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.

However the reason may be because gravity is not propagated by a particle such as a photon but by field properties of space.

The currently accepted view among most cosmologist and physicist is that all forces mediated by particles.  This viewpoint is support the success the Standard Model of Particle Physics has had in explaining and predicting the observed properties of electromagnetic energy, weak, and strong nuclear forces in terms of particles.  It makes very accurate and verifiable predictions of the nature and causality of those forces in terms of particle interactions.

However it falls short of being a complete theory of fundamental interactions because it cannot or does not incorporate the full theory of gravitation as described by General Relativity.  This is because Einstein’s General Theory of Relativity derives gravity in terms of a continuous curvature in the field properties of four-dimensional space-time and not in terms of the discontinuous properties of the quantum.

This fact makes it extremely difficult to conceptually integrate them because something that is discontinuous cannot be by definition continuous.
However it may be possible to integrate gravity with the particle properties of the forces defined in the Standard Model if instead of assuming they are propagated by particles one assumes that the particle properties of all forces are propagated by the fields.

It is easier to explain the mechanism responsible for creating the gravity or quantum of gravitational force by redefine Einstein’s space-time universe into one consisting of only four *spatial* dimensions.

(The reason will become obvious latter in the article)

Einstein gave us the ability to do this when he used he used equation of E=mc^2 and the constant velocity of light to defined gravity in terms geometric properties of space-time because it allows one to convert a unit of time in his space-time universe to a unit of 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 defining the geometric properties of a space-time universe in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

However it allows one to define a physical mechanism that would responsible creating a particle or quanta of space-time in terms of the field properties of four *spatial* dimensions.

For example the article “Why is energy/mass quantized?” Oct. 4, 2007 showed it is possible to explain the discontinuous properties of space by extrapolating the laws classical resonance in a three-dimensional environment to a matter wave on a continuous “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.

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

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

Therefore these discrete or quantized energy of resonant systems in a field consisting of four *spatial* dimensions would be responsible for the particle characteristics the standard model associates with the propagation of gravity electromagnetic energy, weak, and strong nuclear forces.

However, it does not explain how or why we observed them in terms of discontinuous properties of a particle instead of the continuous properties of a field as the above theoretical model and Einstein Theories predicts we should.

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 defines the mechanism responsible for the quantization of the field properties of space associated with energy/mass in the article “Why is energy/mass quantized?“.

Quantum mechanics defines the smallest possible unit of space and increment of energy in terms of Planck’s length “h” while defining the size of an individual quantum of force in terms of the equation E = h c / L. 

In other words the physical size of the fundamental quanta of all forces is not the same as is suggest by the Standard Model of Particle Physics and quantum mechanics but varies with their energy and the higher energy there is the smaller its volume.

However this means the length and therefore the volume of a Graviton would be considerably larger when compared to the volume associated with a quantum unit of the electromagnetic weak or strong forces because of its relatively low energy content with respect to theirs.

The theoretical evidence to support this conclusion is provided by the fact that the energy of a quantum of force is mathematically defined by its frequency and wavelength.  This means a higher energy particle with a shorter wavelength would occupy a smaller volume than lower energy ones.

Observational evidence can be found in the fact that quanta of the strong and weak forces can only be observe in particle accelerators capable of generating the energy required to magnify their environment enough to allow for us to observe them.

In other words the reason why we can observe quanta of the strong and weak forces is because we can create experimental apparatus that can magnify the environment to the point where they become visible.

While a quantum of a less energetic electromagnetic force associated with visible light is observable because it size is comparable to the size to the sensing apparatus in the cones and rods in the eyes use to detect it.

However electromagnetic forced is about a million billion billion billion billion (10^42) times stronger than gravitational.

Using the same logic one reason why we have been unable to observe a Graviton may be because we have been unable to construct an observing platform a million billion billion billion billion (10^42) larger than the one need to observe quanta of electromagnetic force of the same strength. 

However the relatively large size of a Graviton or an individual quanta of gravity predicted by quantum mechanics suggests another reason why we have been unable to observe it.

We know from observations that gravitational forces act on much smaller scales than the physical size of an individual Graviton predicted by quantum mechanics. However this means that we should observe that the orbital energy of objects should also be quantized.

Some may disagree by saying that the size of the quantum unit of gravitational force is too small relative to the mass of objects that the effect of its quantization would be unobservable.

However the equation that defines the size of a Gravitron ( E = h c / L ) tells us that it would relatively large with respect to the orbits of many of the observable planets.  Additionally the force of gravity is always attractive or only acts in one direction therefore the effects of its quantization would be cumulative

In other words if gravity is propagated by the graviton the cumulative effects over the life of the universe should be observable with the increased sensitivity and high resolution of modern instrumentation.

Therefore one must assume that Einstein was correct we he defined gravity in terms of its field and not the quantum properties of space-time because if it was propagated by the Graviton then quantum mechanics tells us due to its relative large size that we should have observed discrete regions of space where orbits of stars planets and moons are not found.

This strongly suggest the reason why we have been unable to observe a Graviton is because gravity is not propagated it but by the field properties of space.

Later Jeff

Copyright Jeffrey O’Callaghan 2013 

The post Finding the graviton appeared first on Unifying Quantum and Relativistic Theories.

In other words in a quantum system Schrödinger wave equation plays the role of Newtonian laws in that it predicts the future position or momentum of a electron in terms of a probability distribution.

However it may be possible to develop a classical understanding of why the four quantum numbers define the arrangement of electron in atoms by converting or transposing Einstein’s space-time universe to one made up of fourth *spatial* dimension.

The reason this is necessary is because the quantum numbers deal more with the spatial than the time properties of three-dimensional space therefore eliminating time will allow for a more direct application of classical laws to the solution.

Einstein gave us the ability to do this when he use the equation E=mc^2 and the constant velocity of light to define the geometric properties of space-time because it provided a method of converting a unit of time in a space time environment  to 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 should allow one to define the physicality of the Principal Quantum number (n),  the Angular Momentum “â„“”  (l), Magnetic (m) and Spin Quantum Number(+1/2 and -1/2) by extrapolating the laws of a classical Newtonian environment to a 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 by extrapolating the laws governing 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.

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 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 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.

However the fact that one can derive the quantum mechanical properties of energy/mass by extrapolating the resonant properties of a wave in three-dimensional environment to a fourth *spatial* dimension means that one should be able to derive the quantum numbers that define the properties of the atomic orbitals in those same terms.

As mentioned earlier there are four quantum numbers.  The first the Principal Quantum number is designated by the letter “n”, the second or Angular Momentum by the letter “â„“” the third or Magnetic by the letter “m” and the last is the Spin or “s” Quantum Number.

In three-dimensional space the frequency or energy of a resonant system is defined by the vibrating medium and the boundaries of its environment.

For example the resonant energy of a standing wave generated when a violin string plucked is determined in part by the length and tension of its strings.

Similarly the energy of the resonant system the article “Why is energy/mass quantized?” associated with atom orbitals would be defined by the “length” or circumference of the three-dimensional volume it is occupying and the tension on the space it is occupying.

Therefore the physicality of “n” or the principal quantum number would be defined by the fundamental vibrational energy of three-dimensional space that article associated with the quantum mechanical properties of energy/mass.

The circumference of its orbital would correspond to length of the individual strings on a violin while the tension on its spatial components would be created by the electrical attraction of the positive charge of the proton.

Therefore the integer representing the first quantum number would correspond to the physical length associated with the wavelength of its fundamental resonant frequency.

However, classical mechanics tells us that each environment has a unique fundamental resonant frequency which is not shared by others.

The reason an electron does not fall into the nucleus is because as was shown in the article “Why is energy/mass quantized?” all energy is contained in four dimensional resonant systems.  Therefore the fundamental frequency or wavelength of four dimensional space would define the minimum energy and therefore the physical size of the first quantum orbital.

This defines physicality of the environment associated with the first quantum number.  (The reason why it is unique for each subdivision of electron orbitals will be developed later) . Additionally observations tell us that resonance can only occur in an environment that contains an integral or half multiples of the wavelength associated with its resonant frequency and that the energy content of its harmonics are always greater than those of its fundamental resonate energy.

This allows one to derive the physicality of the second “â„“” or azimuth quantum number in terms of how many harmonics of the fundament frequency a given orbital can support. 

In the case of a violin the number of harmonics a given string can support is in part determined by its length.   As the length increase so does the number of harmonics because its greater length can support a wider verity of frequencies and wavelengths.  However, as mentioned earlier each additional harmonic requires more energy than the one before it.  Therefore there is a limit to the number of harmonics that a violin string can support which is determined in part by its length.

Similarly each quantum orbital can only support harmonics of their fundamental frequency that will “fit” with the circumference of the volume it occupies.

For example the first harmonic of the 1s orbital would have energy that would be greater than that of the first because as mentioned earlier the energy associated with a harmonic of a resonant system is always greater than that of its fundamental frequency.  Therefore it would not “fit” into the volume of space enclosed by the 1s orbital because of its relatively high energy content.  Therefore second quantum number of the first orbital will be is 0. 

However it also defines why in terms of classical wave mechanics the number of suborbital associated with the second quantum number increases as one move outward from the nucleus because a larger number of harmonics will be able to “fit” with the circumference of the orbitals as they increase is size.

This also shows that the reason the orbitals are filled in the order 1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f, 5s is because the energy of the 3d or second harmonic of the third orbital is higher in energy than the energy of the fundamental resonant frequency of the 4th orbital.  In other words classical wave mechanics tells us the energy of the harmonics of the higher quantum orbitals may be less than that of the energy of the fundamental frequency of preceding one so their harmonics would “fit” into circumference of the lower orbitals

The third or Magnetic (m) quantum number physical defines how the energy associated with each harmonic in each quantum orbital is physically oriented with respect to axis of three-dimensional space.

For example it tells us that the individual energies of 3 “p” orbitals are physically distributed along each of the three axis of three-dimensional space.

The physicality of the fourth quantum or spin number has nothing to do with the resonant properties of space however as was shown in the article “Pauliâ€s Exclusion Principal: a classical interpretation” Feb. 15, 2012 one can derive its physicality by extrapolating the laws of a three-dimensional environment to a fourth *spatial* dimension.

That article it was shown all forms of energy including the angular momentum of particles can be defined in terms of a displacement in a “surface* of three-dimensional space manifold with respect to a fourth *spatial* dimension.

In three-dimensional space one can use the right hand rule to define the direction of the angular momentum of charged particles.  Similarly the direction of that displacement with respect to a fourth *spatial* dimension can be understood in term of the right hand rule.  In other words the angular momentum or energy of an electron with a positive spin would be directed “upward” with respect to a fourth *spatial* dimension while one with a negative spin would be associated with a “downwardly” directed one.
Therefore one can define the physically of the fourth or spin quantum number in terms of the direction a “surface” of three-dimensional space is displaced with respect to a fourth *spatial* dimension.  For example if one defines energy of an electron with a spin of -1/2 in terms of a downward directed displacement one would define a +1/2 spin as an upwardly directed one.

The physical reason why only two electrons can occupy a quantum orbital and why they have slightly different energies can also be derived by extrapolating the laws of a classical three-dimensional environment to a fourth *spatial* dimension.

There a two ways to fill a bucket.  One is by pushing it down and allowing the water to flow over its edge or by using a cup to raise it to the level of the buckets rim.

Similarly there would be two ways fill an atomic orbital according to the concepts presented in that article.  One would be by creating a downward displacement on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* to the energy level associated with the electron while the other would create an upward displacement in that surface.

However the energy required by each method will not be identical for the same reason that it requires slightly less energy to fill a bucket by pushing it down below the surface than it would be to fill one that was above it because the one above the surface would be at a higher gravitational potential.

However it also explains why no two quantum particles can have the same quantum number 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 quantum particles with similar quantum numbers would greater than that caused by a single one.  Therefore, they will repel each other and seek the lower energy state associated with a different quantum number because the magnitude of the force resisting the displacement will be less for them than if they had the same number.

This shows how one can define a physical model for the energy distribution with an atom by extrapolating the deterministic laws of a classical three-dimensional environment to a fourth *spatial* dimension.

Later Jeff

Copyright Jeffrey O’Callaghan 2012

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Later Jeff

Copyright Jeffrey O’Callaghan 2011

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