However this may just be an illusion resulting from a lack of understanding of the quantum environment.

One of the fundament areas where this disconnect appears is in the probabilistic interpretation Schrödinger wave equation

However one could eliminate this disconnect if one could explain the causality of those probabilities in terms of a physical image based on the laws of classical physics similar to how we explain the causality of the movement of the planets around the sun in terms of a physical image of a curvature in space-time.

Granted this will not change the fact that one cannot use quantum mechanics to make precise predictions of future events but it would give us a physical reason why we cannot in terms of our classical understanding of causality.

One way of accomplishing this would be look at the physically observable properties of all quantum systems and determine if by applying the laws of causality in a classical environment one can explain the reason for the probabilities associated with Schrödinger’s equation.

For example in 1924 Louis de Broglie theorized that all quantum objects are physically composed of a wave as was verified by 1927 by Davisson and Germer) when he observed electrons diffracted by crystals.

However, the fact that no one has been able to physically connect the causality of those observable properties to the probabilities of all quantum systems does not change the fact that there must be one because if there wasn’t they could not interact with our environment to create the physically observable properties of the world upon which those probabilities are determined.
One reason for this failure may be due to the fact that those probability are related to the spatial not time dependent properties of the wave function.

If so one may be able to establish the connection by looking at it in terms of its spatial properties instead of the space-time ones associated with Einstein’s theories.

Einstein gave us the ability to do this when defined the geometric properties of space-time in terms of the constant velocity of light because that provided a method of converting a unit of time in a space-time environment of unit of space in four *spatial* dimensions. Additionally because the velocity of light is constant he also defined a one to one quantitative and qualitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

The fact that one can use Einsteinâ€s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with energy in terms of four *spatial* dimensions is one bases for assuming as was done in the article “Defining energy?” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However doing so would have allowed Louis de Broglie to physically define the casualty of the quantum properties associated with Schrödinger equation in terms of a physical or spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension as was done in the article “Why is energy/mass quantized?” Oct. 4, 2007.

Briefly, that article showed the quantized properties of energy/mass are the result of a resonant system formed by a matter “wave” on a “surface” of a three-dimensional space manifold with respect to fourth “spatial” dimension. This is because it showed the four conditions required for resonance to occur in a 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 made up of four.

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* dimension 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 with respect to a fourth *spatial* dimension to oscillate with 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 on a surface of a three-dimensional space manifold.

Yet the classical laws of three-dimensional space tell us the energy of resonant systems can only take on the discontinuous or discreet energies associated with their fundamental or harmonic of their fundamental frequency.

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.

However, these are the similar to the quantum mechanical properties of energy/mass in that they can only take on the discontinuous or discreet energies associated with the formula E=hv where “E” equals the energy of a particle “h” equal Planck’s constant “v” equals the frequency of its wave component.

In other words Louis de Broglie would have been able to physicality connect the properties of his particle waves to the quantum mechanical properties of Schrödinger equation in terms of the discrete incremental energies associated with a resonant system in four *spatial* dimensions if he had assume space was composed of it instead of four dimensional space-time.

Yet it also would have allowed him to define the physical boundaries of a quantum system in terms of the geometric properties of four *spatial* dimensions.

For example in classical physics, a point on the two-dimensional surface of a piece 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?” Oct. 4, 2007.

As mentioned earlier in the article “Defining energy?” Nov 27, 2007 showed all forms of energy can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However assuming the energy associated with Louis de Broglie particle wave is result of a displacement in four *spatial* dimension instead of four dimensional space-time as was done earlier would allow one to define a classical causality for quantum probabilities in terms the observable environment we inhabit.

Classical mechanics tell us that due to the continuous properties of waves the energy the article “Why is energy/mass quantized?” Oct. 4, 2007 associated with a quantum system would be distributed throughout the entire “surface” a three-dimensional space manifold with respect to a fourth *spatial* dimension.

For example Classical mechanics tells us the energy of a vibrating or oscillating ball on a rubber diaphragm would be disturbed over its entire surface while the magnitude of those vibrations would decrease as one move away from the focal point of the oscillations.

Similarly if the assumption that quantum properties of energy/mass are a result of vibrations or oscillations in a “surface” of three-dimensional space is correct then classical mechanics tell us that those oscillations would be distributed over the entire “surface” three-dimensional space while the magnitude of those vibrations would be greatest at the focal point of the oscillations and decreases as one moves away from it.

As mentioned earlier the article “Why is energy/mass quantized?” shown a quantum particle is a result of a resonant structure formed on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Yet Classical Wave Mechanics tells us resonance would most probably occur on the surface of the rubber sheet were the magnitude of the vibrations is greatest and would diminish as one move away from that point,

Similarly a particle would most probably be found were the magnitude of the vibrations in a “surface” of a three-dimensional space manifold is greatest and would diminish as one move away from that point.

This shows that one can define the causality of the probabilities associated Schrödinger wave equation in terms of the laws of causality associated with our observable environment by redefining them in terms of four *spatial* dimensions.

In other words one can eliminate the disconnect between the probabilities associated his equation and a classical environment by defining their causality in terms of the laws of classical physics.

It should be remember Einsteinâ€s genius allows us to choose to define a quantum system in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories thereby giving us a new perspective on the probabilistic properties of a quantum environment and how they physically connected to our observable universe.

Later Jeff

Copyright Jeffrey O’Callaghan 2016

The post The relevance of classical mechanics to a quantum environment. appeared first on Unifying Quantum and Relativistic Theories.

Quantum mechanics defines our observable environment only in terms of the probabilistic values associated with Schrödingerâ€s wave equation.

However it is extremely difficult to define a set of statements which explains how those probabilities are physically connected to it even though it has held up to rigorous and thorough experimental testing.

This may be the reason most physicists consider quantum mechanics only in terms of its mathematical formalization instead trying to understand the meaning of it in terms of the space-time environment we occupy. 
For example in 1924 Louis de Broglie was the first to realize all particles are physically composed of a matter wave as the discovery of electron diffraction by crystals in 1927 by Davisson and Germer) verified.  However in his paper, “Theory of the double solution“ he unsuccessfully attempted to define a physical interpretation of Schrödinger equation in classical terms of space and time.

As is pointed at his biography on the nobleprize.org web site in “1951, he together with some of his younger colleagues made another attempt, one which he abandoned in the face of the almost universal adherence of physicists to the purely probabilistic mathematical interpretation of, Bohr, and Heisenberg.”

However the fact that no has been able to physically connect those probabilities to our environment does not change the fact that there must be one because if there wasn’t they could not interact with it to create the physicality of observable world upon which those probabilities are based.

As mentioned earlier Louis de Broglie and his colleagues tried unsuccessfully to find a physical interpretation of Schrödinger equation in classical terms of space and time.

However the reason for their failure may be due to the fact that it is related to the spatial not time dependent properties of the wave function.

If so one may be able to establish the connection by looking at it in terms of its spatial properties instead of the space-time one Louis de Broglie and his colleagues used.

Einstein gave us the ability to do this defined the geometric properties of space-time in terms of the constant velocity of light and a dynamic balance between mass and energy because that  provided a method of converting a unit of time in a space-time environment of unit of space in four *spatial* dimensions.  Additionally because the velocity of light is constant he also defined a one to one quantitative and qualitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

The fact that one can use Einsteinâ€s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with energy in terms of four *spatial* dimensions is one bases for assuming as was done in the article “Defining energy?” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This would have allowed Louis de Broglie to physically connect the probabilities associated Schrödinger equation to the quantum properties of a matter wave in terms of a physical or spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension as was done in the article  “Why is energy/mass quantized?” Oct. 4, 2007. 

Briefly that article showed that one can do this by assuming they are caused by the formation of a resonant system on a “surface” of a three-dimensional space manifold with respect to fourth “spatial” dimension.  This is because it showed the four conditions required for resonance to occur in a 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 made up of four.

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* dimension 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 with respect to a fourth *spatial* dimension to oscillate with 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 on a surface of a three-dimensional space manifold.

Yet the classical laws of three-dimensional space tell us the energy of resonant systems can only take on the discontinuous or discreet energies associated with their fundamental or harmonic of their fundamental frequency.

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.

However, these are the similar to the quantum mechanical properties of energy/mass in that they can only take on the discontinuous or discreet energies associated with the formula E=hv where “E” equals the energy of a particle “h” equal Planck’s constant “v” equals the frequency of its wave component.

In other words Louis de Broglie would have been able to physicality connect the the quantum mechanical properties of his particle waves to Schrödinger equation in terms of the discrete incremental energies associated with a resonant system in four *spatial* dimensions if he had assume space was composed of it instead of four dimensional space-time.

Yet it also would have allowed him to define the physical boundaries of a quantum system in terms of the geometric properties of four *spatial* dimensions.

For example in classical physics, a point on the two-dimensional surface of a piece 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?” Oct. 4, 2007

As mentioned earlier in the article “Defining energy?” Nov 27, 2007 showed all forms of energy can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However assuming the energy associated with Louis de Broglie particle wave is result of a displacement in four *spatial* dimension instead of four dimensional space-time as was done earlier would allows one to connect the probabilities associated with Schrödinger equation to the physicality of our observable environment we all live in.

Classical mechanics tell us that due to the continuous properties of waves the energy the article “Why is energy/mass quantized?” Oct. 4, 2007 associated with a quantum system would be distributed throughout the entire “surface” a three-dimensional space manifold with respect to a fourth *spatial* dimension.

For example Classical mechanics tells us that the energy of a vibrating or oscillating ball on a rubber diaphragm would be disturbed over its entire surface while the magnitude of those vibrations would decease as one move away from the focal point of the oscillations. 

Similarly if the assumption that quantum properties of energy/mass are a result of vibrations or oscillations in a “surface” of three-dimensional space is correct then classical mechanics tell us that those oscillations would be distributed over the entire “surface” three-dimensional space while the magnitude of those vibrations would be greatest at the focal point of the oscillations and decreases as one moves away from it.

As mentioned earlier the article “Why is energy/mass quantized?” shown a quantum particle is a result of a resonant structure formed on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Yet Classical Wave Mechanics tells us resonance would most probably occur on the surface of the rubber sheet were the magnitude of the vibrations is greatest and would diminish as one move away from that point,

Similarly a particle would most probably be found were the magnitude of the vibrations in a “surface” of a three-dimensional space manifold is greatest and would diminish as one move away from that point.

This shows how one can physically connect the probabilities associated Schrödinger wave equation to our observable environment by redefining it in terms of four *spatial* dimensions.

It should be remember Einsteinâ€s genius allows us to choose to define a quantum system in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories thereby giving us a new perspective on the probabilistic properties of a quantum environment and how they physically connected to our observable universe.

Later Jeff

Copyright Jeffrey O’Callaghan 2015

The post The physical meaning of Schrödinger wave equation appeared first on Unifying Quantum and Relativistic Theories.

Einstein told us that energy and mass are interchangeable however he did not define what mass is.  He only told us how mass interacts with space-time.

As Steven Weinberg said “Mass tells space-time how to curve while space-time tells mass how to move”.

However Einstein’s inability to define or derive the casualty of mass is can be traced to the fact that he chose to define the energy associated with it in terms of four dimension space-time instead of defining the mass associated with energy in terms four *spatial* dimensions.

Yet Einstein gave us the ability to do this when used the equation E=mc^2 and the velocity of light to define the geometric properties of space-time because it allows one to convert a unit of displacement he associated with energy in a four dimensional space-time universe to an equivalent displacement a unit of mass would create in four *spatial* dimensions.  Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words because he defined the geometric relationship between energy and mass in terms of the constant velocity of light means that one can quantitatively and qualitatively define a one to one between the properties of energy in a space-time universe to the physical properties of mass four *spatial* dimensions.

This was the bases for assuming as was done in the article “Defining energy” Nov 27, 2007 that all forms of energy including thermo and inertia or momentum of mass can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of one in a space-time environment.
However changing ones perspective on the geometric structure of the universe form one of space-time to four *spatial* dimensions not only gives one the ability to understand the causality of mass but also give one the ability derive its quantum mechanical properties as was done in the article “Why is energy/mass quantized?” Oct. 4, 2007″ in terms of its wave component and the resonant properties of four *spatial* dimensions.

(Louis de Broglie was the first to predict the existence of the wave properties of mass when he theorized that all particles have a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer).

Briefly that article 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 be meet in one consisting of four.

The existence of four *spatial* dimensions would give a matter wave that Louis de Broglie associated with a particle 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 with respect to a fourth *spatial* dimension at a 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 four *spatial* dimensions.

Classical mechanics tells us that resonant systems can only take on the discrete or quantized energies associated with a fundamental or a harmonic of their fundamental frequency.

However, this does not explain how the boundaries of a particleâ€s resonant structure are defined.

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 geometric boundaries of the resonant system associated with a particle.

Therefore, these resonant systems in a four *spatial* dimensions would define mass and its quantum mechanical properties because of the fact that the volumes of space containing them would have a higher concentration of energy and therefore the mass associated with those volumes would be greater.

This would allow one to, not only understand the causality of the absolute properties of mass such as inertia but it would allow us to derive all of its relativistic ones.

For example one can use these concepts to explain why the corresponding particle types across the three fundamental families of particles in the Standard Model listed in the table below have identical properties except for their mass, which grows larger in each successive family.

As mentioned earlier the article “Why is energy/mass quantized?” showed that one can derive the mass of a particle in terms of the energy contained within a resonant system generated by a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension while the article “Defining energy” showed that one can derive the energy of its environment in terms a displacement in the same three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore using the concepts developed in those articles one could derive the total mass of a particle in terms of the sum of the energies associated with that resonant structure and the displacement in the “surface” of three-dimensional space associated with the energy of the environment it is occupying.

Yet Classical Mechanics tells us there will be specific points in space where the matter wave that Louis de Broglie associated with a particle can interact with the energy content or temperature of its environment to form a resonant system.

Therefore, the mass of each family member would not only be dependent on the energy associated with the resonant system that defined their quantum mechanical properties in the article “Why is energy/mass quantized?” but also on temperature of the environment they are occupying.

Thus suggest the reason “The corresponding particle types across the three families have identical properties except for their mass, which grows larger in each successive family.” is because of an interaction between the resonant properties defined in the article “Why is energy/mass quantized?” and the energy content of the environment they are occupying.

This means the particles in the first family would be found in relativity low energy environments, are relatively stable, and for the most part can be observed in nature.  However, the particles in the second and third families would be for the most part unstable and can be observed only in high-energy environments of particle accelerators.  The exception is the Muon in the second family, which is only observed in the high-energy environment of cosmic radiation.

The relative masses of the fundamental particles increases in each successive family because the higher-energy environments where they occupy would result in the corresponding particles in each successive family to be formed with a greater relative “separation” in the “surfaces” of a three-dimensional space manifold with respect to a fourth *spatial* dimension..

Therefore, the corresponding particles in the second family will have a greater mass than the particles in the first family because the “separation”, with respect to a fourth *spatial* dimension of the three-dimensional space manifold associated with them is greater than the “separation” associated with the first family.

Similarly, the corresponding particles in the third family will have a greater mass than those in the second family because the “separation”, with respect to a fourth *spatial* dimension, of the three-dimensional space manifold associated with them is greater than the spatial “separation” associated with the second family.

Additionally the corresponding particle types across the three families have “identical properties” because as shown in the article “The geometry of quarks” Mar. 15, 2009 they are related to the orientation of the “W” axis of the fourth *spatial* dimension with the axis of three-dimensional space.  Therefore, each corresponding particle across the three families will have similar properties because the orientation of the “W” axis of the fourth *spatial* dimension with respect to the axis of three-dimensional space is the same for the corresponding particles in all of the families.

This explains why “The corresponding particle types across the three families having identical properties except for their mass, which grows larger in each successive family” in terms of the properties of classical resonance and the existence of four *spatial* dimensions.

However it also allows one to derive the absolute properties of mass associated with Newton’s first and second laws of motion because as was shown in the article “The Equivalence Principal: an alternative to space-time” July 15, 2008 all accelerations or forces (including gravitational) can be derive in terms of a curvature in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

(This curvature is analogous to the curvature in space-time Einstein assumed was responsible for gravitational forces.)

Newton’s first law of motion which defines the inertial properties of the mass of an object or particle states that “Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it”

However this is what one would expect if one assumes, as mentioned earlier the momentum of an object is caused by a displacement of a “surface” of a three-dimension space manifold with respect to a fourth *spatial* dimension because according those concepts it would tent to stay rest or once in motion would tend to stay in motion because its displacement would remain constant unless it interacted with an external force or as was shown in the article “The Equivalence Principal: an alternative to space-time” a three dimensional “surface” that was curved with respect to a fourth *spatial* dimension.

However it also allows on to understand the causality of Newton’s second law which defines the relationship between an object’s mass “m”, its acceleration “a”, and why the change in velocity of an object or particle is define by the equation is F = ma because as mentioned earlier, the rest mass of an object is directly proportional to a displacement a “surface” of three-dimensional space manifold with respect to fourth *spatial* dimension.  Therefore, as was shown in the article “Defining energy” there will be a 1 to 1 correspondence between it and the curvature in space associated with the energy required to make a unit change in its displacement with respect to a fourth *spatial* dimension.  Therefore the inertia of an object or its resistance to change in velocity would be directly related to its mass. 

In other words using Einstein’s field equations to redefine his space-time universe in terms of four *spatial* dimension allows one to not only understand and derive the causality of the relativistic properties of mass but also the absolute properties associated with its inertia without the need of assuming the existence of the Higgs Boson.

Later Jeff

Copyright Jeffrey O’Callaghan 2013

The post Deriving mass without the Higgs Boson appeared first on Unifying Quantum and Relativistic Theories.

Therefore the gravitational forces associated with that component of Dark Matter would be “dark” or invisible to our scientific instruments.

However, if Dark Matter or a continuous non-quantized field of energy/mass did make up a significant percentage of the universe’s mass, as observations suggest it does it would have an effect on our understanding of the evolution of the universe for two reasons?  The first is because its attractive properties would affect the evolution of the large scale structures of the universe such as galaxies and galactic clusters.  The second is because of the effect it would have on the propagation of light.

Most scientists are aware that light is shifted towards the red end of the spectrum when it passes though interstellar dust clouds like those found in the Orion Nebula.  However they do not share the same awareness of the effects the existence of a continuous field of energy/mass would have on it.

Yet before we begin to address the reason for those effects it would be beneficial to discuss some other observations that support its existence.

For example in 1927 by Davisson and Germer confirmed Louis de Broglie theory that all particles have a wave component. This is observational proof of the existence of a continuous field of energy/mass because waves are by definition a continuous form of energy and therefore the existence of a continuous field of energy/mass is necessary to support the internal wave component of particles.

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 energy/mass and electromagnetic waves by extrapolating classical 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 in terms of a resonant “system” formed in the continuous field properties of energy/mass in four *spatial* dimensions by extrapolating the laws of classical resonance in a three-dimensional environment to a fourth *spatial* dimension.

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 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 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.

As the article “Why is energy/mass quantized?” showed 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 as is required by the wave properties of the resonant system defined in that article to explain the internal electromagnetic wave properties of a photon in terms of the matter wave that is responsible for its quantum mechanical properties.

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. 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.

Therefore, classical wave mechanics, if extrapolated to four *spatial* dimensions tells us a force would be 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 which will result in its elevated and depressed portions moving towards or become “attracted” to each other.

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

The reason electromagnetic energy 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 the quantized resonant systems called photons.

Yet if it is true that electromagnetic waves are propagated in a continuous field of energy/mass it would affect our present understanding of the evolution of the universe because most of them are based on the fact that light does not interact with space.

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.  

Yet, as mentioned earlier the existence of Dark Matter or a continuous non-quantized field 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 thereby reducing the magnitude of the distance predicted by that law.

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.

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 one can show why low intensity shifts in wavelength of photons can occur when they interacted with a continuous non-quantized form of energy/mass in terms of Classical wave mechanics if one assumes as was done in the article “Why is energy/mass quantized?” that their quantum mechanical properties are a result of a matter wave in a continuous non-quantized field of energy/mass.  This is because the velocity of electromagnetic energy is constant while that of an electron is not. Therefore, the only way to alter the energy, direction or momentum of light is by “degrading” or changing its wavelength. Yet, if the electromagnetic and particle properties of both a photon and electron are a result of a matter wave is as suggested by that article 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 for both an electron and a photon regardless of wavelength.

In other words if it is true that photons do interact with Dark Matter them we will have to reevaluate the distances calculated by Hubble’s law and our understanding of the evolution the universe which is based on it.

Later Jeff

Copyright Jeffrey O’Callaghan 2012

The post Dark Matter and its affect on Hubble’s law appeared first on Unifying Quantum and Relativistic Theories.

For example an electron in certain atoms will spontaneously decay after being excited by emitting pairs of polarized photons such that one is aligned horizontally the other vertically.  According to quantum mechanics these photons are entangled and act of observing one instantly affects the other no matter how far they are apart.
This instantaneous communication between the entangled photons is at the heart of quantum entanglement.  This is the “spooky action at a distance” Einstein believed was theoretically implausible because according to Relativistic theories information cannot be propagated instantaneously but only at the speed of light.

To demonstrate this 1935, Einstein co-authored a paper with Podolsky and Rosen which was intended to show that Quantum Mechanics could not be a complete theory of nature.  The first thing to notice is that Einstein was not trying to disprove Quantum Mechanics in any way.  In fact, he was well aware of its power to predict the outcomes of various experiments.  What he was trying to show was that there must be a “hidden variable” that would allow Quantum Mechanics to become a complete theory of nature

The argument begins by assuming that there are two systems, A and B (which might be two free particles), whose wave functions are known.  Then, if A and B interact for a short period of time, one can determine the wave function which results after this interaction via the Schrödinger equation or some other Quantum Mechanical equation of state.  Now, let us assume that A and B move far apart, so far apart that they can no longer interact in any fashion.  In other words, A and B have moved outside of each other’s light cones and therefore are spacelike separated.

With this situation in mind, Einstein asked the question: what happens if one makes a measurement on system A?  Say, for example, one measures the momentum value for system A.  Then, using the conservation of momentum and our knowledge of the system before the interaction, one can infer the momentum of system B.  Thus, by making a momentum measurement of A, one can also measure the momentum of B.  Recall now that A and B are “spacelike” separated, and thus they cannot communicate in any way.  This separation means that B must have had the inferred value of momentum not only in the instant after one makes a measurement at A, but also in the few moments before the measurement was made.  If, on the other hand, it were the case that the measurement at A had somehow caused B to enter into a particular momentum state, then there would need to be a way for A to signal B and tell it that a measurement took place.  However, the two systems cannot communicate in any way!

If one examines the wave function at the moment just before the measurement at A is made, one finds that there is no certainty as to the momentum of B because the combined system is in a superposition of multiple momentum eigenstates of A and B.  So, even though system B must be in a definite state before the measurement at A takes place, the wave function description of this system cannot tell us what that momentum is!  Therefore, since system B has a definite momentum and since Quantum Mechanics cannot predict this momentum, Quantum Mechanics must be incomplete.

In response to Einstein’s argument about incompleteness of Quantum Mechanics, John Bell derived a mathematical formula that quantified what you would get if you made measurements of the superposition of the multiple momentum eigenstates of two particles.  If local realism was correct, the correlation between measurements made on one of the pair and those made on its partner could not exceed a certain amount, because of each particle’s limited influence.

In other words he showed there must exist inequities in the measurements made on pairs of particles that cannot be violated in any world that included both their physical reality and their separability because of the limited influence they can have on each other when they are “spacelike” separated.

When Bell published his theorem in1964 the technology to verify or reject it did not exist.  However in the early 1980s, Allen Aspect performed an experiment with polarized photons that showed that the inequities it contained were violated.

Many believed this provided experimental verification of the concept of Quantum entanglement.  Additionally it meant that science has to accept that either the reality of our physical world or the concept of separability does not exist.

However this may not be true because in the article “The *reality* of quantum probabilities” Mar. 31 2011 it was shown the probability functions quantum mechanics associates the wave function can be understood by assuming it is physically a result of a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Very briefly the article “Why is energy/mass quantized?” Oct. 4, 2007 showed that one can derive the quantum mechanical properties energy/mass by extrapolating the laws of classical resonance to a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

(Louis de Broglie was the first to predict the existence of a continuous form of energy/mass when he theorized all particles have a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.)

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 be meet in one consisting of a continuous non-quantized field of energy/mass and 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 space (the substance) to oscillate with 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 it.

Observations of a three-dimensional environment show the energy associated with resonant system 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.

Therefore this defines a physical mechanism responsible for why energy/mass is quantized in terms of a matter wave move on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

In an earlier article “Embedded dimensions” Oct. 4, 2007 it was shown that one can derive all forms of energy including that of quantum systems in terms of displacement in a *surface*that manifold

However assuming its energy is result of a displacement in four *spatial* dimension allows one to derive, the probability distribution associated with the wave function of individual particles by extrapolating the laws of a three-dimensional environments to a fourth *spatial* dimension.

Classical mechanics tell us that because of the continuous properties of space the oscillations the article “Why is energy/mass quantized?” associated with a quantum system would be distributed throughout the entire “surface” a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This would be analogous to what happens when one vibrates a rod on a continuous rubber diaphragm.  The oscillations caused by the vibrations would be felt over its entire surface while their magnitudes would be greatest at the point of contact and decreases as one moves away from it.

However, this means if one extrapolates the mechanics of the rubber diaphragm to a “surface” of a three-dimensional space manifold one must assume the oscillations associated with each individual quantum system exists everywhere in three-dimensional space.  This also means there would be a non-zero probability they could be found anywhere in our three-dimensional environment.

As mentioned earlier the article “Why is energy/mass quantized?” showed a quantum mechanical system is a result of a resonant structure formed on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Yet Classical Wave Mechanics tells us that resonance would most probably occur on the surface of the rubber diaphragm were the magnitude of the vibrations is greatest and would diminish as one move away from that point,

Similarly a quantum system would most probably be found were the magnitude of the vibrations in a “surface” of a three-dimensional space manifold is greatest and would diminish as one move away from that point,

However this also means each individual particle in a quantum system has its share its wave and probably function with all other particles and therefore the total probability of a quantum system being in a given configuration when observed would be equal to the sum of the individual probability functions of eachone  in that system.

As mentioned earlier Allen Aspect verified that Bell inequities were violated by the quantum mechanical measurements made on pairs of polarized photons that were spacelike separated or in different local realities.

Yet, as just mentioned the wave or probability function of a quantum system is a summation of the probably function of all of the particles it contains.  Therefore, two particles which originated in the same quantum system and were moving in opposite directions would have identical wave or probability functions even if they were not physically connect.

The measurements Allen Aspect made on the polarized photon that verified that Bells inequity was violated involved finding a correlation between the probabilities of each particle being in a given configuration based on the concepts of quantum mechanics.  When this correlation was found many assumed that somehow they must be entangled or physical connected even though they were in different local realities.  In other words the Newtonian concept separability does not apply to quantum environment. 

However, this may not be true.

According to quantum mechanics act of measuring the state of one of pair of entangled photons instantly affects the measurement of the other no matter how far they are apart.  Yet if it is true as mentioned earlier that each particle shares an identical wave or probably function as it move through space the measurement of the state of one particle would be reflected in the measurement of the other because those measured states will have the same probability of occurring in each particle.

In other words the reason why Bell’s inequity is violated in quantum system is not because they are physically entangled or connected at the time of measurement but because their individual wave or probability functions were “entangled” or identical at the time of their separations and remained that way as they moved apart.  Therefore even though they are not physical connected measurements based on their quantum mechanical probability function would be.

Additionally quantum entanglement is defined in terms probability. Therefore, there would be a non-zero probably that bellâ€s inequity will be violated when measuring the influence of one particle on another because those measurement are based on probabilities. Therefore, one could mathematical quantify the scenario proposed above because the probability of this occurring should mirror the individual quantum mechanical probability function of each individual particle.

But to say that the correlation between measurements of the quantum characteristics of two particles is because they are entangle or are physically connected is like saying the correlation between the color characteristics of the hair of identical twins is because they have been physically connect throughout their entire life.

This shows how one can by extrapolating the classical laws governing a three-dimensional environment to a fourth *spatial* dimension define a mechanism responsible for the correlation of the quantum mechanical measurements of particles that exist in non-local environments while maintaining the classical concepts of reality and separability.

Later Jeff

Copyright Jeffrey O’Callaghan 2011

The post Quantum entanglement: A Classical non-locality appeared first on Unifying Quantum and Relativistic Theories.

One is that it would allow one to understand why a proton and an election have different masses even though the absolute magnitude of their charge is the same in terms of the laws of classical three-dimensional space.
In the article “Why is energy/mass quantized?” Oct. 4, 2007 it was showed one can derive its quantum mechanical properties by extrapolating the laws of classical resonance in a three-dimensional environment to a matter wave in a continuous non-quantized field of energy/mass moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

(Louis de Broglie was the first to predict the existence of a continuous field of energy/mass when he theorized that all particles had a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.)

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 a matter wave the ability to oscillate spatially on a “surface” between a third and fourth *spatial* dimension 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 with respect to a fourth *spatial* dimension to oscillate with 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 discrete quantized values associated with its resonant or a harmonic of its resonant frequency.

The article “Why is energy/mass quantized?” showed why these resonant systems in four *spatial* dimensions are responsible for the discrete quantized energies associated with protons and electrons.

However, one can also use the above concept of four *spatial* dimensions to understand the physical boundaries of a proton and electron.  

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 internal structure of quarks, a fundament component of particles was derived in the article “The geometry of quarks” Mar. 15, 2009 in terms of an interaction between a continuous energy/mass component of space and the geometry of four *spatial* dimensions.)

Meanwhile in the article “The reality of the fourth *spatial* dimension” Dec. 1, 2010 it was shown that one can derive all forms of energy including gravity in terms of a displacement or curvature in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This curvature is analogous to the space-time curvature “The General Theory of Relativity” hypothesized is responsible for gravitational energy.

One advantage, as will be shown below to defining the universe in terms of four *spatial* dimensions is that allows for a bidirectional spatial movement of a “surface” of a three-dimensional space manifold whereas defining it in terms of four dimensional space-time does not.  This is because one can move in two directions up or down, forwards or backwards in a spatial dimension but in only one direction, forward in a time dimension.

For example in the article “Electromagnetism in four *spatial* dimensions” Sept. 27, 2007 showed one can derive the polarity and absolute magnitude of the charge on a proton and electron in terms of a bidirectional displacement of a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

It derived the positive charge of a proton in terms of a “downward” displacement  in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  While the negative the charge of an electron will be derived in terms of oppositely directed “upward” displacement in that surface.

One can understand how these displacements would define their electrical properties by extrapolating the laws of classical mechanics of displacements in water to it.

Classical mechanics tell us that if one lifts a bucket full of water or pushes down on an empty one a force will be developed that will cause the bucket raised above or the one that was pushed down below its surface to move or become “attracted” to its surface.

Similarly if one lifts or pushed down on a “surface” of three-dimensional space manifold a force will be developed that will cause the raised or depressed regions to become attracted to its surface.

Therefore, one could derive why the unlike charges attract each other in terms of a classical mechanism if one assumes that they are a result oppositely directed of a displacement  in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

Additional classical mechanics also tells us there is a direct relationship between the magnitudes of a displacement in the surface of water to the magnitude of the energy resisting that displacement.

For example the force resisting the further displacement of an empty bucket in water is directly related to the depth of that displacement.

This defines why like charges repel each other because the displacement in a “surface” of a three-dimensional space manifold 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 energy resisting the displacement will be greater for two identical charges than it would be for a single charge.

The mechanism responsible for generating this movement was defined in the article “The reality of the fourth *spatial* dimension” were it was shown when mass is converted to energy or energy to mass, the “surface” of a three-dimensional space manifold either “expands” or “contracts” with respect to a fourth *spatial* dimension.  This would result in the movement of that “surface” respect to it.

The effects these movements have on the density of continuous energy/mass component of the resonant systems that defined the quantum mechanical properties of a proton and electron in the article “Why is energy/mass quantized?” are analogous to the effects high and low pressure areas in the earth’s atmosphere have on density of air molecules.

In a high-pressure area, the energy of air molecules is directed downwards towards the surface of the earth.  This results in the density of the air molecules at the apex of a high-pressure area to be greater than their density in the volume of air adjacent to it.

Conversely, in a low-pressure area the energy of the air molecules is directed upward away from the surface of the earth which results in their density at the apex of a low-pressure area to be less than the density of the air molecules in the volume of air adjacent to it.

A similar effect would occur in space with respect to the density of their continuous energy/mass component

In a dimensional “high-energy volume” associated with the positive charge of a proton, the energy of the continuous energy/mass component of space would be directed “downward” with respect to a fourth *spatial* dimension, towards the “surface” of a three-dimension space manifold.  This results in its density in the resonant system of a proton to be greater relative to its density in the volume adjacent to it.

This is analogous to how the air molecules at the apex of a high-pressure area in the earth’s atmosphere would be denser than the air molecules in the volume of air adjacent to the apex of a high-pressure area.

Conversely in a dimensional “low-energy volume” associated with the negative charge of an electron, the energy of the continuous energy/mass component of space would be directed “upward” with respect to a fourth *spatial* dimension, away from the “surface” of a three-dimension space manifold.  This results in its density in the resonant system of an electron to be less relative to its density in the volume adjacent to it.

Therefore, the density of the continuous energy/mass component of the resonant system of a proton will be greater than that of an electron even though the absolute magnitude electrical energy or charge is the same.

This is analogous to why the density of air molecules in a high-pressure area is greater that in a low-pressure area even though the magnitude of their energy is same but oppositely directed.

In the article “Gravity and electromagnetism linked in four *spatial* dimensions” Dec 14, 2007 it was shown that the mass of a particle or object is directly related to the density or concentration of the continuous field of energy/mass contained in the volume of a particle or object.

Therefore because the density, as mentioned earlier of the continuous non-quantized field of energy/mass is greater in a proton than that of an electron its mass will also be greater than that of an electron.

This shows that one of the theoretical advantages to define the space in terms of a continuous field of energy/mass and four *spatial* dimensions instead of four dimensional space time is that it would allow one to understand why the relative mass of a proton is greater than that of an electron even though the absolute magnitude of their charge is the same by extrapolating the laws of a classical environment to four *spatial* dimensions.

Later Jeff

Copyright Jeffrey O’Callaghan 2011

The post The relative masses of a proton and electron appeared first on Unifying Quantum and Relativistic Theories.

One is that it would allow to understand why it is not necessary to assume there must be “hidden variable” that would allow Quantum Mechanics to become a complete theory of nature in order to maintain the classical concepts of separability.

In 1935, Einstein co-authored a paper with Podolsky–Rosen which came to be called the EPR Paradox.  Its intent was to show that Quantum Mechanics could not be a complete theory of nature.  The first thing to notice is that Einstein was not trying to disprove Quantum Mechanics in any way.  In fact, he was well aware of its power to predict the outcomes of various experiments.  What he was trying to show was that there must be a “hidden variable” that would allow Quantum Mechanics to become a complete theory of nature

The argument begins by assuming that there are two systems, A and B (which might be two free particles), whose wave functions are known.  Then, if A and B interact for a short period of time, one can determine the wave function which results after this interaction via the Schrödinger equation or some other Quantum Mechanical equation of state.  Now, let us assume that A and B move far apart, so far apart that they can no longer interact in any fashion.  In other words, A and B have moved outside of each other’s light cones and therefore are spacelike separated.

With this situation in mind, Einstein asked the question: what happens if one makes a measurement on system A?  Say, for example, one measures the momentum value for it.  Then, using the conservation of momentum and our knowledge of the system before the interaction, one can infer the momentum of system B.  Thus, by making a momentum measurement of A, one can also measure the momentum of B.  Recall now that A and B are spacelike separated, and thus they cannot communicate in any way.  This separation means that B must have had the inferred value of momentum not only in the instant after one makes a measurement at A, but also in the few moments before the measurement was made.  If, on the other hand, it were the case that the measurement at A had somehow caused B to enter into a particular momentum state, then there would need to be a way for A to signal B and tell it that a measurement took place.  However, the two systems cannot communicate in any way!

If one examines the wave function at the moment just before the measurement at A is made, one finds that there is no certainty as to the momentum of B because the combined system is in a superposition of multiple momentum eigenstates of A and B.  So, even though system B must be in a definite state before the measurement at A takes place, the wave function description of this system cannot tell us what that momentum is!  Therefore, since system B has a definite momentum and since Quantum Mechanics cannot predict this momentum, Quantum Mechanics must be incomplete.

In response to Einstein’s argument about incompleteness of Quantum Mechanics, John Bell derived a mathematical formula that quantified what you would get if you made measurements of the superposition of the multiple momentum eigenstates of two particles.  If local realism was correct, the correlation between measurements made on one of the pair and those made on its partner could not exceed a certain amount, because of each particle’s limited influence.

In other words he showed there must exist inequities in the measurements made on pairs of particles that cannot be violated in any world that included both their physical reality and their separability because of the limited influence they can have on each other when they are “spacelike” separated.

When Bell published his theorem in1964 the technology to verify or reject it did not exist.  However in the early 1980s, Allen Aspect performed an experiment with polarized photons that showed that the inequities it contained were violated.

This meant that science has to accept that either the reality of our physical world or the concept of separability does not exist.

Many would prefer to assume the separability defined by Newtonian physics does not exist instead of reality of our particle world because without that “reality” Einstein and many others believe science would have little meaning.

However in the article “The *reality* of quantum probabilities”  it was shown the probability functions quantum mechanics associates the wave function of a particle is a result of a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Very briefly the article “Why is energy/mass quantized?” Oct. 4, 2007 showed that one can derive the quantum mechanical properties energy/mass by extrapolating the laws of classical resonance to a matter wave in a continuous non-quantized field of energy/mass moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

(Louis de Broglie was the first to predict the existence of a continuous form of energy/mass when he theorized all particles have a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.)

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 be meet in one consisting of a continuous non-quantized field of energy/mass and 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 continuous non-quantized field of energy/mass to oscillate with 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 it.

These resonant systems are responsible for the quantum mechanical properties energy/mass.

In earlier article “Embedded dimensions” Oct. 4, 2007 it was shown that one can derive all forms of energy including that of a quantum system in terms of displacement in a *surface* of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However assuming its energy is result of a displacement in four *spatial* dimension allows one to derive, the probability distribution associated with its wave function of individual particles by extrapolating the laws of a three-dimensional environments to a fourth *spatial* dimension.

Classical mechanics tell us that because of the continuous properties of waves the article “Why is energy/mass quantized?” associated with a quantum particle its energy would be distributed throughout the entire “surface” a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This would be analogous to what happens when one vibrates a rod on a continuous rubber diaphragm.  The oscillations caused by the vibrations would be felt over its entire surface while their magnitudes would be greatest at the point of contact and decreases as one moves away from it.

However, this means if one extrapolates the mechanics of the rubber diaphragm to a “surface” of a three-dimensional space manifold one must assume the oscillations the associated with each individual quantum system must simultaneously exists everywhere in three-dimensional space.  This also means there would be a non-zero probability they could be found anywhere in our three-dimensional environment.

As mentioned earlier the article “Why is energy/mass quantized?” showed a quantum mechanical system is a result of a resonant structure formed on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Yet Classical Wave Mechanics tells us that resonance would most probably occur on the surface of the rubber sheet were the magnitude of the vibrations is greatest and would diminish as one move away from that point,

Similarly a quantum system would most probably be found were the magnitude of the vibrations in a “surface” of a three-dimensional space manifold is greatest and would diminish as one move away from that point,

However this means each individual particle in a quantum system has its own wave and probably function and therefore the total probability of a quantum system being in a given configuration when observed would be equal to the sum of the individual probability functions of each particle in that system.

As mentioned earlier Allen Aspect verified that Bell inequities were violated by the quantum mechanical measurements made on pairs of polarized photons that were space like separated or in different local realities.

Yet, as just mentioned the wave or probability function of a quantum system is a summation of the probably function of all of the particles it contains.  Therefore, two particles which originated in the same quantum system and were moving in opposite directions would have identical wave or probability functions even if they were not physical connected.

The measurements Allen Aspect made on the polarized photon that verified that Bells inequity was violated involved finding a correlation between the probabilities of each particle being in a given configuration based on the concepts of quantum mechanics.  When this correlation was found many assumed that somehow they must be entangled or physical connected even though they were in different local realities.  In other words the Newtonian concept separability does not apply to quantum environment. 

However, this may not be true.

According to quantum mechanics act of measuring the state of a pair of entangled photons instantly affects the other no matter how far they are apart.  Yet if it is true as mentioned earlier that each particle has an identical wave or probably function as it moves through space the measurement of the state of one particle would be reflected in the measurement of the other because those measured states would have the same probability of occurring in each particle.

In other words the reason why Bell’s inequity is violated in quantum system is not because they are physically entangled or connected at the time of measurement but because their individual wave or probability functions were “entangled” or identical at the time of their separations and remained that way until a measurement was made.

But to say the correlation of the quantum characteristics of two particles are identical because they are entangle or are physically connected is like saying the correlation between the color characteristics of the hair of identical twins is because they have been physically connect throughout their entire life.

This shows that Quantum Mechanics can be consider “complete theory of nature”, contrary to what Einstein believed because one can define a mechanism responsible for the correlation of the quantum characteristics of particles that exist in non-local environments by extrapolating the “reality” of our three dimensional world to a fourth *spatial* dimension.

Later Jeff

Copyright Jeffrey O’Callaghan 2011

The post The Reality behind the EPR Paradox appeared first on Unifying Quantum and Relativistic Theories.

If so one should be able to derive the strong force in those terms.

The strong force, also known as the strong interaction, is the strongest force in the universe, 10³⁸ times stronger than gravity and 100 times stronger than the electromagnetic force.  However, it is only effective on length-scales of the atomic nucleus and drops rapidly off as the distance from the nucleus increases.

Earlier in the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown that one can derive the quantum mechanical properties of energy/mass by extrapolating the laws of classical resonance in a three-dimensional environment to a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
(Louis de Broglie was the first to predict the existence of a matter wave when he theorized that all particles have a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.)

Briefly it was shown 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 be meet by a matter wave in an environment 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 with respect to a fourth *spatial* dimension to oscillate 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 in four *spatial* dimensions.

These resonant systems are responsible for the quantum mechanical properties energy/mass.

Later in the article “The geometry of quarks” Mar. 15, 2009 it was shown that one can understand why a particle is made up of three quarks of different “colors” again by extrapolating the geometric of three-dimensional space to a fourth while the article “Embedded dimensions” Oct. 22. 2007 showed it is possible to define all forms of energy including electrical in terms of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Using the concepts developed in those articles one derive the mechanism responsible for why observe of particles are made up of distinct components called quarks of which there are six types, the UP/Down, Charm/Strange and Top/Bottom.  The Up, Charm and Top have a fractional charge of 2/3.  The Down, Strange and Bottom have a fractional charge of -1/3.  Scientists have also determined that quarks can take on one of three different configurations they have designated by the colors red, blue, and green.

The explanation is based in part on the fact that we as three-dimensional beings can only observe three of the four *spatial* dimensions.  Therefore, the energy associated with a displacement in its “surface” with respect to a fourth *spatial* dimension will be observed by us as being directed along that “surface”.  However, because two of the three-dimensions we can observe are parallel to that surface we will observe it to have 2/3 of the total energy associated with that displacement and we will observe the other 1/3 as being directed along the signal dimension that is perpendicular to that surface.

This means the 2/3 fractional charge of the Up, Charm and Top may be related to the energy directed along a “surface” of a displaced three-dimensional space manifold with respect to a four *spatial* dimension while the -1/3 charge of The Down, Strange and Bottom may be associated with the energy that is directed perpendicular to that “surface”.

The reason why quarks come in three configurations or colors with a fractional charge of 1/3 or 2/3 may be because, as was shown in the article “Embedded dimensions” there are three ways the individual axis of three-dimensional space can be oriented with respect to a fourth *spatial* dimension.  Therefore, the configuration or “colors” of each quark may be related to how its energy is distributed in three-dimensional space with respect to a fourth *spatial* dimension.

However, it also explains why it takes three quarks of different “colors” to form a particle because, as mentioned earlier one can define a particle in terms of a resonant system on a “surface” a three-dimensional space manifold with respect to a fourth *spatial* dimension.  If the colors of each quark represent the central axis associated with its charge then to form a stable resonate system would require three quarks that have different central axis to balance its energy with respect to the axes of three-dimensional space.  A particle could not exist if two quarks have the same central axis or color because it would cause an energy imbalance along that axis.  Therefore, a particle consisting of anything but quarks of three different colors would not be stable.

A proton contains two up Quarks with a +2/3 charge and one down quark with a -1/3 charge.  This tells us because they are stable that the resonant interaction of their geometries contains more energy that the electrical repulsive energy associated with their positive charge.

It is this excess resonant binding energy associated with their dimensional properties defines the causality of the strong force and the stability of a nucleus.

However, its components or protons and neutrons must be physically close enough for them to share this excess energy to create a stable one.

The sharing of this excess binding energy is also responsible for the creation of neutrons because geometrically it takes less energy for a volume to contain the two up quarks and two down quarks of a proton and neutron instead of four up quarks and two down quarks of two protons. In other words their electrical repulsive energy associated with the quarks is cut in half when the volume contains a proton and neutron instead of two protons and therefore energy/mass component of that volume will be in the lowest energy state possible.

However, the addition of a neutron to a nucleus adds the excess binding energy associated with its resonant system without the repulsive effects associated with of the positive charge of a proton.

Therefore, the existence of neutrons in a nucleus allows for creation of larger ones consisting of multiple positively charged protons because they add the binding energy associated with their resonant system without adding any repulsive electrical charge.

Yet this indicates that the binding energy of the strong force would be related to the size of the nucleus after a certain atomic weight is reached a nucleus will become physically too large for the individual resonant “structures” associated with the protons and neutron to uniformly share the energy require to maintain its structure.  This will result in that nucleus expelling the energy/mass required to reduce its physical size to a point where a stable nucleonic structure can be maintained.  Therefore, any nucleus that is physically larger than this critical value will be radioactive.

Additionally, the nucleus of atoms that have an atomic weight less than the critical value would increase its weight and size by “absorbing” energy/mass from an external source.  This will result in increasing the size and atomic number of that nucleus.

This indicates that the effectiveness of the strong nuclear force in absorbing or emitting energy/mass would only be effective on length-scales of the atomic nucleus and would drop rapidly off as the distance from the nucleus increases.

This shows how one can derive mechanism responsible for the strong nuclear force by extrapolating the classical laws governing resonance in a three-dimensional environment to one made up of four.

Later Jeff

Copyright Jeffrey O’Callaghan 2011

The post The Strong force in four *spatial* dimensions appeared first on Unifying Quantum and Relativistic Theories.

If so one should be able to define the weak force in those terms.

The weak force is responsible for changing to one quark to another or a lepton to another lepton – the so-called “flavor changes” when particles undergo radioactive decay.  In Physics speak the weak interaction involves the exchange of the intermediate vector bosons, the W and the Z.

Earlier in the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown that one can derive the quantum mechanical properties of energy/mass by extrapolating the laws of classical resonance in three-dimensional space to a matter wave on a surface of a three dimensional space manifold with respect to four *spatial* dimension.
(Louis de Broglie was the first to predict the existence of a matter wave when he theorized that all particles have a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer. )

Briefly it was shown 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 be meet by a matter wave in an environment 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 with respect to a fourth *spatial* dimension to oscillate 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 four *spatial* dimensions.

These resonant systems are responsible for the quantum mechanical properties energy/mass.

Later in the article “The geometry of quarks” Mar. 15, 2009 it was shown that one can understand why a particle is made up of three quarks of different “colors” again by extrapolating the geometric of three-dimensional space to a fourth while the article “Embedded dimensions” Oct. 22. 2007 showed it is possible to define all forms of energy including electrical in terms of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Using the concepts developed in those articles one derive the mechanism responsible for why observe of particles are made up of distinct components called quarks of which there are six types, the UP/Down, Charm/Strange and Top/Bottom.  The Up, Charm and Top have a fractional charge of 2/3.  The Down, Strange and Bottom have a fractional charge of -1/3.  Scientists have also determined that quarks can take on one of three different configurations they have designated by the colors red, blue, and green.

The explanation is based in part on the fact that we as three-dimensional beings can only observe three of the four *spatial* dimensions.  Therefore, the energy associated with a displacement in its “surface” with respect to a fourth *spatial* dimension will be observed by us as being directed along that “surface”.  However, because two of the three-dimensions we can observe are parallel to that surface we will observe it to have 2/3 of the total energy associated with that displacement and we will observe the other 1/3 as being directed along the signal dimension that is perpendicular to that surface.

This means the 2/3 fractional charge of the Up, Charm and Top may be related to the energy directed along a “surface” of a displaced three-dimensional space manifold with respect to a four *spatial* dimension while the -1/3 charge of The Down, Strange and Bottom may be associated with the energy that is directed perpendicular to that “surface”.

The reason why quarks come in three configurations or colors with a fractional charge of 1/3 or 2/3 may be because, as was shown in the article “Embedded dimensions” there are three ways the individual axis of three-dimensional space can be oriented with respect to a fourth *spatial* dimension.  Therefore, the configuration or “colors” of each quark may be related to how its energy is distributed in three-dimensional space with respect to a fourth *spatial* dimension.

However, it also explains why it takes three quarks of different “colors” to form a particle because, as mentioned earlier one can define a particle in terms of a resonant system on a “surface” a three-dimensional space manifold with respect to a fourth *spatial* dimension.  If the colors of each quark represent the central axis associated with its charge then to form a stable resonate system would require three quarks that have different central axis to balance its energy with respect to the axes of three-dimensional space.  A particle could not exist if two quarks have the same central axis or color because it would cause an energy imbalance along that axis.  Therefore, a particle consisting of anything but quarks of three different colors would not stable.

This suggests that the stability of the energy/mass components of particles are related to a resonant interaction between the components of three and fourth *spatial* dimensions.

As mentioned earlier the weak force manifests itself in the transmutation of a quark from one flavor or color to another when nuclear particles decays and manifest itself by changing one quark to another, or a lepton to another lepton, the so-called “flavor or color changes”.

However this is what one would expect if their stability was related to, as mentioned above the geometric configuration of their central axis because the only thing that distinguishes their color or flavor is how their central axes in the fourth *spatial* dimension orientated with respect to three-dimensional space.   If the individual quark components of a particle were not in the lowest energy configuration they would rotate around that axis until they were. 

However, as mentioned earlier a particleâ€s stability is related to how the central axis of its component quarks are oriented with respect to a fourth *spatial* dimension.  Therefore the weak force could be defined in terms of the energy associated with their most stable geometric configuration.  In other words to form a stable particle the central axis of its quarks would have to rotate around their fourth dimensional axis until the particle they were a part of had obtained the lowest geometric energy configuration possible with respect to a fourth *spatial* dimension. 

Hence one could derive the casualty of the transmutation or the flavor or color change of quarks from to another in terms of the reconfiguration of its central axis with respect to a fourth *spatial* dimension required to form a stable particle.

This is analogous to the central axis of a wind vane rotates in three-dimensional towards the direction of the wind to reduce the amount of force or energy on its two-dimensional surface by the wind.

Similarly the three-dimension axis of quarks will rotate in four *spatial* dimensions to reduce the energy content of a particle to its lowest level.

As mentioned earlier the binding energy holding quarks together is dependent on the resonant interaction their central axis.  Therefore, magnitude of weak nuclear force binding them together would be associated with the flavor or color change that occurs when an atomic decay takes place.

The reasons the weak force manifests itself in the exchange the vector particles called the W and  Z bosons is because as was shown in the article “Why is energy/mass quantized?” all energy is propagated in discrete resonant structures.  Therefore, it will have particle properties that article associates with them.

This shows how one can derive mechanism responsible for the weak force by extrapolating the classical laws governing resonance in a three-dimensional environment to one made up of four *spatial* dimensions.

Later Jeff

Copyright Jeffrey O’Callaghan 2011

The post The weak force in four *spatial* dimensions 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.