Einstein was able to define the origins of gravity and potential energy associated with rest mass in terms of curvature or the changing geometry of a space-time manifold but he did not tell us anything about the causality of kinetic energy.

For example he told us that gravity is caused by curvature or distortion in a space-time manifold however he did not due the same for kinetic energy associated with constant relative motion.

Yet its casualty is central to our understand of our universe because it along with gravity and Dark Energy are assumed to be responsible for evolution of the universe.

However one reason may be because kinetic energy of relative motion is constant with respect to both distance and time.  In other words the energy of an object in constant motion always moves the same distance in a given time interval.

As was just mentioned one of the difficulties in defining the kinetic energy in terms of the space-time environment defined by Einstein is that its magnitude is determined only by the distance an object moves through space within a constant time interval.  In other words it is only dependent on the spatial not on time parameters of its movement.

However redefining Einstein’s space-time universe in terms of its spatial properties would allow one to define the energy of constant motion in terms of those spatial properties.

Einstein gave us the ability to do this when he define the displacement or curvature he associated with the potential energy of rest mass in terms of the equation E=mc^2 and the constant velocity of light because that gave us the ability to redefine a unit of time in his space-time universe to an equivalent unit of space in a universe consisting of only four *spatial* dimensions.

This fact is the bases for assuming as was done in the article “Defining energy” Nov. 26, 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.

Using those concepts one could define the energy of rest mass in terms of magnitude of a physical displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension cause by a objects mass while defining the kinetic energy of two masses in relative motion in terms of the spatial displacements cause by that motion. 

In other words the “surface” of three dimensional space associated with objects in relative motion would exist on different three dimensional plains with respect to a fourth *spatial* dimension.

For example magnitude of kinetic energy of two masses would be defined the relative magnitude of their displacement in “surface’ of three dimensional space with respect to a fourth *spatial* dimension 

In other words it allows one to mathematically derive the causality of relativistic motion in terms of the geometry of either four *spatial* dimensions or four dimensional space-time space because when Einsteinâ€s defined his space-time universe in terms of energy/mass and the constant velocity of light he allow to chose one or the other and get the same end results.

Einstein in his General Theory of Relativity derived the causality of gravity in terms of a curvature or displacement in a space-time manifold however in his Special Theory of Relativity he only told us the effects of relative motion has on an environment not what caused the energy of that motion.  However as was shown above one can use his theoretical concepts to mathematically define its casual in terms physical displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension thereby give a more complete understanding of the relativistic environment encompassed by his theories.

This is significant because understanding the spatial properties of relative motion is the first step in understanding how Newton’s laws of motion are physically connected to Einstein’s space-time environment.

Later Jeff

Copyright 2018 Jeffrey Oâ€Callaghan

The post What is the origin of kinetic energy and why should we care? 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 particle in terms of a probability distribution by assuming that it simultaneously exists everywhere in three-dimensional space. 

This accentuates difference between quantum and classical mechanics because it derives the evolution of a particle in terms of it being in one place both before and after a measurement was taken whereas quantum mechanics derives its finial resting place in terms of an infinite number of possible starting points.

However one may be able to reconcile these two conflicting concepts by observing how matter and energy interact in terms of the classical properties of space-time.

But it will be easier if we first transpose or covert Einstein’s space-time universe to one consisting of only four *spatial* dimensions.

This is because it will allow us to define the mechanism responsible for the superpositioning of particles it in terms of a geometry which is directly related their position or spatial properties instead of its non-positional or temporal components.

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 that provided a method of converting a unit of space-time associated with energy to unit of space associated with position.  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.

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

This will allow as the article “Why is energy/mass quantized?” Oct. 4, 2007 to understand the physicality of the quantum properties energy/mass 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 spatially with the frequency associated with the energy of that event.

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

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

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

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

Yet it also allows one to define the boundary 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 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?“

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 its energy is result of a displacement in four *spatial* dimension allows one to derive the the most probable position of a particle in terms of its wave function by extrapolating the observations and classical laws associated with a three-dimensional environment to a fourth *spatial* dimension.

Classical mechanics tell us that due to 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.

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

Similarly if the assumption that quantum properties of energy/mass are a result of vibration 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 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 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.

In other words a particle appears to be superpositioned because its wave energy is distributed in probabilistic manner throughout the entire universe.

This suggests the reason why particles appear to be superpositioned is not due to the mathematical probabilities associated with Schrödinger wave equation but due to a classical interaction of the wave properties of a quantum system with the  geometry of a universe of a consisting either four dimensional space-time or four *spatial* or time dimension.

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 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 causality of the quantum mechanical properties of energy/mass

Later Jeff

Copyright Jeffrey O’Callaghan  2015

The post A classical explanation of Quantum Superposition 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.

We think so.

Many including Albert Einstein and Erin Schrödinger, had difficulty accepting the “reality” of quantum mechanics because many of its concepts appear to contradict those of our observable universe.

For example in a quantum system Schrödinger’s wave equation defines the field properties of its environment and predicts the future distribution of a particle’s position only in terms of the abstract properties of probabilities.

However many including Einstein and Schrödinger define reality in terms of what they see or touch.

For example, Einstein used the observable “reality” of the interactions of electromagnetic energy with a photoelectric material to derive the quantum mechanical properties of energy/mass while using the observable properties of light in our three-dimensional environment to define his space-time universe.

In other words his conclusion that electromagnetic energy is quantized was based on the physical “reality” of the environment sounding the photoelectric material and how electromagnetic energy interacted with it, not on the abstract probabilities associated with quantum fields.

However the abstract properties of probabilities do share a common characteristic with Einstein’s space-time universe in that time or a space-time dimension have never be seen or touched and therefore they like the probability functions of quantum field theory are, by definition abstract quantities.

Fortunately they also have a common element, as mentioned earlier in the physically observable non-abstract properties of the *spatial* dimensions because the probabilities associated with Schrödinger’s wave equation are expressed in terms of the spatial properties of position.

Therefore because they share a common connection to the observable “reality” of our three-dimensional spatial environment one should be able to define the physical “reality” of both Einstein space-time dimension and the field properties of quantum mechanics in terms of their non-abstract spatial components.
Einstein gave us the ability to do this when he used the constant velocity of light in the equation E=mc^2 to define geometric properties of energy/mass because it allows one to convert a unit of time in his four dimensional space-time universe to a unit of space in a one consisting of only 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.

The fact that one can use the Einsteinâ€s equations to qualitatively and qualitatively derive the spatial properties of energy in a space-time universe 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. 

One of the theoretical advantages of modeling the existence of energy/mass on four *spatial* dimensions instead of four dimension space-time is it allows one to derive the “reality” of a quantum fields in terms of the observable non-abstract properties of our three-dimensional environment.

The physical “reality” of the field properties energy/mass in 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 field consisting of four *spatial* dimensions.

Briefly it showed that one can derive its field properties by extrapolating the observable non-abstract properties of a three-dimensional environment to a fourth *spatial* dimension.

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 observations  of our three dimensional “reality”, 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 non-abstract mechanism for understanding why similar charges repel each other because observations of wave on the surface of water tell us 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, observations of our three dimensional environment tell 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 continuous field properties of electromagnetism by extrapolating the observable non-abstract properties of our 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* dimension can also be derived by extrapolating the observable non-abstract resonant properties of a three-dimensional environment to one consisting of four *spatial* dimension.

There are 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.

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 quantum and electromagnetic field theories.

However if true one must also show how the probabilities associated with Schrödingerâ€s equation could have evolved out of those field properties.

Classical mechanics tell us that because of the continuous properties of waves, the energy the article “The Photon: a matter wave?” Oct. 1, 2007 associated with all quantum systems such as a photon would be distributed throughout the entire “surface” a three-dimensional space manifold with respect to a fourth *spatial* dimension similar to how the wave generated by a vibrating ball on a surface of a rubber diaphragm are disturbed over its entire surface while the magnitude of the displacement it causes will decrease as one moves away from the focal point of the balls oscillations.

However, this means if one extrapolates the mechanics of the rubber diaphragm to a “surface” of three-dimensional space one must assume the oscillations associated with each individual quantum system must be disturbed thought the entire universe while the spatial displacement associated with its energy; defined in the in the article “Defining energy?” Nov 27, 2007 would decrease as one moves away from its focal point.  Therefore their is a non-zero probability they could be found anywhere in our three-dimensional environment. 

Classical Wave Mechanics also 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 an observer would most probably find a quantum system 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 is exactly what is predicted by Quantum mechanics in that one can only define a particle’s position or momentum in terms of the probabilistic values associated with vibrations of its wave function.

This shows how one can define the “reality” of the continuous field associated with Schrödinger’s wave equation and its associated probabilities in terms of a physical mechanism based on the observable non-abstract “reality” of our three-dimensional environment.

Latter Jeff

Copyright 2013 Jeffrey O’Callaghan

The post The reality of Quantum Fields appeared first on Unifying Quantum and Relativistic Theories.