Inverse Compton scattering also exists, where the photon gains energy (decreasing in wavelength) upon interaction with matter. Since the wavelength of the scattered light is different from the incident radiation, it is an example of inelastic scattering,  The amount the wavelength changes is called the Compton shift.  

The effect is important because it demonstrates that light cannot be explained purely as a wave phenomenon.  Thomson scattering, the classical theory of an electromagnetic wave scattered by charged particles, cannot explain low intensity shifts in wavelength. (Classically, it is assumed that light of sufficient intensity for the electric field to accelerate a charged particle to a relativistic speed will cause radiation-pressure recoil and an associated Doppler shift of the scattered light, but the effect would become arbitrarily small at sufficiently low light intensities regardless of wavelength.)  In other words the results of Compton’s experiment convinced physicists that light behaves as a stream of particle-like objects (quanta) whose energy is proportional to the frequency.

However one can integrate the quantum or photonic properties of light such as Compton scattering with its wave properties by extrapolating the laws of a Classical three-dimensional environment to fourth *spatial* dimension.
For example In the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown one can derive the quantum mechanical properties of energy/mass and a photon in terms of a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension by extrapolating the classical laws of resonance in a three-dimensional environment to one of four.

Briefly it showed the four conditions required for resonance to occur in a classical Newtonian three dimensional environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in one of consisting of only four *spatial* dimensions.

The existence of four *spatial* dimensions would give a “surface” of a three-dimension space manifold (the substance) the ability to oscillate spatially on a “surface” between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or a photon interacting with an electron.  This would force the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

Therefore, these oscillations in space, would meet the requirements mentioned above for the formation of a resonant system or “structure” in it. 

The energy associated with resonant system in three-dimensional space can only take on the incremental or discreet values associated with a fundamental or a harmonic of the fundamental frequency of its environment.

Similarly the energy associated with resonant systems in four *spatial* dimensions could only take on the incremental or discreet values associated a fundamental or a harmonic of the fundamental frequency of its environment.

These resonant systems in four *spatial* dimensions are responsible for the incremental or discreet energies associated with photon and all other quantum mechanical systems.

While one can derive the electromagnetic wave properties of a photon as was done in the article “Electromagnetism in four *spatial* dimensions” Sept. 27, 2007 by extrapolating the laws of classical wave mechanics to a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly a wave on the two-dimensional surface of water causes a point on that surface to be become displaced or rise above or below the equilibrium point that existed before the wave was present. Classical wave mechanics tells us a force will be developed by the differential displacement of the surfaces, which will result in the elevated and depressed portions of the water moving towards or become “attracted” to each other and the surface of the water.

Similarly a matter wave on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension would cause a point on that “surface” to become displaced or rise above and below the equilibrium point that existed before the wave was present.

However, as just mentioned classical wave mechanics, if extrapolated to four *spatial* dimensions tells us the force developed by the differential displacements caused by a matter wave moving on a “surface” of three-dimensional space with respect to a fourth *spatial* dimension will result in its elevated and depressed portions moving towards or becoming “attracted” to each other.

This defines the causality of the attractive forces of unlike charges associated with the electromagnetic wave component of a photon in terms of a force developed by a differential displacement of a point on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, it also provides a classical mechanism for understanding why similar charges repel each other because observations of water show that there is a direct relationship between the magnitudes of a displacement in its surface to the magnitude of the force resisting that displacement.

Similarly the magnitude of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by two similar charges will be greater than that caused by a single one. Therefore, similar charges will repel each other because the magnitude of the force resisting the displacement will be greater for two similar charges than it would be for a single charge.

One can define the causality of electrical component of electromagnetic radiation in terms of the energy associated with its “peaks” and “troughs” that is directed perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that perpendicular displacement.

However, Classical Mechanics also tells us a horizontal force will be developed by that perpendicular or vertical displacement which will always be 90 degrees out of phase with it. The attractive force associate with this horizontal displacement is called magnetism.

This is analogous to how the vertical force pushing up of on mountain also generates a horizontal force, which pulls or attracts matter horizontally towards from the apex of that displacement.

Yet as shown in the article “Why is energy/mass quantized?” the matter wave responsible for the propagation of electromagnetic energy must travel through space in quantized resonant structures that is responsible for the quantum mechanical properties of a photon.

Therefore the articles “Why is energy/mass quantized?” and “Electromagnetism in four *spatial* dimensions” explain both the electromagnetic and wave properties of a photon and electron because it defines one in terms of the other.

Yet it also allows one to explain how the low intensity shifts in wavelength of X and gamma rays occur when they interact with charged particles in terms of Classical wave mechanics because if the causality of their electromagnetic and particle properties are as suggested above related to the resonant properties of a matter wave then it tells us that interference will occur no matter how small the intensity of their interaction is.

This is because the velocity of all forms of electromagnetic energy including gamma and X rays is constant and therefore it cannot change after an interaction occurs with particles such as an electron while an electron’s can be altered by a change in its velocity.   Therefore, the only way to alter the energy, direction or momentum of a gamma or x-ray is by “degrading” or changing their wavelength.  Yet, if the electromagnetic and particle properties of both a photon and electron are a result of a matter wave is as suggested above then classical wave mechanics could define their interaction in terms of the interference of their electromagnetic wave properties.  However this also tells us their scattering at very low light intensities could take on any arbitrarily small value regardless of wavelength. 

In other words if one assumes the electromagnetic and particle characteristics of both a photon and electron is a property of a physical displacement created by a matter wave on in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension as is done here then one can Classically explain why it is not necessary to accelerate a charged particle to a relativistic speed to cause the low intensity shifts in wavelength associated with the Compton effect.

This shows how one can explain the inelastic scattering of photons in matter which results in the decrease in energy (increase in wavelength) of an X-ray or gamma ray photon, called the Compton Effect by extrapolating the laws of classical wave mechanics to a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Later Jeff

Copyright Jeffrey O’Callaghan 2012

The post Compton scattering: A Classical approach appeared first on Unifying Quantum and Relativistic Theories.

One is that it would allow one to quantifiably derive the origins of our present universe in terms of a cycle of expansions and contractions by extrapolating the laws of a classical environment to four *spatial" dimensions.

The Standard Cosmological Model of the Universe hypothesis the universe evolved from a small compact "ball" of energy/mass which began a rapid expansion based in part on a frequency shift in the spectral lines in light called the red shift.

In 1929 Edwin Hubble observed the characteristic colors, or spectral lines emitted by the stars in the galaxies do not have exactly the same wavelengths observed in the laboratory; rather they are systematically shifted to longer wavelengths, toward the red end of the spectrum.

He correctly assumed this change in the observed frequency of light occurs in part because its source i.e. galaxies and observer are in motion relative to each other, with the frequency increasing when the source and observer approach each other and decreasing when they move apart.  Therefore, he assumed the red shift he observed in the spectrum of galaxies meant that they were moving way.

However, he also found the further a galaxy is away from the Earth the larger its redshift and therefore its recessional velocity form the Earth is proportional to their distance from it.  Astronomers still use the formula called Hubble law he derived from these observations to predict the rate at which the universe is expanding.  It states that it is directly related to distance times a constant known as the Hubble Constant.

As mentioned earlier there are several theoretical advantages to assuming the existence of four *spatial* dimension and a continuous non-quantized field of energy/mass.

The first, as was shown in the article "What is Dark Matter?" Sept 10, 2007 is that it would allow one to explain the invisible gravitational component of Dark matter because being up of mass it would exert a gravitational potential yet being continuous it would be invisible to modern instrumentation which are only calibrated to detect mass in its particle form.

That article listed several other observations that support its existence such as the fact that electromagnetic energy in itself is not quantized because a photon can have any frequency and therefore any energy greater than zero or less than infinity and the equation defining the relationship between mass and energy, E=m*c^2 indicates that mass is completely convertible to one or more photons with energies greater than zero or less than infinity.

This suggests that a continuous non-quantized field of energy/mass must be available to support the continuous properties associated with energy of the electromagnetic spectrum.

However one of the strongest arguments that can be made for its existence when combined with four *spatial* dimensions instead of four dimensional space-time is that it allows one to theoretically derive the quantum mechanical properties of a energy/mass and a photon by extrapolating the observations of a three-dimensional environment to a fourth *spatial* dimension.

In the article "Why is energy/mass quantized?" Oct. 4, 2007 it was shown that one can derived the quantum mechanical properties of energy/mass and a photon by extrapolating the laws of classical resonance in a three dimensional environment to the discrete energies associated with a resonant "system" formed in four *spatial* dimensions created by a matter wave in a continuous non-quantized field of energy/mass.  However, it also showed all energy must be propagated through space in these quantized resonant systems.

Briefly it showed the four conditions required for resonance to occur in a classical three-dimensional environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in one consisting of four *spatial* dimensions.

The existence of four *spatial* dimensions would give the continuous field of energy/mass the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the continuous field of energy/mass to oscillate with respect to a fourth *spatial* dimension at the frequency associated with the energy of that event.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established in a continuous field of energy/mass.

Classical mechanics tells us the energy of a resonant system can only take on the quantized values associated with its resonant or a harmonic of its resonant frequency.

It was shown these resonant systems in a continuous field of energy/mass are responsible for the quantum mechanical properties of a photon and energy/mass.

However, it is also possible to use the existence of a continuous non-quantized form of energy/mass and four *spatial* dimension to explain electromagnetic properties of a photon in terms of the matter wave that the article "Why is energy/mass quantized?" showed was responsible for its quantum mechanical properties.

In the article "Electromagnetism in four *spatial* dimensions" Sept.27, 2007 it was shown that one can define the propagation of electromagnetic energy in terms of oscillations in a continuous non-quantized field of energy/mass generated by a matter wave moving at the velocity of light on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

How this is possible can be understood by comparing a matter wave in a continuous field of energy/mass that article hypothesizes is responsible for electromagnetic energy to a wave on water.

In a classical world, the trough of a wave on water displaces the vertical volume of water below its surface with air while its peak displaces the air above it with water.

Additionally, classical wave mechanics tells us a force will be developed by the differential displacement of its surfaces, which will result in the elevated and depressed portions of the water moving towards or become "attracted" to each other and the surface of the water.

Similarly, the "trough" of a matter wave in a continuous field of energy/mass would displace a volume of three-dimensional space below its "surface" with a component of four-dimensional space.  While its "peak" would displace a "volume" of four-dimensional space above a "surface" of a three-dimensional space manifold with three-dimensional space.

However, as mentioned earlier classical wave mechanics when extrapolated to a fourth *spatial* dimension tells us that a force would be developed by the differential displacements of the continuous field of energy/mass, which will result in the elevated and depressed portions "moving" towards or becoming "attracted" to each other.

Therefore, by extrapolating the laws of classical wave mechanics to four *spatial* dimensions one can derive the causality of the attractive forces of unlike electromagnetic charges in terms of a force developed by the differential displacement of a continuous field of energy/mass caused by a matter wave on that "surface".

However, it also provides a classical mechanism for understanding why similar charges repel each other because observations of water show that there is a direct relationship between the magnitudes of a displacement in its surface to the magnitude of the force resisting that displacement.

Similarly, the magnitude of a displacement in a continuous field of energy/mass caused by two similar charges will be greater than that caused by a single one.  Therefore, similar charges will repel each other because the magnitude of the force resisting the displacement will be greater for two similar charges than it would be for one.

The reason an electromagnetic wave is observed to be made up of discrete quantized units called photons and not a continuous wave is because, as mentioned earlier article "Why is energy/mass quantized?" showed the energy of a matter wave forms resonant "system" formed in four dimensional space.  Therefore, its energy will propagated in quantized resonant systems called photons.

However, the existence of Dark Matter or a continuous non-quantized form of energy/mass would affect our understanding of the evolution of the universe because it would interact with the wave properties of a photon causing them to be red shifted.  How and why this interaction occurs requires an understanding of how and why it could interact with a photon to generate a red shift which as mentioned earlier is the basis for many of the currently accepted cosmological models of its origin.

(It should be remember, we do agree with many cosmologists that the universe is presently in an overall state of expansion however, we disagree with the currently accepted rates at which this expansion is occurring and define this expansion not in terms of a "big bang" but in terms of cycle of expansions and contractions in four *spatial* dimension.)

One way of accomplishing this is to compare the interaction of the matter wave component of a photon with a continuous non-quantized form of energy/mass to the interaction of a wave on water to water.

The frequency and energy content of a water wave decreases as it moves along its surface due, in part, to its interaction with the inertial mass of the water which causes it to heat up.  The greater the distance it travels on the water the greater the decrease in its energy and frequency.

Similarly the frequency of the matter wave component of a photon would decrease as it moved along a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension due to its interaction with a continuous non-quantized energy/mass component of space.  The greater the distance it travels the greater the decrease in its energy and frequency.

However this "Tired Light" concept of the energy loss associated with the red shifting of photons by its interaction with space has been dismissed by many because no Compton scattering is observed in them.

Compton scattering is a type of scattering that X-rays and gamma rays undergo in matter.  The inelastic scattering of photons in matter results in a decrease in energy (increase in wavelength) of an X-ray or gamma ray photon, called the Compton Effect.  Part of the energy of the X/gamma ray is transferred to a scattering electron, which recoils and is ejected from its atom (which becomes ionized), and the rest of the energy is taken by the scattered, "degraded" photon.

Inverse Compton scattering also exists, where the photon gains energy (decreasing in wavelength) upon interaction with matter.  Since the wavelength of the scattered light is different from the incident radiation, Compton scattering is an example of inelastic scattering, but the origin of the effect can be considered as an elastic collision between a photon and an electron.  The amount the wavelength changes by is called the Compton shift.  Although nuclear Compton scattering exists Compton scattering usually refers to the interaction involving only the electrons of an atom.  The Compton Effect was observed by Arthur Holly Compton in 1923 at Washington University in St. Louis and further verified by his graduate student Y. H. Woo in the years following.  Compton earned the 1927 Nobel Prize in Physics for the discovery.

Many feel it demonstrates that light cannot be explained purely as a wave phenomenon.  Thomson scattering, the classical theory of an electromagnetic wave scattered by charged particles, cannot explain low intensity shifts in wavelength (Classically, light of sufficient intensity for the electric field to accelerate a charged particle to a relativistic speed will cause radiation-pressure recoil and an associated Doppler shift of the scattered light, but the effect would become arbitrarily small at sufficiently low light intensities regardless of wavelength.)  Light must behave as if it consists of particles to explain the low-intensity Compton scattering.  Compton’s experiment convinced physicists that light can behave as a stream of particle-like objects (quanta) whose energy is proportional to the frequency.

The reason why many astronomers believe the entire redshift of a star is the result of its movement away from an observer is as just mentioned classical theory of charged particles interacting with an electromagnetic wave, cannot explain any shift in wavelength.

Therefore, if the red shift was caused by a particle interaction one should observed Compton scattering in red shifted light.  Since no Compton scattering is observed in light coming from a star it is assumed by many astronomers it can only be caused by the movement of an object away from an observer because as mentioned earlier it is the only way they can explain it.

Yet as was shown in the article "Why is energy/mass quantized?" if the quantum mechanical properties of photons are a result of a resonant system generated by a matter wave in a continuous non-quantized field of energy/mass then Classical Wave theory tells us that a portion of the redshift may be caused by the interaction of its wave properties with a continuous non-quantized energy/mass component of space.

This would mean that the assumption that the entire redshift in a star’s spectrum is a result of its movement away from us may be invalid because the energy loss due to the interaction of the wave component of a photon with a dark matter or a continuous non-quantized field of energy/mass would result in it being redshifted.

However the law of conservation of energy/mass tells us that it must be conserved.  In other words if a photon is redshifted or loses energy to a continuous non-quantized form of mass as it move through an environment it tells us the mass component of that environment must increase.

Yet this means that interaction will result in an increase the continuous non-quantized mass component in the environment where that energy loss took place.  The magnitude of this interaction is quantified by the experimentally verified equation E=mc^2.

However as has been showed throughout the Imaginers Chronicles a volume of three-dimensional space is made up of a continuous field of mass therefore if one increases the quantity of it in a given region of space the volume associated with that region will expand.

Therefore the rate of expansion of the universe due to a conversion electromagnetic energy to a continuous non-quantized field of mass would be related to the non-linear formula of E=mc^2.

Therefore, if this mechanism does define one of the expansive components of the universe the rate of the expansion would be less than that predicted by many cosmologists because one of its components would be defined by the non-linear formula of E=mc^2 and not by the linear recessional velocity of galaxies.  This would result in a reduction of the calculated rate of expansion which is based on the assumption that the entire energy loss of associated with the red shift in light is due to the recessional velocity of galaxies.

(The force called Dark Energy is a result of the fact that one must add the non-linear expansion caused by the creation of a continuous non-quantized field mass to the linear expansion associated with the recessional velocity of galaxies making it appears as though the expansion of the universe is accelerating.)

However, it should be remember we are not saying that the universe is not expanding, but we are saying that rate of that expansion may be less than predict by many of todayâ€s cosmologists.

Presently the universe appears to be in an overall state of expansion with respect to a fourth *spatial* dimension, due to the recessional velocity of galaxies.

However, someday this expansion will crease and it will enter a contraction phase.

This is primarily due to the mechanism defined earlier in which light or electromagnetic energy is converted to continuous non-quantized field of mass.  This will result in increasing in the total mass content of the universe, with a corresponding increase in its total gravitational contractive forces.

The universe will begin to contract when the contractive force associated with the gravitation potential of this increase mass exceeds the expansive forces associated with the recessional velocity of the galaxies.

However, the contraction or "compression" of the universe will generate heat for the same reason as heat is generated by the "contraction" or compression of a gas.

The heat of a contracting gas generates an expansive force that opposes further contraction of the gas.

Similarly, the heat generated by the contraction of the universe will cause an expansive force that will oppose gravitationally forces that are causing the universe to contact.

The velocity of contraction will increase until the momentum of the galaxies, planets, and the continuous non-quantized mass components of the universe equals the expansive forces generated by the heat generated by its contraction.

At this point in time the total expansive energy of the universe would be equal to the total mass equivalent of that energy or E=mc^2, where "E" equals the total expansive energy of the universe and "m" equals the total energy/mass content of the universe.  From this point on the velocity of the contraction will slow and be maintained by the momentum associated with its remaining energy/mass component.

However, after a certain point in time the heat generated by its contraction will cause its mass component to be converted back to electromagnetic radiation.  This will reduce the total mass content of the universe and attractive gravitational forces associated with it.

This will result in the universe entering an expansive phase because the radiation pressure generated by heat of its collapse will exceed the contractive forces associated with its remaining energy/mass. 

Earlier it was shown that the interaction of an electromagnetic wave with a continuous non-quantized field of energy/mass results in increasing the quantity of a continuous non-quantized field of mass in the volume of space where the interaction occurred.

Therefore, the quantity of a continuous non-quantized field of mass in the universe will increase as it expands due to its interaction with an electromagnetic wave.

Hence the expansion will continue until the total gravitational attractive forces of the mass in the universe exceeds the total expansive forces cause by the heat generated by its contraction.

At this point, the contraction phase will begin again.

Since the universe is a closed system, the amplitude of the expansions and contractions will remain constant because the law of conservation of mass/energy dictates the total mass and energy in a closed system remains constant.

This results in the universe experiencing in a never-ending cycle of expansions and contractions of equal magnitudes.

Many cosmologists do not accept the cyclical scenario of expansion and contractions because they believe a collapsing universe would end in the formation of a singularity similar to the ones found in a black hole and therefore, it could not re-expand.

However, according to the first law of thermodynamic the universe would have to begin expanding before it reached a singularity because that law states that energy in an isolated system can neither be created nor destroyed.

Therefore, because the universe is by definition an isolated system; the energy generated by its gravitational collapse cannot be radiated to another volume but must remain within it.  This means the radiation pressure exerted by its collapse must eventually exceed momentum of its contraction and the universe would have to enter an expansion phase.  This will cause the mass/energy of the universe to oscillate around a point in space. 

This would be analogous to the how momentum of a mass on a spring causes it spring to stretch beyond its equilibrium point resulting it osculating around it. 

There can be no other interoperation if one assumes the validity of the first law of thermodynamics which states that the total energy of the universe is defined in terms of heat and the momentum of its components.  Therefore, when one decreases the other must increase and the universe must oscillate around a point in space if it does enter a contraction phase.

The reason a singularity can form in black hole is because it is not an isolate system therefore the thermal radiation associated with its collapse can be radiated into the surrounding space.  Therefore, its collapse can continue because momentum of its mass can exceed the radiation pressure cause by its collapse in the volume of space surrounding a black hole.

According to this scenario the heat generated by its collapse would have to raise the temperature enough to completely ionize its energy/mass, making it opaque to radiation to account for the observer properties of the Cosmic Background Radiation. 

This would make the Cosmic Background Radiation an integral part of each cycle and provides for observation method to quantify the process.  This is because one could use the first law of thermodynamics to determine if the momentum of the collapsing of energy/mass of the universe would generate enough heat to ionize enough of the universe’s baryonic matter to account for its observed properties.

Later Jeff

Copyright Jeffrey O’Callaghan 2011

The post Dark Matter and the Evolution of the universe appeared first on Unifying Quantum and Relativistic Theories.

The ability to define a mechanism which can resolve the conflict between Maxwell’s classical wave theory of light and the quantization of the electromagnetic field confirmed by the photoelectric effect is one of them.

In the article “Why is mass and energy quantized?” Oct 4, 2007 it was shown that one can understand and derive both the quantum mechanical and wave properties of energy/mass by extrapolating the laws of a classically resonating three-dimensional environment to a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  Additionally it was showed why all forms of energy must be propagated in these resonant systems.

(The concept of a particle having a wave component was first formulated in 1924, when Louis de Broglie he theorized they have a wave properties.  However he was unable to resolve the conflict between it and the quantum mechanical properties of a photon associated with the photoelectric effect.)  

Briefly it showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in one consisting of four spatial dimensions.

The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a “surface” between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the “surface” of a three-dimensional space manifold to oscillate spatially with the frequency associated with the energy of that event.

The oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established space.

Therefore, these oscillations in a “surface” of a three-dimensional space manifold would meet the requirements mentioned above for the formation of a resonant system or “structure” in four-dimensional space if one extrapolated them to that environment. 

Classical mechanics tells us the energy of a resonant system can only take on the discrete or quantized values associated with its fundamental or a harmonic of its fundamental frequency.

Hence, these resonant systems in four *spatial* dimensions would be responsible for the discrete quantized energy associated with the quantum mechanical systems.

Additionally it also tells us why in terms of the physical properties four dimensional space-time or four *spatial* dimensions an electron cannot fall into the nucleus is because, as was shown in that article all energy is contained in four dimensional resonant systems. In other words the energy released by an electron “falling” into it would have to manifest itself in terms of a resonate system. Since the fundamental or lowest frequency available for a stable resonate system in either four dimensional space-time or four spatial dimension corresponds to the energy of an electron it becomes one of the fundamental energy units of the universe.

Yet one cans also define the boundary of a quantum system in terms of the spatial properties of four spatial dimensions.

For example in classical physics, a point on the two-dimensional surface of paper is confined to that surface.  However, that surface can oscillate up or down with respect to three-dimensional space. 

Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate “up” or “down” with respect to a fourth *spatial* dimension.

The confinement of the “upward” and “downward” oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries associated with a particle in the article “Why is energy/mass quantized?“

The photoelectric effect is perhaps the most direct and convincing evidence of the existence of photons and the “corpuscular” nature of light and electromagnetic radiation.  That is, it provides undeniable evidence of the quantization of the electromagnetic field and the limitations of the classical field equations of Maxwell.

This conclusion is based on the observation that the emission of electrons begin as soon as electromagnetic energy of a given frequency strikes the photoelectric material.  This is inconsistent with the wave theory of light because it predicts the delayed emissions of electrons.

In addition, it was observed that varying the intensity of the light does not change the velocity of the electrons ejected but only their numbers, however increasing the frequency does.

Einstein in 1905 successfully explained these observations by assuming the incident light consisted of individual quanta, called photons, that interacted with the electrons in the metal like discrete particles, rather than as continuous waves and that each one carried the energy E = hf, where h is Planck’s constant and f is the frequency.  Therefore, increasing the intensity of the light corresponded to increasing the number of incident photons per unit time (flux), while the energy of each photon remained the same (as long as the frequency of the radiation was held constant). 

These assumptions explain why varying the intensity of the light does not change the velocity of the electrons ejected but only their numbers because according Einstein’s photonic concepts that would result in increasing the number of photons with the same energy thereby causing a greater number of electrons to be ejected.  However, because each photon has the same energy the electrons effect by them would carry the same average energy when ejected.  Additionally it would also explain why increasing the frequency “f” of the incident radiation would increase their average energy because that would increase the average energy of the photons striking the photoelectric material thereby their increasing average energy.

However, assuming as we have done that the quantization of the electromagnetic field is a result of a resonant system formed by a matter wave on “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension allows one to resolve the conflict between those properties and Maxwell’s classical wave interpretation of light.  This is because, it allows one to extrapolate the laws classical wave mechanics in a three-dimensional environment to a fourth *spatial* dimensions to explain its quantization.

Classical Wave Mechanics tells us resonant system must be quantized or have the discrete energies associated with their fundamental or a harmonic of their fundamental frequency.

Yet this means that one could interpret Planck’s constant or “h” in the equation Einstein used to calculate the energy of photon as the energy associated with the fundamental resonant frequency in four *spatial dimensions that defined a photon in the article “Why is mass and energy quantized?”.  Therefore, every photon would have a multiple “h” of that energy.

The reason why, as Einstein noted, “increasing the intensity of the incident radiation causes greater numbers of electrons to be ejected, each carrying the same average energy” is because each photon had the identical frequency and therefore, as was shown in the article “Why is mass and energy quantized?” would contain the same energy.  However this means that increasing the intensity of the incident radiation must mean a proportional an increase in the number of photons striking the photo electric material.  Therefore it follows that increasing the intensity of the incident radiation would cause greater numbers of electrons to be ejected, each carrying the same average energy.   However it allows his concepts to integrated into Maxwell’s wave theory of light because as was shown in that article the energy of a photon is related to the wave properties of its resonant structure.

Additionally, as Einstein also noted as one increased the frequency the average energy of the emitted electrons increases.  This is consistent with the classical wave interpretation of the resonant system associated with a photon in the article “Why is mass and energy quantized?” because it defines their quantized energy in terms of the frequency of a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimensions.  This means that according to Classical Wave Mechanics its quantized energy will be directly related to its frequency of that matter wave and therefore increasing its frequency will also increase the energy of the ejected elections.

The reason why delayed emission is not observed is because as was shown in that article energy can only be propagated in these resonant systems.  Therefore if the energy associated with a quantized resonant “system” of a photon of a given frequency is sufficient it will instantly eject an individual electron off a photoelectric surface while none will be f it is not.

This shows how one can resolve the conflict between Maxwell’s wave theory of light and the quantization of the electromagnetic field confirmed by the photoelectric effect by assuming that the quantization of an electromagnetic field is caused by a resonant system formed by a matter wave moving on a “surface” of three-dimensional space manifold with respect to a fourth *spatial* dimension.

Later Jeff

Copyright Jeffrey O’Callaghan 2011

The post Resolving the conflict between the photoelectric effect and Maxwell’s wave theory of light appeared first on Unifying Quantum and Relativistic Theories.