Optica!
Ben Ito
10-12-05
The wave and particle duality theory of light is described. The aperture diffraction, transmission & reflection (T&R), polarization, and particle structures, based on a wave structure of light, violated logic. The optic particle theory of light is formed where the propagation, aperture diffraction and linear polarization effects of light are described using optic particles. The structure, energy and mass of an optic particle are described. This paper will prove that light has only a particle structure.
1. Introduction
The wave and particle problem of light is described. Huygens observed water waves and assumed that light propagated by the formation of secondary wavelets yet Huygens' propagation mechanism formed a secondary wavelet problem. Fresnel used interfering secondary wavelets to describe the aperture diffraction mechanism of light yet the constructively interfering secondary wavelets also formed a secondary wavelet problem. In 1888, Hertz discovered radio waves. Maxwell's equations were used to describe Hertz's radio waves. Maxwell then assumed that light also had a transverse EM (electromagnetic) wave structure; however, in 1898, the photoelectric effect proved that light was composed of particles which contradicted Maxwell's structure of light since Maxwell's structure is not a particle structure. Planck and Einstein indirectly used Maxwell's structure of light to derive discrete energy equations that were used to imply a particle (photon) structure of light yet Maxwell's structure of light cannot be used, in any form, to imply a particle structure of light. The quantum electrodynamics (QED) particle structures of light was derived by enclosing a segment of an EM wave in an infinitesimal size box (normalization); however, the field structure outside the box was not included in the QED box normalization. There are numerous problems associated with the wave and particle duality theory of light.
The optic particle theory of light is formed where the propagation, aperture diffraction and linear polarization effects of light are described using optic particles. The energy of an optic particle is represented with the photoelectric energy equation, and the photoelectric constant is derived using the atomic ionization energy. The mass equation of an optic particle is derived using the kinetic energy equation. This paper will prove that light has only a particle structure.
2. Huygens Principle
Huygens principle described the propagation of light. Huygens' candle flame formed secondary wavelets that originated from within the volume of a candle flame. Huygens did not know the wavelength of light and assumed that the wavelength of light was one third the width of the candle flame (fig 1) yet the wavelength of light is five orders of magnitude shorter than the width of the candle flame. The extremely short wavelength secondary wavelets, that originate from the volume of a candle flame cannot form Huygens' initial summed wave front.
A candle flame forms chromatic light yet Huygens propagation mechanism was based on mono-chromatic light. Huygens' propagation mechanism cannot describe the propagation of chromatic light. Consequently, Huygens principle is invalid.
Huygens' wave front formed secondary wavelets that propagated a distance of a wavelength. The far tangent points of the secondary wavelets' structures were combined (summed) to form the new wave front. When the new wave front was formed, the majority of the secondary wavelets' structures were arbitrarily eliminated (fig 2) which formed Huygens' secondary wavelet problem.
Huygens' secondary wavelets formed away from the source which implied that light created it's own energy which is not physically possible since a light beam is not a physical source. Huygens' propagation mechanism's secondary wavelets, that form away from the source, violated logic.
Wave theory used the spherical wave structure to derive the aperture diffraction intensity equation (Hecht, p. 464); consequently, Huygens' secondary wavelets were described with spherical waves. A spherical wave radiated structure in a radial pattern; consequently, spherical waves formed a retrogressive wave (fig 3) yet the retrogressive wave was not experimentally observed; a light beam propagating in the forward direction does not form a light beam that propagated in the reverse (retrogressive) direction. Kirchhoff eliminated the retrogressive wave by deriving a spherical wave that only formed structure in the forward direction (Longhurst, p. 223); however, by definition, a spherical wave forms structure in a radial pattern that includes the retrogressive direction. Kirchhoff's elimination of the retrogressive wave is invalid. The physical structure of a spherical wave has precedence over Kirchhoff's formulation. The non-existence of the retrogressive wave is experimental proof that Huygens' secondary wavelets are not spherical waves.
3. Huygens-Fresnel Principle
Huygens-Fresnel principle described the aperture diffraction effects of light. Fresnel used Huygens principle; the only difference was that the secondary wavelets interfere. Huygens' secondary wavelets undergo constructive and destructive interference. Fresnel implied that the destructive interfering secondary wavelets solved Huygens secondary wavelet problem; however, Huygens-Fresnel secondary wavelets also undergo constructive interference. When the new wave front was formed, the portions of the secondary wavelets' structures that formed constructive interference were arbitrarily eliminated which formed Huygens-Fresnel secondary wavelet problem.
Huygens-Fresnel aperture diffraction secondary wavelets described with spherical waves formed a forward and reverse (retrogressive) wave yet the retrogressive wave was not experimentally observed (fig 4); half of the aperture diffracted light does not propagate in the reverse direction. The non-existence of the retrogressive wave is experimental proof that the Huygens-Fresnel secondary wavelets are not spherical waves which conflicts with the derivation of the small square aperture diffraction intensity equation (Hecht, p. 464) that used the spherical wave equation to describe the secondary wavelets that form the aperture diffraction effect of light.
Huygens-Fresnel aperture diffraction mechanism's interfering secondary wavelets' formed an intensity problem. Huygens-Fresnel aperture diffraction pattern was formed by the interfering secondary wavelets. The formation of the dark fringes of the diffraction pattern were formed by destructive interference which would result in a reduction of the intensity of the diffraction pattern since the destructive interfering portions of the secondary wavelets do not contribute to the intensity. In the small circular aperture diffraction effect, 40% of the diffraction pattern is composed of dark fringes (fig 8); consequently, the destructive interference would result in more than a 40% reduction in the intensity of the diffraction pattern yet a significant reduction in the intensity is not experimentally observed. The intensity that enters the aperture equals the intensity that formed the aperture diffraction pattern which is experimental proof that Fresnel's interfering secondary wavelets do not form the aperture diffraction effects of light.
4. Fresnel's T&R Equations
The derivation of Fresnel's transmission-reflection (T&R) equations is described. The incident, transmission and reflection plane waves were represented with cosine wave structures (Hecht, p. 111). The boundary continuity of the cosine plane wave structures was represented with,
Icos(k'z) + Rcos(k'z) = Tcos(k"z).......................................1
The first boundary equation was derived using z = 0 in equation 1,
I + R = T.........................................................................2
The second boundary equation is (Hecht, p. 114) (Klein, p. 571),
n'I - n'R = n"T...................................................................3
Equation 2 and 3 were used to derive Fresnel's T&R amplitude equations,
T = (2n')/(n' + n")...........and........R = (n' - n")/(n' + n").........4a,b
For an air/glass surface, n' = 1 and n" = 1.5, the second boundary equation (equ 3) becomes,
I - R = (1.5)T....................................................................5
Using equations 2 and 5, the following inequality is formed,
I - R = (1.5)T > T = I + R ..................................................6
which forms,
-R > R............................................................................7
Equations 7 is invalid; consequently, equations 2 and 3 cannot be used to derive Fresnel's T&R equations. In addition, a air/glass surface forms a negative reflection amplitude (equ 4b), since n">n', which conflicts with the positive reflection amplitude of equation 2. The derivation of Fresnel's T&R equations, that used equations 2 and 3, is invalid.
The derivation of the T&R intensity equations are described. A light beam is incident normal to an air/glass boundary surface, n' = 1 (air) and n" = 1.5 (glass), forms the T&R amplitudes of,
T = (2n')/(n' + n") = .8.....&......R = (n' - n")/(n' + n") = -.2..... 8a,b
Squaring the results of equations 8a,b form the T&R intensities,
I = /T/^2 = .64.....&.......I = /R/^2 = .04....... ........................9a,b
Normalizing the result of equations 9a,b forms the T&R intensities of 94.9% and 5.1% which conflicts with the experimental T&R intensities of 96% and 4%. There is a 20% discrepancy between the theoretical (5.1%) and experimental (4%) reflection intensities; therefore, Fresnel's T&R equations cannot be used to derive the air/glass surface transmittance (96%) and reflectance (4%) intensities (Hecht, p. 121).
5. Polarization
The structure of natural light is described. The description of linear polarized light used natural light to represent non-polarized light. Natural light is composed of plane waves that electric field oscillation are pointing in various directions perpendicular to the axis of propagation (fig 6) which would annihilate the majority of the field structure. The structure of natural light is not physically possible.
The linear polarization effects of light, using two linear polarization filters, is described (Cutnell, p.736). The alleged structure of natural light interacted with the first linear polarization filter. The plane waves, of natural light, that field structures were oscillating along the linear polarization filter's transmission axis, propagated through the first polarization filter. Wave theory arbitrarily created the components of linear polarized light to explain the oscillating field structure that was emitted through the second polarization filter (fig 7); consequently, wave theory's mechanism of linear polarized light violated logic.
Circular and elliptical polarized light is described. The structure of circular and elliptical polarized light required a transverse plane wave of Maxwell's structure of light to describe the rotation of circular and elliptical polarized light. Maxwell's structure of light originated from an oscillating electric point source that formed a horizontal plane wave. A horizontal electric plane wave cannot form the rotation of circular and elliptical polarized light.
6. Maxwell's Structure of Light
The derivation of Maxwell's structure of light is described. Maxwell's structure of light was derived using Maxwell's equations,
Curl x E = dB/dt........&.........Curl x B = (-1/c) dE/dt..........10a,b
Equations 10a,b were expanded using Cartesian coordinate system (Hecht, p. 44), (Jenkins, p. 411),
(dE-z)/dy - (dE-y)/dz = -(dB-y)/dt,............(dE-x)/dz - (dE-z)/dx = -(dB-y)/dt........11
(dE-y)/dx - (dE-x)/dy = -(dB-z)/dt ............(dB-z)/dy - (dB-y)/dz = 1/c (dE-d)/dt..12
(dB-x)/dz - (dB-z)/dx = 1/c (dE-y)/dt..........(dB-y)/dx - (dB-x)/dy = 1/c (dE-z)/dt..13
The differential components that do not represent a field structure oscillating perpendicular to the z-axis were eliminated,
(dE-z)/dy, (dE-z)/dx, (dB-z)/dy, (dB-z)/dx . .......................14
The remaining differential components were used to derive Maxwell's structure of light,
E = E'cos(k'z - wt)x......&.......B = B'cos(k'z - wt)y............15a,b
Maxwell's structure of light originated from an oscillating electric point source. When an oscillating point source formed a positive charge, an electric field structure that points radially outward is formed (fig 8); consequently, an oscillating electric point source forms a horizontal electric plane wave. In addition, the oscillating field structure formed within an LRC circuit capacitor is a horizontal wave.
Maxwell's equation (10b) was derived using Ampere's law,
int(B dot dl) = u int[(J + a dE/dt)dS]....................................16
The (J) variable of Ampere's law (equ 16) is the current density. Maxwell stated that the electric displacement current density,
J = a dE/dt.........................................................................17
was formed between the plates of the capacitor. Maxwell's electric "current" density (equ 17) is invalid since "current" is not flowing across the plates of the capacitor (fig 9). The first charging capacitor plate accumulates electrons that induces a charge on the adjacent plate; the induced charge forms a current in the wire attached to the second plate; consequently, no current is propagating across the plates of the capacitor. Maxwell's equation (equ 10b) derived using equation 17 is invalid.
The continuous EM field structure, formed by an oscillating electric point source, is not a particle structure nor are the continuous EM planes of Maxwell's plane wave structure of light composed of discontinuous particles (fig 16). The photoelectric effect proved that light was composed of particle; consequently, Maxwell's structure of light is physically invalid.
7. Planck's Black-body Radiation
Planck's description of the black-body radiation is described. Planck derived a discrete energy equation by implying that standing waves of Maxwell's structure of light formed inside the cavity of the black-body (Eisberg, p. 8). An EM wave originated from a surface atom. The EM wave propagated to the adjacent surface and returned back to the original position. At all times, nodes of the EM wave formed at both surfaces yet the peaks and nodes of an EM wave propagate. A propagating EM wave cannot maintain the nodes of the standing wave at the surfaces. Consequently, Planck's standing wave structure is not physically possible. An EM wave is not a guitar string.
Planck implied that the alleged standing waves formed discrete energies describe with (Eisberg, p. 16).
E = hf.............................................................................18
Planck then assumed that the discrete energies of equation 18 represented a particle (photon) structure of light yet the alleged standing waves only formed within the cavity of the black-body; consequently, Planck's photon structure of light does not apply to light outside the black-body. In addition, Planck's discrete energy equation (equ 18) is derived using standing waves of Maxwell's 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 of light.
The derivation of Planck's black-body average total energy equation is described. Boltzmann's gas molecule kinetic energy distribution equation was used,
P(E) = [e^(-E/kT)]/kT.........................................................19
where
E = (1/2)mv^2.........................................................20
There is a problem with Boltzmann's equation (equ 19); at zero energy (v = 0), the maximum number of gas molecules is formed yet experimentally the energy that represents the maximum number of gas molecules is between zero velocity and the maximum velocity; therefore, Boltzmann's equation is invalid. The law of equipartition of energy derived using Boltzmann's equation is also invalid.
The law of equipartition of energy was derived using Boltzmann's equation (equ 19),
E = {int[EP(E)dE]}/{int[P(E)dE]} = kT...........................21
.......(limits 0 to infinity)
Planck implied that as the frequency approached zero, the energy approached the law of equipartition of energy (kT),
E ---> kT.....(f ---> 0).......................................................22
Planck also stated that as the frequency approached infinity, the total energy of the black-body emission approached zero (Eisberg, p. 15),
E --->0........(f ---> oo)......................................................23
Planck was comparing equations 22 and 23 with the law of equipartition of energy equation yet the law of equipartition of energy equation was derived using Boltzmann's equation that was a function of the velocity (equ 19 and 20). The derivation of the law of equipartition of energy cannot be used to derive the frequency dependent black-body average total energy equation.
Planck used the discrete energy equation (equ 18) in equation 21 and replaced the integrations (int) with summations (sum) to form the black-body average total energy equation that was a function of the frequency,
E(f) = {sum[EP(E)]}/{sum[P(E)] = hf/[(e^(hf/kt) - l]...............24
.........(summation from 0 to infinity)
The alleged black-body average total energy equation (equ 24) was used to derive Planck's black-body intensity equation,
p(f) = {[8(pi)f^2]/c^2} {hf/[(e^(hf/kt) - l]}.................................25
Planck's black-body intensity equation (equ 25) represents the energy emissions formed by the black-body; however, when the temperature is constant (T = 5000 degrees), heat (kinetic energies of gas molecules) is not included in Planck's black-body intensity equation since the kinetic energies of gas molecules are not dependent on the frequency. Planck's black-body intensity equation omits the most predominate energy emission formed within the black-body; consequently, Planck's black-body intensity equation is invalid.
8. Einstein Energy Quanta
The derivation of Einstein's energy quanta equation (1905) used Wien's black-body radiation equation (Nye, p. 468),
p = a(f^3)e^(-bf/T)............................................................26
Wien's black-body radiation equation (equ 26) was used in the derivation of the entropy equation,
S = vY(p,f)df = E/bf ln{[E/(vaf^3df )] - l}...............................27
The change in entropy was represented with,
S - S' = [E/(bf)] ln(v/v').....................................................28
which formed,
S - S' = [R/N] ln[(v/v')^(NE/Rbf)]........................................29
The NE/Rbf of equation 29 was equated to one,
NE/Rbf = 1 -------------> E = Rbf/N......................................30a,b
Einstein's energy quanta equation (equ 30b) was used to imply a particle (photon) structure of light. Einstein's derivation of the energy quanta equation used Wien's black-body radiation equation (equ 26). Wien's black-body radiation equation described radio waves and light emissions; consequently, the frequency variable of Wien's black-body radiation equation implied Maxwell's 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; consequently, Einstein's energy quanta equation cannot be used to imply a particle (photon) structure of light.
Einstein's energy quanta equation was derived using Wien's black-body radiation equation (equ 26) that was a function of the frequency. Wien's black-body radiation equation does not include heat energy emissions since heat energy (kinetic energies of gas molecules) is not a function of the velocity. The most predominate energy emission of the black-body radiation effect was not include in Wien's black-body radiation equation; consequently, the derivation of Einstein's energy quanta equation is invalid.
9. Quantum Electrodynamics
The derivation of the quantum electrodynamic (QED) particle structure of light is described (Marcuse, p. 60). An electromagnetic (EM) wave structure of light was enclosed in an infinitesimal size box (normalization) yet the majority of the field structure was not included in the QED box normalization. Consequently, the QED particle structure of light is invalid.
10. Optic Particle Theory
The propagation of light is described using optic particles. The velocity of light is measured at approximately 3 x 10^8 m/s, and the photoelectric effect prove that light is composed of optic particles; consequently, a stream of optic particle that compose a light beam are propagating at the velocity of light.
The aperture diffraction effect of light is described using optic particles. Only when light contacts the aperture edge does the aperture diffraction effect occur. A laser beam that passes through an aperture, without contacting the aperture edge, does not form a diffraction pattern; consequently, the interaction of light with the aperture edge is an essential component in the formation of the aperture diffraction effect of light. Also, the total light intensity that enters the aperture equals the total light intensity that forms the aperture diffraction pattern; consequently, optic particles do not interfere with each other to form the aperture diffraction pattern. The optic particles that contact the aperture edge activate the aperture edge atoms which forms an aperture edge effect. The aperture edge effect forms in the aperture and directs the optic particles, that enter the aperture, to the intensity points of the diffraction pattern (fig 10).
The linear polarization effects of light formed by two linear polarization filters is described using optic particles. Non-polarized light is composed of optic particles that are randomly distributed in the light beam. The first linear polarization filter aligns the optic particles, in rows, with the transmission axis (fig 11). The second polarization filter reads the alignment (rows) of the polarized light and shifts the alignment to the second polarization filter's transmission axis. The angle (A) formed between the first and second linear polarization filters' transmission axes forms the polarization alignment shift that determines the intensity emitted through the second polarization filter where I' is the maximum intensity emitted through the polarization filters when the polarization filters' transmission axes are aligned,
I = I' cos(A) ............................................................31
The structure of an optic particle is described. To form the photoelectric effect of light, the optic particle's structure must completely interact with a single photoelectric surface atom to transfers the entire structure (energy) of the optic particle to a single surface atom; consequently, the frontal diameter of the optic particle must be smaller than the diameter of the photoelectric surface atom.
The energy of an optic particle is described with the frequency dependent photoelectric energy equation,
E = Cf............................................................................32
The derivation of the photoelectric optic particle's energy is based on the entire structure (energy) of an optic particle being absorbed by a single photoelectric atom. The energy of the optic particle ionizes the surface atom and forms the emitted electron's kinetic energy; consequently, the sum of the atomic ionization energy (IE) and the emitted electron's maximum kinetic energy (KE) are used to derive the energy (E) of an optic particle,
IE + KE = E ...................................................................33
A sodium photoelectric atom is used to derive the energy (E) of an optic particle. The ionization energy (IE) of a sodium atom is 5.14 eV. A 420 nm light beam emits a .65 eV maximum kinetic energy (KE) electron when interacting with a sodium surface . The energy of a 420 nm optic particle is derived using equation 33,
5.14eV + .65eV = 5.8eV..................................................33
The photoelectric constant is derived using a 5.8 eV energy (420 nm) optic particle that forms a frequency of 6.1 x 10^14 Hz,
C = E/f = (5.8eV)/(6.1 x 10^14) = 9.5 x 10^(-16) eV-s..........34
The mass equation of an optic particle is derived. Lebedeve's light experiment (1901) proved that the optic particles that compose a light beam have a mass. A thin mirror is suspended with a torsion string (fig 12). A light beam incident on the mirror rotates the mirror which proves that the optic particle that composes a light beam have a mass. The mass equation of an optic particle is derived using the kinetic energy equation,
m = 2E/c^2.....................................................................35
The mass of a 5.8 eV optic particle is derived using equation 35,,
m = 2(5.8 Ev)/c^2 = 1 x 10^(-35) kg...................................36
11. Conclusion
Huygens principle formed a secondary wavelet problem; when the new wave front was formed, the majority of the secondary wavelets' structures were arbitrarily eliminated. In addition, Huygens secondary wavelets described with spherical waves formed a retrogressive wave that was not experimentally observed. The non-existence of the retrogressive wave is experimental proof that Huygens secondary wavelets are not spherical waves.
Huygens-Fresnel principle described the aperture diffraction effects of light yet when the new wave front was formed, the constructive interfering portions of the secondary wavelets structure were arbitrarily eliminated which formed Huygens-Fresnel's secondary wavelet problem. Huygens-Fresnel principle also formed a retrogressive wave problem; therefore, wave theory's aperture diffraction intensity equations, that used the spherical wave equation, are invalid.
The continuous EM planes of Maxwell's structure of light are not composed of discontinuous particles. The photoelectric effect proved that light was composed of discontinuous particles which conflicted with Maxwell's structure of light. The photoelectric effect of light proved that Maxwell's structure of light does not represent the physical structure of light.
Planck used standing waves of Maxwell's structure of light to derive a discrete energy equation. Planck then assumed that the discrete energy equation represented a particle (photon) structure of light; however, Maxwell's structure of light is not a a particle structure and cannot be used, in any form, to imply a particle structure; consequently, Planck's implied particle (photon) structure of light is invalid.
Einstein also derived an energy quanta equation that was used to imply a particle (photon) structure of light; however, Einstein used Wien's black-body radiation equation. The frequency variable of Wien's black-body radiation equation implied Maxwell's structure of light; consequently, the Einstein's energy quanta equation cannot be used to imply a particle (photon) structure of light.
The optic particle theory of light proves that light has only a particle structure. The aperture diffraction effects of light are formed by optic particles that activate the aperture edge atoms and produce an aperture edge effect. The aperture edge effect forms in the aperture and directs the optic particles, that enter the aperture, to the intensity points of the diffraction pattern.
The linear polarization effects of light formed by two linear polarization filters is described using optic particles. Non-polarized light is composed of optic particles that are randomly distributed in the light beam. The first linear polarization filter aligns the optic particles, in rows, with the transmission axis. The second polarization filter reads the alignment (rows) of the polarized light and shifts the alignment to the second polarization filter's transmission axis.
The photoelectric constant is derived using a sodium surface. The energy of a 420 nm optic particle is derived by adding the ionization energy and the emitted electron's maximum kinetic energy,
5.14eV + .65eV = 5.8eV.
The photoelectric constant is derived using a 5.8eV (420 nm) optic particle,
C = E/f = 9.5 x 10^(-16) eV-s.
Lebedeve's light experiment (1901) proved that the optic particles that compose a light beam have a mass. The mass equation of an optic particle is derived using the kinetic energy equation,
m = 2E/c^2.
The mass of a 5.8 eV optic particle is,
m = 2(5.8 eV)/c^2 = 1 x 10^(-35) kg.
The propagation, aperture diffraction and linear polarization effects of light are described with optic particles. The optic particles structure, mass, and energy are describe; consequently, light has only a particle structure.
12. References
John Cutnell & Kenneth Johnson. "Physics". 6th ed. John Wiley.
Robert Eisberg and Robert Resnick. "Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles". John Wiley & Sons. 1974.
Eugene Hecht. "Optics". 4th ed. Addison-Wesley. 2002.
Miles Klein. "Optics". John Wiley. 1970.
Francis A. Jenkins and Harvey White. "Fundamentals of Optics". 3rd ed. McGraw-Hill. 1957.
R.S. Longhurst. "Geometrical and Physical Optics". 2nd ed. John Wiley. 1986.
Dietrich Marcuse. "Engineering Quantum Electrodynamics". Harcourt, Brace & World. 1970.
Mary Jo Nye. "The Question of the Atom". Tomash. 1984.
Mahatma Gandhi