The post The quantization of space appeared first on The Imagineer's Chronicles.
]]>Quantum mechanics defines our observable physical environment only in terms of the probabilistic values associated with Schrödinger’s wave equation.
More specifically it defines a particle in terms of the instantaneous collapse of a wave function which it assumes extends form one edge of the universe to the other.
However this definition appears to contradict two very basic properties of our observable reality: the fact that particles appear to have a physical presents and how it can be simultaneously be in many places at the same time. In other words if Schrödinger’s wave equation does define our observable environment one should be able to explain how a mathematical probability obtains a physical presents when observed and how that physical presents can exist in different places at the same time.
Einstein gave us the answer to the second question in his formula for relativistic length contraction L = L0((1 – v2/c2))1/2 because it tells the distance between every point along the trajectory of all forms of energy which are moving at the speed when viewed by an outside observer including that associated with the wavefunction is zero. Additionally because time stops for anything traveling at the speed of light it would have enough time to travel from the perspective of an outside observer from one end of the universe to the other. In other words according to Einstein’s theory the particle associated with the wave function when viewed by an outside observer simultaneously exist in many places because the distance between its end points when viewed by him or her is zero
However it is extremely difficult to define a set of statements which explains how those probabilities can be connected to physical properties of particles even though it has held up to rigorous and thorough experimental testing.
This may be the reason most physicists consider quantum mechanics only in terms of its mathematical formalization instead trying to understand the meaning of it in terms of the spacetime environment we occupy.
For example in 1924 Louis de Broglie was the first to realize all particles are physically composed of a matter wave as the discovery of electron diffraction by crystals in 1927 by Davisson and Germer) verified. However in his paper, “Theory of the double solution“ he could not define a physical interpretation of Schrödinger equation in classical terms of space and time.
As is pointed at his biography on the nobleprize.org web site in "1951, he together with some of his younger colleagues made another attempt, one which he abandoned in the face of the almost universal adherence of physicists to the purely probabilistic mathematical interpretation of, Bohr, and Heisenberg."
However the fact that no has been able to physically connect those probabilities to our environment does not change the fact that there must be one because if there wasn’t they could not interact with it to create the physicality of observable world upon which those probabilities are based.
As mentioned earlier Louis de Broglie and his colleagues tried unsuccessfully to find a physical interpretation of Schrödinger equation in classical terms of space and time.
However the reason for their failure may be due to the fact that quantum properties of particles are related to the spatial not a time dependent properties of the wave function.
If so one may be able to establish the connection Louis de Broglie was looking for it in terms of a spatial instead of the time or spacetime property of the wave function
Einstein gave us the ability to do this when he defined the geometric properties of spacetime in terms of the constant velocity of light and a dynamic balance between mass and energy because that provided a method of converting a unit of time in a spacetime environment to a 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 spacetime universe and one made up of four *spatial* dimensions.
The fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the curvature in spacetime 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 threedimensional space manifold with respect to a fourth *spatial* dimension.
This would have allowed Louis de Broglie to physically connect the probabilities associated Schrödinger equationto the observable properties of particles in terms of a physical or spatial displacement in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension as was done in the article "Why is energy/mass quantized?" Oct. 4, 2007.
Briefly that article showed that one can do this by assuming they are caused by the formation of a resonant system created by the wave component of particles on a "surface" of a threedimensional space manifold with respect to fourth "spatial" dimension. This is because it showed the four conditions required for resonance to occur in a threedimensional 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 threedimensional 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 threedimensional space manifold.
Yet the classical laws of threedimensional 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.
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 quantum mechanical properties of his particle waves to Schrödinger equation in terms of the discrete incremental energies associated with a resonant system in four *spatial* dimensions if he had assume space was composed of it instead of four dimensional spacetime.
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 twodimensional surface of a piece of paper is confined to that surface. However, that surface can oscillate up or down with respect to threedimensional space.
Similarly an object occupying a volume of threedimensional 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 threedimension 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 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 threedimensional 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 spacetime as was done earlier allows one to connect the probabilities associated with Schrödinger equation to the observable properties of particles. In other words it can explain how one can be observed at a specific point in space even though its wave energy is distributed throughout a relatively large volume of space.
For example 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 threedimensional space manifold with respect to a fourth *spatial* dimension.
It also 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 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 threedimensional space is correct then classical mechanics tell us that those oscillations would be distributed over the entire "surface" threedimensional 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 particle is a result of a resonant structure formed on the "surface" of a threedimensional 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 observed were the magnitude of the vibrations in a "surface" of a threedimensional space manifold is greatest and would diminish as one move away from that point.
Additionally it also gives us a classical expiation of how a particle can simultaneously exist in many different place and why the probability of finding it in a give volume of space is what it is because as mentioned earlier according to Einstein’s theory the distance between end points of the particle wave when viewed by an outside observer is zero even though it may extend from one end of the universe to the other because it is traveling at the speed of light. In other words according to Einstein’s theory the wave function when viewed by an outside observer simultaneously exist in many places therefore there is a probability of finding the resonant structure associated with its particle properties any where in that space.
This shows how one can connect the properties with Schrödinger’s equation to our observable environment by assuming that space is quantized by the resonate system created by a physical wave in either spacetime dimension or a "surface" of a threedimension space manifold with respect to fourth "spatial" dimension and observing it causes it to collapse into the smaller volume of a resonant structure Quantum Mechanics associates with a particle.
It should be remember Einstein’s genius allows us to choose to define a quantum system in either a spacetime environment or one consisting of four *spatial* dimension when he defined the geometry of spacetime 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 2017
The post The quantization of space appeared first on The Imagineer's Chronicles.
]]>The post Einstein in four *spatial* dimension appeared first on The Imagineer's Chronicles.
]]>But even more damaging is that assuming it is composed of four *spatial* dimensions instead of fourdimensional spacetime, would allow physicists more logical and consistent explanation based on physical observations or our environment for time dilation, length foreshortening, the mass increases associated with relative velocities, gravitational and kinetic energy than can be provided by spacetime concepts of the Special and General Theories of Relativity.
Einstein himself defined a universe composed of four *spatial* dimension and one of fourdimensional spacetime when he mathematically defined its geometric properties in terms of the constant velocity of light. This is because it allows one to redefine a unit of time he associated with energy in his spacetime universe to unit of space in a one consisting of only four *spatial* dimensions.
However as was mentioned earlier viewing the universe in terms of four *spatial* dimensions instead of fourdimensional spacetime, would allow one to define the mechanism responsible for time dilation, length foreshortening, the mass increases associated with relative velocities, and gravity based on the physical observations instead of the abstract mathematical properties of the Special and General Theories of Relativity.
One of the advantages of deriving all forms of energy in terms of their spatial instead of their time or space time properties is that it allows one to form a physical image of the opposing nature of kinetic and gravitational forces in terms of our observable properties of our environment
For example we observe that the kinetic energy associated a satellite opposes the gravitational energy of the object it is orbiting.
However because of observations of our threedimensional environment tell us one can move in two directions upward or downwards in a *spatial* dimension one can form a clearer image of opposing properties of these forces by defining gravity in terms of a "downward directed" displacement in a surface of a threedimensional space manifold with respect to a fourth spatial dimension while define kinetic energy in terms of oppositely or upward directed or up displacement in that surface. Granted the one can do the same using the properties of a spacetime dimension however it is much more difficult to understand the opposing nature of these force because we only observe time to move in one direction forward.
This is the observational basis for defining, as was done in the article "Defining potential and kinetic energy?" gravitational and kinetic energy in terms of oppositely directed movements or displacements in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension.
In other words if one defined the energy/mass in a volume associated with mass in terms of downward directed displacement in a "surface" of a threedimensional space manifold with respect to a four *spatial* dimension one would define the energy associated with its relative motion in terms of an oppositely or upward displacement in that "surface".
This would allow one to form a physical image of the relative mass increase due to relative velocities based on observation of our threedimensional world because according to the concepts contained in that article the total energy/mass of an object would be equal to the sum of the displacements of a "surface" of a threedimensional space manifold caused by its rest mass and that caused by their relative velocities.
However defining space in terms of four spatial dimension not only provides observational basis for causality of the gravity and kinetic energy but it also provides an explanation for the casualty of time dilation and the length foreshortening in gravitational environments and moving reference frames based on physical observations made in a threedimensional environment.
The following analogy can be used to understand and define the relativistic properties length and time based on observations made in a threedimensional environment.
Assume that two "2 dimensional creatures” are living on the surface of two pieces of paper resting on a desktop.
Also, assume the two creatures can view the surfaces of the other piece of paper, which are separated a pencil.
If the diameter of the pencil is increased, the curvature between the surfaces of the two pieces of paper will increase.
Each of these creatures, when viewing the other piece of paper will only perceive the twodimensional translation of the threedimensional curvature generated by the pencil.
Therefore, each will view the distance between two points on the surface of the other as shorter since they will view that distance as a twodimensional translation of a threedimensional curvature in the surface of the paper. Therefore each will measure the distance between them on their piece of paper as being longer as the diameter of the pencil increases then they would if they viewed it on the other piece.
Similarly, because threedimensional beings could only "view" a threedimensional translation of a "curvature" or displacement in four *spatial* dimension caused by the relative motion of a reference frame they will measure distance or length in them as being longer than they would be if viewed as an observer who is in relative motion to it.
This is the mechanism responsible for the relativistic properties of length in terms of the geometry of four *spatial* dimensions.
The twodimensional creatures in the earlier example will also notice that time is effected by a curvature in the surface of their paper.
Each of them will view the others “time” as moving slower because the threedimensional curvature in the paper makes the distance between events longer than the two dimensional translation of that curvature. Therefore, it will take longer for events "move" through a curvature in threedimensional space on the surface of the others piece of paper relative to the time it would take for it to move thought the twodimensional translation of that curvature.
Earlier it was mentioned that time can be defined as only being the measure or the "distance between" the sequential ordering of the causality of an event.
Therefore time would be dilated with respect to a reference frame that is external to a gravitational field or was in motion because as mentioned earlier the length of the arc generated in threedimensional space by a gravitational field or the kinetic energy of relative motion to be longer than the cord of that arc. Therefore, the distance between events would be greater for an observer in those reference frames than for one who is outside of it. However, this means an observer outside of those reference frames would measure the time between those events as being dilated with respect to an observer who is inside because the time required for objects to move between events in that reference frame will be longer.
As mentioned earlier article both “Gravity” and kinetic energy can be define in terms of a displacement in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension as well as one in a spacetime manifold.
However, this means that one can define the foreshortening of the length of an object in relative motion or in a gravitational field in terms of the cord to the arc generated by that curvature. This is because the cord of an arc created by that displacement is always shorter than the arc itself and since threedimensional beings can only observe the threedimensional cord of an arc in fourdimensional space they would view the length of the objects to be shorter when viewed in relative motion or in a gravitational field.
However it would also provide a mechanism for the time dilatational associated with gravity and motion that is consistent with our observations of threedimensional space.
This shows one the benefits of viewing Einstein relativistic theories in terms of four *spatial* dimension is that it allows one to form a more logical and consistent explanation based on physical observations or our environment for time dilation, length foreshortening, the mass increases associated with relative velocities, gravitational and kinetic energy than can be provided by the spacetime concepts of the Special and General Theories of Relativity.
As was shown earlier Einstein’s mathematics allows us to choose to define our universe in terms of either a spacetime environment or one consisting of only four *spatial* dimension when he defined its geometry in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories thereby giving us a new perspective on its relativistic properties.
Later Jeff
Copyright 2007 Jeffrey O’Callaghan
Anthology of 

The Imagineer’s 
The Imagineer’s Chronicles Vol. 5 — 2014 Paperback $14.84 Ebook $9.97 
The Imagineer’s 

The Imagineer’s 
The Imagineer’s 
The Imagineer’s 

The post Einstein in four *spatial* dimension appeared first on The Imagineer's Chronicles.
]]>The post A Relativistic Quantum Mechanics appeared first on The Imagineer's Chronicles.
]]>Many interpret this as meaning a particle and all other objects exists in a world of probabilities and only become connected to the environment when observed. Additionally it assumes that a particle is distributed or simultaneous exists form one edge of the universe to the other because it tells us there is a probability it can be found anywhere in it.
However it is extremely difficult to define a set of statements which explains how those probabilities can be physically connected to that environment even though it has held up to rigorous and thorough experimental testing.
Yet Einstein gave us a an explanation for this connection in his relativistic formulas for length contraction L = L0((1 – v2/c2))1/2 because it tells us the distance between every point along the trajectory of all forms of energy which are moving at the speed including that associated with the wavefunction is zero for an observer who is outside of its reference frame. In other words since the energy associated with Schrödinger’s equation which is moving at the speed of light the distance between the each end of the universe for it relative to an outside observer is zero.
However because the probabilities associated with Schrödinger’s equation involve the spatial properties of position, to fully understand the ramifications of that equation to our understanding of quantum mechanics one must transpose it to the spatial equivalent.
Einstein gave us the ability to do this when he defined the geometric properties of spacetime in terms of the constant velocity of light and a dynamic balance between mass and energy because that provided a method of converting a unit of time in a spacetime 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 spacetime universe and one made up of four *spatial* dimensions.
The fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the curvature in spacetime 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 threedimensional space manifold with respect to a fourth *spatial* dimension.
However this would allow one to physically the connect the probabilities associated Schrödinger’s equation to our observable environment in terms of a physical or spatial displacement in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension as was done in the article "Why is energy/mass quantized?" Oct. 4, 2007.
Briefly that article showed that the observable properties of particles can be caused by the formation of a resonant system on a "surface" of a threedimensional space manifold with respect to fourth "spatial" dimension. This is because the four conditions required for resonance to occur in a threedimensional 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 threedimensional 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 threedimensional space manifold.
Yet the classical laws of threedimensional 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.
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 fundamental resonate frequency of space defined by the equation E=hv where "E" equals the energy of a particle "h" equal Planck’s constant "v" equals the frequency of its wave component.
Yet it also allows one 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 twodimensional surface of a piece of paper is confined to that surface. However, that surface can oscillate up or down with respect to threedimensional space.
Similarly an object occupying a volume of threedimensional 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 threedimension 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 threedimensional space manifold with respect to a fourth *spatial* dimension.
However as mentioned earlier assuming the probabilities associated with Schrödinger’s equation are the result of a displacement caused by a matter wave moving on a "surface" of a threedimension space manifold with respect to a four *spatial* dimension allows one to connect them to the physicality of the observable environment we all live in.
Classical mechanics tell us that due to the continuous properties of the wave energy the article "Why is energy/mass quantized?" Oct. 4, 2007 associated with a quantum system would be distributed throughout the entire "surface" a threedimensional 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 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 threedimensional space caused by matter wave is correct then classical mechanics tell us that those oscillations would be distributed over the entire "surface" threedimensional 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 because
However, as was mentioned earlier Einstein in his formula for length contraction L = L0((1 – v2/c2))1/2 tells us that a particle would simultaneously exist everywhere throughout the entire universe because of the fact that wave energy is continuous it would extend to each end of the universe. Therefore the distance between the each end of the universe relative to an observer outside of that reference frame would be zero. Additionally because time stops for anything traveling at the speed of light it would appear to exist simultaneously at every point in the universe of an outside observer.
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 threedimensional 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 threedimensional space manifold is greatest and would diminish as one move away from that point.
In others words one can explain how the probabilities associated with Schrödinger’s equation are connected to our physical world and the fact that particles simultaneously exist everywhere in the universe before it is observed by applying the concepts of Einstein Theory of Relativity to the quantum environment.
It should be remember Einstein’s genius allows us to choose to define a quantum system in either a spacetime environment or one consisting of four *spatial* dimension when he defined the geometry of spacetime 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 2017
Anthology of 
The Reality of the Fourth Spatial Dimension Paperback $9.77 Ebook $6.24 

The Imagineer’s

The Imagineer’s Chronicles Vol. 5 — 2014 Paperback $14.84 Ebook $9.97 
The Imagineer’s 

The Imagineer’s 
The Imagineer’s 
The Imagineer’s 

The post A Relativistic Quantum Mechanics appeared first on The Imagineer's Chronicles.
]]>The post The quantum properties of nonpoint particles appeared first on The Imagineer's Chronicles.
]]>We know that everything in the universe including particles have physical size.
Even so for the past 50 years, the Standard Model of particle physics which many say has given us the most complete mathematical description of the particles and forces that shape our world ignores this fact and treats them all as size less dimensionless mathematical points.
Many physicists feel this way because it predicts with so much accuracy the microscopic properties of particles and the macroscopic ones of stars and galaxies that it must be a correct physical model that even though as was just mentioned it treats all particles and their interactions not in term of their physical size but in terms of mathematic points.
However in 1924 Louis de Broglie’s showed that it cannot be when he theorized that all particle’s have a wave component and that one must take this into account when one defines how they interact with their environments. This fact becomes irrefutable when in 1927 Davisson and Germer observed that electrons were diffracted by crystals. Later it was determined the equation E = hν which defines the wavelength and therefore the physical volume occupied by a particle could be used to calculate the magnitude of that diffraction. In other words one must take into consideration the physical size of a particle to determine how they interact with a crystal.
This means that one cannot assume as the Standard Model does that a particle can be defined as points and expect to develop a complete description of how and why force and particles interact in our observable environment.
In other words one to understand the properties of point particles one must take into consideration their spatial extended properties.
For example in the article "Why is energy/mass quantized?" Oct. 4, 2007 where it was shown the quantum mechanical properties of particles can be defined by extrapolating the laws classical resonance in a threedimensional environment to a matter wave on a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension.
(Einstein gave us the ability to do this when he defined geometric properties of a space time universe 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 spacetime universe to unit of space in one consisting of only four *spatial* dimensions. )
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 be meet by a matter wave in 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 threedimensional 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
Source: 
Therefore the discrete or quantized energy of resonant systems is responsible for the discrete quantized quantum mechanical properties of particles.
However, it did not explain how the boundaries of a particle’s resonant structure are created in free space.
In other words why is electromagnetic energy not perceived to have the properties of a continues wave moving though space but those of particle
In classical physics, a point on the twodimensional surface of paper is confined to that surface. However, that surface can oscillate up or down with respect to threedimensional space.
Similarly an object occupying a volume of threedimensional 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 threedimension volume with respect to a fourth *spatial* dimension is what defines the geometric boundaries of the resonant system associated with a particle in the article "Why is energy/mass quantized?"
However one can also understand why we perceive there locations in terms of the probabilities associated with quantum mechanics.
The reason why we do not observe energy in its extended wave form is that, as mentioned earlier all energy is propagated through space in discrete components associated with its resonant structure. Therefore, its energy appears to originate from a specific point in space associated with where an observer samples or observes that that energy.
This is analogous to how the energy of water in a sink is release by allowing it to go down the drain. If all we could observe is the water coming out of the drain we would have to assume that it was concentrated in the region of space defined by the diameter of the drain. However, in reality the water occupies a much larger region.
However this also gives one the ability to understand in terms of a physical image the probabilistic interpretation of quantum mechanic interns of where the energy of this matter wave is obverse or measured.
Classical wave mechanics tells us a wave’s energy is instantaneously constant at its peaks and valleys or the 90 and 270degree points as its slope changes from positive to negative while it changes most rapidly at the 180 and 360degree points.
Therefore, the precise position of a particle could be only be defined at the "peaks" and "valleys" of the matter wave responsible for its resonant structure because those points are the only place where its energy or "position" is stationary with respect to a fourth *spatial* dimension. Whereas its precise momentum would only be definable with respect to where the energy change or velocity is maximum at the 180 and 360degree points of that wave. All points in between would only be definable in terms of a combination of its momentum and position.
However, to measure the exact position of a particle one would have to divert or "drain" all of the energy at the 90 or 270degree points to the observing instrument leaving no energy associated with its momentum left to be observed by another instrument. Therefore, if one was able to precisely determine position of a particle he could not determine anything about its momentum. Similarly, to measure its precise momentum one would have to divert all of the energy at the 180 or 360 point of the wave to the observing instrument leaving none of its position energy left to for an instrument which was attempting to measure its position. Therefore, if one was able to determine a particles exact momentum one could not say anything about its position.
The reason we observe a particle as a point mass instead of an extended wave is because, as mentioned earlier the article when we observe or "drain" the energy continued in its wave function, whether it be related to its position or momentum it will appear to come from a specific point in space similar how the energy of water flowing down a sink drain appears to be coming from a "point" source with respect the extended volume of water in the sink.
As mentioned earlier, all points inbetween are a dynamic combination of both position and momentum. Therefore, the degree of accuracy one chooses to measure one will affect the other.
For example, if one wants to measure the position of a particle to within a certain predefined distance "m" its wave energy or momentum will have to pass through that opening. However, Classical Wave Mechanics tells us that as we reduce the error in our measurement by decreasing the predefine distance interference will cause its energy or momentum to be smeared our over a wider area thereby making its momentum harder to determine. Summarily, to measure its momentum "m"kg / s one must observe a portion the wavelength associated with its momentum. However, Classical wave mechanics tell us we must observe a larger portion of its wavelength to increase the accuracy of the measurement of its energy or momentum. But this means that the accuracy of its position will be reduced because the boundaries determining its position within the measurement field are greater.
However, this dynamic interaction between the position and momentum component of the matter wave would be responsible for the uncertainty Heisenberg associated with their measurement because it shows the measurement of one would affect the other by the product of those factors or m^2 kg / s.
Yet because of the time varying nature of a matter wave one could only define its specific position or momentum of a particle based on the amplitude or more precisely the square of the amplitude of its matter wave component.
This shows that one can develop a complete description for how particles can exist as a point as the Standard Model assumes they do while at the same time have the spatial properties need to define our reality
Later Jeff
Copyright Jeffrey O’Callaghan 2017
Anthology of 
The Reality of the Fourth Spatial Dimension 

The Imagineer’s

The Imagineer’s Chronicles Vol. 5 — 2014 Paperback $14.84 Ebook $9.97 
The Imagineer’s 

The Imagineer’s 
The Imagineer’s 
The Imagineer’s 

The post The quantum properties of nonpoint particles appeared first on The Imagineer's Chronicles.
]]>The post A relativistic Quantum Mechanics appeared first on The Imagineer's Chronicles.
]]>Many interpret this as meaning a particle and all other objects exists in a world of probabilities and only become connected to the environment when observed. Additionally it assumes that a particle is distributed or simultaneous exists form one edge of the universe to the other because it tells us there is a probability it can be found anywhere in it.
However it is extremely difficult to define a set of statements which explains how those probabilities can be physically connected to that environment even though it has held up to rigorous and thorough experimental testing.
Yet Einstein gave us a an explanation for this connection in his relativistic formulas for length contraction L = L0((1 – v2/c2))1/2 because it tells us the distance between every point along the trajectory of all forms of energy which are moving at the speed including that associated with the wavefunction is zero for an observer who is outside of its reference frame. In other words since the energy associated with Schrödinger’s equation which is moving at the speed of light the distance between the each end of the universe for it relative to an outside observer is zero.
However because the probabilities associated with Schrödinger’s equation involve the spatial properties of position, to fully understand the ramifications of that equation to our understanding of quantum mechanics one must transpose it to the spatial equivalent.
Einstein gave us the ability to do this when he defined the geometric properties of spacetime in terms of the constant velocity of light and a dynamic balance between mass and energy because that provided a method of converting a unit of time in a spacetime 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 spacetime universe and one made up of four *spatial* dimensions.
The fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the curvature in spacetime 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 threedimensional space manifold with respect to a fourth *spatial* dimension.
However this would allow one to physically the connect the probabilities associated Schrödinger’s equation to our observable environment in terms of a physical or spatial displacement in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension as was done in the article "Why is energy/mass quantized?" Oct. 4, 2007.
Briefly that article showed that the observable properties of particles can be caused by the formation of a resonant system on a "surface" of a threedimensional space manifold with respect to fourth "spatial" dimension. This is because the four conditions required for resonance to occur in a threedimensional 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 threedimensional 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 threedimensional space manifold.
Yet the classical laws of threedimensional 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.
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 fundamental resonate frequency of space defined by the equation E=hv where "E" equals the energy of a particle "h" equal Planck’s constant "v" equals the frequency of its wave component.
Yet it also allows one 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 twodimensional surface of a piece of paper is confined to that surface. However, that surface can oscillate up or down with respect to threedimensional space.
Similarly an object occupying a volume of threedimensional 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 threedimension 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 threedimensional space manifold with respect to a fourth *spatial* dimension.
However as mentioned earlier assuming the probabilities associated with Schrödinger’s equation are the result of a displacement caused by a matter wave moving on a "surface" of a threedimension space manifold with respect to a four *spatial* dimension allows one to connect them to the physicality of the observable environment we all live in.
Classical mechanics tell us that due to the continuous properties of the wave energy the article "Why is energy/mass quantized?" Oct. 4, 2007 associated with a quantum system would be distributed throughout the entire "surface" a threedimensional 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 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 threedimensional space caused by matter wave is correct then classical mechanics tell us that those oscillations would be distributed over the entire "surface" threedimensional 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 because
However, as was mentioned earlier Einstein in his formula for length contraction L = L0((1 – v2/c2))1/2 tells us that a particle would simultaneously exist everywhere throughout the entire universe because of the fact that wave energy is continuous it would extend to each end of the universe. Therefore the distance between the each end of the universe relative to an observer outside of that reference frame would be zero. Additionally because time stops for anything traveling at the speed of light it would appear to exist simultaneously at every point in the universe of an outside observer.
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 threedimensional 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 threedimensional space manifold is greatest and would diminish as one move away from that point.
In others words one can explain how the probabilities associated with Schrödinger’s equation are connected to our physical world and the fact that particles simultaneously exist everywhere in the universe before it is observed by applying the concepts of Einstein Theory of Relativity to the quantum environment.
It should be remember Einstein’s genius allows us to choose to define a quantum system in either a spacetime environment or one consisting of four *spatial* dimension when he defined the geometry of spacetime 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 2017
Anthology of 
The Reality of the Fourth Spatial Dimension Paperback $9.77 Ebook $6.24 

The Imagineer’s

The Imagineer’s Chronicles Vol. 5 — 2014 Paperback $14.84 Ebook $9.97 
The Imagineer’s 

The Imagineer’s 
The Imagineer’s 
The Imagineer’s 

The post A relativistic Quantum Mechanics appeared first on The Imagineer's Chronicles.
]]>The post Should we allow imagination to define physics? appeared first on The Imagineer's Chronicles.
]]>Most if not all explanatory models of reality rely to some extent on ones imagination because they use unobservable quantities to support them.
For example Einstein used the concept of a spacetime dimension to define gravity. However no one has ever directly observed a spacetime dimension.
Similarly quantum mechanics describes the interactions of particles in terms of the mathematical probabilities associated with a wavefunction which like a spacetime dimension is also unobservable.
In other words both of these theories have imagination as a core component of their explanatory structure.
However there is distinct difference in how they apply it to the environment they are attempting to explain.
For example Einstein in his the "General Theory of Relativity" uses imagination and mathematics to expand a curvature in our observable threedimension environment to define a fourdimensional spacetime universe.
In other words even though its explanatory mechanism is based the existence of a spacetime dimension that can only exist in our imagination he was able by using Riemannian geometry mathematically connect to our observable environment.
Similarly Quantum mechanics also uses imagination and mathematics to very accurately describe the particle interaction based on probabilities.
But unlike Relativity it uses a mathematical construct know as the wavefunction to describe the mechanism responsible for the future position of a particle which has no counterpart in our observable environment.
As Steven Weinberg mentioned in his book "Dreams of a Final Theory" the reason this difference in methodology is important is because mathematics in itself is never the explanation of anything because it is only the means by which we use one set of facts to explain another. This is true even though it may be the only the language in which we express them. In other words mathematics should not be used to justify the mathematics of an explanatory model.
However as was just mentioned quantum mechanics uses the mathematics associated with a wavefunction to explain the mathematical mechanism it assumes is responsible for particle interaction.
Why then when mathematics in itself is never the explanation of anything do so many tell us that the mathematical properties of a wavefunction explain the quantum environment.
They do so because to this date it is the only way available to explain and predict how, among many other things chemical process occur and why the particles that were present in the Big Bang, evolved to create the universe we live in even though its entire theoretical structure is based purely on the imagination of those who developed it.
Some may question using the term imagination to describe the mathematical properties of the wavefunction. However its definition of "being the faculty or action of forming new ideas, or images or concepts of external objects not present to the senses" is applicable to them.
This is true even though science can use its abstract mathematical properties to accurately predict the evolution of particle system.
However as we have shown throughout the Imagineer’s Chronicles there may be more to the wavefunction than just mathematics. In other words by using the imagination one may be able to explain or expand the abstract mathematical properties of the wavefunction to the observable properties of our environment similar to how Einstein was able to expand a curvature in our observable threedimension environment using Riemannian geometry to define a fourdimensional spacetime universe.
For example in the article "Why is energy/mass quantized?" Oct. 4, 2007 it was shown one can understand how and why energy/mass is quantized in terms of the observable properties of resonant systems in our three dimensional environment.
Other articles like "Quantum entanglement: a classical explanation" July 15, 2015 clearly shows that the "spooky action at a distance, as Einstein called it can be explained in terms of the laws of classical causality. In other words it is merely an illusion resulting from a lack of understanding of a classic physicality of a quantum environment
Many of the 250 articles published in the Imagineer’s Chronicles over the past nine years show that one can apply the classical laws of our observable environment to a quantum one to explain hoe the mathematical properties of the wavefunction physically describe how particles interact.
Imagination as was mentioned earlier is a critical component of all modern theoretical models of physics. But we must not allow it to be only the only one because it can result in defining an environment that does not describe the reality we are attempting to define.
In other words similar to how Einstein was able to expand a curvature in our observable threedimension environment to define a fourdimensional spacetime universe one must, as we have tried to do make an effort to expand the physical properties of our observable environment to explain the world of quantum mechanics and the wavefunction that defines its environment.
Later Jeff
Copyright Jeffrey O’Callaghan 2016
The universe’s most powerful enabling tool is not
knowledge or understanding but imagination
because it extends the reality of one’s environment.
However its scientific effectiveness is closely
related to how strongly it is
anchored in the reality it defines.
Anthology of 
The Reality of the Fourth Spatial Dimension Paperback $9.77 Ebook $6.24 

The Imagineer’s

The Imagineer’s Chronicles Vol. 5 — 2014 Paperback $14.84 Ebook $9.97 
The Imagineer’s 

The Imagineer’s 
The Imagineer’s 
The Imagineer’s 

The post Should we allow imagination to define physics? appeared first on The Imagineer's Chronicles.
]]>The post Time travel: is it possible? appeared first on The Imagineer's Chronicles.
]]>The laws of physics in the microscopic world suggest that it is because the physical processes they define at the subatomic level appear to be either entirely or mostly time symmetric. In other words the theoretical statements that describe them remain true if the direction of time is reversed. However, the opposite is true in the macroscopic world in that there is an obvious direction (or flow) of time. In others words, process in our macroscopic environment are observed to be asymmetric with respect to the direction of time appearing to rule out the possibility of traveling backwards in it.
Therefore, one way to understand why we as a civilization have been unable devise a mechanism for traveling back in time may be to understand difference between the macroscopic and microscopic worlds with respect to it because in one it seems possible while in the other it appears not to be.
Entropy appears to be the only quantity in the macroscopic world that "picks" a particular direction for time. As one goes "forward" in time, the second law of thermodynamics says the entropy or disorder of an isolated system will increase when no energy is consumed. In other words many in the scientific community believe the reason a system composed of multiple units must always move in forward with respect to time because to go back to a previous configuration one must add energy to it.
However, one cannot apply the concept of entropy to the microscopic world of atoms to determine its direction with respect to time because the entropy or relative disorder of system composed of signal entities such as an atom does not spontaneously increase as it moves through it. Therefore, one cannot use it to define its direction in microscopic systems because it does not quantifiably change as one "moves" through time.
Yet both these definitions define the direction or flow of time in terms of the physical configuration of its spatial components. For example, entropy or relative disorder of system composed of a signal atom does not spontaneously increase as it moves through time because its spatial position can only be reference to itself. This differs form systems that contain multiple entities in that the spatial configuration of its units can be compared to others in that system. The only difference between them with regards to defining their entropy with respect to the movement of time is what their spatial locations are reference to.
However the fact that we have been unable to move backwards in time in the microscopic universe suggests the casualty of time in that environment may not be related to the physical movement of an entity but to the causality of a quantifiable change in the spatial components of a system similar to the one that gives us direction for time in a macroscopic system.
For example in a multiunit system the causality of the increased entropy associated with the forward movement of time is directly related to its thermodynamic energy because it is what quantifies the direction of the changing spatial disorder in a system. Similarly in a single component system the sequential ordering of the causality of it moving to the left and then to the right will always define the direction of time in terms of its changing spatial position. In other words on can define the direction of time in both in terms of the causality of the systems spatial components.
As was mentioned earlier the second law of thermodynamics which defines the passage of time in the macroscopic world is based on a statistical definition was developed by Ludwig Boltzmann does not hold with strict universality: any system can fluctuate to a state of lower entropy.
However scientists have observed billions of particle collisions in which two particles collide to produce other particles however they have never observed two particles spontaneous coming together to form one particle even though statistically speaking they should happen much more often than in multi particle systems because they have considerably less complexity.
Therefore understanding the causality of the change in the position component of entities in both macro and microscope system may tell us if travel time travel is possible.
As was shown in the earlier article "Defining what time is" Sept. 20, 2007 defining the direction of time in terms of the sequential ordering of the causality of events would a provide a consistent direction for time in all environments because the causality of an atom moving to the left in both single or multiple component system would always be proceeded by the causality of that the same atom moving to the right; even though, as was mentioned earlier the behavior of the atom is not qualitatively different in either case. This would be true in both our physical and mathematical perceptions of time.
In other words defining it in terms of the sequential ordering of the causality of an event is consistent with the observation that events appear to always move forward in time in both the macroscopic universe and the microscopic world of particle accelerators because the casualty of particle breaking up into different parts must always proceed those parts coming together.
Some might think that it is not possible to tell the order in which events occurred without using time as a reference. However one can use the spatial properties of a system to determine it because the first event in a series would only be connected to the one before it while all other would be connected not only to that one but to the one after it. In other words one could determine the order in which the events occurred by referencing them to the one that has only one spatial connection and following the single line of events back towards there origin.
However this also rules out any possibility of one traveling through time because if it is only a measure of the sequential ordering of the causality of events then similar to all measurements it does not have physical properties so because one cannot travel through or in something that does not have a physical structure time travel is physically possible.
Is time travel possible?
The laws of physics in the microscopic world suggest that it is because the physical processes they define at the subatomic level appear to be either entirely or mostly time symmetric. In other words the theoretical statements that describe them remain true if the direction of time is reversed. However, the opposite is true in the macroscopic world in that there is an obvious direction (or flow) of time. In others words, process in our macroscopic environment are observed to be asymmetric with respect to the direction of time appearing to rule out the possibility of traveling backwards in it.
Therefore, one way to understand why we as a civilization have been unable devise a mechanism for traveling back in time may be to understand difference between the macroscopic and microscopic worlds with respect to it because in one it seems possible while in the other it appears not to be.
Entropy appears to be the only quantity in the macroscopic world that "picks" a particular direction for time. As one goes "forward" in time, the second law of thermodynamics says the entropy or disorder of an isolated system will increase when no energy is consumed. In other words many in the scientific community believe the reason a system composed of multiple units must always move in forward with respect to time because to go back to a previous configuration one must add energy to it.
However, one cannot apply the concept of entropy to the microscopic world of atoms to determine its direction with respect to time because the entropy or relative disorder of system composed of signal entities such as an atom does not spontaneously increase as it moves through it. Therefore, one cannot use it to define its direction in microscopic systems because it does not quantifiably change as one "moves" through time.
Yet both these definitions define the direction or flow of time in terms of the physical configuration of its spatial components. For example, entropy or relative disorder of system composed of a signal atom does not spontaneously increase as it moves through time because its spatial position can only be reference to itself. This differs form systems that contain multiple entities in that the spatial configuration of its units can be compared to others in that system. The only difference between them with regards to defining their entropy with respect to the movement of time is what their spatial locations are reference to.
However the fact that we have been unable to move backwards in time in the microscopic universe suggests the casualty of time in that environment may not be related to the physical movement of an entity but to the causality of a quantifiable change in the spatial components of a system similar to the one that gives us direction for time in a macroscopic system.
For example in a multiunit system the causality of the increased entropy associated with the forward movement of time is directly related to its thermodynamic energy because it is what quantifies the direction of the changing spatial disorder in a system. Similarly in a single component system the sequential ordering of the causality of it moving to the left and then to the right will always define the direction of time in terms of its changing spatial position. In other words on can define the direction of time in both in terms of the causality of the systems spatial components.
As was mentioned earlier the second law of thermodynamics which defines the passage of time in the macroscopic world is based on a statistical definition was developed by Ludwig Boltzmann does not hold with strict universality: any system can fluctuate to a state of lower entropy.
However scientists have observed billions of particle collisions in which two particles collide to produce other particles however they have never observed two particles spontaneous coming together to form one particle even though statistically speaking they should happen much more often than in multi particle systems because they have considerably less complexity.
Therefore understanding the causality of the change in the position component of entities in both macro and microscope system may tell us if travel time travel is possible.
As was shown in the earlier article "Defining what time is" Sept. 20, 2007 defining the direction of time in terms of the sequential ordering of the causality of events would a provide a consistent direction for time in all environments because the causality of an atom moving to the left in both single or multiple component system would always be proceeded by the causality of that the same atom moving to the right; even though, as was mentioned earlier the behavior of the atom is not qualitatively different in either case. This would be true in both our physical and mathematical perceptions of time.
In other words defining it in terms of the sequential ordering of the causality of an event is consistent with the observation that events appear to always move forward in time in both the macroscopic universe and the microscopic world of particle accelerators because the casualty of particle breaking up into different parts must always proceed those parts coming together.
Some might think that it is not possible to tell the order in which events occurred without using time as a reference. However one can use the spatial properties of a system to determine it because the first event in a series would only be connected to the one before it while all other would be connected not only to that one but to the one after it. In other words one could determine the order in which the events occurred by referencing them to the one that has only one spatial connection and following the single line of events back towards there origin.
However this also rules out any possibility of one traveling through time because if it is only a measure of the sequential ordering of the causality of events then similar to all measurements it does not have physical properties so because one cannot travel through or in something that does not have a physical structure time travel is physically possible.
Latter Jeff
Copyright 2016
of the Fourth
Spatial Dimension
Paperback
$9.77
Ebook
$6.24
The Imagineer’s
Chronicles
Vol. 7 — 2016
The Imagineer’s
Chronicles
Vol. 6 — 2015
Paperback
$12.25
Ebook
$9.89
The Imagineer’s
Chronicles
Vol. 5 — 2014
Paperback
$14.84
Ebook
$9.97
The Imagineer’s
Chronicles
Vol. 4 — 2013
Paperback
$14.95
Ebook
$7.99
The Imagineer’s
Chronicles
Vol. 3 — 2012
Paperback
$11.54
Ebook
$6.55
The Imagineer’s
Chronicles
Vol. 2 — 2011
Paperback
$9.24
Ebook
$6.57
The Imagineer’s
Chronicles
2007 thru 2010
Paperback
$15.43
Ebook
$7.82
The post Time travel: is it possible? appeared first on The Imagineer's Chronicles.
]]>The post Quantum mechanics as an emergent property of spacetime. appeared first on The Imagineer's Chronicles.
]]>Quantum mechanics assumes that it is fundamental because it defines all interactions within it in terms of its quantized properties while one could say that Einstein’s General Theory of Relativity defines it in terms of an emergent property of continuous spacetime manifold because that’s how it defines reality.
Most would agree the best way of which to determine which one is fundamental would be to see if one can be explain in terms of the other.
Richard Feynman Physics Lecture 01 – Photons, Corpuscles of Light 
For example it is impossible to explain the apparent continuous properties of spacetime in terms of the discrete properties quantum mechanics associates with energy/mass because by definition something that is discrete cannot by definition be continuous. However it is possible to explain how the continuous properties of spacetime can be broken up into the discrete components of energy/mass that allows quantum mechanics to define it in those terms.
Quantum mechanics assumes that energy/mass is quantized based, in part on Schrödinger wave equation which is used to predict and define the quantized energy distribution of electrons in an atom in terms of the Principal number (n), the Angular Momentum “ℓ” (l), Magnetic (m) and Spin Quantum Number(+1/2 and 1/2).
However as mentioned earlier it may be possible to define an emergent mechanism based on the reality of four dimensional spacetime that can explain why the energy distribution in a atom is quantized.
Yet because quantum mechanics defines its operational environment in terms of the spatial properties of position or momentum and not in terms of temporal properties of time or a spacetime environment it would be easier to understand how by redefining that environment in terms of its spatial equivalentEinstein gave us the ability to qualitatively and quantitatively convert the relativistic properties of a spacetime environment to an equivalent one consisting of only four *spatial* dimensions when he defined its geometric properties 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 spacetime universe to unit of space in one consisting of only four *spatial* dimensions.
In other words by defining the geometric properties of a spacetime universe in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining his spacetime universe in terms of the geometry of four *spatial* dimensions.
However this would allow explain how the spatial characteristics of the energy distribution quantum mechanics associated with the four quantum numbers can emerge from reality of environment consisting of four dimensional spacetime or its four *spatial* dimension equivalent.
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 threedimensional environment to a matter wave moving on a “surface” of a threedimensional 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 threedimensional 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 threedimensional 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 threedimensional space, would meet the requirements mentioned above for the formation of a resonant system or “structure” in space.
Observations of a threedimensional 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.
In other words this defines the quantization or the particle properties of energy/mass in terms of an emergent property of four *spatial* dimensions.
However the fact that one can derive the quantum mechanical properties of energy/mass by extrapolating the resonant properties of a wave in threedimensional environment to a fourth *spatial* dimension means that one should also 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 ” ℓ” the third or Magnetic by the letter “m” and the last is the Spin or “s” Quantum Number.
In threedimensional space the frequency or energy of a resonant system is defined by the vibrating medium and the boundaries of its environment.
For example the 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 threedimensional 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 threedimensional 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.
Additionally it also tells us why in terms of the physical properties four dimensional spacetime 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 spacetime or four spatial dimension corresponds to the energy of an electron it becomes one of the fundamental energy unit of the universe.
This defines physicality of the environment associated with the first quantum number in terms of an emergent property of four *spatial* dimensions and why it is unique for each subdivision of electron orbitals. 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 “ℓ” 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 threedimensional space.
For example it tells us that the individual energies of 3 “p” orbitals are physically distributed along each of the three axis of threedimensional 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 “Pauli’s Exclusion Principal: a classical interpretation” Feb. 15, 2012 one can derive its physicality by extrapolating the laws of a threedimensional environment to a fourth *spatial* dimension.
Briefly the article “Defining potential and kinetic energy?” Nov. 26, 2007 showed all forms of energy including the angular momentum of particles can be defined in terms of a displacement in a “surface* of threedimensional space manifold with respect to a fourth *spatial* dimension. In threedimensional 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 threedimensional 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 threedimensional 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 the article “Defining potential and kinetic energy?”. One would be by creating a downward displacement on the “surface” of a threedimensional space manifold with respect to a fourth *spatial* to the level associated with the electron in that orbital while the other would be raise it up to that energy level .
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 of water by pushing it down below its surface than using a cup to fill it.
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 threedimensional 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 if they had the same number.
This shows how one can derive the physicality of the four quantum numbers of an emergent property of four *spatial* dimension or its spacetime equivalent.
Later Jeff
Copyright Jeffrey O’Callaghan 2016
Anthology of 
The Reality of the Fourth Spatial Dimension 

The Imagineer’s

The Imagineer’s Chronicles Vol. 5 — 2014 Paperback $14.84 Ebook $9.97 
The Imagineer’s 

The Imagineer’s 
The Imagineer’s 
The Imagineer’s 

The post Quantum mechanics as an emergent property of spacetime. appeared first on The Imagineer's Chronicles.
]]>The post The conservation of spacetime. appeared first on The Imagineer's Chronicles.
]]>However these laws suggest the existence of another more fundamental one that physically defines their causality.
Einstein’s General Relativity, from 1905 to 2005 – Kip Thorne – 
For example Einstein told us that time dilates and space contracts as the energy and momentum of reference frames increase.
In other words there appears to a one to one correspondence between the effects momentum and energy has on the dimensional properties of spacetime.
However the fact that the energy and momentum have a common effect on those properties suggests there may be a physical connection between them and their conservation laws.
For example Einstein told us the mass of a particle created in accelerators increases the curvature in spacetime causing the physical distance between two points external to it to decrease by a measurable amount. If that particle decays that curvature returns to where it was before that mass was created. In other words physical properties of space are conserved in the creation, destruction or redistribution of mass. Additionally he also told us that concentrating it in the form of a particle causes time to dilate by a measurable amount with respect to its external spacetime environment and when that particle decays time is returned to normal rate of change.
In other words in all reactions involving mass the physical properties of spacetime are conserved because they always return to their original value before it was either created or destroyed.
One can also connect the causality of the law of conservation of all forms of energy to the physical properties of a spacetime environment.
For example it can be shown the causality of charge conservation is also directly related to the symmetries of the spacetime environment defined by Einstein.
However it will be easier to explain if one coverts it to its equivalent in four *spatial* dimensions.
(The reason will become obvious later on in this discussion.)
Einstein gave us the ability to do this when defined the geometric properties of spacetime in terms of the constant velocity of light because that provided a method of converting a unit of time in a spacetime environment to a 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 spacetime universe and one made up of four *spatial* dimensions.
The fact that one can use Einstein’s theories to qualitatively and quantitatively derive the displacement he associated with energy in a spacetime universe in terms of four *spatial* dimensions is the bases for assuming as was done in the article “Defining energy” Nov 27, 2007 that all forms of energy including those associated with charge can be derived in terms of a spatial displacement in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension.
This allows one to derive the physical properties of charge in terms a displacement in that "surface" with respect to a fourth *spatial* dimension.
For example if one raises a cup of water above its surface it will be given a measurable amount of potential energy with respect to that surface while at the same time a force will be developed that will be directed downward towards it. Additionally the level of the water will be lowered by the exact amount that was removed by the lifting of the cup above its surface. If one pours the water back the levels will return it original depth. In other words the level of the water is conserved due to the symmetry of its surface levels.
However as was shown in the article “Defining energy” Nov 27, 2007 if one raises, with respect to a fourth *spatial* dimension the volume of threedimension space associated with a charge it will be given a measurable amount of potential energy with respect to that "surface" while at the same time a force will be developed that will be directed downward towards it. Additionally the energy level of threedimensional space not associate with that charge will be lowered by the exact same amount. If one calls the volume space that was raised up a negative charge one would call the lowering of the "surface" of three dimension space caused by that a positive charge. If one neutralizes the negative charge by bring it in contact with that "surface" it will return to its original level and the charge will be neutralized. This shows how one can derive the causality of charge conservation in term of the symmetry imposed by Einstein theories.
In other words symmetry imposed by Einstein’s spacetime environment means that charge must be conserved because the creation of one must always be offset by the other.
This is true in environments consisting of either four *spatial* dimensions or four dimensional spacetime because as was shown earlier they are quantitative and qualitative interchangeable.
However it also allows one to understand how the conservation laws of nature are physically connected to each other in terms of the physical geometry of our universe.
It should be remember Einstein’s genius allows us to choose to derive the conservation laws either a spacetime environment or one consisting of four *spatial* dimension when he defined their environments in terms energy and the constant velocity of light. This interchangeability broadens the environment encompassed by his theories thereby giving us a new perspective on the origins of the conservation laws of physics.
Later Jeff
Copyright Jeffrey O’Callaghan 2016
The post The conservation of spacetime. appeared first on The Imagineer's Chronicles.
]]>The post Seeing time appeared first on The Imagineer's Chronicles.
]]>
What Is Time? Determinism, Quantum Physics, Consciousness, Free Will, Causality. 
However physicists are not afforded the option of an abstract definition because they have defined gravity in terms of the physical curvature in a spacetime dimension. For example, a physical curvature in spacetime is viewed by many physicists to be causality of the force of gravity.
In other words to be consistent they should be able to define it in terms of its physicality.
Yet it is possible that time may be something which cannot be defined by a what but may be an effect similar to how color is not a something but is an effect cause by how light is reflected by a something. If this is true physicist’s would have to find another way to define gravity other that one that depends on the interactions of space and time defined by Einstein.
Another question that is difficult to answer is if nothing in the universe changed would time still exist.
Answering this question may provide an answer as to what time is because if change is the causality of our perception of time then understanding what causes it in the spacetime environment that physicist’s say we live may help us to understand how it is connected to our environment.
However, as Einstein suggested in the following quote time cannot not be physically connected to the process of change because it is a rigid unchanging component of a spacetime environment defined by both his Special and General Theories of Relatively and therefore could not be responsible of the dynamic process associated with change.
"Since there exists in this four dimensional structure [spacetime] no longer any sections which represent "now" objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four dimensional existence, instead of, as hitherto, the evolution of a threedimensional existence."
In other words according to Einstein the structure of spacetime is ridge while the changes we associated with time are merely an illusion similar to the illusion of change created in a flip book when one rapidly flips through its pages containing series of pictures that vary gradually from one page to the next.
Yet this means if, as he suggested the time dimension is not responsible for the "evolution of a threedimensional existence" some other geometric property of the our universe must be physically connected to it to allow change to propagated through it.
Therefore to understand the "evolution of a threedimensional existence" one would have to explain how the change propagates through it without referring to a time dimension.
Einstein gave us the ability to do this when he defined the energy associated with the evolution of a spacetime environment in terms of the equation E=mc^2 the constant velocity of light because that provided a method of converting a unit time and redefine the energy in that environment to its equivalent 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 spacetime universe and one made up of four *spatial* dimensions.
In other words he tells the physical properties of a spacetime geometry are related to an observer’s interpretation similar to how the measurements of their magnitudes are related an observer’s velocity. This is because, as was show above one can reinterpret the mathematics associated with the time dimension in an environment consisting of four dimensional spacetime with a spatial one to create one in only four *spatial* dimensions with identical properties. However one must be careful not to think of this as the physical replacement of the time dimension in Einstein’s universe with a spatial one because according to his mathematics they coexist in the same geometric plain.
Additionally the fact that the equation E=mc^2 allows us to quantitatively derive energy in a spacetime environment in terms of four *spatial* dimensions is the bases for assuming as was done in the article “Defining energy” Nov 27, 2007 that all forms of change can be derived in terms of a displacement in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension instead of one in a spacetime manifold.
Doing would also allow physicists to define gravity and energy in terms that do not depend on time or the interactions of space and time defined by Einstein.
Additionally it would allow one to understand how the geometric properties of space interact to create the change associated with time in terms of a physical image without using it because we can "see" or perceive how a void in space created by any displacement causes change where, as was mentioned earlier we cannot with time.
For example, we can physically observe how the energy stored in the displacement of water in dam causes change in an environment when it is released or allowed to flow over it. In other words we can form a physical image of the causality of the changing level of water in a dam in terms of its movement through the spatial void between its top and bottom.
Similarly one can form a clear physical image of how and why change occurs in our threedimensional environment by assuming the energy stored in a spatial displacement in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension is released though the "void" that displacement creates in four dimensional space.
This suggest the change most associate with time may be an effect caused by an interaction of a fourth spatial dimension with our three dimension environment.
In other words similar to how an the color of an apple is an effect created by an interaction between light and its surface time may be the effect of a physical interaction of our threedimensional environment with a four *spatial* dimension.
It should be remember Einstein’s mathematical model which defines the physical geometry of our universe tells us that an all objects must simultaneously exist in both a spacetime environment and one consisting of four spatial dimension because as was shown above one can use his mathematics to define two identical universes; one in four dimensional time and another made up of only four *spatial* dimensions. Which one we use to define our reality is dependent on how an observer interprets his mathematics.
Later Jeff
Copyright Jeffrey O’Callaghan 2016
Anthology of 

The Imagineer’s

The Imagineer’s Chronicles Vol. 5 — 2014 Paperback $14.84 Ebook $9.97 
The Imagineer’s 

The Imagineer’s 
The Imagineer’s 
The Imagineer’s 

The post Seeing time appeared first on The Imagineer's Chronicles.
]]>