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.

In other words can one use our everyday experiences to understand the irrationality behind many of the assumptions made by quantum mechanics and integrate them into the space-time environment in which we all live

For example the paradoxical wave–particle behavior of energy/mass, one of the fundamental concepts defining Quantum mechanics defies the “reality” of the four dimensional world we live in because of its inability to describe/define how quantum-scale objects can simultaneously exist as waves and particles.  Many have tried to explain it as a fundamental property of the Universe, while alternative interpretations explain the duality as an emergent, second-order consequence of various limitations of the observer.

However, it is possible to explain the wave–particle duality of the quantum world in terms of the “reality” of classical concepts and four dimensional space-time by redefining Einstein’s space-time environment to its equivalent four spatial dimension counterpart because it will allow one to directly apply classical concepts of Newtonian space to the wave properties quantum mechanics associates with particles.

(The reasons will become obvious latter.)

Einstein gave us the ability to do this when he used the velocity of light to define the geometric properties of space-time because it allows one to convert a unit of time in his four dimensional space-time universe to a unit of a space in an environment consisting  four spatial dimensions which identical to those of our three-dimensional space.  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 by mathematically defining the geometric properties of time in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of four *spatial* dimensions and gave us the ability to redefine the curvature or displacement he associated with energy/mass in a space-time environment to a spatial displacement in a fourth *spatial* dimension.

This, as mentioned earlier will allow us to understand the reasons behind the paradoxical wave–particle duality of light when it is partially reflected by two surfaces, as outlined on pages 17 thru 23 of Richard P Feynman book “QED The Strange Theory of Light and Matter” in terms of the laws of classical physics.

On those pages he writes that by placing two glass surfaces exactly parallel to each other one can observe how the photons of light reflected from the bottom surface interact with those reflected from the top surface.  Depending on the distance between the glass surfaces he can determine, by using a photo detector, that four percent or 4 out of 100 photons reflected from the lower surface of the glass could add up to as many as 16 or none at all when they interact with the photons reflected from the upper surface of the glass because of the reinforcement of the reflected wave energy from the bottom and top surfaces of the glass.

In other words the 4 photons reflected from the surface of the bottom piece of glass would interact with the incident ones to that surface creating from 0 to 8 photons while the 4 photons reflected from the surface of the top piece of glass would interact with the incident ones to it creating 0 to 8 more photons for a total of 0 to 16 photons.

These observations by Mr. Feynman support a wave theory of electromagnetic radiation because according to it, the energy associated with the interference of the 4 photons reflected from the bottom surface with 4 from the top will result in energy variations that corresponds to the energy of 0 to 16 photons.

However, wave theory also predicts the energy variations should be continuous.

In other words, the energy of the reflected photons should be able to take on any value between 0 and the combined energies associated with 16 photons.

Unfortunately, for the wave theory of light, the energy of the reflected photons Richard Feynman observed in the above experiment only took on integral values equal to the energy of the photons that originally struck the surface of the glass.  This indicates that their energy is not transmitted by a wave but by a particle.

However this observational paradox can be resolved if particles are, as mentioned earlier are viewed in terms four *spatial* dimension instead of four dimensions space-time because it shows their behavior can be described in terms of a resonant “structure” generated by a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

For example in the article “Why is energy/mass quantized?” Oct. 10, 2007 it was shown one can derive both the wave and particle properties of energy/mass and a photon by extrapolating the laws of classical of resonance in a three-dimensional environment to a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  Additionally it showed that all energy must be propagated in these resonant systems.

Briefly it showed the four conditions required for resonance to occur in a classical Newtonian environment, an object, or substance with a natural frequency, a forcing function at the same frequency as its natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet by a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

The existence of four *spatial* dimensions would give the “surface” of three-dimensional space (the substance) the ability to oscillate spatially with respect to a 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.

Therefore if one extrapolates the laws of classical wave mechanics to a fourth *spatial* dimension these oscillations in a “surface” of a three-dimensional space manifold would generate a resonant system or “structure” in space. 

Classical mechanics tell us resonant system can only have the incremental or discrete energy associated with its fundamental or a harmonic of its fundamental frequency.

Similarly the incremental or discrete energies associated with individual photons in Richard Feynman’s experiment could be explained by assuming that they are a result of the fundamental or a harmonic of the fundamental frequency resonant properties of four *spatial* dimensions.

This shows how one can derive the quantum mechanical properties of energy/mass and a photon by extrapolating the laws of classical wave mechanics to a matter wave on a “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension.

However, one can also describe the physicality of a particle in terms of the wave properties of its resonant structure.

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?“

This provides the ability to understand how and why a photon can have the properties of both a wave and a particle because it clearly defines their interdependence in terms of the laws of Classical wave mechanics

However it also defines the physical reality of particle-wave duality in terms of the classical properties of a matter wave moving on the “surface” of a three dimension space manifold with respect to a fourth *spatial* dimension or four dimensional space-time environment because remember, as was show earlier they are equivalent

For example, the wave like interference of photons he observed would be due to the wave properties of the resonant “system” defined in the article “Why is energy/mass quantized?“.

If the distance between the two glass surfaces in Richard Feynman’s experiment is equal to half of the wavelength of the resonant “system” associated with a photon, classical wave mechanics tell us the interference of its wave properties would interfere and will, as mentioned earlier yield the energy associated with 0 photons.

If the distance between two glass surfaces is equal to its wavelength of they will reinforce each other and yield the energy associated with 16 photons.

However, it also tells us the reason the energy variations caused by their interference are quantized and not continuous as wave theory predicts they should is because, as was shown in the article “Why is energy/mass quantized?” the resonant properties of four *spatial* dimensions means that their energy would be propagated in the discrete quantized values associated with the fundamental or harmonic of fundamental frequency of four *spatial* dimensions or space-time environment they are occupying.

Yet this also defines the reason the wave properties of 8 reflected photons reinforce themselves to create the energy associated with16 photons is because Classical wave mechanics tells us that when two waves of the same frequency interact their frequency will or does not change.  Therefore if energy is propagated in discrete quantized values associated with the wavelength or frequency of a resonant system the reinforcement of the wave properties of 8 photons must be carried away in the integral or discreet energies associated with resonant systems of up to 16 photons of the same frequency as those original 8 photons.

This indicates that viewing the quantum mechanical world of wave–particle duality in terms of the geometric properties of a resonant “system” generated by a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension allows one to derive its “reality” by extrapolating the laws of classical mechanics in three-dimensional environment to a fourth *spatial* dimension.

It should be remember Einsteinâ€s genius allows us to chose if we want to resolve all paradoxes between the microscopic world of quantum mechanics and the macroscopic world of Relativity either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of energy/mass and the constant velocity of light. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the spatial as well as the time properties of our universe thereby giving us a new perspective on the physical relationship of particles and waves

Later Jeff

Copyright Jeffrey O’Callaghan 2014

The post The geometry of a particle wave appeared first on Unifying Quantum and Relativistic Theories.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Later Jeff

Copyright Jeffrey O’Callaghan 2012

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

At this point, the contraction phase will begin again.

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

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

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

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

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

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

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

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

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

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

Later Jeff

Copyright Jeffrey O’Callaghan 2011

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

One of them is that it would allow one to explain the” reality” of the probabilities associated with quantum mechanical wave function in terms of the classical laws of three-dimensional space.
Quantum mechanics assumes that one cannot define a particle in terms of its exact position or momentum but only in terms of the probabilistic values associated with its wave function.  This is in stark contrast to the Classical “Newtonian” assumption that one can assign precise values of future events based on the knowledge of their past. 

For example In a quantum system Schrödinger wave equation plays the role of Newtonian laws in that it predicts the future position or momentum of a particle in terms of a probability distribution by assuming that it simultaneously exists everywhere in three-dimensional space. 

This accentuates the fundamental difference between quantum and classical mechanics because the latter defines the reality of future events in terms of the effects of pervious events whereas quantum mechanics defines them based on the “non-classical” reality of the sum total of all possible events that can occur.  

However, as mentioned earlier one can define the classical “reality” of quantum probabilities by extrapolating the laws of a classical three-dimension environment to one consisting of four *spatial* dimensions.

In the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown one can define why energy/mass is quantized by extrapolating the laws of classical wave mechanics 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.

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 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 it 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.

This cannot be done in four-dimensional space-time because time or a space-time dimension is only observed to move in one direction forward therefore it cannot support the bidirectional movement require to define classical resonance.

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

In an 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, as mentioned earlier the probability distribution associated with its wave function 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 energy 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 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 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?” shown 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 a 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 as mentioned earlier this is exactly what is predicted by Quantum mechanics in that one can define a particle’s exact position or momentum only in terms of the probabilistic values associated with vibrations of its wave function.

This shows how one can define the classical “reality” of the quantum mechanical probability functions by extrapolating the laws of classical mechanics to four *spatial* dimensions.

Later Jeff

Copyright Jeffrey O’Callaghan 2011

The post The *reality* of quantum probabilities 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.