the magnitude of the ether wind increases from 463 m/s to 30,463 m/s for the time interval of 6:00 pm to 12:00 am yet Michelson's experiment is based on a constant magnitude of the ether wind. Furthermore, Michelson's experiment is unnecessary since the glass vacuum tube experiment is definitive and irreversible experimental proof Fresnel's ether, composed of matter, does not physically exist.
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§ 5. Lorentz
In Lorentz's paper "Simplified Theory of Electrical and Optical Phenomena in Moving Systems" (1899), Lorentz is justify Maxwell's theory by altering the dimensions of Maxwell's equations using px .
"dBz/dy - dBy/dz = 4πq(px + vx) + 4π(d/dt - px d/dx) Ex..............................................8
dBx/dz - dBz/dx = 4πpqvy + 4π(d/dt - px d/dx) Ey.....................................................9
dBy/dx - dBx/dy = 4πqvz + 4π(d/dt - px d/dx) Ez........................................................10
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4πV2(dEz /dy - dEy/dz) = - (d/dt - px d/dx) Bx..............................................................11
4πV2(dEx/dz - dEz /dx) = - (d/dt - px d/dx) By..............................................................12
4πV2(dEy/dx - dEx/dy) = - (d/dt - px d/dx) Bx...............................................................13
...In most applications p would be the velocity of the earth in its yearly motion." (Lorentz, § 3).
x' = [V/(V2 - px2)1/2]x,....................................................................................................14
y' = y,...........................................................................................................................15
z' = z,...........................................................................................................................16
t' = t - x px /(V2 - px2).....................................................................................................17
Lorentz justifying Maxwell's electromagnetic theory of light using Maxwell's equations but manipulating the coordinate system of Maxwell's equations does not alter the fact that Maxwell's equations are derived using Faraday's induction effect that is not luminous, nor is induction an ionization or particle effect which is experimental proof light is not an electromagnetic phenomenon.
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Lorentz alters the dimensions of Michelson's experimental apparatus to reverse the negative result of Michelson's experiment to justify the existence of Fresnel's ether, composed of matter (Michelson, p. 120).
"§ 9. Hitherto all quantities of the order p2x /V2 have been neglected. As is well known, these must be taken into account in the discussion of Michelson's experiment, in which two rays of light interfered after having traversed rather long paths, the one parallel to the direction of the earth's motion, and the other perpendicular to it. In order to explain the negative result of this experiment Fitzgerald and myself have supposed that, in consequence of the translation, the dimensions of the solid bodies serving to support the optical apparatus, are altered in a certain ratio." (Lorentz, § 9).
Lorentz is reversing the negative result of Michelson's ether experiment to justify the existence of Fresnel's optical ether by contracting the x dimension of the interferometer's armature, using the constant magnitude of the earth's tangential velocity vector px but at the surface of the earth, the magnitude of the earth's tangential velocity vector px in not constant.. At 6:00 pm, the magnitude of the earth's tangential velocity px is 464 m/s (fig 7); at 7:00 pm; because of the earth's daily and yearly motions, the magnitude of px increases to 5,077 m/s. At midnight, the earth's yearly tangential velocity vector px increases to 30,463 m/s; consequently, the earth tangential velocity vector px increases from 463 m/s to 30,463 m/s from 6:00 pm to 12: 00 am yet Lorentz's transformation is based on a constant value of the translational velocity px which proves Lorentz's transformation is physically invalid.
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§ 6. Planck
In Planck's paper, "On the Law of Distribution of Energy in the Normal Spectrum" (1901), Planck is supporting Maxwell's electromagnetic theory of light.
"In any case the theory requires a correction, and I shall attempt in the following to accomplish this on the basis of the theory of electromagnetic radiation which I developed." (Planck, Intro).
"In my last article4 I showed that the physical foundations of the electromagnetic radiation theory, including the hypothesis of "natural radiation", withstand the most severe criticism" (Planck, Intro).
Planck uses the blackbody radiation effect and Boltzmann's thermodynamic entropy in the derivation of the energy element (hv) that represents the energy of an electromagnetic photon emitted by the blackbody radiation effect but Maxwell's expanding electromagnetic field cannot maintain a particle structure of a electromagnetic photon.
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Planck's energy element (hv) is derived using Boltzmann's thermodynamic entropy equation,
S = k log R................................................................................................18
that is used with Planck's blackbody electron (resonator) kinetic energy distribution ratio (Planck, § 3),
R = (N + P)N + P/ NN · PP...........................................................................1
to form (Planck, § 5)
SN = k{N + P) log (N + P) - N log N - P log P)............................................20
Using UN = NU and UN = Pe, equation 20 becomes,
S = k{(1 + U/e) log (1 + U/e) - U/e log U/e}.................................................21
Equation 21 is represented as,
S = f(U/e)....................................................................................................22
The second entropy equation is derived using (Planck, § 8
T = γ · f(U/γ)...............................................................................................23
The following equation (Planck, § 9)
1/T = dS/dU................................................................................................24
and equations 24 are used to form,
dS/dU = 1/γ · f(U/γ)...................................................................................25
Integrating equation 25,
S = f(U/γ)...................................................................................................26
Comparing the variables of equations 22 and 26, a proportionality is formed,
e α γ...........................................................................................................27
Planck's energy element is derived using equation 27.
"§10. If we apply Wien's displacement law in the latter form to equation (6) for the entropy S, we then find that the energy element e must be proportional to the frequency v, thus:
e = hγ".......................................................................................................28
(Planck, § 10). Planck uses a proportionality (equ 27) to equate the kinetic energy (e = 1/2 mv2) of the blackbody surface electrons that possess a mass with the energies of massless electromagnetic photon (hv) in the derivation of the energy element (e = hv) since Planck's constant h = 6.6 × 10-34 m2 kg/s contains the units of the mass (kg) yet light is composed of massless light particles that energy cannot be represented with the units of the mass. Plus, Planck's derivation of the energy element uses Boltzmann's closed system thermodynamic entropy S = k log (V/Vo) which conflicts with the open system of the blackbody radiation effect which proves the derivation of Planck's energy element is physically invalid.
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§ 7. Einstein's Photoelectric
In Einstein's photoelectric paper, "On a Heuristic Viewpoint Concerning the Production and Transformation of Light" (1905), Einstein is supporting Maxwell's electromagnetic theory of light.
"By contrast, the electromagnetic state of a region of space is described by continuous functions and, hence, cannot be determined exactly by any finite number of variables. Thus, according to Maxwell's theory, the energy of purely electromagnetic phenomena (such as light) should be represented by a continuous function of space. By contrast, the energy of a material body should be represented by a discrete sum over the atoms and electrons; hence, the energy of a material body cannot be divided into arbitrarily many, arbitrarily small components. However, according to Maxwell's theory (or, indeed, any wave theory), the energy of a light wave emitted from a point source is distributed continuously over an ever larger volume." (Einstein1, Intro).
"These electrons also interact with the free molecules and electrons by conservative potentials when they approach very closely. We denote these electrons, which are bound at points of space, as "resonators", since they absorb and emit electromagnetic waves of a particular period." (Einstein1, § 1).
Einstein is represent the energy of an electromagnetic photon with the energy quanta but Maxwell's expanding electromagnetic field cannot maintain a particle structure of a propagating electromagnetic photon.
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Einstein uses Wien's blackbody intensity equation (Einstein1, § 4),
p = α v3 e-βv/T............................................................................................29
to derive a blackbody entropy equation,
S - So = (E/βv) ln V/Vo..............................................................................30
Einstein uses Boltzmann's thermodynamic entropy,
S - So = (R/N) ln W....................................................................................31
"Monochromatic radiation of low density behaves---as long as Wien's radiation formula is valid--in a thermodynamic sense, as if it consisted of mutually independent energy quanta of magnitude Rβv/N." (Einstein1, § 6).
Einstein is equating equations 30 and 31 to derive the energy quanta,
E = Rβv/N...................................................................................................32
Einstein's energy quanta (Rβv/N) contains Boltzmann's gas molecule constants R and N that represent gas molecules which have a mass that cannot be used in an energy equation that represents the energy of a massless electromagnetic photon that is used to represent the result of Lenard's photoelectric effect.
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§ 8. Einstein Electrodynamics
In Einstein's paper, "On the Electrodynamics of Moving Bodies" (1905), Einstein is justifying Maxwell's electromagnetic theory of light using Maxwell's equations.
"Let the Maxwell-Hertz equations for empty space be valid for the system at rest K, so that we hav
dX/dt = dN/dy - dM/dz.....................dL/dt = dY/dz - dZ/dy...............................33a,b
dY/dt = dL/dz - dN/dx.....................dM/dt = dZ/dx - dX/dz...............................34a,b
dZ/dt = dM/dx - dL/dy.....................dN/dt = dX/dy - dY/dx...............................35a,b
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........................................................39
Applying equation 39 to the coordinate system of Maxwell's equations,
"X' = X.......................................... L' = L...................................................................40a,b
Y' = β[Y - (v/c)N].......................... M'= β[M + (v/c)Z]..................................................41a,b
Z' = β[Z + (v/c)M],..........................N' = β[N - (v/c)Y]"................................................42a,b
(Einstein2, § 6). Einstein justifies Maxwell's electromagnetic theory of light but altering the dimensions of Maxwell's equations does not change the fact that Maxwell's equations are derived using Faraday's induction effect that is not luminous nor is induction an ionization or particle effect.
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§ 9. Einstein's Inertial Mass
In Einstein's paper, "Does the Inertia of a Body depend upon its Energy Content?" (1905), Einstein describes the inertial mass.
"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." (Einstein3, p. 641).
Einstein uses the inertial mass L/V2 to structurally unify Maxwell's electromagnetic field with matter but Einstein's inertial mass (m = L/V2) is massless since L represents the energy of an electromagnetic photon. Einstein is attempting to use the inertial mass to structural unify Maxwell's electromagnetic field with Fresnel's optical ether, composed of matter.
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§ 10. Minkowski
In Minkowski's paper, "The Fundamental Equations for Electromagnetic Processes in Moving Bodies" (1908), Minkowski represents the aether with Maxwell's equations.
"§ 2. The Fundamental Equations for Æther.
curl m - dE/dt = pm........................................43
div e = p.........................................................44
curl e + dm/dt = 0...........................................45
div m = 0........................................................46
(Minkowski, Part 1, § 2). Minkowski is representing the aether with Maxwell's equations to depict an electromagnetic aether but Maxwell's equations are derived using Faraday's induction effect that is not luminous.
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§ 11. Einstein's Electromagnetic Ether
In Einstein's paper, "The Principle of Relativity and Its Consequences in Modern Physics" (1910), Einstein describes an electromagnetic ether.
"When it was realized that a profound analogy exists between the elastic vibrations of ponderable matter and the phenomena of interference and diffraction of light, it could not be doubted that light must be considered as a vibratory state of a special kind of matter. Since, moreover, light can propagate in places devoid of ponderable matter, one was forced to assume for the propagation of light a special kind of matter that is different from ponderable matter, and that was given the name "ether." (Einstein4, § 1).
"The introduction of the electromagnetic theory of light brought about a certain modification of the ether hypothesis. At first the physicists did not doubt that the electromagnetic phenomena must be reduced to the modes of motion of this medium. But as they gradually became convinced that none of the mechanical theories of ether provided a particularly impressive picture of electromagnetic phenomena, they got accustomed to considering the electric and magnetic fields as entities whose mechanical interpretation is superfluous. Thus, they have come to view theses fields in the vacuum as special states of the ether" (Einstein4, § 1).
Einstein describes an electromagnetic ether but Maxwell's electromagnetic field originates from Faraday's induction effect that is not luminous. Also, Maxwell's massless electromagnetic field that is propagating at the velocity of light conflicts with Fresnel's wave theory of light that represents diffraction using light waves formed by the vibration of a stationary ether, composed of matter.
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§ 12. Relativity: Special and General Theory
In Einstein paper, "Relativity: Special and General Theory" (1917), Einstein describes the inertial mass (m).
"XV. General Results of the Theory
IT is clear from our previous considerations that the (special) theory of relativity has grown out of electrodynamics and optics. In these fields it has not appreciably altered the predictions of theory, but it has considerably simplified the theoretical structure, i.e. the derivation of laws, and—what is incomparably more important—it has considerably reduced the number of independent hypotheses forming the basis of theory. The special theory of relativity has rendered the Maxwell-Lorentz theory so plausible, that the latter would have been generally accepted by physicists even if experiment had decided less unequivocally in its favor." (Einstein6, § 15).
"Hence we can say: If a body takes up an amount of energy Eo, then its inertial mass increases by an amount
Eo/c2.......................................................................................................47
the inertial mass of a body is not a constant, but varies according to the change in the energy of the body. The inertial mass of a system of bodies can even be regarded as a measure of its energy. The law of the conservation of the mass of a system becomes identical with the law of the conservation of energy, and is only valid provided that the system neither takes up nor sends out energy. Writing the expression for the energy in the form
mc2 + Eo/ (1 - v2/c2)1/2.............................................................................48
we see that the term mc2, which has hitherto attracted our attention, is nothing else than the energy possessed by the body before it absorbed the energy Eo." (Einstein6, § 15).
Einstein energy equation Eo = mc2 is another attempt at structurally unifies Maxwell's electromagnetic field with matter to justify Fresnel's ether, composed of matter, that is the foundation of the wave theory of light, using the inertial mass Eo/c2 (equ 59) but Einstien's inertial mass (m = Eo/c2) is massless since Eo represents the energy of a massless electromagnetic photon.
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Einstein is justifying the existence of Fresnel's ether, composed of matter, using the reversal of the negative result of Michelson-Morley experiment based on Lorentz's theory.
"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 is using the reversal of Michelson-Morley experiment to justify the existence of Fresnel's ether (Michelson-Morley, p. 333) but Lorentz uses the constant magnitude of the earth's yearly tangential velocity vector px but at the surface of the earth, the magnitude of the earth's tangential velocity vector px is formed by the earth's daily and yearly motions; consequently, the earth's tangential velocity vector is not constant.. At 6:00 pm, the magnitude of the earth's tangential velocity px is 463 m/s (fig 7); at 7:00 pm; because of the earth's daily and yearly motions, the magnitude of px increases to 5,077 m/s. At midnight, the earth's tangential velocity vector px increases to 30,463 m/s. As time increases, the earth's tangential velocity px increases from 463 m/s to 30,463 m/s for the time interval of 6:00 pm to 12:00 am yet Lorentz's transformation is based on a constant value of px (Lorentz, § 3) which proves Lorentz's transformation is physically invalid. In addition, the glass vacuum tube experiment proves Michelson-Morley ether experiment cannot be reversed which proves Fresnel's wave theory of light is physically invalid.
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§ 13. Conclusion
Fresnel's wave theory of light is based on an optical ether, composed of matter, yet diffraction forms in vacuum that is void of matter. Maxwell's electromagnetic theory based on Faraday's induction effect was introduced since induction forms in vacuum but induction is not luminous nor is induction an ionization or particle effect. Minkowski and Einstein describe an electromagnetic ether but Maxwell's massless electromagnetic field that propagates at the velocity of light conflicts with Fresnel's stationary' ether, composed of matter. Einstein energy equation Eo = mc2 is an attempt at structurally unifies Maxwell's electromagnetic field with Fresnel's ether, composed of matter, using the inertial mass Eo/c2 (equ 59) but Einstien's inertial mass (m = Eo/c2) is massless since Eo represents the energy of a massless electromagnetic photon. Furthermore, Lenard proves light is composed of particles which conflicts with the continuity of Maxwell's electromagnetic field and, an expanding electromagnetic field cannot maintain the particle structure of an electromagnetic photon. Modern physics uses the gauge transformation of Maxwell's equations but representing Maxwell's equations with a gauge potential does not change the fact that Maxwell's equations are derived using Faraday's induction effect that is not luminous, nor is induction an ionization or particle effect. In an experiment, a laser beam enters an aperture without the laser beam's intensity contacting the aperture edge results in no diffraction effect but when the laser's intensity contacts the aperture edge a diffraction effect is formed. The interaction of the laser beam's intensity with the aperture edge is an essential component in the aperture diffraction mechanism. I predict that the optic particles of a laser beam that contacts the aperture edge activate the aperture edge atoms forming an aperture edge effect that re-directs the optic particles that enter the aperture to only the intensity areas of the diffraction pattern; the scalar energy of the re-directed optic particles forms the intensity of the diffraction pattern (fig 20) without involving an ether or wave interference.
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§ 14. Reference
Einstein1, Albert. On a Heuristic Point of View about the Creation and Conversion of Light. Annalen der Physik. 17:132. 1905. http://en.wikisource.org/wiki/On_a_Heuristic_Point_of_View_about_the_Creation_and_Conversion_of_Light
Einstein2, Albert. On the Electrodynamics of Moving Bodies. Annalen der Physik. 17:891-921. 1905. https://www.fourmilab.ch/etexts/einstein/specrel/www/
Einstein3, Albert. Does the Inertia of a Body depend upon its Energy Content? 1905.
Einstein4, Albert. The Principle of Relativity and its Consequences in Modern Physics. 1910.
Einstein5, Albert. Relativity: Special and General Theory. Brauschweig. 1917. http://en.wikisource.org/wiki/Relativity:_The_Special_and_General_Theory
Fresnel, Augustin. Memorie su la Diffraction de la Lumiere. French Academy of Science. 1819.
Faraday, Michael. Experimental Researches in Electricity. Philosophical Transactions of the Royal Society of London. 1831-1838 http://www.gutenberg.org/files/14986/14986-h/14986-h.htm
Hertz, Heinrich. Annalen der Physik. 1887.
Huygens, Christiann. Treatise on Light. Translated by Silvanus P. Thompson. French Academy of Science. 1690. http://www.gutenberg.org/files/14725/14725-h/14725-h.htm
Lenard, Philipp. Ueber die lichtelektrische Wirkung. 5:142-150. Annalen der Physik. 1902.
Lorentz, Hendrik. Simplified Theory of Electrical and Optical Phenomena in Moving Systems. Proceedings of the Royal Netherlands Academy of Arts and Sciences 1:427-442. 1899. http://en.wikisource.org/wiki/Simplified_Theory_of_Electrical_and_Optical_Phenomena_in_Moving_Systems
Maxwell, Clerk. A Dynamical Theory of the Electromagnetic Field. Philosophical Magazine. 1864. https://en.wikisource.org/wiki/A_Dynamical_Theory_of_the_Electromagnetic_Field
Michelson, Albert. The Relative Motion of the Earth and the Luminiferous Ether. American Journal of Science. 22:120-129, 1881. http://en.wikisource.org/wiki/The_Relative_Motion_of_the_Earth_and_the_Luminiferous_Ether
Minkowski, Hermann. The Fundamental Equations for Electromagnetic Processes in Moving Bodies. Mathematisch-Physikalische Klasse. pp. 53-111. 1908. http://en.wikisource.org/wiki/Translation:The_Fundamental_Equations_for_Electromagnetic_Processes_in_Moving_Bodies
Planck, Max. On the Law of Distribution of Energy in the Normal Spectrum. Annalen der Physik. 4:553. 1901. http://www.chemteam.info/Chem-History/Planck-1901/Planck-1901.html
Poynting, John. The Transfer of Energy in the Electromagnetic Field. Philosophical Transactions of the Royal Society of London. 175:343-361. 1884. http://en.wikisource.org/wiki/On_the_Transfer_of_Energy_in_the_Electromagnetic_Field
1
Optica!
Ben T. Ito
May 19, 2017
This paper will analyze the wave theory of light.
§ 1. Introduction
Huygens (1690) describes the propagation of light using light waves formed by the motion of an Ethereal matter (Huygens, p. 11). Bradley's (1725) stellar aberration is used to justify the existence of Huygens' ether but aberration does not alter the fact that light propagates through a glass vacuum tube that is void of matter. Also, the change in the position of Bradley's star is determined using two times that Bradley is viewing a specific star but the time measurement uncertainty of a 1725 pendulum clock is 60 seconds for 24 hours which produces a position uncertainty of the measurement of the position of Bradley star that is larger than the position change of Bradley's star which proves Bradley's stellar aberration is physically invalid. Fresnel (1819) established the wave theory of light by representing diffraction using interfering light-waves created by the vibration of an elastic fluid (Fresnel, 43) despite the fact that diffraction forms in vacuum that is void of matter which contradicts Fresnel's diffraction mechanism that is the foundation of the wave theory of light. Maxwell's (1864) electromagnetic theory of light based on Faraday induction effect was introduced since induction forms in vacuum but Faraday's induction effect is not luminous. Maxwell's theory is based on the assumption that since light and the radio induction effect propagate at the same velocity that light has an electromagnetic field structure but the velocity of light does not change the fact that Maxwell's theory is based on Faraday's induction effect that is not luminous. Poynting (1884) supports Maxwell's theory by deriving an electromagnetic energy equation (Poynting, p. 358) but Poynting's current wire is not luminous. Hertz (1887) attempts to structurally unite light with induction using a spark gap experiment that produces light and the radio induction effect but Hertz's spark gap emits electrons yet Faraday's induction effect is also not an ionization effect. The generation of light by a light source is always accompanied by the emission of electrons yet Maxwell's electromagnetic theory of light is based on Faraday's induction effect that is not an ionization effect which proves light is not an electromagnetic phenomenon. In addition, Lenard (1899-1902) proves light is composed of particles which conflicts with the continuity of Maxwell's electromagnetic field. Planck (1901) addresses Lenard's photoelectric effect by deriving an energy element (hγ) that represents the energy of an electromagnetic photon but Maxwell's expanding electromagnetic field cannot maintain a particle structure of a propagating electromagnetic photon. In Einstein's (1905) electrodynamics (special relativity), Einstein supports Maxwell's electromagnetic theory of light using Maxwell's equations but Maxwell's equations are derived using Faraday's induction experiment that is not luminous nor is induction an ionization or particle effect. Furthermore, Einstein's translation velocity varies form 463 m/s to 30,463 m/s for the time interval from 6:00 pm to 12:00 am yet special relativity is based on a constant value of the translational velocity. In Einstein's paper "Does the Inertia of a Body Depend Upon its Energy Content?" (1905), Einstein uses the inertial mass (L/V2) to structurally unify Maxwell's electromagnetic field with matter to structurally unify Maxwell's electromagnetic field with Fresnel's ether, composed of matter but Einstein's inertial mass (m = L/V2) is massless since L represents the energy of a massless electromagnetic photon. Einstein (1910) describes an electromagnetic ether but Maxwell's electromagnetic field originates from Faraday's induction effect that is not luminous; also, Maxwell's massless electromagnetic field that is propagating at the velocity of light conflicts with Fresnel's stationary ether composed of matter.
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§ 2. Fresnel
In Fresnel's paper, "Memorie su la Diffraction de la Lumiere" (1819), Fresnel describes diffraction using interfering light waves formed by the vibration of the elastic fluid (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 is describing diffraction using interfering light waves formed by the motion of an elastic fluid (ether) but diffraction forms in vacuum that is void of matter which contradicts Fresnel's diffraction mechanism.
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Fresnel describes diffraction using secondary waves that are formed by the wave AMI (fig 6).
"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 and interfering secondary waves when the bottom of the wave AMI touches the diffraction object. The expanding secondary light waves propagate to the diffraction screen and interfere forming the diffraction pattern but the creation of secondary waves (energy) away from the light source by the wave AMI is representing the wave AMI as a light source that is arbitrarily generating secondary waves which violates energy conservation.
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Fresnel derives a diffraction intensity equation by summating the interfering light waves' amplitudes, at the diffraction screen, using a line integral (equ 1).
"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 "..................................1
(Fresnel, 53). Fresnel is using a line integral to summate (equ 1) the interfering light waves' amplitudes at the diffraction screen (fig 2) but a line integral can only be used to represent the length of the wave AMI. In addition, the limits of Fresnel's line integral represents the length of the wave AMI yet in Fresnel's derivation, the wave amplitudes at a point P on the diffraction screen are summate yet the point P on the diffraction screen is not within the limits of the line integral which proves Fresnel's derivation is mathematically invalid. In addition, during the diffraction effect of light, the crests and nodes of Fresnel's propagating light waves propagate in the forward direction. At the diffraction screen point P, the propagating light waves' amplitudes would oscillate forming an average resultant amplitude of zero that would eliminate the diffraction pattern. Fresnel omits the time element from the derivation since propagating light waves eliminate the diffraction pattern but one of the most important physical characteristic of light is omitted from Fresnel's derivation since propagating light waves eliminate the intensity of the diffraction pattern.
The wave theory of light is based on light waves that energy is dependent on the magnitude of the wave amplitude. The bigger the wave amplitude the larger in intensity (energy) of the light wave. Fresnel is using the interfering light waves' amplitudes, at a point P, on the diffraction screen to represent the intensity (energy) of the diffraction effect which depicts 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 (Lenard, Intro). The varying intensity of a light ray is used to justify that the energy of a light wave is dependent on the wave amplitude but in Fresnel's derivation the interfering light waves are interacting at a point P on the diffraction screen which represents a light particle energy that is dependent on only the frequency which proves Fresnel's diffraction mechanism is physically invalid.
The formation of the small rectangular aperture diffraction pattern (fig 3) is represented using wave interference but the destructive interference of the light waves' amplitudes (energy) used to form the dark fringes of the diffraction pattern represents the destruction of energy which violates energy conservation; furthermore, the destruction of the light waves' amplitudes (intensity) would result in a reduction in the total light intensity of the diffraction pattern since the destroyed light waves' amplitudes do not contribute to the total light intensity of the diffraction pattern yet more than 80% of the small rectangular aperture diffraction pattern is composed of dark areas which would result in at least a 60% reduction in the total light intensity of the diffraction pattern yet experimentally, the total light intensity that enters a small rectangular aperture (dt = 1s) is equal to the total light intensity of the diffraction pattern.
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§ 3. Maxwell
In Maxwell's paper, "Dynamical Theory of the Electromagnetic Field" (1864), Maxwell states the ether 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 and heat, and it is because the transmission of these radiations is not greatly altered when transparent bodies of measurable density are substituted for the so-called vacuum, that we are obliged to admit that the undulations are those of an ethereal substance, and not of the gross matter, the presence of which merely modifies in some way the motion of the ether." (Maxwell, Intro).
Fresnel's wave theory of light is based on light waves formed by the vibration of an ether, composed of matter, but light propagates through a glass vacuum tube that is void of matter which contradicts Fresnel's wave theory of light. When confronted with the problem of how the ether, composed of matter, exists in the glass vacuum tube, Maxwell uses hyperbole to justify the ether, composed of matter, existing in vacuum forming light waves.
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Maxwell's equations are derived using Faraday's induction effect.
"PART III. - GENERAL EQUATIONS OF THE ELECTROMAGNETIC FIELD." (Maxwell, Part III).
"the total electromagnetic momentum of the circuit, or the number of lines of magnetic force which pass through it, the variations of which measure the total electromotive force in the circuit. This electromagnetic momentum is the same thing to which Professor Faraday has applied the name of the Electrotonic State. If the circuit be the boundary of the elementary area dydz." (Maxwell, Part III).
"Equations of Magnetic Force.
uα = dH/dy - dG/dz............................................2
uβ = dF/dz - dH/dx.............................................3
uλ = dG/dx - dF/dy.............................................4
Equations of Currents...
dλ/dy - dβ/dz = 4πp'............................................5
dα/dz - dλ/dx = 4πq'............................................6
dβ/dx - dα/dy = 4πr'............................................7
We may call these the Equations of Currents." (Maxwell, Part III).
Maxwell's equations are derived using Faraday's induction effect produced by the magnetic flux (α, β, λ) and internal conduction wire electric field (F, G, H) that forms Faraday's induction current in a wire loop.
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Maxwell's electromagnetic theory of light is based on Maxwell's equations.
"ELECTROMAGNETIC THEORY OF LIGHT" (Maxwell, Part VI).
"(93) If we combine the equations of Magnetic Force (B) with those of Electric Force (B) with those of Electric Current" (Maxwell, Part VI).
Maxwell's electromagnetic theory of light based on Faraday's induction effect was introduced since induction forms in vacuum but Faraday's induction effect is not luminous. Maxwell uses the velocity of light to justify the structural unification of light with induction but the velocity of light does not change the fact that Faraday's induction effect is not luminous. Poynting (1884) supports Maxwell's theory by deriving an electromagnetic energy equation using a current wire but Poynting's current wire is not luminous. Hertz (1887) attempts to structurally unite light with induction but Hertz's spark gap emits electrons yet Faraday's induction effect is also not an ionization effect. The production of the light is always accompanied by the emission of electrons yet induction is not an ionization effect which proves light is not an electromagnetic phenomenon. In addition, Lenard proves light is composed of particles which conflicts with the continuity of Maxwell's electromagnetic field since as a light ray propagates, the optic particles that compose a light ray form spaces between optic particles that distances between optic particles increase due to the dispersion of a light. Furthermore, the radio induction effect (radio waves) produces an intensity that is dependent on the inverse of the fifth order of the distance I = K/r5 yet the dispersion of a laser beam is less than the inverse of the second order of the distance I = K/r2. Experimentally, a 2.3 W laser beam with a diameter of one inch after propagating to the moon forms a diameter of four miles yet a one meter diameter 1000 W radio signal that originates from the surface of the earth forms a width of more than one million miles after propagating to the moon which is experimental proof light is not an electromagnetic phenomenon.
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§ 4. Michelson
In Michelson's paper, "The Relative Motion of the Earth and the Lumiferous Ether" (1881), Michelson tests for the effects of the ether wind formed by the earth's motion through Fresnel's ether, composed of matter.
"The undulatory theory of light assumes the existence of a medium called the ether, whose vibrations produce the phenomena of heat and light, and which is supposed to fill all space. According to Fresnel, the ether, which is enclosed in optical media, partakes of the motion of these media, to an extent depending on their indices of refraction. For air, this motion would be but a small fraction of that of the air itself and will be neglected." (Michelson, p. 120).
"Assuming then that the ether is at rest, the earth moving through it, the time required for light to pass from one point to another on the earth's surface, would depend on the direction in which it travels." (Michelson, p. 120).
"The interpretation of these results is that there is no displacement of the interference bands. The result of the hypothesis of a stationary ether is thus shown to be incorrect, and the necessary conclusion follows that the hypothesis is erroneous." (Michelson, p. 128).
Michelson is testing for the existence of Fresnel's optical ether, composed of matter, using an ether wind produced by the earth's daily and yearly rotational motions through Fresnel's stationary ether, composed of matter. At a point on the surface of the earth, the earth's daily and yearly motions interaction with Fresnel's stationary ether form an ether wind that is directed tangent to the earth's surface. An ach lamp is used to form two light rays using a beam splitter. One light ray propagates parallel to the direction of the ether wind and the second ray propagates perpendicular to the ether wind. According to Michelson, only the velocity of the ray that is propagating parallel to the ether wind is affected by the ether wind. Both light rays are recombined to form an interference effect but rotating Michelson's experimental apparatus, at certain angles, both light rays velocities would be altered by the ether wind which would result in the shift of the interference effect but after the rotation of the interferometer no change in the interference effect is observed which represents the negative result of Michelson's experiment. The velocity of light (3 x 108 m/s) is four order of magnitude greater than the maximum velocity of the ether wind (Vmax = 30,463 m/s); consequently, the ether wind cannot produce the shift of the interference effect which proves Michelson's ether experiment has no scientific value. Furthermore, Michelson's experiment is based on a constant magnitude of the ether wind but the magnitude of the ether wind varies as time increases. At 6:00 pm, the magnitude of the earth's tangential velocity vector formed by the earth daily and yearly motions that forms the ether wind is 463 m/s (fig 7), and, the magnitude of the ether wind increases to 5,077 m/s at 7:00 pm. At midnight, the earth' tangential velocity vector equals 30,463 m/s; consequently, the magnitude of the ether wind increases from 463 m/s to 30,463 m/s for the time interval of 6:00 pm to 12:00 am yet Michelson's experiment is based on a constant magnitude of the ether wind. Furthermore, Michelson's experiment is unnecessary since the glass vacuum tube experiment is definitive and irreversible experimental proof Fresnel's ether, composed of matter, does not physically exist.
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§ 5. Lorentz
In Lorentz's paper "Simplified Theory of Electrical and Optical Phenomena in Moving Systems" (1899), Lorentz is justify Maxwell's theory by altering the dimensions of Maxwell's equations using px .
"dBz/dy - dBy/dz = 4πq(px + vx) + 4π(d/dt - px d/dx) Ex..............................................8
dBx/dz - dBz/dx = 4πpqvy + 4π(d/dt - px d/dx) Ey.....................................................9
dBy/dx - dBx/dy = 4πqvz + 4π(d/dt - px d/dx) Ez........................................................10
..............................................................................................................
4πV2(dEz /dy - dEy/dz) = - (d/dt - px d/dx) Bx..............................................................11
4πV2(dEx/dz - dEz /dx) = - (d/dt - px d/dx) By..............................................................12
4πV2(dEy/dx - dEx/dy) = - (d/dt - px d/dx) Bx...............................................................13
...In most applications p would be the velocity of the earth in its yearly motion." (Lorentz, § 3).
x' = [V/(V2 - px2)1/2]x,....................................................................................................14
y' = y,...........................................................................................................................15
z' = z,...........................................................................................................................16
t' = t - x px /(V2 - px2).....................................................................................................17
Lorentz justifying Maxwell's electromagnetic theory of light using Maxwell's equations but manipulating the coordinate system of Maxwell's equations does not alter the fact that Maxwell's equations are derived using Faraday's induction effect that is not luminous, nor is induction an ionization or particle effect which is experimental proof light is not an electromagnetic phenomenon.
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Lorentz alters the dimensions of Michelson's experimental apparatus to reverse the negative result of Michelson's experiment to justify the existence of Fresnel's ether, composed of matter (Michelson, p. 120).
"§ 9. Hitherto all quantities of the order p2x /V2 have been neglected. As is well known, these must be taken into account in the discussion of Michelson's experiment, in which two rays of light interfered after having traversed rather long paths, the one parallel to the direction of the earth's motion, and the other perpendicular to it. In order to explain the negative result of this experiment Fitzgerald and myself have supposed that, in consequence of the translation, the dimensions of the solid bodies serving to support the optical apparatus, are altered in a certain ratio." (Lorentz, § 9).
Lorentz is reversing the negative result of Michelson's ether experiment to justify the existence of Fresnel's optical ether by contracting the x dimension of the interferometer's armature, using the constant magnitude of the earth's tangential velocity vector px but at the surface of the earth, the magnitude of the earth's tangential velocity vector px in not constant.. At 6:00 pm, the magnitude of the earth's tangential velocity px is 464 m/s (fig 7); at 7:00 pm; because of the earth's daily and yearly motions, the magnitude of px increases to 5,077 m/s. At midnight, the earth's yearly tangential velocity vector px increases to 30,463 m/s; consequently, the earth tangential velocity vector px increases from 463 m/s to 30,463 m/s from 6:00 pm to 12: 00 am yet Lorentz's transformation is based on a constant value of the translational velocity px which proves Lorentz's transformation is physically invalid.
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§ 6. Planck
In Planck's paper, "On the Law of Distribution of Energy in the Normal Spectrum" (1901), Planck is supporting Maxwell's electromagnetic theory of light.
"In any case the theory requires a correction, and I shall attempt in the following to accomplish this on the basis of the theory of electromagnetic radiation which I developed." (Planck, Intro).
"In my last article4 I showed that the physical foundations of the electromagnetic radiation theory, including the hypothesis of "natural radiation", withstand the most severe criticism" (Planck, Intro).
Planck uses the blackbody radiation effect and Boltzmann's thermodynamic entropy in the derivation of the energy element (hv) that represents the energy of an electromagnetic photon emitted by the blackbody radiation effect but Maxwell's expanding electromagnetic field cannot maintain a particle structure of a electromagnetic photon.
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Planck's energy element (hv) is derived using Boltzmann's thermodynamic entropy equation,
S = k log R................................................................................................18
that is used with Planck's blackbody electron (resonator) kinetic energy distribution ratio (Planck, § 3),
R = (N + P)N + P/ NN · PP...........................................................................1
to form (Planck, § 5)
SN = k{N + P) log (N + P) - N log N - P log P)............................................20
Using UN = NU and UN = Pe, equation 20 becomes,
S = k{(1 + U/e) log (1 + U/e) - U/e log U/e}.................................................21
Equation 21 is represented as,
S = f(U/e)....................................................................................................22
The second entropy equation is derived using (Planck, § 8
T = γ · f(U/γ)...............................................................................................23
The following equation (Planck, § 9)
1/T = dS/dU................................................................................................24
and equations 24 are used to form,
dS/dU = 1/γ · f(U/γ)...................................................................................25
Integrating equation 25,
S = f(U/γ)...................................................................................................26
Comparing the variables of equations 22 and 26, a proportionality is formed,
e α γ...........................................................................................................27
Planck's energy element is derived using equation 27.
"§10. If we apply Wien's displacement law in the latter form to equation (6) for the entropy S, we then find that the energy element e must be proportional to the frequency v, thus:
e = hγ".......................................................................................................28
(Planck, § 10). Planck uses a proportionality (equ 27) to equate the kinetic energy (e = 1/2 mv2) of the blackbody surface electrons that possess a mass with the energies of massless electromagnetic photon (hv) in the derivation of the energy element (e = hv) since Planck's constant h = 6.6 × 10-34 m2 kg/s contains the units of the mass (kg) yet light is composed of massless light particles that energy cannot be represented with the units of the mass. Plus, Planck's derivation of the energy element uses Boltzmann's closed system thermodynamic entropy S = k log (V/Vo) which conflicts with the open system of the blackbody radiation effect which proves the derivation of Planck's energy element is physically invalid.
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§ 7. Einstein's Photoelectric
In Einstein's photoelectric paper, "On a Heuristic Viewpoint Concerning the Production and Transformation of Light" (1905), Einstein is supporting Maxwell's electromagnetic theory of light.
"By contrast, the electromagnetic state of a region of space is described by continuous functions and, hence, cannot be determined exactly by any finite number of variables. Thus, according to Maxwell's theory, the energy of purely electromagnetic phenomena (such as light) should be represented by a continuous function of space. By contrast, the energy of a material body should be represented by a discrete sum over the atoms and electrons; hence, the energy of a material body cannot be divided into arbitrarily many, arbitrarily small components. However, according to Maxwell's theory (or, indeed, any wave theory), the energy of a light wave emitted from a point source is distributed continuously over an ever larger volume." (Einstein1, Intro).
"These electrons also interact with the free molecules and electrons by conservative potentials when they approach very closely. We denote these electrons, which are bound at points of space, as "resonators", since they absorb and emit electromagnetic waves of a particular period." (Einstein1, § 1).
Einstein is represent the energy of an electromagnetic photon with the energy quanta but Maxwell's expanding electromagnetic field cannot maintain a particle structure of a propagating electromagnetic photon.
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Einstein uses Wien's blackbody intensity equation (Einstein1, § 4),
p = α v3 e-βv/T............................................................................................29
to derive a blackbody entropy equation,
S - So = (E/βv) ln V/Vo..............................................................................30
Einstein uses Boltzmann's thermodynamic entropy,
S - So = (R/N) ln W....................................................................................31
"Monochromatic radiation of low density behaves---as long as Wien's radiation formula is valid--in a thermodynamic sense, as if it consisted of mutually independent energy quanta of magnitude Rβv/N." (Einstein1, § 6).
Einstein is equating equations 30 and 31 to derive the energy quanta,
E = Rβv/N...................................................................................................32
Einstein's energy quanta (Rβv/N) contains Boltzmann's gas molecule constants R and N that represent gas molecules which have a mass that cannot be used in an energy equation that represents the energy of a massless electromagnetic photon that is used to represent the result of Lenard's photoelectric effect.
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§ 8. Einstein Electrodynamics
In Einstein's paper, "On the Electrodynamics of Moving Bodies" (1905), Einstein is justifying Maxwell's electromagnetic theory of light using Maxwell's equations.
"Let the Maxwell-Hertz equations for empty space be valid for the system at rest K, so that we hav
dX/dt = dN/dy - dM/dz.....................dL/dt = dY/dz - dZ/dy...............................33a,b
dY/dt = dL/dz - dN/dx.....................dM/dt = dZ/dx - dX/dz...............................34a,b
dZ/dt = dM/dx - dL/dy.....................dN/dt = dX/dy - dY/dx...............................35a,b
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........................................................39
Applying equation 39 to the coordinate system of Maxwell's equations,
"X' = X.......................................... L' = L...................................................................40a,b
Y' = β[Y - (v/c)N].......................... M'= β[M + (v/c)Z]..................................................41a,b
Z' = β[Z + (v/c)M],..........................N' = β[N - (v/c)Y]"................................................42a,b
(Einstein2, § 6). Einstein justifies Maxwell's electromagnetic theory of light but altering the dimensions of Maxwell's equations does not change the fact that Maxwell's equations are derived using Faraday's induction effect that is not luminous nor is induction an ionization or particle effect.
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§ 9. Einstein's Inertial Mass
In Einstein's paper, "Does the Inertia of a Body depend upon its Energy Content?" (1905), Einstein describes the inertial mass.
"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." (Einstein3, p. 641).
Einstein uses the inertial mass L/V2 to structurally unify Maxwell's electromagnetic field with matter but Einstein's inertial mass (m = L/V2) is massless since L represents the energy of an electromagnetic photon. Einstein is attempting to use the inertial mass to structural unify Maxwell's electromagnetic field with Fresnel's optical ether, composed of matter.
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§ 10. Minkowski
In Minkowski's paper, "The Fundamental Equations for Electromagnetic Processes in Moving Bodies" (1908), Minkowski represents the aether with Maxwell's equations.
"§ 2. The Fundamental Equations for Æther.
curl m - dE/dt = pm........................................43
div e = p.........................................................44
curl e + dm/dt = 0...........................................45
div m = 0........................................................46
(Minkowski, Part 1, § 2). Minkowski is representing the aether with Maxwell's equations to depict an electromagnetic aether but Maxwell's equations are derived using Faraday's induction effect that is not luminous.
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§ 11. Einstein's Electromagnetic Ether
In Einstein's paper, "The Principle of Relativity and Its Consequences in Modern Physics" (1910), Einstein describes an electromagnetic ether.
"When it was realized that a profound analogy exists between the elastic vibrations of ponderable matter and the phenomena of interference and diffraction of light, it could not be doubted that light must be considered as a vibratory state of a special kind of matter. Since, moreover, light can propagate in places devoid of ponderable matter, one was forced to assume for the propagation of light a special kind of matter that is different from ponderable matter, and that was given the name "ether." (Einstein4, § 1).
"The introduction of the electromagnetic theory of light brought about a certain modification of the ether hypothesis. At first the physicists did not doubt that the electromagnetic phenomena must be reduced to the modes of motion of this medium. But as they gradually became convinced that none of the mechanical theories of ether provided a particularly impressive picture of electromagnetic phenomena, they got accustomed to considering the electric and magnetic fields as entities whose mechanical interpretation is superfluous. Thus, they have come to view theses fields in the vacuum as special states of the ether" (Einstein4, § 1).
Einstein describes an electromagnetic ether but Maxwell's electromagnetic field originates from Faraday's induction effect that is not luminous. Also, Maxwell's massless electromagnetic field that is propagating at the velocity of light conflicts with Fresnel's wave theory of light that represents diffraction using light waves formed by the vibration of a stationary ether, composed of matter.
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§ 12. Relativity: Special and General Theory
In Einstein paper, "Relativity: Special and General Theory" (1917), Einstein describes the inertial mass (m).
"XV. General Results of the Theory
IT is clear from our previous considerations that the (special) theory of relativity has grown out of electrodynamics and optics. In these fields it has not appreciably altered the predictions of theory, but it has considerably simplified the theoretical structure, i.e. the derivation of laws, and—what is incomparably more important—it has considerably reduced the number of independent hypotheses forming the basis of theory. The special theory of relativity has rendered the Maxwell-Lorentz theory so plausible, that the latter would have been generally accepted by physicists even if experiment had decided less unequivocally in its favor." (Einstein6, § 15).
"Hence we can say: If a body takes up an amount of energy Eo, then its inertial mass increases by an amount
Eo/c2.......................................................................................................47
the inertial mass of a body is not a constant, but varies according to the change in the energy of the body. The inertial mass of a system of bodies can even be regarded as a measure of its energy. The law of the conservation of the mass of a system becomes identical with the law of the conservation of energy, and is only valid provided that the system neither takes up nor sends out energy. Writing the expression for the energy in the form
mc2 + Eo/ (1 - v2/c2)1/2.............................................................................48
we see that the term mc2, which has hitherto attracted our attention, is nothing else than the energy possessed by the body before it absorbed the energy Eo." (Einstein6, § 15).
Einstein energy equation Eo = mc2 is another attempt at structurally unifies Maxwell's electromagnetic field with matter to justify Fresnel's ether, composed of matter, that is the foundation of the wave theory of light, using the inertial mass Eo/c2 (equ 59) but Einstien's inertial mass (m = Eo/c2) is massless since Eo represents the energy of a massless electromagnetic photon.
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Einstein is justifying the existence of Fresnel's ether, composed of matter, using the reversal of the negative result of Michelson-Morley experiment based on Lorentz's theory.
"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 is using the reversal of Michelson-Morley experiment to justify the existence of Fresnel's ether (Michelson-Morley, p. 333) but Lorentz uses the constant magnitude of the earth's yearly tangential velocity vector px but at the surface of the earth, the magnitude of the earth's tangential velocity vector px is formed by the earth's daily and yearly motions; consequently, the earth's tangential velocity vector is not constant.. At 6:00 pm, the magnitude of the earth's tangential velocity px is 463 m/s (fig 7); at 7:00 pm; because of the earth's daily and yearly motions, the magnitude of px increases to 5,077 m/s. At midnight, the earth's tangential velocity vector px increases to 30,463 m/s. As time increases, the earth's tangential velocity px increases from 463 m/s to 30,463 m/s for the time interval of 6:00 pm to 12:00 am yet Lorentz's transformation is based on a constant value of px (Lorentz, § 3) which proves Lorentz's transformation is physically invalid. In addition, the glass vacuum tube experiment proves Michelson-Morley ether experiment cannot be reversed which proves Fresnel's wave theory of light is physically invalid.
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§ 13. Conclusion
Fresnel's wave theory of light is based on an optical ether, composed of matter, yet diffraction forms in vacuum that is void of matter. Maxwell's electromagnetic theory based on Faraday's induction effect was introduced since induction forms in vacuum but induction is not luminous nor is induction an ionization or particle effect. Minkowski and Einstein describe an electromagnetic ether but Maxwell's massless electromagnetic field that propagates at the velocity of light conflicts with Fresnel's stationary' ether, composed of matter. Einstein energy equation Eo = mc2 is an attempt at structurally unifies Maxwell's electromagnetic field with Fresnel's ether, composed of matter, using the inertial mass Eo/c2 (equ 59) but Einstien's inertial mass (m = Eo/c2) is massless since Eo represents the energy of a massless electromagnetic photon. Furthermore, Lenard proves light is composed of particles which conflicts with the continuity of Maxwell's electromagnetic field and, an expanding electromagnetic field cannot maintain the particle structure of an electromagnetic photon. Modern physics uses the gauge transformation of Maxwell's equations but representing Maxwell's equations with a gauge potential does not change the fact that Maxwell's equations are derived using Faraday's induction effect that is not luminous, nor is induction an ionization or particle effect. In an experiment, a laser beam enters an aperture without the laser beam's intensity contacting the aperture edge results in no diffraction effect but when the laser's intensity contacts the aperture edge a diffraction effect is formed. The interaction of the laser beam's intensity with the aperture edge is an essential component in the aperture diffraction mechanism. I predict that the optic particles of a laser beam that contacts the aperture edge activate the aperture edge atoms forming an aperture edge effect that re-directs the optic particles that enter the aperture to only the intensity areas of the diffraction pattern; the scalar energy of the re-directed optic particles forms the intensity of the diffraction pattern (fig 20) without involving an ether or wave interference.
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§ 14. Reference
Einstein1, Albert. On a Heuristic Point of View about the Creation and Conversion of Light. Annalen der Physik. 17:132. 1905. http://en.wikisource.org/wiki/On_a_Heuristic_Point_of_View_about_the_Creation_and_Conversion_of_Light
Einstein2, Albert. On the Electrodynamics of Moving Bodies. Annalen der Physik. 17:891-921. 1905. https://www.fourmilab.ch/etexts/einstein/specrel/www/
Einstein3, Albert. Does the Inertia of a Body depend upon its Energy Content? 1905.
Einstein4, Albert. The Principle of Relativity and its Consequences in Modern Physics. 1910.
Einstein5, Albert. Relativity: Special and General Theory. Brauschweig. 1917. http://en.wikisource.org/wiki/Relativity:_The_Special_and_General_Theory
Fresnel, Augustin. Memorie su la Diffraction de la Lumiere. French Academy of Science. 1819.
Faraday, Michael. Experimental Researches in Electricity. Philosophical Transactions of the Royal Society of London. 1831-1838 http://www.gutenberg.org/files/14986/14986-h/14986-h.htm
Hertz, Heinrich. Annalen der Physik. 1887.
Huygens, Christiann. Treatise on Light. Translated by Silvanus P. Thompson. French Academy of Science. 1690. http://www.gutenberg.org/files/14725/14725-h/14725-h.htm
Lenard, Philipp. Ueber die lichtelektrische Wirkung. 5:142-150. Annalen der Physik. 1902.
Lorentz, Hendrik. Simplified Theory of Electrical and Optical Phenomena in Moving Systems. Proceedings of the Royal Netherlands Academy of Arts and Sciences 1:427-442. 1899. http://en.wikisource.org/wiki/Simplified_Theory_of_Electrical_and_Optical_Phenomena_in_Moving_Systems
Maxwell, Clerk. A Dynamical Theory of the Electromagnetic Field. Philosophical Magazine. 1864. https://en.wikisource.org/wiki/A_Dynamical_Theory_of_the_Electromagnetic_Field
Michelson, Albert. The Relative Motion of the Earth and the Luminiferous Ether. American Journal of Science. 22:120-129, 1881. http://en.wikisource.org/wiki/The_Relative_Motion_of_the_Earth_and_the_Luminiferous_Ether
Minkowski, Hermann. The Fundamental Equations for Electromagnetic Processes in Moving Bodies. Mathematisch-Physikalische Klasse. pp. 53-111. 1908. http://en.wikisource.org/wiki/Translation:The_Fundamental_Equations_for_Electromagnetic_Processes_in_Moving_Bodies
Planck, Max. On the Law of Distribution of Energy in the Normal Spectrum. Annalen der Physik. 4:553. 1901. http://www.chemteam.info/Chem-History/Planck-1901/Planck-1901.html
Poynting, John. The Transfer of Energy in the Electromagnetic Field. Philosophical Transactions of the Royal Society of London. 175:343-361. 1884. http://en.wikisource.org/wiki/On_the_Transfer_of_Energy_in_the_Electromagnetic_Field
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