User:Printinghome/sandbox

§ 6. Kirchhoff

In Fresnel's diffraction mechanism, spherical waves form in the aperture and propagate to the diffraction screen forming the interference pattern but Fresnel's spherical waves form retrogressive waves that would produce an diffraction pattern in the backwards direction yet the retrogressive diffraction pattern is not experimentally observed which proves Fresnel's diffraction mechanism of light is physically invalid.

"10-4. Defects of Fresnel's Theory...

3. To these difficulties regarding the nature of the secondary sources there is added the difficulty of explaining the existence of the obliquity factor and, in particular, why the sources do not radiate backwards....In addition, one can easily "forget" the backwave." (Longhurst, p. 188).

The diffraction effect of light described using light waves form a retrogressive wave that is not experimentally observed which is experimental proof Fresnel's diffraction mechanism is physically invalid.

--

In Kirchhoff's formulation of Huygens' Principle (1883), Kirchhoff eliminates the retrogressive wave, using Green's theorem,

"8.3 Kirchhoff's diffraction theory

8.3.1 The integral theorem of Kirchhoff

The basic idea of the Huygens-Fresnel theory is that the light disturbance at a point P arises from the superposition of secondary waves that proceed from a surface situated between this point and the light wource. This idea was put on a sounder mathematical basis by Kirchhoff†....................If U' is any other function which satisfies the same continuity requirements as U, we have by Green's theorem" (Born and Wolf, p. 417-418).

"∭(ψ2∇2ψ1 - ψ1∇2ψ2)dV = ∬(ψ2[dψ1/dn] - ψ1[dψ2/dn])dS:..............................29

(Longhurst, p. 190). In Green's theorem (equ 29), the volume integral, that represents a volume, is equated to the surface integral, that represents an area, which is physically invalid and proves Kirchhoff's elimination of the retrogressive wave using the obliquity factor is physically and mathematically invalid.

--

Kirchhoff uses equation 29 to derive an obliquity factor that is used to eliminates the retrogressive wave formed by a spherical wave,

"10-7. Application to Spherical Waves

Equation (10-15) was derived for a surface S which enclosed the point P but not the source (since it was assumed in applying Green's theorem that ψ remains finite throughout the volume of integration). It can be shown that the same result follows if S encloses the source but not the point P. Thus in the case of a single point source the closed surface S may be taken as a spherical wavefront." (Longhurst, p. 192).

"1. The integrand includes an obliquity factor 1/2(1 + cos θ) which is unity in the forward direction (θ = 0) and zero in the reverse direction (θ = π). The amplitude factor a/λ is also present as was seen to be necessary." (Longhurst, p. 193).

Kirchhoff is mathematically eliminating the unwanted structure of the retrogressive wave that propagates in the reverse (backwards) direction, using Green's theorem, but a spherical wave has a radial structure that forms a retrogressive wave which proves Kirchhoff's mathematical elimination of the retrogressive wave is invalid. In quantum mechanics, the atomic orbitals are derived by manipulating the spherical coordinate system where the atomic orbital are not spheres centered around the origin which violates the use of a spherical coordinate system. A spherical coordinate system can to applied to a structure that has a spherical shape that is centered around the origin or a segment of a sphere centered around the origin. Quantum mechanics is manipulating the spherical coordinates system which is similar to Kirchhoff method where a spherical wave structure is being manipulated, using Green's theorem. Furthermore, Maxwell's equations, represent a spherical wave, that form a longitudinal wave yet Maxwell's equations are manipulated to form the electromagnetic transverse wave equations of light. Again, Maxwell's equations that represent a spherical wave are used to derive non-spherical wave structures by using manipulation that originates from Kirchhoff derivation since Kirchhoff is being allow to arbitrarily eliminate the structure of a spherical wave when the structure is representing a spherical wave. Both the quantum mechanics derivation of the atomic orbitals, and the derivation of the electromagnetic transverse wave equations of light are based on a deceptive manipulation that originates from Kirchhoff's formulation of Huygens' principle.

-

--

§ 10. 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 by quantizing Maxwell's electromagnetic field.

"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 is supporting Maxwell's electromagnetic theory of light but Maxwell's theory is based on Henry induction effect that is not luminous. Consequently, Planck seeks to structurally unify light with induction using the blackbody radiation effect, that emits light and the radio induction effect, but the blackbody radiation effect also emits electrons which is experimental proof Planck's unification and quantization of Maxwell's electromagnetic field is invalid since Henry induction effect is not an ionization effect.

Planck's discontinuous light particles that energy is represented with an energy element conflicts with the continuity of Maxwell's electromagnetic field; consequently, Planck used a thermodynamic analogy to justify light particles forming light waves since discrete air molecules form sound waves but air molecules are propagating in random directions and exchange velocities forming sound waves yet light particles, in a light ray, are not propagating in random directions and do not exchange velocities. Furthermore, air, that forms sound waves, produces a longitudinal wave that conflicts the Maxwell's electromagnetic transverse wave structure of light.

"Heisenberg wrote in (1929), that "the existence of the electron" is as unintelligible to the wave mechanical theory as the "existence of the light quantum" to Maxwell's theory." (Miller, p. 18).

--

Planck's blackbody derivation is based on the blackbody surface electrons, oscillating a diathermic medium (optical ether), at the frequency of light, forming EM light waves, that energy is represented with Planck's energy element (hv).

"§ 7. We now want to examine what Wien's displacement law states about the dependence of the entropy S of our resonator on its energy U and its characteristic, particularly in the general case where the resonator is situated in an arbitrary diathermic medium. For this purpose we next generalize Thiesen's form of the law for the radiation in an arbitrary diathermic medium with the velocity of light c. Since we do not have to consider the total radiation, but only the monochromatic radiation, it becomes necessary in order to compare different diathermic media to introduce the frequency v instead of the wavelength λ." (Planck, Part 1, § 7).

"Now according to the well-known Kirchoff-Clausius law, the energy emitted per unit time at the frequency v and temperature T from a black surface in a diathermic medium is inversely proportional to the square of the velocity of propagation c2; hence the energy density U is inversely proportional to c3 and we have:" (Planck, Part 1, § 7).

"the entropy of a resonator vibrating in an arbitrary diathermic medium depends only on the variable U/v, containing besides this only universal constants. This is the simplest form of Wien's displacement law known to me." (Planck, Part 1, § 9).

The blackbody radiation effect forms in vacuum that is void of a diathermic medium, composed of matter, which contradicts Planck's blackbody derivation. In addition, Planck's derivation describes the blackbody surface electrons oscillates at the frequency of light which is physically invalid since electrons that have a mass cannot oscillate at the frequency of light. Furthermore, Planck states that the blackbody surface electrons are propagating at the velocity of light which is also physically invalid since massless light and the radio induction effect propagates at the velocity of light. There is no experimental evidence that justifies Planck's assumption that electrons that have a mass can propagate at the velocity of light.

Planck's energy element (hv) is derived using Boltzmann's thermodynamic entropy equation,

S = k log R...............................................................................39

that is used with Planck's blackbody electron (resonator) kinetic energy distribution ratio (Planck, § 3),

R = (N + P)N + P / NN · PP..........................................................40

to form (Planck, § 5)

SN = k{N + P) log (N + P) - N log N - P log P)........................41

Using UN = NU and UN = Pe, equation 39 becomes,

S = k{(1 + U/e) log (1 + U/e) - U/e log U/e}.................................................42

Equation 40 is represented as,

S = f(U/e)....................................................................................................43

--

The second entropy equation is derived using (Planck, § 8),

T = v · f(U/v)......................................................................44

The following equation (Planck, § 9),

1/T = dS/dU..........................................................................45

and equations 42 are used to form,

dS/dU = 1/v · f(U/v)...........................................................45

Integrating equation 44,

S = f(U/v)...............................................................................47

Using equations 41 and 45, a proportionality is formed,

e α v......................................................................................48

Planck's energy element is derived using equation 46.

"§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 = hv"....................................................................................49

(Planck, § 10). Planck's derivation of the energy element (equ 47) is based on Boltzmann's thermodynamic entropy equation (equ 37) that represents the change of a closed initial volume Vo to a closed final volume V, that contains gas molecules, in a thermodynamic equilibrium. Planck replaces Boltzmann's volume ratio V/Vo with a blackbody surface electron kinetic energy distribution ratio (equ 38) which violates Boltzmann's thermodynamic entropy equation. Also, the blackbody surface electrons occupy a surface yet Boltzmann's thermodynamics entropy equation represents the change of a volume that is incompatible with the blackbody surface electrons which existence on a surface.

Planck uses S = f(U/e) and S = f(U/v) to form a proportionality (e α v), that is used in the derivation of Planck's energy element (e = hv) but the complete equation of S = f(U/v), that is not used in the derivation of Planck's energy element is derived after Planck derives the energy element since the complete equation of S = f(U/v) is derived using the energy element (hv) in equations 40 but equations 40 is also used in the derivation of Planck's energy element, which proves Planck's derivation, of the energy element, is a deceptive manipulation. Also, the derivation of Planck's energy element, using the proportionality, is equating the blackbody surface electrons kinetic energy with the motion of the diathermic medium (optic ether), composed of matter, that forms Planck's EM photons that energy is represented with Planck's energy element but the blackbody radiation effect forms in vacuum that is void of Planck's diathermic medium which is experimental proof Planck's blackbody derivation is physically invalid.

Planck's entropy equation S = f(U/e), (equ 41) represents the kinetic energy distribution of the blackbody surface electrons. The glowing hot blackbody surface electrons dissipate excessive energy, in the form of the blackbody emissions, to form a constant total kinetic energy distribution of the blackbody surface electrons, but the blackbody emissions represented with S = f(U/v) does not form a constant total energy since, as time increases, since the total energy of the blackbody emissions increases yet both S = f(U/e) and S = f(U/v) are used together to form a proportionality that is used to derive Planck's energy element which is physically invalid since the blackbody emissions, of S = f(U/v), represents an ever increasing total energy, as time increases yet S = f(U/e) represent a constant total energy since the excessive energy is being dissipated, in the form of the blackbody emissions. Also, Boltzmann's entropy represents a closed system which conflicts with the open system of blackbody emission represented with S = f(U/v) that cannot be represented with an Boltzmann's entropy since the blackbody emission represents a open system that energy emission cannot form an equilibrium that is required in the use of Boltzmann's thermodynamics entropy equation.

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

Planck's blackbody intensity equation is derived using the energy element (hv) in equation 40,

S = k{(1 + U/hv)log(1 + U/hv) - U/hv log U/hv}.....................................50

Differentiating equation 48 with respect to U using,

1/T = dS/dU.........................................................................................51

forms,


 * $$U_\nu(T) = \frac{hv}{e^\frac{h\nu}{k_\mathrm{}T} - 1}$$..........................................52

Equation 50 is used to derive Planck's blackbody intensity equation,


 * $$u_\nu(T) = \frac{ 2 h \nu^3}{c^2} \frac{1}{e^\frac{h\nu}{k_\mathrm{}T} - 1}$$....................................53

that represents the emission of light and the radio induction effect, outside the blackbody, but equation 26, is derived using Boltzmann's thermodynamic entropy equation (equ 37) that represents a closed system which conflicts with the open system of the blackbody radiation effect, that is continuous emitting the blackbody radiation outside the blackbody, as time increases. Using a closed system blackbody radiation effect, that is the foundation of Boltzmann's entropy equation, would result in the blackbody melting or exploding. In addition, the complete equation of S = f(U/v), that is used in the derivation of Planck's blackbody intensity equation (equ 51), is derived by using the energy element (hv) in equation 40 to derive equation 48. The derivation of the complete equation of S = f(U/v), represented with equation 48, is derived uses Planck's energy element (hv), in the blackbody surface electron energy distribution equation (equ 40) but the blackbody emissions, represented with hv, that total energy is increase, as time increases, does not correspond with the blackbody surface electrons constant total energy distribution of equation 40.

§ 11. Einstein's Energy Quanta

In Einstein's photoelectric paper, "On a Heuristic Viewpoint Concerning the Production and Transformation of Light" (1905), Einstein supports Maxwell's theory and Planck's quantization of Maxwell's electromagnetic field, by deriving an energy quanta that is used to represent an electromagnetic photon which is used to describe Lenard's photoelectric effect ((Einstein1, § 7).

"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 supporting Maxwell's theory that is based on Ampere's law that is not luminous, nor is induction an ionization effect which contradicts Maxwell's theory. Also, Einstein is describing the absorption and emission of an EM photon, by a photoelectric electron, to justify the quantization of Maxwell's electromagnetic field but continuous electromagnetic field structure cannot form a particle structure of light that is absorbed by Lenard's photoelectric electron.

---

Einstein uses Wien's blackbody intensity equation (Einstein1, § 4),

p = α v3 e-βv/T.................................................54

to derive a blackbody entropy equation,

S - So = (E/βv) ln V/Vo..............................................................................55

Einstein uses Boltzmann's thermodynamic entropy equation,

S - So = (R/N) ln W....................................................................................56

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 53 and 54 in the derivation of the energy quanta,

E = Rβv/N...................................................................................................57

Einstein derives the energy quanta by equating of equations 53 and 54 that represents the structural equating of gas molecules, that have a mass, with massless light particles, since Einstein energy quanta (E = Rβv/N) contains Boltzmann's thermodynamics constants R and N which prove Einstein derivation of the energy quanta is physically invalid. In the following statement, Einstein is stating that the energy of light particles is the same as the energy of a thermodynamics gas molecules but the energy of a thermodynamics gas molecule is dependent on the velocity that conflicts with Einstein's energy quanta that is dependent on the frequency.

"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" (Einstein1, § 6).

"Einstein's earliest scientific work dealt with electromagnetism, thermodynamics, and a statistical approach to the entropy function. His 1905 paper "On the Movement of Small particles Suspended in a Stationary Liquid Demanded by the Molecular-Kinetic Theory of Heat" provided crucial support for the physical validity of Avogadro's hypothesis and molecular-kinetic theory. The photoelectric-effect paper, "On a Heuristic Point of View about the Creation and Conversion of Light," demonstrated the necessity of incorporating the atomistic (or quantum) idea into the electromagnetic theory of light. Here Einstein demonstrated that the mathematical description for the entropy of black-body radiation in a closed volume is identical to that for a gas in the same volume. By analogy, then, electromagnetic radiation may be treated as a dynamic collection of particles, as is the case for a gas, where the energy of the electromagnetic or light particles is proportional to the frequency of radiation." (Nye, p. 460).