On the one hand quantum physics tells that the universe is made up of discrete units of energy/mass while relativistic physics tells us it is composed of a continuous field of space-time

Unfortunately these two ideas do not work well together because a continuous field by definition cannot be made up of discrete parts as is suggested by quantum mechanics.
Some have tried to merge them by defining what is has come to be called a relativistic quantum field theory.  It assumes that particles can be understood as the quanta of some quantum field which in essence elevates fields to the most fundamental objects in nature and that each type of field generates its own particular type of particle.

However, you cannot have it both ways because by definition a field is continuous and saying they can be understood in terms of some quantum field does not mean that you have connected them to the continuous properties of a relativistic space-time field or any field for that matter.  All it does is elevate its size to that of the entire universe because by definition a field is continuous throughout its entire domain.  Therefore if the fundamental component of the universe is a quantum field as quantum field theory suggests then it could only contain one quantum entity because if it contained more the continuity of the field would be broken.  In words saying one can understand the continuous properties of a field in terms of a quantum field is like saying that one can understand why a circle is round is because it is a circle. 

Another reason why it is so difficult to conceptually to integrate Quantum theory with the field properties of Einstein’s theories is because it defines space in terms of a field consisting of time or a space-time dimension while Quantum theory defines itself in terms of its spatial properties of energy/mass.  

For example Schrödinger’s wave equation only defines the probability of a particle will be located in a given volume of space without giving a reference to time while Einstein defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2.

Yet one can overcome the difficultly by redefining the field properties of space-time Einstein associated with energy/mass to its spatial properties Quantum field theory associates with it. 

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 spatial displacement it 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 space four *spatial* dimensions.

One of the theoretical advantages to assuming that the universe is made up of four *spatial* dimensions instead of four dimensional space-time is that it allows one to derive the quantum mechanical properties of energy/mass in terms of the field properties of four *spatial* dimensions instead of defining the field properties of space in terms of its quantum mechanical properties as is done in quantum field theory.

The field properties of four *spatial* dimension was developed in the article “Electromagnetism in four *spatial* dimensions” Sept 27, 2007 where it was shown the forces associated with an electromagnetic field can be explained and predicted in terms of matter wave on a continuous field consisting of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly it showed that one can derive its properties by extrapolating the laws of Classical Wave Mechanics to a field consisting of fourth *spatial* dimensions.

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 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 become “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 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 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.  This force is called magnetism.

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

This shows how one can explain and predict the electrical and magnetic field properties of an electromagnetic wave by extrapolate the laws of classical wave mechanics 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.

However, as was shown in the article “The Photon: a matter wave?” Oct. 1, 2007 the quantum field properties of four *spatial* dimensions can be explained and predicted by extrapolating the resonant properties of field in a three-dimensional environment to one consisting of four *spatial* dimension.

There are 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.

The existence of four *spatial* dimensions would give the continuous surface or field of three-dimensional space manifold (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, these oscillations in four *spatial* dimensions, would meet the requirements mentioned above for the formation of a resonant system or “structure” in space. 

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.

These resonant systems in four *spatial* dimensions are responsible for the incremental or discreet field energies associated with relativistic quantum field theories.

This shows that it is possible to logically and consistently explain and predict the quantum mechanical field properties energy/mass in a microscopic environment by assuming that space is composed of four *spatial* dimensions instead of four dimensional space-time.

However it also shows it is more logical and consistent with observations to assume that our universe is fundamentally composed of fields not quanta of energy/mass as is assumed by quantum field theory

It should be remember Einsteinâ€s genius allows us to choose whether to define the energy of all systems in either a space-time environment or one consisting of four *spatial* dimension when he defined it and the geometry of space-time in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories making them applicable to both the field as well as the quantum properties of our universe thereby giving us a new perspective on its causality.

Latter Jeff

Copyright 2013 Jeffrey O’Callaghan

The post Particles or fields you cannot have it both ways appeared first on Unifying Quantum and Relativistic Theories.

To this point physicists have identified six types of quarks, called the UP/Down, Charm/Strange and Top/Bottom. The Up, Charm and Top have a fractional charge of 2/3 while the Down, Strange and Bottom have a fractional charge of -1/3.

They assume each quark carries a charge called “color” which like electric charge is always conserved. However, unlike electric charge, the color charge (the chromo in Chromodynamics) comes in three varieties or red, green, and blue and that each quark comprising a particle must have a different color, red, green, or blue.

The reason is because Pauliâ€s exclusion principle says no particle can be made up of components with identical quantum states.  They incorporate this principal into Quantum Chromodynamics theoretical structure by assigning a color to individual quarks and adopting a rule that says for a stable particle to exist the colors of their components must combine to make a colorless particle.  This requires particles to conform to Pauliâ€s exclusion principle because colorless or white light only exist if it is made up of one part red, blue, and green light.  Therefore a stable particle can only exist it is made up of three different types of quarks with colors of red blue and green.

However as of yet no one has been able to define the reason for their fractional charge or their color component in terms of the physicality of the environment they occupy.

Yet as was show in the article “The geometry of quarks” Mar. 15, 2009 one can derive a physical reason for their fractional charge and color properties if one assumes as was done in the article “Why is energy/mass quantized?” Oct 4, 2007 that the quantum mechanical properties of energy/mass can be derived in terms of a resonant structure formed by a matter wave on “surface” a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly that article 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 the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in four spatial dimensions.

The existence of four *spatial* dimensions would give space (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 “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 space.

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.

These resonant systems in four *spatial* dimensions are responsible for the incremental or discreet energy associated with quantum mechanical systems.

The only way to dampen the frequency of a classically resonating system is to add or remove energy from it, which results in changing the characteristics of that system.

Additionally the energy in a classically resonating system is, as mentioned earlier is discontinuous and can only take on the discrete values associated with its fundamental or harmonic of its fundamental frequency.

However, these properties of a classically resonating system are the same as those found in a particle in that they are made up of discreet or discontinuous packets of energy/mass and when energy is either added or removed from it, its characteristics changed.

But if space was made up of four *spatial* dimensions one should also be able to explain why quarks have a fractional charge and how their color properties interact to form stable particles in terms of the geometry four *spatial* dimension.

The article Defining energy Nov. 26, 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.

However, 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 Nov. 22, 2007 there are three ways the individual axis of three-dimensional space can be oriented with respect to a fourth *spatial* dimension.  Therefore, the geometric configuration or “colors” of individual quarks may be related to how its energy is distributed in three-dimensional space with respect to a fourth *spatial* dimension.

However, it may also explain why it takes three quarks of different “colors” to form a stable 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 shows how one can put the color and therefore the Chromo in Quantum Chromodynamics by assuming that space is composed of four *spatial* dimensions instead of four dimensional space-time.

Later Jeff

Copyright 2012 Jeffrey O’Callaghan

The post Putting the Chromo in Quantum Chromodynamics appeared first on Unifying Quantum and Relativistic Theories.

One is that it would allow for the integration of the quantum mechanical and wave properties of energy/mass by extrapolating the classical laws of a three-dimensional environment to a fourth *spatial* dimension.
In 1924 Louis de Broglie was the first to theorize that all particles had a transverse matter wave component.  In his paper, “Theory of the double solution“ he attempted to define a causal interpretation of their wave properties in the classical terms of space and time.  He later abandoned it in the face of the almost universal adherence of physicists to the theories presented by Born, Bohr, and Heisenberg regarding the uncertainties and probabilistic interpretation of quantum particles.

One of the difficulties he may have faced in this endeavor is that he assume along with most other scientists of his day the universe was composed of four-dimensional space-time.

This presented a problem because observations of a space-time environment indicate that time or a space-time dimension can only move in one direction, forward.  Therefore, it could not support bidirectional movement required for the propagation of a transverse wave. 

However Einstein provided a solution to this problem when he use the equation E=mc^2 and the constant velocity of light to define the geometric properties of space-time because that gave a method of converting a unit of time associated with energy to its equivalent unit of space in four *spatial* dimensions.  Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

This may have allowed Louis de Broglie to define the quantum or particle properties, as was done in the article “Why is mass and energy quantized?” Oct. 4, 2007 of the transverse wave he theorized they were made up of in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly that article showed that 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 be satisfied by a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

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.

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

As was shown in that article these resonant systems in a continuous form of mass/energy are responsible for its quantum mechanical properties.

He then many have been able defined a causal interpretation of the Quantum Mechanical equation for a particles energy or E=hv (where “h” is Planck’s constant “v” is a particles frequency and “E” is the magnitude or its energy) based on the existence of these resonant systems

Classical mechanics tells us that the energy of a resonant system is quantized in terms of multiples of the harmonics of the fundamental frequency of its environment. 

Therefore, he could have interpreted the equation E=hv as defining the quantization of a particle’s energy in terms of the incremental energies “h” associated with the fundamental or harmonic of the resonant frequency of an environment consisting of four *spatial* dimensions..

However, this would have also allowed him to define a casual mechanism responsible for the uncertainty principal and the probability functions of Quantum Mechanics, again by extrapolating the three-dimensional laws of classical resonance to four *spatial* dimensions.

Because he may have realized the causality of the uncertainty in oneâ€s ability to define the exact position or momentum of a particle was due to the fact that the resonant system that the article “Why is mass and energy quantized?” derived was responsible for the quantum mechanical properties of energy/mass is distributed over the finite volume associated with the wavelength of its resonant system.  Therefore, one could only define its specific position or momentum in terms of an uncertainty related to where relative to its finite extended volume a measurement is made.

This indicates may have been able to derive a causal interpretation of the quantum mechanical properties of energy/mass in terms of classical properties of a matter wave if he had assumed there were a result of the geometric property of four *spatial* dimensions.

However, as mentioned earlier this cannot be done if one assumes space it made up of four-dimensional space-time because its geometry cannot support the transverse wave properties Louis de Broglie associated with particles.

Later Jeff

Copyright Jeffrey O’Callaghan 2010

The post The geometry of Quantum Mechanics appeared first on Unifying Quantum and Relativistic Theories.

One is that it would allow one understand quantum tunneling or how particles can tunnel or move through potential barriers that are higher than their energy in terms of the laws of classical physics.

Quantum tunneling is defined “as a microscopic phenomenon in which a particle violates the principles of classical mechanics by penetrating or passing through a potential energy barrier or impedance higher than its potential energy.  A barrier, in terms of quantum tunneling, may be a form of energy state analogous to a “hill” or incline in classical mechanics, which classically suggests that passage through or over such a barrier would be impossible without sufficient energy.  However, on the quantum scale, objects exhibit wave-like behavior.  Therefore, in quantum theory, quanta moving against a potential energy “hill” can be described by their wave function, which represents the probability amplitude of finding that particle in a certain location at either side of the “hill”.  If this function describes the particle as being on the other side of the “hill”, then there is the probability that it has moved through, rather than over it, and has thus “tunneled“.
However, does this behavior really violate the laws of classical mechanics because there are numerous examples of how energy can be relocated or tunneled through what appears to be an impenetrable barrier for the potent energy of the mediums associated with the transmission of that energy?

For example, classical wave mechanics tells us that the energy of wave on the surface of water can be transmitted or “tunnel” through a flexible steel plate separating two volumes of water by the flexing of that plate.  This plate acts as a potential energy barrier between the water in each tank because it is “higher than the potential energy” of the two volumes however due to steel plate’s ability to flex its energy can be transmitted beyond it.

This demonstrates that due to the spatial properties of a wave, its energy can penetrate or be transmitted to other side of a flexible steel plate without the water having to go over it.

However, as was showed in the article “Why is energy/mass quantized?” Oct 4, 2007 on can define the energy of a quantum mechanical system in terms of a resonant system or “structure” generated by a matter wave on a “surface” of a three-dimensional space manifold with respect to fourth *spatial* dimension.

In other words one can derive its physical structure in terms of the classical properties of a wave

(Louis de Broglie was the first to realize this when 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. )

This means the energy associated with a particle could tunnel through a potential energy barrier that had an energy “higher” than it and still not violate the laws of classical mechanics for the same reason as the energy associated with the water, in the earlier example could tunnel though a potential energy barrier that was higher than its potential energy and not violate those laws. 

In other words, the physical wave component that Davission and Germer observed a particle to have could “penetrate or pass through a potential energy barrier or impedance higher than its potential energy” for the same reason as the energy of a wave on water can penetrate one

The reason why quantum tunneling appears to contradict the laws of Classical Mechanics is because Quantum Mechanics does not define a particle in terms of its wave prosperities but only in terms of a rigid structure of a particle. 

However, as was shown in the article “Why is energy/mass quantized?” a particle can be defined in terms of the dynamics of a resonant wave on a “surface” of a three-dimensional space manifold with respect a fourth *spatial* dimension. 

This means, on a quantum level a particle does not have the rigid point like structure quantum mechanics associates with it but a dynamic spatial one associated with a classical wave.  Therefore, its energy can “tunnel” through a potential barrier or impedance higher than the energy associated with the point in space quantum mechanics associated with a particle for the same reason the energy of a water wave can tunnel through the flexible steel plate in the earlier example.

The probability function quantum mechanics uses to predict whether or not a particle will tunnel through a potential energy barrier can be thought of as a measure of the energy distribution in the space surrounding a particle because as was shown in the article “Why is energy/mass quantized?” a particles volume would be defined by wave properties. 

Therefore, according to classical mechanics its position could not be determined with an accuracy smaller than the wavelength of the resonant system associated with a particle.  This means classical mechanics tells us that the probability a particle can be observed on either side of an energy barrier will depend on the “energy width” of that barrier.

Additionally classical mechanics tells us that due to the time variant properties of waves one could only determine its position in a probabilistic manner defined by were one observed it in that time varying environment.

This shows because particles have wave-like properties on a quantum scale they can quantum tunnel or penetrate through a potential barrier or impedance higher than the energy of the particle without violating the laws of classical mechanics.

Later Jeff

Copyright 2008 Jeffrey O’Callaghan

The post Quantum tunneling: a classical interpretation appeared first on Unifying Quantum and Relativistic Theories.

One of these observations is called the Casimir effect.
The Casimir effect is a small attractive or repulsive force which acts between two close parallel-uncharged conducting plates, which many physics believe is due to quantum vacuum fluctuations of the electromagnetic field.

According to modern physics, a vacuum is full of fluctuating electromagnetic waves of all possible wavelengths, which imbue it with a vast amount of energy.  Casimir realized that between two plates, only those electromagnetic waves whose wavelengths fit a whole number of times into the gap should be counted when calculating the vacuum energy.  As the gap between the plates is narrowed, fewer waves can contribute to the vacuum energy and so the energy density between the plates falls below the energy density of the surrounding space.  This generates either an attractive or a repulsive force depending on the specific arrangement of the two plates.  This is because Quantum theory requires that each of these vibrations be quantized and therefore the field, at each point in space would be a simple harmonic oscillator that has the energy of the particle associated with the force that Casimir observed to be pushing the plates together.

In the article ”The Photon: a matter wave?” Oct. 1, 2007 it was shown that one can derive the quantum mechanical properties of an electromagnetic wave by extrapolating the laws of classical resonance in a three-dimensional environment to resonant system in a continuous non-quantized field of energy/mass and four *spatial* dimension.

(Louis de Broglie was the first to predict the existence of a continuous non-quantized form of energy/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, 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 composed 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* 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.

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 non-quantized field of energy/mass.

As was shown it the article ”Why is mass and energy quantized?“ Oct.4, 2007 these resonant systems are responsible for the quantum mechanical properties of energy/mass.

Yet it can also be shown they are responsible for the Casimir effect because observations of resonant systems in a classical environment indicate the number of simple harmonic oscillators that can be established in a given environment is dependent on the distance or “gap” between the “end points” of their environments.

But same concept can be applied to two uncharged metallic plates in a vacuum, because even without any external electromagnetic field the electromagnetic components of the atoms in each plate are vibrating or have thermal energy because they are not at absolute zero.  These random vibrations of their electromagnetic components will result in a random electromagnetic field to be generated between the plates.

However, classical wave mechanics tells us these random electromagnetic vibrations would be reinforced only at certain points in space.  The number of simple harmonic oscillators in the space between two plates formed by this reinforcing would decreases as the gap between them decreases.  In other words, the smaller the gap between the plates the fewer number of quantum fields or particles that gap could support.

This means as was shown in the article ”Why is energy/mass quantized?“ there will be a greater number simple harmonic oscillators impacting the plates from outside of the gap than between it.  This will cause a force that will push the plates together because the energy density associated with the harmonic oscillations outside of the gap would be greater than inside of it.

However, it also tells us there will be also be places where the distance between the plates will be equal to the wavelength associated with a fundamental or harmonic of the fundamental frequency of a quantum fluctuation.  At those distances their energy will reinforce force each other and push them apart.

Therefore, if one assumes as us done here that the quantum mechanical properties of energy/mass are a result of a resonant system in four *spatial* dimension one can understand why the specific arrangement of the two plates causes an attractive or repulsive force to be developed by extrapolating the properties of a three-dimensional environment to a fourth *spatial* dimension.

Later Jeff

Copyright Jeffrey O’Callaghan 2008

The post The Casimir effect appeared first on Unifying Quantum and Relativistic Theories.

“From before 1920 until his death in 1955, Einstein struggled to find laws of physics far more general than any known before. In his theory of relativity, the force of gravity had become an expression of the geometry of space and time. The other forces in nature, above all the force of electromagnetism, had not been described in such terms. But it seemed likely to Einstein that electromagnetism and gravity could both be explained as aspects of some broader mathematical structure. The quest for such an explanation — for a “unified field” theory that would unite electromagnetism and gravity, space and time, all together — occupied more of Einsteinâ€s years than any other activity“.

Unfortunately, Einstein did not have access to the data concerning the quantum “qualities” of mass and electromagnetic energy when developing his theories as we do today, such as the Louis de Broglieâ€s observation made in 1924 that all particles have a wave component.  If he had he may have chosen to define gravity in terms of four *spatial* dimensions instead of four-dimensional space-time because, as was shown in the article “Gravity in four *spatial* dimensions” Dec. 15, 2007 he could have done it that way.

This is because even the smallest particle, according to Broglie observations must have a wave component.  Therefore, a continuous medium must be available to support it.  Einstein would have realized this medium would have to be made up of a continuous non-quantized field of energy/mass because by definition a wave can only be propagated on a continuous surface.

He also may have due to the spatial properties of a transverse of the energy/mass wave Louis de Broglie observed chose to define energy in our environment in terms of its spatial not time properties because a transverse wave can only be propagated by a spatial displacement with respect to the surface it is moving on.

However Einstein gave us the option to qualitatively and quantitatively convert the geometric properties of his space-time environment to an equivalent one consisting of only four *spatial* dimensions when he defined the geometric properties of a space-time universe and the dynamic balance between mass and energy in terms of the equation E=mc^2 and the constant velocity of light. This is because it allows one to redefine a unit of time he associated with energy in his space-time universe to unit of space we believe he would have associated with mass in a universe consisting of only four *spatial* dimensions.

In other words by defining the geometric properties of a space-time universe in terms of the equation E=mc^2 and the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe and gravity in terms of the geometry of four *spatial* dimensions.

Additionally this would have provided a way to integrate quantum properties of energy/mass into both his Special and General Theories of Relativity using the concepts of classical physics.

For example in the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown one can explain the quantum mechanical properties of energy/mass by extrapolating the “reality” of 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.

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 the “surface” of a three-dimensional space manifold (the substance) the ability to oscillate spatially with respect to it 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, these oscillations on a “surface” of three-dimensional space, would meet the requirements mentioned above for the formation of a resonant system or “structure” in space.

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 discreet or incremental values associated a fundamental or a harmonic of the fundamental frequency of its environment.

Additionally it also tells us in terms of the physical properties four dimensional space-time or four *spatial* dimensions the reason 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 unit of the universe.

However redefining Einstein’s space time concepts in terms of four *spatial* dimensions would also allow one to integrate electromagnetism into them.

For example 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 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 become “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 charges than it would be for a single charge

The electrical component of electromagnetic energy is a result of the force associated with the “slope” of a curvature created by the “peaks” and “troughs” of a matter wave that is perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that “vertical” displacement

Classical Mechanics tells us a horizontal force will be developed by a vertical displacement which will always be 90 degrees out of phase with it.  This force is called magnetism.

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

As was shown above redefining Einstein’s space-time concepts in terms of their spatial equivalent allows one to not only allows one to ingrate the quantum properties of energy/mass into the continuous field properties of his space time universe but also give one classical understanding of how to incorporate electromagnetism into it.

Later Jeff

Copyright Jeffrey O’Callaghan 2008

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