Optica!

Ben Tsutomu Ito

12-14-04

I will prove that the wave-particle duality theory of light is invalid then form a particle theory of light that describes the aperture diffraction, and transmission & reflection effects of light. The optic particle's energy is represented with the photoelectric energy equation; the constant (h) is derived using the atomic ionization energy and emitted electron's kinetic energy. In addition, the optic particle's mass equation is derived using the kinetic energy equation.

1. Introduction

This paper addresses the wave and particle problem of light. The reason that the wave and particle problem of light exist is because of the enormous velocity and infinitesimal size of the optic particles that composed a light beam make the isolation of a single optic particle difficult.

"during most of time, diverse opinions have been held, based on conflicting theories and speculations or on apparently conflicting experimental evidence." (Monk, p. 100)

The photoelectric effect proves that light is composed of particles which conflicts with Maxwell's EM [electromagnetic] plane wave structure of light.

"we will soon encounter evidence [photoelectric effect] that light and other radiation carry energy in discrete units a fact that cannot be explained by a wave theory." (Michels, p. 357)

The justification of the wave theory of light is the assumption that interacting waves form the wave effects of light [aperture diffraction and T&R], and that Maxwell's plane wave structure of light forms a discrete energy and structure [Planck's blackbox]; consequently, the wave theory of light becomes the wave-particle duality theory of light where light has both wave and particles properties.

"a wave-particle [duality] is "against common sense" or "paradoxical" or, worse still, that "scientists cannot make up their minds"." (Asimov, p. 136)

The wave-particle duality theory of light is justified with Huygens's principle, Fresnel's T&R [transmission & reflection] equations, polarization, Maxwell's structure of light, Einstein's photoelectric quanta, quantum mechanic wave packet, and quantum electrodynamics (QED).

I will prove that the wave theory of light is invalid. I will then form a particle theory of light that describes the aperture diffraction, and T&R [transmission & reflection] effects of light. The optic particle's energy is described using the photoelectric energy equation; the constant (h) of potassium surface is derived using the potassium atom's ionization and emitted electron's kinetic energies. The optic particle's mass equation is derived using the kinetic energy equation.

2. Huygens Principle

a. Wave Front

Huygens's principle describes wave theories' propagation, and aperture diffraction mechanisms of light. Huygens implies that a candle flame emits spherical waves that when summed form a wave front (fig 1). However, a candle flame cannot form a wave front since:

1. A candle flame's alleged spherical wave emissions are chromatic.

2. Light has very short wavelengths and originates from within the volume of a candle flame.

Huygens's implies that the point source emission described with spherical waves, when summed, forms a coherent wave front (fig 2) yet candle light is chromatic. Chromatic spherical waves have different wavelengths; whereas, coherent light is mono-chromatic. The sum of different wavelength spherical waves cannot form a coherent wave front as implied by Huygens's principle. Candle light cannot form a coherent wave front.

Huygens's spherical wave emissions originate from within the volume of a candle flame which cannot form the alignment, of the spherical waves, required to form a coherent wave front (fig 3). The point source emissions are randomly distributed within the volume of the candle flame. Randomly distributed point sources within a volume cannot form the coherency of a wave front. The short wavelengths of light do not allow the volume of a source to from a wave front.

"But notice what happen as the waves move farther from there source. The chaos of ripples smooths out, and if one imagines not three particles but million, it becomes smoother still. By the time they reach us from a distant star theory will have formed a single, simple ripple." (Park, p. 217)

Huygens and Parks are assuming that the unaligned chromatic spherical waves' structures becomes aligned after propagating a large distance. However, the original spherical wave emissions are unaligned and chromatic. Since the spherical wave originate from a volume, a large distance of propagation cannot align the spherical waves' structures. The alignment of the spherical waves, that is required to form a coherent wave front, is create at the source. Huygens and Parks are assuming that the wavelengths of candle light are large compared to the thickness of the candle flame thus forming a coherent wave front by using a large distance from the source, however, that argument is only valid if the emitted wavelengths are larger than the volume that the spherical wave originate from. However, the thichness of the candle flame and the volume of the star is much larger than the wavelengths of light. Consequently, candle and star light do not form a coherent wave structure as implied by Huygens.

b. Propagation

Huygens's propagation mechanism of light requires the existence of Huygens's wave front. Huygens's alleged wave front becomes a LOPS [line-of-point-sources]. The point-sources are described with secondary wavelets that structure disperse (propagate) a distance of a wavelength (Resnick, p. ) only in the forward direction. The sum of infinitesimal size segments, of the outer portion of the secondary waves form the next wave front (fig 4). The newly created wave front becomes another LOPS. This mechanism repeats over and over, at intervals of a wavelength (fig 5).

"light was propagated by secondary actions. This is the basic concept that later was attributed to Huygens. The main reason for Girmaldi's objection was that if this type of propagation were true, then the points reached by light would also become sources of light" (Ronchi, p. ).

The majority (99%) of the LOPS secondary wavelets' structures are eliminated after each new wave front is formed since only infinitesimal size segments, of the LOPS' secondary wavelets, form the next wave front. Huygens's propagation mechanism repetitively destroys the majority of the LOPS secondary wavelets' structures then repetitively recreating the entire LOPS secondary wavelets at intervals of a wavelength. Consequently, each wave front becomes a source; the energy of the source created then destroyed, at intervals of a wavelength in Huygen's propagation mechanism. Huygens's propagation mechanics is an extreme violation of the law of conservation of energy. Huygens's propagation mechanism does not describe the physical propagation of light.

c. Retrogresive Wave

Huygens's aperture diffraction mechanism is described. Huygens's alleged wave front forms in the aperture and becomes a LOPS [line-of-point-sources] that produces the aperture diffraction effects of light. Huygens's aperture diffraction mechanism forms a LOPS in the plane of the aperture. Huygens's LOPS secondary wavelets are described with spherical waves.

"Thus is the case of a single point source the closed surface S may be taken as a spherical wave front." (Longhurst, p. 192)

A spherical wave has a symmetric structure; therefore, the LOPS described with spherical waves forms a retrogressive wave that propagates in the reverse direction (fig 6). Huygens assumed that the retrogressive wave does not exist.

"Huygens simply assumed that such "reflected" [retrogressive] waves do not exist, that is in effect, that the amplitude of the secondary wavelets in the backwards direction is zero" (Reimann, p. 914)

The retrogressive wave is not experimentally observed; half of the aperture diffracted light does not propagate in the reverse [retrogressive] direction.

"Had we drawn the [secondary wavelets] as spheres, there would have been a backward [retrogressive wave] moving toward the source-something that is not observed." (Hecht, p. 105)

Kirchhoff's formulation of Huygens's principle (Longhurst, p. 193) eliminates the retrogressive wave by deriving a non-symmetric spherical wave structure described with an obliquity factor.

"The absence of the direct back-wave [retrogressive wave] is taken care of by the obliquity factor" (Longhurst, p. 193)

Kirchhoff's non-symmetric spherical waves are used to eliminate the retrogressive wave.

"It is obviously necessary to postulate the existence of an obliquity factor in the amplitude of the secondary wavelets whose value is maximum in the forward direction an falls away with increasing angle made with this direction, to become zero in the backward [retrogressive] direction." (Reimann, p. 915).

However, by definition, a spherical wave has a symmetric structure.

"a description of spherical waves, waves that are spherically symmetrical" (Hecht, p. 29)

Huygens's LOPS's spherical waves forms a retrogressive wave yet experimentally, the retrogressive wave is not observed. Kirchhoff's formulation of Huygens's principle (Longhurst, p. 193) is used to justify the non-existence of the retrogressive wave by implying that a spherical wave does not form a symmetric structure yet by definition a spherical wave has a symmetric structure. The experimental non-existence of the retrogressive wave is physical proof that Huygens's LOPS do not physically exist.

d. Aperture diffraction

According to Huygens, the intensity and dark areas of the aperture diffraction pattern are formed by the partial and complete annihilation of the diffracted waves that interact at the diffraction screen. The partial and completely annihilated waves do not contribute to the total intensity of the diffraction pattern. The formation of the intensity and dark areas, by the partial and complete annihilation of the diffracted waves would substantially reduce the total intensity of the aperture diffraction effect yet a significant reduction in the aperture diffraction effect's total intensity is not experimentally observed. In the small square aperture diffraction experiment, 80% of the aperture diffraction pattern is formed of dark areas (fig 8) which would reduce the total intensity of the aperture diffraction pattern by more than 80%, using Huygens's aperture diffraction mechanism, yet a significant reduction in the aperture diffraction effect's total intensity is not experimentally observed which is physical proof that Huygens's aperture diffraction interacting wave mechanism does not describe the aperture diffraction effects of light.

3. Fresnel's T&R Equations

The derivation of Fresnel's T&R equations is described. An incident light beam that interacts normal to a flat glass surface is used. The incident(I), transmission(T), and reflection(R) light beams are represented with the following plane wave equations (Hecht, p. 111),

I = I'cos(kz - wt), (equ l)

T = T'cos(kz - wt), (equ 2)

R = R'cos(kz - wt).(equ 3)

Hecht states that "at the boundary at any time and any point" (Hecht, p. 112)

I' + R' = T'.(equ 4)

However, equation 4 is only valid for t=0; example, when wt = .1 equation 4 is not formed; therefore, Hecht statement that equation 4 represents the boundary condition at any time (t) is false. Hecht then states that

"the continuity of the tangential component of B/u requires"

that at the glass surface, the derivative of the incident and reflection plane waves equal the derivative of the transmission plane wave (Hecht, p. 113).

-I'k'cos(kz - wt) + R'k'cos(kz - wt) = T'k"cos(kz - wt) (equ 5)

However, the derivative of a cosine is a sine. The cosine incident, transmission and reflection plane waves (equ 1,2 & 3) do not form equation 5. Example, using incident plane wave (equ 1) and z=0 and t = 0,

(d/dz)I'cos(kz - wt) = -kI'sin(kz - wt) = 0. (equ 6)

Consequently, equation 5 cannot be derived using the derivatives of equations 1,2 and 3. Fresnel's T&R derivation is based on a contradiction. To form equation 4, the incident, transmission and reflection plane waves must be represented with cosine yet to form equation 5 the plane waves must be represented with sine. Both equations 4 and 5 are the foundation of Fresnel's T&R derivation. Wave theory uses the imaginary exponential to represent the sinusoidal plane wave representation yet when the imaginary exponential is expanded,

e^(iA) = cos(A) - isin(A), (equ 7)

the plane wave is either a sine or cosine structure not both. Consequently, Fresnel's uses conflicting sinusoidal structures to form equations 4 and 5.

Fresnel's then uses equations 4 and 5, to derive the Fresnel's equations. Using z=0 and t=0, in equation 5,

-I'k' + R'k' = T'k". (equ 8)

Using

I' + R' = T', (equ 9)

equation 8 and n' = k' and n" = k", Fresnel's equations are derived,

r = (n' - n")/(n' + n"), (equ 10)

t = 2n'/(n' + n"). (equ 11)

However, when n' = 1 and n" = 1.5,

r = .2 and t = .8 (equ 12a,b).

The intensity of lignt is

I = E^2 (equ 13)

since Fresnel's equations represent the amplitude of the waves at the glass surface, Fresnel's equations are used in equation 13 to derive the intensity equation. Squaring equations 12a,b,

r^2 = .04 and t^2 = .64 (equ 14)

Fresnel's T&R equations have a problem. The experimental reflection of light through glass is approximately 4% and the transmission is 96%.

Wave theory than invents a reflectance and transmittance equations that are used to describe the intensity,

R = [(n' - n")/(n' + n")]^2, (equ 15)

T = 4n'n"/(n' + n")^2. (equ 16)

The amplitude of the electric field of Fresnel's equations (equ 10 & 11) determines the intensity of the reflection and transmission light beams (equ 13). The square root of equation 15 and 16 would from Fresnel's amplitude equations. However, the transmittance equation does not form Fresnel's transmission equation when squared rooted,

[4n'n"/(n' + n")^2]^(1/2) =/ 2n'/(n' + n"). (equ 17)

(n'n")^(1/2) = n' (equ 18).

The reflectance and transmittance equations do not represent the transmission and reflection intensities of light.

The incident (I) and reflection (R) light beams are propagating in opposite directions. The addition of the incident and reflection light beams' amplitudes cannot be described with equation 4 since the amplitude of the propagating waves are changing, at a fix point, on the glass surface. The propagation of light would not form equation 4. Fresnel's boundary equation (equ 4) is derived using non-propagating plane wave structure (t=0) yet light experimentally propagates.

The derivation of Fresnel's transmission/reflection equations, and the reflectance/transmittance equations are invalid and conflict with the propagation of light.

4. Polarization

The polarization of light is described. According to polarization, the incident (natural) light is composed of many plane waves that field structures oscillate in different directions (fig 9) which is physically not possible since the sum of natural light's field structures would annihilated.

Wave theories' two filter polarization mechanism is described. The alleged nature light is emitted through a linear polarization filter and is said to form polarized light. According to wave theory, the polarization filter only emits the nature light that plane waves resultant field structure oscillates along the transmission axis of the polarization filter. A second polarization filter is placed in the path of the polarized light (fig ). As the second polarization filter is rotated, the intensity of the light that exist the second filters is altered. Wave theory implies that the components of the resultant wave are emitted thought the second filter; consequently, wave theory uses two completely different polarization mechanism to explain the polarization effects of light. The first filter only emits waves that resultant field structure is oscillating along the first polarization filter's transmission axis yet the second filter emits light that is not aligned with the transmission axis. The second polarization filter allows the components of the resultant vector to exist the second polarization filter is which is a completely different mechanism then the mechanism that describes light that is emitted by the first polarization filter.

"to develop an understanding of the techniques used to generate, change, and manipulate it to fit our needs." (Hecth, P. 331).

Wave theory has created a new wave structure of (nature) light and is using two completely different and contradicting mechanisms to describe the polarization effects of light.

Circular polarized light is described. Left-circular polarized light is represented with (Hecht, p. 328),

E = E'[cos(kz - wt)i - sin(kz -wt)j], (equ 19)

However, two field structures do not act independently as implied by the mechanism of circular polarized light. The field structure described with equation 19 would superposition and a resultant field structure would form. Circular polarized light is implying that two electric fields act independently which is not physically possible. When the field structure of equation 19 are summed the frequency and wavelength of the circular polarized light would change; however, experimentally, when light is emitted through a circular or elliptical polarization filter the frequency and wavelength of the emitted light beam does not change; therefore, the mechanism of circular and elliptical polarization are invalid.

4. Maxwell's Structure of Light

Maxwell's structure of light described. Maxwell's structure of light is derived from Maxwell's equations (Jenkins, p. 408),

(delta)xE = - dB/dt and (delta)xB = ue(dE)/dt. (equ 20a,b)

A continuous and dispersive field structure of an EM [electromagnetic] spherical wave is represented with Maxwell's equations. The current displacement is not related to Maxwell's derivation of the EM plane wave structure of light since the electric field formed by the two plates of the current displacement only occurs between the plates (fig 10). Maxwell's EM plane wave structure of light has an arbitrary length that is not bounded by two plates. Therefore, Maxwell's structure of light is not derived from the current displacement.

Maxwell's derivation of the EM plane wave structure of light describes. A spherical wave that is formed by an oscillating point source is approximated with a plane wave structure (fig 11). As the distance from the source increase the spherical wave's dispersive and continuous EM field structure can be approximated with a plane wave structure by mathematically by expanding equations 20a,b using rectangular coordinate system then eliminating the expanded differentials (dE(z)/dt, dB(z)/dy,.........) that do not form a field structure on the x-y plane (fig 12); consequently, Maxwell's plane wave approximation eliminates the majority of the spherical waves field structure. The plane wave approximation is only valid if light has a non-discrete structure since the elimination of the plane wave approximation is based on a continuous nono-discrete structure of an EM spherical wave. If light has a discrete structure then the all of the field structure must be included, and the plane wave approximation would not be possible. The plane wave approximation's remaining differentials equations are differentiated a second time to form a second order differential equations that solution produce Maxwell's EM plane wave structure of light,

E = E'cos(kz - wt)y and B = cos(kz - wt)x (equ 21a,b)

Using the same elimination method, the plane waves propagating in the x and y direction can also be derive,

E = E'cos(kx - wt)y and B = cos(kx - wt)z (equ 22a,b)

E = E'cos(ky - wt)x and B = cos(ky - wt)z (equ 23a,b)

Maxwell's equations represent the symmetric structure of a spherical wave. The continuous and dispersive field structure of an EM spherical wave is approximated with Maxwell's plane wave structure of light (equ 21,22 or 23). The derivation of the plane wave from a spherical wave is base on a continuous structure of light. According to the wave theory of light, Maxwell's plane wave structure of light is structurally identical to a radio wave; the only difference being the wavelengths since Maxwell's structure of light is derived from Maxwell's (radio wave) equations,

"In 1873 Maxwell advanced his theory that light waves where electromagnetic waves and, apart from wavelength, theory were identical with all waves [radio waves] which could be obtained by radiation from electrical circuits" (Ronchi, p. 263)

Yet continuous and dispersive EM field structure is not a particle structure; therefore, Maxwell's structure of light is not a particle structure yet the photoelectric effect proves that light is composed of particles.

"we will soon encounter evidence [photoelectric] that light and other radiation carry energy in discrete units a fact that cannot be explained by a wave theory." (Michels, p. 357)

In the photoelectric effect experiment, when the intensity of the incident beam is increased, expected, using Maxwell's structure of light, is an increase in the kinetic energy of the emitted photoelectric electrons; however, experimentally the photoelectric electron's kinetic energy is unaffected by the change in the incident beam's intensity.

"According to Maxwell, a light waves energy is proportional to its brightness or as scientist say, its intensity. By increasing the beam's intensity one should be hitting the zinc with arbitrarily large amounts of energy. Something should happen. Below the threshold frequency nothing did. For the same reason, once the electrons are effected, increasing the light intensity should increase the electron energy. Again nothing." (Rothman, p. 155)

The photoelectric effect proves that light is composed of particles since only a particle structure of light can explain the results of the photoelectric effect of light.

The double slit aperture diffraction experiment proves that Maxwell's continuous plane wave structure of light cannot not be used to represent light. Maxwell's plane wave structure of light is formed of a continuous EM plane structure. If Maxwell's plane wave is used to represent the physical structure of light then a laser beam's width would represent the width of the plane wave. During the double slit diffraction experiment, when a laser beam is represented with Maxwell's plane wave structure of light, the plane wave interacts with both slits. Light is emitted through both slits, (fig 13)

"How can one photon pass through two slits? One way to restate the question is, how can light have both particle and wave properties in the same experiment (Orear, p. 306).

A photon described with a plane wave cannot interact with the two slits of the double slit aperture diffraction effect of light. The double slit experiment prove that light has a discrete structure since the double slit experiment emits two discrete structures from a plane of the alleged plane wave structure of light.

Maxwell assumed that since radio waves and light propagated at the same velocity that both have the same continuous EM structure.

"he [Maxwell] obtained a numerical result equal to the measured speed of light! The conclusion was inescapable---light was "an electromagnetic disturbance in the form of waves" (Hecht, p. 6)

Light and radio waves may propagate at the same velocity; however, this does not justify that both light has the continuous structure of a radio wave.

"Maxwell jumped to a conclusion. He concluded that light is one form of electromagnetic wave. He had no real evidence of this, but he felt that the coincidence of that "tremendous speed was not a coincidence at all." (Bova, p. 159)

Maxwell's structure of light is based on the assumption that since light and EM radio waves have the same velocity that their structures are also identical yet the photoelectric effect and the double slit aperture diffraction experiments prove that light is a composed of particles which conflicts with Maxwell's plane wave structure of light since a particle structure is diametrical to a continuous structure of a plane wave. Yet quantum radio frequency physics is used to justify that a continuous radio wave is composed of particles.

"It [quantum frequency radio physics] is based on the phenomenon of resonant interaction with matter of electromagnetic radiation in the microwave and RF [radio frequency] regions. As a result of this interaction, a quantum of electromagnetic energy is either radiated or absorbed." (Stepin, p. 23)

"Radio waves are generated and detected as an oscillating electric or magnetic field, and it is unusual (but not unknown) to hear a physicists refer to a quantum process in the radio frequency spectrum. (Smith, p. 1)

However, an emitted "quantum" of an EM radio wave always disperses during propagation; consequently, an emitted quantum of a radio wave is not a a particles structure since a dispersive and continuous EM field structure is not a particle structure. A particle structure requires that the structure remains discrete after propagating yet a radio waves structure always disperses during propagation. The photoelectric effect proves that light is composed of particles. Light and a radio waves are not related as implied when Maxwell's structure of light is derived from Maxwell's equations. Light does not have the characteristics of an EM radio wave since:

1. Light is composed of particles yet a radio wave has a continuous EM structure.

2. Light forms the photoelectric effect; whereas, a radio wave does not from the photoelectric effect.

3. Light forms wavelengths between 390nm-790nm; however, radio waves have wavelengths between lm-100km.

4. Light forms a visible intensity yet a radio waves intensity is not visible.

5. Light does not propagate through an opaque medium yet a radio wave propagates through a non-conducting opaque medium.

Consequently, light is not an electromagnetic phenomenon as implied by Maxwell.

The energy of Maxwell's structure of light is described. The fundamental problem with Maxwell's structure of light is that an EM plane wave has an arbitrary length.The arbitrary length of Maxwell's plane wave structure of light is required in the derivation of the aperture diffraction intensity equations. The distance between the aperture and the diffraction screen point where the plane wave interacts determines the length of the plane wave; These distances vary for each point in the aperture. The distance between a point in the aperture and the diffraction screen point where the plane wave interacts determines the length of the plane wave; therefore, Maxwell's structure of light must have an arbitrary length to describe the aperture diffraction effect of light yet an arbitrary length field structure forms two different energies since the total length of a field structure determines the energy. A (5 x 10^14 Hz) plane wave the length of 10.000 cm and 10.001 cm interact at the diffraction screen. The total electric field structure and the frequency determines the energy of a plane wave yet the photoelectric effect proves that light has a discrete energy that is determine only by the frequency yet Maxwell's plane wave that forms two different length field structure, 10.00 cm and 10.001 cm, that are described with the same energy which violates logic. Maxwell's plane wave does not represent the physical structure of light.

The coherency of Maxwell's structure of light is described. Maxwell's EM plane wave structure of light is used to describe a light beam formed by a point source. Light from a candle flame, sun, and a laser originate from within a volume that allegedly emit point sources. The point sources emit spherical waves that are summed and approximated with Maxwell's plane wave structure of light. Yet to form a coherent wave front, the alignment of emitted spherical waves field structures is required to form the coherency of a the wave front. The coherency of the wave front requires both the vertical and horizontal coherency:

1. The vertical coherency of Maxwell's structure of light requires that the plane waves' electric field structures oscillate in positive and negative vertical directions. (fig 14)

2. The horizontal coherency of Maxwell's plane wave requires that the summed plane waves EM field structures' peaks and nodes occur at the same positions along the horizontal length(fig 15).

Radio waves form a coherent plane wave since a radio wave originates from the surface of a radio antenna. The wavelengths of a radio wave are long (lm-100km), and the point source emissions along the length of the antenna, at any time, all have the same wavelength, which allows for a radio antenna to form the vertical and horizontal alignment of a plane waves that when summed form the wave front of a radio plane wave. The vertical coherency is formed since the radio antenna atoms are bounded to one another. However, candle, sun and laser light are formed by point source emissions that are suspended in a volume; therefore, the unbounded point source emissions within a gaseous volume cannot form the vertical coherency since the point sources are unbounded. The vertical coherency would require that all of the spherical wave emissions emit an electric field structure that electric field oscillate in the positive or negative vertical directions. Yet the point sources, within a volume, are not connected to one another as is with the point source emissions of a radio wave anntena's atoms. In addition, the horizontal coherency requires that the electric fields' nodes and peaks of the emitted wave structures occur at the same position along the horizontal length which when summed would form a plane wave. Yet sun and candle light are chromatic, therefore, cannot form the horizontal coherency of a summed plane waves describe with Maxwell's structure of light. MAXWELL'S STRUCTURE OF LIGHT ONLY DESCRIBES MON-CHROMATIC LIGHT. Chromatic light has many wavelengths which cannot form a coherent wave structure; therefore, chromatic star and candle light cannot form the coherency of Maxwell's plane wave structure of light. Laser light is mono-chromatic yet laser light originates from the gas molecules that would not form the horizontal alignment required in forming the coherency of Maxwell's plane wave structure of light. Therefore, light cannot from the coherency of Maxwell's structure of light.

The derivation of wave theories aperture diffraction intensity equations is described. A non-propagating plane wave structure of light is used to describe the aperture diffraction effects of light. The time variable (t) of equations 21a,b are used to represent the propagation of the plane waves EM field structure. However, the average field electric effect effect of a propagating plane waves field structure, at a point (z'), on the diffraction screen is zero,

E(ave) = E'sin(k'z' - wt) = 0 (equ 24)

All of wave theories aperture diffraction derivation use a non-propagating plane wave structure of light using t=0 yet light experimentally propagates; therefore, wave theories aperture diffraction derivation conflict with the experimental propagation of light. The wave theories aperture diffraction mechanism is invalid since:

1. The LOPS [line-of-point-sources] describe with secondary wavelet form a retrogressive wave that is not experimentally observed.

2. Fresnel's aperture diffraction intensity derivations use non-propagating plane waves (t=0) yet light experimentally propagates.

3. The dark areas of the aperture diffraction pattern formed by the annihilation of the interacting waves would substantially reduce the total intensity.

4. The photoelectric effect prove that the light is composed of particles; however, particles cannot form the wave structure that is used to describe the aperture diffraction effects of light.

Maxwell's plane wave structure of light does not describe the physical structure of light.

5. Planck's Blackbox Emission Derivation

Planck's blackbox emission derivation (1900) is described. Planck's uses the standing wave mechanism of Maxwell's structure of light to describe light emitted within the blackbox,

"a set of simple harmonic oscillating standing waves in thermal equilibrium in a blackbox cavity"(Eisberg, p. 15)

The standing wave mechanism originates form Rayleigh-Jean's blackbox emission derivation.

"We assumed for simplicity that the metallic wall cavity filled with electromagnetic radiation" (Eisberg, p. 8)

"the radiation inside the cavity must exist in the form of standing waves with nodes at the metallic surface."(Eisberg, p. 8)

The standing wave mechanism requires that Maxwell's EM plane wave structure of light is emitted normal to the glowing hot metallic emission surface, maintain nodes of Maxwell's plane wave structure of light at both emission surfaces, and resonate between both red hot emission surfaces. Light cannot physically form standing waves since:

1. Light does not always propagate normal to the emission surface.

2. The majority of the emitted wavelengths cannot form wave structures that produce nodes at both surfaces (fig 17).

3. The propagation of the standing waves field structure cannot maintain nodes at both surfaces.

4. The string standing wave analogy is inappropriate since Maxwell's structure of light is a field structure.

5. The superposition of the standing waves EM field structure would annihilate.

Light does not always propagate normal to the emission surface. In an experiment, a flat metallic surface is heated red hot. If the light emissions only propagated normal to the emission surface then the light emissions, formed by the red hot surface, would only be visible viewed perpendicular to the emission surface yet the red hot metallic surface is visible from all outward angles. The light emissions are not all propagating normal to the emission surface as implied by Planck's standing wave mechanism. Secondly, the standing wave mechanism requires that the plane waves form nodes at both surfaces yet the majority of the emitted wavelengths do not form nodes at both surfaces. Example, if a 550nm wavelength plane wave emission formed nodes at both surfaces, in a 5.5 cm blackbox, then a 551nm and 552nm wavelength plane waves would not form nodes at both surfaces. The majority of the emitted wavelengths do not form the standing waves that form nodes at both emission surfaces. Thirdly, the plane wave structure of light must propagate. It would not be possible for for the standing waves composed of plane waves to maintain the nodes at both surfaces and also propagate yet experimentally light propagates. Consequently, wave theory use a standing wave string analogy to describe the standing wave of light yet an EM standing wave is formed by field structure which cannot be compared with a standing wave formed by a string since a string is not a field structure. The EM plane waves that form the standing waves have a constant maximum amplitude yet according to the standing wave string analogy the maximum amplitude of the string changes when a string forms a standing wave. Therefore, a string standing wave cannot be compared to an EM standing wave of light. Finally, the superposition of the standing waves field structure would annihilate and no field effect would form from a standing wave of light formed by Maxwell's EM plane wave structure of light. Light does not physically form standing waves.

Planck uses the standing waves of Maxwell's structure of light to derive Planck's discrete energy equation.

"The energies of the entities in the system we are considering, a set of simple harmonic oscillating standing waves in thermal equilibrium in a blackbody cavity, are governed by (1-20)." (Eisberg, p. 15).

Planck is assuming that the formation of the standing wave forms the discrete energy yet it is not physically possible for light to form standing waves within a blackbody. The derivation of Planck's discrete energy equation

E = hf (equ 25)

derived from standing waves is invalid.

The derivation of Planck's blackbox average total energy equation is described. The discrete energies emitted by the blackbox emission effect are represented with Boltzmann's thermodynamic kinetic energy distribution equation (Eisberg, p. 15),

e^(-E/kT)

P(E) = -------------- (equ 26)

kt

The law of equipartition of energy equation is derive using energies from 0 to infinity and equations 26,

inte[EP(E)dE]

E(T) = --------------------- = kT (equ 27)

inte[P(E)dE]

Planck then states that as the frequency (f), of the blackbox emission effect, approaches infinity,

f ---> infinity (equ 28)

the total energy of the blackbox emission effect approaches zero (Eisberg, p. 15),

E ---> 0.(equ 29)

"Planck was led to consider the possibility of a violation of the law of equipartition of energy on which the theory [blackbox] was based." (Eisberg, p. 14)

Planck implies that since equation 29 violates the law of equipartition of energy (equ 27) that the average total energy of the blackbox emission effect is a function of the frequency.

"Planck realized that, in the circumstances that prevail for the case of blackbody radiation, the average energy of the standing waves is a function of frequecy E(f) have the properties indicated by (equ 27) and (equ 29)" (Eisberg, p. 15)

However, the law of equipartition of energy (equ 27) is derived using the entire range of emission wavelengths, from X-rays to radio waves. When Planck uses frequencies that approaches infinity, (equ 28), only short wavelengths emission are represented,

wavelength ---> 0. (equ 30)

Planck is assuming that equation 29, E ---> 0 when f --> (infinity) represents the entire range of wavelength emissions of the blackbox effect yet equation 29 only represents an infinitesimal range of wavelength emissions, wavelength --> 0 (equ 30). Consequently, equation 29 does not violate the law of equipartition of energy that Planck's blackbox emission derivation is based on. Planck's justification that the average total energy is a function of the frequency is invalid.

Planck replaces the integrations that form the law of equipartition of energy equation (equ 27) with summations which forms Planck's average total energy equation that is a function of the frequency (Eisberg, p. 16),

sum[EP(E)dE] hf

E(f) = --------------------- = ------------------- (equ 31)

sum[P(E)dE] e^(hf/kT) - l

However, mathematically, a summation is an approximation of an integration. Replacing the integration used to derive law of equipartition of energy equation (equ 27) with Planck's summation cannot substantially change the resulting equation yet Planck's average total energy equation (equ 31) is a function of the frequency; whereas, the law of equipartition of energy equation (equ 27) is a function of the temperature. Consequently, Planck's derivation of the blackbox average total energy equation (equ 31) is invalid.

Planck uses the average total energy equation (equ 31) to derive the blackbox intensity equation, L = wavelength (Eisberg, p. 19),

8(pi)hc dL

I(L) = --------- -------------------- (equ 32)

L^5 e^(hc/LkT) - 1

Planck uses equation 32 and the experimental blackbox emission curve to obtain the value of the constant (h) of Planck's energy equation (equ 25). To justify that and electromagnetic wave of Maxwell's structure of light forms a discrete energy and particle structure. However, the blackbox intensity curve (fig 17) 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

The results of five completely different measurement devises cannot be represented on the same graph. The intensity of light is visible yet the intensity of a radio wave are not visible. If the blackbox emission intensity curve equation (equ 32) and the resulting experimental graph are invalid then Planck's derivation of the constant (h) is also invalid.

6. Einstein's Photoelectric Quanta

The derivation of Einstein's photoelectric quanta equation is described.

"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 of 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. Einstein's revolutionary paper made clear that the "atomistic" or discontinuous nature of matter is characteristic of energy as well, generalizing Planck's recent work on the existence of discontinuities, or "quanta" of energy in black-body radiation. (Nye, p. 460)

In Einstein's photoelectric effect paper (1905), Einstein uses Wien's gas molecule analogy.

"We now wish to compare the average magnitude of the "blackbox" energy quanta with the average kinetic energy of the translational motion of a molecule at the same temperature." (Einstein's paper, Nye, p. 472)

However, it is physically inappropriate to use a gas molecule analogy to describe light since:

1. Gas molecules exist within a container yet optic particles are emitted from the red hot surfaces of the metallic container.

2. Gas molecules have varying velocities that are substantially affected by the temperature yet optic particles have a constant velocity that velocity is not substantally affect by the change in temperture.

3. Gas molecules kinetic energies are dependent on the temperature and frequency yet the energy of the optic particles are determined by only the frequency.

4. Gas molecules kinetic energy varies depending on the temperature; however, after the optic particles are emitted, the temperature does not substantially affect the energy of the optic particles.

It is physically inappropriate to use Wien's gas molecule analogy to describe light since light does not have the physical characteristics of gas molecules.

In section 5 of Einstein paper, Einstein implies that the probability is a "statistical probability".

W = (v/v')^n (equ 33)

where

"Let us consider a number, n, moving points (e.g., molecules) in a volume v." (Nye, p. 470)

Einstein describes the probability (W) with the following equation,

W = (v/v')^NE/Rbf. (equ 34)

"Monochromatic radiation of low density behaves--as long as Wein's radiation formula is valid---in a thermodynamic sense, as if it consisted of mutually independent energy quanta of magnitude Rbf/N." (Nye, p. 472)

Einstein is assuming that the NE/Rbf of equation 34 is equal to one,

NE/Rbf = l ---------------> E = Rbf/N (equ 35a,b)

However, using equation 35, when NE/Rbf =1 then n of equation 33 represent a single gas molecule. Therefore, the volume v' is the volume of a single gas molecule.

Einstein uses the probability in the thermodynamic work-dependent entropy equation,

(delta)S = (R/N)ln[V'/V"] (equ 36)

Einstein uses the probability equation (equ 34) in place of the work of the thermodynamic entropy equation,

(delta)S = nRln{[v/v']^(NE/Rbf)}. (equ 37)

Einstein derives the energy quanta equation by assuming that the NE/Rbf of equation 37 is equal to one. Yet if NE/Rbf is equal to one this would imply that v' is the volume of a gas molecule which would form a tremendously large change in the entropy of equation 37. However, the volume, number of gas molecules, and the temperature of Einstein's system are constant; therefore, the thermodynamic change in the entropy of Einstein's system is zero. The energy quanta equation cannot be derived from the thermodynamic change in the entropy equation as implied by Einstein. Einstein's gas molecule analogy that implies that an electromagnetic wave forms a particle effect of the blackbox emission effect is invalid.

7. Quantum Mechanic Wave Packets and Quantum Electrodynamics (QED) of Light

The quantum mechanic wave packet structure of light is describe. Quantum mechanics is a wave theory yet "quantum" implies a particle theory.

"the basic conceptual framework of the subject [quantum mechanics] has been considered by many scientists to be unsatisfactory" (Rae, p. 222)

The problem with quantum mechanics is that a continuous wave structures are used to describe a particle structure yet a continous EM wave structure is the opposite of a particle structure. The quantum mechanic wave packet structure of light is an attempt at forming a particle structure from Maxwell's plane wave structure of light. The quantum mechanic wave packet structure of light is formed by the,

"superpositioning, that is sum of plane waves [Maxwell] of different frequencies and amplitudes" (Brandt, p. 21)

Two plane waves of slightly different angular frequencies are superpositioned which forms wave packets along the horizontal length (fig ). The wave packets formed are not a particle structures since two plane waves can form more than two wave packets. Quantum mechanics then uses 14 plane waves of different frequencies and amplitudes to form a quantum mechanic wave packet. A single wave packet formed by 14 plane waves is used to represent a quantum mechanic wave packet structure of light. Yet according to the wave theory of light, a plane wave represents the structure of a photon. Using 14 plane waves to form a QM wave packet that describe a particle structure of a photon when a single plane wave is used to describe a single photon is questionable physics.

"It seems to me that far from there being only one interpretation of quantum mechanics, there is today no fully satisfactory way of understanding this theory." (Healey, p. 2)

The quantum mechanic wave packet structure of light does not describe the physical structure of light.

QED [quantum electrodynamics] of light is described. QED is another attempt at quantizing Maxwell's EM plane wave structure of light. QED quantizes Maxwell's structure of light by enclosing a segment of a plane wave's EM field structure within a box (normalization).

QED quantizes the length and the plane (width) of the plane wave. Yet Maxwell's plane wave structure of light is formed of a continuous EM field structure. If Maxwell's plane wave is used to represent the physical structure of light then a laser beam's width would represent the width of the plane wave. During the double slit diffraction experiment, when a laser beam is represented with Maxwell's plane wave structure of light, the plane wave interacts with both slits and emits light through both slits. (fig 13)

"How can one photon pass through two slits? One way to restate the question is, how can light have both particle and wave properties in the same experiment (Orear, p. 306).

QED particle structure of light is not a continuous structure. Yet Maxwell's structure of light is derived form a continuous structure of a spherical wave; therefore, the derivation of the QED discrete quantum structure of light using Maxwell's plane wave structure of light is not physically possible since the original spherical wave structure is not a particle structure. QED quantum structure of light conflicts with the continuous structure that is describe with Maxwell's equations.

8. Particle Theory of Light

The particle theory of light is describe. The photoelectric effect of light proves that light is composed of particles. I will prove that the aperture diffraction effect of light is a particle effect. In an experiment, a small diameter laser passes through a small circular aperture without contacting the aperture edge; the aperture diffraction pattern is not formed when the incident light does not contact the aperture edge. Consequently, the interaction of the optic particles with the aperture edge atoms is an esstential part of the aperture diffraction mechanism. I predict that the interaction of light with the aperture edge atoms form an "aperture effect" that diffracts the optic particles that enter the aperture.

In an experiment, a photomultiplier is used to test the light that forms the small aperture diffraction effect of light. A photomultiplier is placed in the aperture, and between the aperture and the diffraction screen.

"a photomultiplier that utilize the photoelectric effect is used to test a single photon" (Orear, p. 34)

The photomultiplier experiment proves that, in the plane of the aperture, the optic particles are directed to the intensity areas and not allowed in the areas where the dark areas of the aperture diffraction pattern. Consequently, I predict that the optic particles that contact the aperture edge forms an "aperture effect", in the plane of the aperture, that directs the optic particles, that enter the aperture, to the intensity areas of the diffraction pattern. In addition, the intensity of light that enter the aperture is approximately equal to the intensity formed by the diffraction pattern. The intensity is spread out on the diffraction screen by the aperture effect. The aperture diffraction effect of light is a particle effect.

The T&R [transmission& reflection] effect of light is also a particle effect. In the T&R experiment of light, a photomultiplier is placed in front of the glass plate and embedded in the glass medium. The photomultiplier experiment prove that the incident, transmission and reflected light beams are composed of particles. Consequently, the T&R effects of light is a particle effect. I predict that the glass surface molecules act as an atomic grid. When the optic particle are incident normal to the glass surface the full face of the atomic grid is exposed; 94% of the incident beam's optic particles are transmitted through the glass surface atomic grid and 4% of the optic particles are reflected when interacting with the atomic grid. When the incident angle measured from the glass surface normal increases, the atomic grid's effect on the incident beams' optic particles increases and decreases the transmission beam's intensity. Consequently, the T&R effect of light is a particle effect.

The constant (h) of the photoelectric energy equation is derived using the ionization energy. The energy required to release (ionize) the electron from the surface atom and the kinetic energy of the emitted photoelectric electron represents the total energy of an optic particle. To ionize a potassium atom 4.3 eV (Lide, p. 10-215) of energy is required. A (5 x 10 ^14 Hz) optic particle emits a .5 eV kinetic energy electron from a potassium atom (Hecht, p. 1123). Consequently, the total energy of a 5 x 10^14 Hz optic particle is derived by adding the atomic ionization (IE) and emitted electron's kinetic (KE) energies,

(IE) + (KE) = 4.3 eV + .5 eV = 4.8 eV. (equ 38)

Using a 5 x 10^14 Hz optic particle's energy of 4.8 eV (equ 38) in the photoelectric energy equation, the approximate value of the constant (h) is derived for a potassium surface,

h = E/f = 4.8eV/(5 x 10^14 Hz) = 9.6 x 10^(-15) eV-s. (equ 39)

The mass of a 5 x 10^14 Hz optic particle is derived using the kinetic energy equation,

E = (1/2)mv^2 -----------------> m = 2E/c^2 (equ 40)

The mass of a 5 x 10^14 Hz optic particle is derived using v=c= 3 x 10^8 m/s, and E = 4.8 eV or 7.7 x 10^19 J in equation 40,

m = 2(7.7 x 10^(-19)J)/c^2 = 1.69 x 10^(-34) kg. (equ 41)

9. Conclusion

Huygens's principle describe the propagation and aperture diffraction mechanisms of light. Huygens's propagation mechanism, repetitively, destroys the majority of the LOPS secondary wavelets' structures after every wave fronts is formed, at intervals of a wavelength. Huygen's propagation mechanism is an extreme violations of the law of conservation of energy. Huygen's aperture diffraction mechanism's interaction wave mechanism would substantially reduce the total intensity of the diffraction pattern. A substantially reduction in the total intensity of the diffraction pattern is not experimentally observed; therefore, Huygen's aperture diffraction mechanism does not describe the aperture diffraction effects of light.

The derivation of Fresnel's equations is based on conflicting structures. A cosine wave structures are required in forming the boundary equation,

I' + R' = T',

yet a sine plane wave structures are require in forming the tangental equation,

-I'k' + R'k' = T'k".

Both equations are used to derive Fresnel's T&R equations. The derivation of Fresnel's T&R equations is invalid since Fresnel's derivation uses conflict structures to describe the incident, transmission, and reflection plane waves. In addition, Fresnels derivation of the T&R [transmission and reflection] equations of light uses non-propagating plane waves (t=0) yet experimentally light propagates. Fresnel's derivation of the T&R equations uses conflicting structures and uses a wave structure that does not propagate using t=0. The derivation of Fresnel's T&R equations is invalid.

Maxwell's structure of light is derived form Maxwell's (radio wave) equations where a infinitesimal size segment of an EM spherical wave is approximated with a continuous EM plane wave structure of light. Maxwell's structure of light is not a particle structure yet the photoelectric effect prove that light has a particle structure. According to Maxwell light has a continuous structure yet a continuous structure of a plane wave interact with both slits of the double slit aperture diffraciton experiment. The emission of light through both slits is experimental proof that light is composed of particles which conflict with Maxwell's continuous EM plane wave structure of light. Maxwell's structure of light originated form radio waves. Maxwell believe that since light and radio waves have the same velocity that both have an electromagnetic structure. However, an EM field structure is a continuous structure and the photoelectric effect and the double slit aperture diffraction experiments prove that light is composed of particles which conflict with Maxwell's structure of light. Maxwell's structure of light also forms a coherency problem since candle light, star, and laser light originate from the volume of point source emission that are suspended within a volume. The short wavelengths of light and the volume that the point sources originate do not form a coherent structure of Maxwell's plane wave structure of light. The reason for Maxwell's structure of light is to describe the aperture diffraction effects of light, a wave effect. All of wave theories aperture diffraction derivation use a non-propagating plane wave structure of light using t=0 yet light experimentally propagates; therefore, wave theories aperture diffraction derivation conflict with the experimental propagation of light. In addition:

1. The LOPS [line-of-point-sources] describe with secondary wavelet form a retrogressive wave that is not experimentally observed.

2. Fresnel's aperture diffraction intensity derivations use non-propagating plane waves (t=0) yet light experimentally propagates.

3. The dark areas of the aperture diffraction pattern formed by the annihilation of the interacting waves would substantially reduce the total intensity.

4. The photoelectric effect prove that the light is composed of particles; however, particles cannot form the wave structure that is used to describe the aperture diffraction effects of light.

Maxwell's plane wave structure of light does not describe the physical structure of light.

Planck's blackbox emission derivation is described. Planck assume that light within the blackbox forms standing waves; however, it is not physically possible for light to form standing waves within a blackbox since:

1. Light does not always propagate normal to the emission surface.

2. The majority of the emitted wavelengths cannot form wave structures that produce nodes at both surfaces (fig 17).

3. The propagation of the standing waves field structure cannot maintain nodes at both surfaces.

4. The string standing wave analogy is inappropriate since Maxwell's structure of light is a field structure.

5. The superposition of the standing waves EM field structure would annihilate.

Planck uses the standing waves to derive a discrete energy equation yet it is physically not possible for light to form standing waves. Planck's derivation of the discrete energy equation, based on the formation of standing waves, is invalid. Planck then derives the average energy equation by replaces the integrations of the law of equipartition of energy with summations. A summation is an approximation of an integration, replacing the integrations with summations cannot substantially change the original equation yet Planck's derivation of the average total energy equation does not resemble the original law of equipartition of energy equation. Planck derivation of the average total energy equation is mathemically invalid.

Einsteins photoelectric quanta equation derivation (1905) is described. Einstein uses a gas molecule analogy to describe light within the blackbox emission effect. However, it is inappropriate to use thermodynamic gas molecules to describe light since light and gas molecule a physically unrelated.

1. Gas molecules exist within a container yet optic particles are emitted from the red hot surfaces of the metallic container.

2. Gas molecules have varying velocities that are substantially affected by the temperature yet optic particles have a constant velocity that velocity is not substantally affect by the change in temperture.

3. Gas molecules kinetic energies are dependent on the temperature and frequency yet the energy of the optic particles are determined by only the frequency.

4. Gas molecules kinetic energy varies depending on the temperature; however, after the optic particles are emitted, the temperature does not substantally affect the velocity of the optic particles.

Einstein replaces the work (V'/V") of the thermodynamic entropy equation with a probability equation (W),

dS = nRln([v/v']^(NE/Rbf).

then implies that NE/Rbf of the previous equation is equal to one,

NE/Rbf = 1 ------> E = (Rbf)/N.

Einstein uses an improper substitution; the probability is not equivalent to work and cannot be used in an entropy equation. The volume, number of gas molecules and temperture of Einstein system is constant; therefore, the change in entropy of Einstein's system is zero. Einsteins derivation of the energy quanta equation is derive from a system that change in entropy is zero.

The QM [quantum mechanic] wave packets of light are described. The QM wave packet is an attempt at forming a particle structure from Maxwell's plane wave structure of light by superpositioning plane waves of different frequencies and amplitudes. Plane waves form more wave packets than the number of plane waves used; therefore, quantum mechanic wave packets do not from a particle structure. Quantum mechanics then uses 14 plane waves to describe a "quantum" structure of light; yet using 14 plane wave to derive a single "quantum" structure of light violates logic since a single plane wave is used to describe a photon. The QM wave packet structure of light is invalid. QED [quantum electrodynamics] of light is another attempt at quantizing Maxwell's structure of light. QED quantizes Maxwell's structure of light by enclosing a segment of a plane wave within a box (normalization). However, the plane of a plane wave structure of light represent the width of the light beam; therefore, the quantumization of Maxwell's structure of light would effect the continuity of Maxwell's plane wave structure of light. Consequently, the QED particle structure of light conflict with the continuity of Maxwell's EM plane wave structure of light.

The particle theory of light is described. The photoelectric effect proves that light is composed of particles; therefore, the aperture diffraction effect of light is a particle effect. I predict that the optic particles that contact the aperture edge form an aperture effect that directs the optic particles, to the intensity areas of the diffraction pattern and does not allow the diffracted optic particles in the dark areas. Using a photomultipier, a light that enter the aperture are directed to the intensity areas of the diffraction pattern and not allowed the dark areas. The photomultiplier experiment proves that the aperture diffraction effect of light is a particle effect.

The constant (h) of of the photoelectric energy equation is derived using the atomic ionization energy (IE) and emitted electron's kinetic energy (KE).

(IE) + (KE) = 4.3 eV + .5 EV = 4.8 eV

Using a 5 x 10^14 Hz optic particle's energy of 4.8 eV, the value of the constant (h) is derived for a potassium surface,

h = E/f = (4.8 eV)/(5 x 10^14 Hz) = 9.6 x 10^1- eV-s.

Using the kinetic energy equation the mass of a (5x 10^14 Hz) optic particle is derived,

m = 2E/c^2 = 2(7.7 x 10^(-19)J)/c^2 = 1.69 x 10^(-34) kg.

9. References

Isaac Asimov. "Understanding Physics Vol 11." George Allen & Unwin Ltd. 1966.

Ben Bova. "The Beauty of Light." John Wiley. 1988.

Siegmend Branddt and Hans Dieter Dahmen. "Quantum Mechanics". 3rd ed. Springer