7. Planck's Black-body Radiation
Planck's derivation of the black-body radiation discrete energy and average total energy equations are described (Eisberg, p. 8). Planck derives a discrete energy equation by describing light within the black-body with standing waves of Maxwell's structure of light. The standing wave mechanism requires that an EM wave structure of light maintain nodes at both surfaces, at all times, yet the peaks and nodes of an EM wave propagate. The propagation of the nodes of an EM wave cannot form Planck's standing wave structure.
The standing wave mechanism also requires that the resonating (propagating) EM wave returns back to the exact position that it originated. This would result in the standing waves remaining in the cavity of the black-body yet experimentally light exits the black-body. To explain the light that exists the black-body wave theory implies that the ray of the EM wave, ricochets off the interior surfaces of the black-body, at various angles, and consequently existing the black-body through an aperture (fig ). The various angles of the ricocheting EM wave is not forming the standing wave structure. The standing wave structure requires that the EM wave structure propagates back to the origin position. Wave theory is using two conflicting mechanisms to describe the light within the black-body. The standing wave structure and the ricocheting wave structure are two incompatible and contradicting structures of light which violates logic.
Planck's standing wave mechanism originated from standing waves formed by an oscillating rope yet an oscillating rope is a mechanical wave that does not have the physical properties of and EM wave. The ends of a rope are connected to a stationary object. The vibrating rope forms standing waves by forming integer number wavelengths between ends. The rope is used as a medium that propels the energy of the wave to form the standing wave yet an EM wave is not a rope. The nodes of an EM wave propagate and do not form always form nodes at both surfaces as required in forming a standing wave structure; therefore, it is not physically possible for Maxwell's structure of light to form a standing wave structure.
There is no physical proof that light forms standing waves. Wiener (1890) used fringes formed on a photographic film to demonstrate the existence of standing waves of light yet Wiener explanation would require that the incident light beam is coherent; however, sun and candle light also form fringes on a photographic film yet sun and candle light is not coherent; therefore, Wiener justification that light forms standing waves is invalid.
Planck assumed that the energy of the standing waves could take on only certain discrete values,
E = 0, dE, 2dE, 3dE, 4dE...........................................31
Planck than stated that the energy dE was proportion to the frequency,
dE oc f....................................................................32
The discrete energies of equation 31 are represented with,
dE = hf' - hf"..............................................................33
Consequently, Planck's discrete energy equation is derived from equations 32 and 33,
E = hf........................................................................34
Planck assumed that the EM wave that are contained within a box could only form discrete energy that are describe with a frequency since the standing waves are only formed at specific wavelengths. It is required that the length of the box and therefore the length of the standing wave is constant since the constant length of the standing wave forms the discrete energies. Example, using a 6 cm box, 600nm, 300nm and 200nm wavelengths form the alleged standing waves. A 600 nm wavelength standing wave froms a frequency of 5 x 10^14 Hz. A 300nm wavelength standing wave that forms the frequency of 1 x 10^15 Hz and the 200 nm standing wave forms a frequency of 1.5 x 10^15 Hz. Using equation 33, the energy dE for the wavelengths, 300nm and 600nm, is derived,
dE = hf' - hf" = .66 eV - .33 eV = .33 eV......................35
Using equation 33, the energy dE for the wavelengths, 200nm and 300nm, is derived,
dE = .66 eV - .99 eV = .33 eV....................................36
Planck's standing wave mechanism for a 6 cm box does not include the wavelengths between 600nm and 300nm yet experimentally 422nm light is emitted from a black-body. Planck's standing wave mechanism conflicts with the light emissions that are experimentally observed. Wave solve this problem by stating that the EM waves do not propagate normal to the surface and can form varying length standing waves yet the constant length of the standing waves forms the discrete energies; therefore, the assertion that the EM waves propagate in various direction within the black-body to explain the wavelength emission between 600 nm and 300 nm conflicts with Planck's standing wave mechanisms; therefore, Planck's standing wave mechanism conflicts with the experimental light emissions of the black-body effect.
The structure of light, within the black-body, is represented with standing waves of Maxwell's structure of light that is used to derive a discrete energy equation. Planck's discrete energy equation is then used to imply a particle structure of light yet Maxwell's structure of light is not a particle structure and cannot be used, in any form, to imply a particle structure. In addition, Planck's standing wave structure of light implies that the physical boundary, of the volume within the black-body, form the discrete energies. The wavelength of the wave structure determines rather or not a wave can form nodes at both surfaces, that form the standing wave structure, which forms Planck's discrete energy yet candle light forms the photoelectric effect and a candle flame is not forming standing waves; therefore, Planck's black-body discrete energy equation cannot be used to imply the discrete energy of light formed by a candle flame or any light outside the black-body. Planck discrete energy equation does not apply to light outside the black-body; consequently, Planck's discrete energy equation cannot be used to imply a particle (photon) structure of light.
The derivation of Planck's black-body spectrum equation is described. Boltzmann's gas molecule kinetic energy distribution equation,
P(E) = [e^(-E/kT)]/kT.........................................................37
where
E = (1/2)mv^2.................................................................38
Equation 34 is used to derive the law of equipartition of energy. The law of equipartition of energy is a gas molecule kinetic energy equation.
E = {inter[EP(E)dE]}/{inter[P(E)dE]} = kT..........................39
.......(limits 0 to infinity)
There is a problem with Boltzmann's equation (equ 26). At the zero energy when the velocity of the gas molecule is zero, the maximum number of gas molecules is described which is not experimentally observed. The maximum number of gas molecule energies is a value between zero velocity and the maximum velocity. Boltzmann's equation implies that the maximum number of gas molecule energies is formed when the velocity of the gas molecules is zero which is not experimentally observed. Therefore, Boltzmann's equations is invalid and the law of equipartition of energy using Boltzmann's equation are invalid.
Planck implies as the frequency approaches zero that the law of equipartition of energy approaches kT,
E ----> kT.....(f --->0)...................................40
Planck also states that as the frequency (f), approaches infinity, the total energy of the black-body emission approaches zero (Eisberg, p. 15),
E -----> 0......(f ----> oo).......................................41
Planck implies that euations 40 and 41 represent the law of equiparition of energy; however, equation 40 and 41 do not describe the law of equipartition of energy since the law of equipartition of energy is not a function of the frequency. Planck's justification is based on incompetence. The law of equipartition of energy describes gas molecules energy distribution that are a function of the velocity; therefore, the law of equipartition of energy cannot be used, in any form, to describe the energy emissions of the black-body radiation effect; consequently, Planck's justification that the average total energy of the black-body emission effect is a function of the frequency is invalid.
Planck uses the discrete energy equation (equ 34) in equation 39 and replaces the integrations (inter), of equation 39, with summations (sum) to form the average total energy equation that is a function of the frequency,
E(f) = {sum[EP(E)]}/{sum[P(E)] = hf/[(e^(hf/kt) - l]................42
.........(summation from 0 to infinite)
Planck's derivation of average total energy equation is invalid since the law of equipartition of energy is a function of the velocity. Planck uses the average total energy equation (equ 42) to derive the black-body intensity equation,
p(f) = {[8(pi)f^2]/c^2} {hf/[(e^(hf/kt) - l]}.................................43
Equation 30 represents the energy emissions formed by the black-body; however, heat (kinetic energies of gas molecules) is not included in Planck's black-body spectrum equation. When the black-body temperature is constant, the kinetic energies of gas molecules are not dependent on the frequency. The energies distrubution of a gas molecules is determined by the velocity; therefore, Planck's black-body spectrum equation omits the most predominate energy emission formed within the black-body; consequently, Planck's black-body spectrum equation (equ 43) is invalid. Planck's black-body derivation is an intentional deception and manipulation.
The black-body intensity curve is formed using five different measuring devises:
1. Radio waves (circuits)
2. Microwaves (crystal)
3. Infrared (bolometer)
4. Light & UV (photomultiplier)
5. X-rays (ionization chamber)
Planck's, black-body intensity curve using a constant temperture (Eisberg, p. 19), leaves out heat energy since heat energy is not a function of the frequency yet heat energy is the most predominate energy emitted by the black-body. Consequently, Planck's black-body emission intensity curve is invalid.