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.
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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.
Later Jeff
Copyright Jeffrey O’Callaghan 2016
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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
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Einstein’s General Relativity, from 1905 to 2005 – Kip Thorne – 
However these laws suggest the existence of another more fundamental one that physically defines their causality.
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
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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
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But as Charles Seife mentions on page 142 of his book Alpha & Omega "Taken literally the plain vanilla form of the Standard model does not say anything about particle mass at all: in fact if theorists try to put mass in to its equations they blowup and become meaningless."
In 1964 Peter Higgs showed that one can solve this problem and explain why particles have inertial or rest mass if one assumes space is permeated by what is called a Higgs field.
He was able to show that if the particles called boson change their velocity or accelerate, then the Higgs field should exert a certain amount of resistance or drag which according to his theory is the origin of mass. In a slightly more precise terminology, the origin of mass is an interaction between a particle and the (nonzero) Higgs field. It also assumes the disturbance created by mass as it moves through this field would break it’s symmetry triggering the Higgs mechanism, causing the bosons it interacts with to have mass and generate the particle called the Higgs boson.
In 4 July 2012, the ATLAS and CMS experiments at CERN’s Large Hadrons Collider announced they had each observed a new particle the Higgs boson which many physicists tell us confirms the existence of the Higgs field.
However the Standard model’s explanation of mass as a broken symmetry of a spatial environment does not tell us what it is symmetrical to. In other words it does not answer the question "What spatial boundary or axis are the components of the Higgs field asymmetrical to?"
As was mentioned earlier the addition of the Higges field to the Standard Model gives us an almost complete mathematical description of the particles and forces that shape our world in terms of broken symmetries because it does not incorporate the gravitational forces into it.
Einstein on the other hand mathematically derived the causality of gravity in terms of an asymmetrical property of a spacetime environment.
However the fact that Einstein used the broken symmetry of a spacetime environment to derive gravity or the forces associated with mass suggests he may have provided a method of defining the physical mechanism responsible for the symmetry breaking the Standard Model assumes is responsible for that mass.
This is true even though time is only observed to move in one direction forward and never appears to stop so therefore does not have a boundary by which one can define asymmetries.
However he gave us the ability redefine the asymmetries in a spacetime environment responsible for mass in terms of their spatial properties when he defined them in terms of the constant velocity of light because that provided a method of converting a unit of time to its equivalent unit of space in four *spatial* dimensions.
Additionally because the velocity of light is constant it also defined a one to one quantitative and qualitative correspondence between his spacetime universe and one made up of only four *spatial* dimensions.
The fact that one can use Einstein’s theories to qualitatively and quantitatively define the displacement he associated with gravitational energy and mass in a spacetime environment in terms of four *spatial* dimensions is bases for assuming as was done in the article “Defining energy” Nov 27, 2007 that all forms of energy including that associated with mass can also be defined in terms of a spatial displacement in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension.
This would allow one to define the asymmetrical properties or broken symmetries Einstein associated with gravity in terms of a spatial displacement in the "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimensions.
However it also allows the Standard Model to use Einstein theories define the asymmetry associated with the energy of the mass component of particles in terms of their spatial instead the time properties of space.
For example the symmetry of the mathematics of the Standard Model tells us that particles and antiparticles are always created in pairs. However the only way to explain this in a spacetime environment is to assume that they are moving backwards in time. Yet, as was mentioned earlier no one has ever observed time to move backwards.
Yet if one interprets the symmetry of the Standard Model in terms of its spatial instead of its spacetime properties as was shown above to be possible one would realize that because we can move in two direction upwards and downwards in the spatial dimensions one can easily define the symmetrical boundary between particles and antiparticles in terms the equal distance they would occupy above and below the physical "surface" of a threedimensional space manifold with respect to fourth *spatial* dimension.
Yet one can also define asymmetrical properties of the Higgs field the Standard Models assumes is responsible for mass in terms of object or particle occupying the volume either above or below the physical "surface" of a three dimensional space manifold with respect to fourth *spatial* dimension.
In other words converting or transposing Einstein spacetime theories to their spatial equivalent as was done above shows that the asymmetries the Standard Model associates with mass and those Einstein associated with gravity share a common property of the geometry of space.
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 a solution to a problem, as mentioned earlier is only dependent on how an observer interprets his mathematics.
Later Jeff
Copyright Jeffrey O’Callaghan 2016
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Additionally defining or describing what time is extremely difficult. Some define it only in the abstract saying that is an invention of the human consciousness that gives us a sense of order, a before and after so to speak of the changes that occur in our environment. However one can define or describe space in terms of the void we can see between objects that it contains.
Fay Dowker Public Lecture – Spacetime Atoms and the Unity of Physics 
In other words time and space do not appear to share any physical qualities.
Even so physicists have derived the physical structure of the universe in terms of a mathematical model that combines space and time into a single interwoven spacetime continuum.
However it is difficult to understand how in a spacetime environment they can physically interact when, as was just mentioned neither of them have any common properties.
Granted using mathematics one can explain how they do in terms of abstract concepts but it does not explain how and why they do in physical terms.
Yet one can use the fact that the one of the primary functions of time is to define change to form a physical image of how it interacts with space to create it.
Einstein gave us the ability to do this when he defined the energy contained in a volume of spacetime in terms the constant velocity of light because that provided a method of converting a unit of time to its equivalent unit of space in four *spatial* dimensions. Additionally because the velocity of light is constant it also defined a one to one quantitative and qualitative correspondence between his spacetime universe and one made up of only four *spatial* dimensions.
In other words he tells the physical properties of space and time are relative to an observer’s interpretation similar to how the measurements of their magnitudes are relative to an observer’s velocity because, as was show above one can reinterpret the mathematics associated with the spacetime environment of both the General and Special Theories of Relativity purely in terms of its spatial components to create an identical one in only four *spatial* dimensions. However one must be careful not to think of this as the physical replacement of the time dimension in Einstein’s spacetime universe with a spatial one because according to his mathematics they simultaneously coexist in the same geometric plain.
However the fact that one can use Einstein’s theories to qualitatively and quantitatively define the displacement he associated with energy in a spacetime universe in terms of four *spatial* dimensions is 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.
Doing would also allow one to form a physical image of how the geometric properties of space or time interact to create change because as mentioned earlier we can form a clear physical image of how a void in four spatial dimensions created by that displacement would cause change.
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 the dam in terms of its movement through the spatial void between the top and bottom of the dam.
Similarly one can form a clear physical image of how and why change would occur in our three dimensional environment by assuming the energy stored in a spatial displacement in a "surface" of a three dimensional space manifold with respect to a fourth *spatial* dimension is released though the void that displacement creates in four dimensional space.
As was mentioned earlier it is difficult to form physical image of how time can interact with space because of its abstract properties.
However one can from a very clear image of how it does when one realizes that according Einstein theories the physical properties of space and time which as was shown above are relative to an observer coexist on in the same dimensional plain. Therefore an observer who looks at his theories form a spatial perspective can easily understand how change occurs in a space timeenvironment in terms of the physical example of water flowing over a dam.
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 a solution to a problem, as mentioned earlier is only dependent on how an observer interprets his mathematics.
Later Jeff
Copyright Jeffrey O’Callaghan 2016
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Have you ever wondered why so many seeming rational scientists make seemly irrational assumptions to explain why our universe behaves the way it does and why Einstein was unable see, as Robert Oerter pointed out in his book "The Theory of Almost Everything: the magic of relativistic Quantum electrodynamics or QED.
For example he tells one reason he may have felt this way is because it defines the charge around a solitary electron as being caused by the spontaneous creation and evaporation of virtual electronpositron pairs which then instantaneously disappear. In other words when a virtual electronpositron pair is created near the (real) electron, the (imaginary) virtual positron will be attracted toward the real electron, while the virtual electron is repelled. Therefore there should be a resulting separation of charge
I think most rational people would consider someone irrational if they tried to convince l us the reason why they were late for work was because a swam of virtual or imaginary cars were blocking the road and disappeared after we showed up.
Shouldn’t we hold our scientists to the same degree of rationality?
Most who have studied the history of science are aware that Einstein was vehemently opposed to many of the fundamental components of quantum mechanics such as the existence of virtual particle’s to explain an isolated charge.
This was true even though he was able, in his General Theory of Relativity to derive the force of gravity in terms of the geometry of space and time while being unable to do the same for electromagnetism and charge, as was documented by the American Institute of Physics.
"From before 1920 until his death in 1955, Einstein struggled to find laws of physics far more general than any known before. In his Theory of Relativity, the force of gravity had become an expression of the geometry of space and time. The other forces in nature, above all the force of electromagnetism, had not been described in such terms. But it seemed likely to Einstein that electromagnetism and gravity could both be explained as aspects of some broader mathematical structure. The quest for such an explanation — for a "unified field" theory that would unite electromagnetism and gravity, space and time, all together — occupied more of Einstein’s years than any other activity".
One reason why it was difficult of him to visualize electromagnetic fields including those around a single charge may have been because he chose to define the universe in terms of four dimensional spacetime instead of four *spatial* dimensions because, as will be shown below it easier to visualize the properties of electrometric waves and charge in terms of their spatial rather time or spacetime properties.
However he did provide a method of understanding them in terms of their common properties when he chose to define gravity in a spacetime environment in terms of the equation E=mc^2 and constant velocity of light because that give him the ability to redefined it terms of the spatial properties of 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 gravity in terms of four *spatial* dimensions is one bases for assuming as was done in the article “Defining energy?” Nov 27, 2007 that all forces can be derived in terms of a spatial displacement in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension.
One of the advantages to using this technique is that it allows one to define the physicality of gravitational and electrical forces including those around a single electron in the same terms.
For example In the article "Gravity in four spatial dimensions" Dec. 15, 2007 it was shown one can derive gravitational forces in terms of curvature or physical displacement in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension as well as one in a four dimensional spacetime environment.
However the article "What is electromagnetism?" Sept, 27 2007 showed one can also derive the forces associated with electromagnetism in terms of a similar displacement in the "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension.
Briefly that article showed it is possible to derive the forces associated with an electromagnetic wave by extrapolating the laws of Classical Wave Mechanics in a threedimensional environment to a matter wave moving on a "surface" of threedimensional space manifold with respect to a fourth *spatial* dimension.
A wave on the twodimensional surface of water causes a point on that surface to be become displaced or rise above or below the equilibrium point that existed before the wave was present. A force will be developed by the differential displacement of the surfaces, which will result in the elevated and depressed portions of the water moving towards or become "attracted" to each other and the surface of the water.
Similarly a matter wave on the "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension would cause a point on that "surface" to become displaced or rise above and below the equilibrium point that existed before the wave was present.
Therefore, classical wave mechanics, if extrapolated to four *spatial* dimensions tells us a force will be developed by the differential displacements caused by a matter wave moving on a "surface" of threedimensional space with respect to a fourth *spatial* dimension that will result in its elevated and depressed portions moving towards or become "attracted" to each other.
This defines the causality of the attractive forces of unlike charges associated with the electromagnetic wave component of a photon in terms of a force developed by a differential displacement of a point on a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension.
However, it also provides a classical mechanism for understanding why similar charges repel each other because observations of water show that there is a direct relationship between the magnitudes of a displacement in its surface to the magnitude of the force resisting that displacement.
Similarly the magnitude of a displacement in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension caused by two similar charges will be greater than that caused by a single one. Therefore, similar charges will repel each other because the magnitude of the force resisting the displacement will be greater for two charges than it would be for a single charge.
One can define the causality of electrical component of electromagnetic radiation in terms of the energy associated with its "peaks" and "troughs" that is directed perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that perpendicular displacement.
However, Classical Mechanics tells us a horizontal force will be developed by that perpendicular or vertical displacement which will always be 90 degrees out of phase with it. This force is called magnetism.
This is analogous to how the vertical force pushing up of on mountain also generates a horizontal force, which pulls matter horizontally towards the apex of that displacement.
However, as was mentioned earlier gravity can also be explain in terms of a differential force caused by a displacement in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension.
This shows how one can define a common mechanism for the causality of both electromagnetism and gravity in terms of a "unified field" consisting of four *spatial* dimension by extrapolating the laws of classical mechanics in a threedimensional environment to four *spatial* dimensions.
In other words one can visualize the fact that unlike charge attract each other while like ones repel in terms of the asymmetrical properties of spacetime or four spatial dimensions.
Einstein was unable to accomplish this in terms of fourdimensional spacetime because time is only observe to move in one direction forwards and therefore making it difficult to visualize the bidirectional movement of the spatial component of a matter wave moving on its "surface" that is responsible for electromagnetism .
However it also give a more rational explanation of the charge around a solitary electron than the spontaneous creation and evaporation of virtual electronpositron pairs because it shows that it can be understood in terms of a physical displacement in a "surface" of a threedimension space manifold with respect to fourth spatial dimension.
In other words it shows that electric forces are related to a physical displacement in a surface of a three dimensional space manifold with respect to a either a higher spatial or time dimension thereby eliminating the need to evoke the existence of virtual electronpositron pairs to understand the behavior of a charge around a solitary electron.
It should be remember Einstein’s genius allows us to choose to define charge in either a spacetime environment or one consisting of four *spatial* dimension when he defined that environment in terms mass energy and the constant velocity of light. This interchangeability broadens the environment encompassed by his theories thereby giving us a new perspective on the physicality of charge.
Latter Jeff
Copyright Jeffrey O’Callaghan 2016
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Einstein referred to this as "spooky action at a distance" because it assumed that particles can interact instantaneously, regardless of distance separating them which according to his perception of reality this was not possible.
However if one accepts the reality of the spacetime universe defined by Einstein one would realize that according the core principals of his theories there is nothing spooky about action at distance relative to an observers velocity.
Even so he was so convince that he coauthored a paper with Podolsky–Rosen whose intent was to show that if Quantum Mechanics was a valid theory it could not be complete because it does not agree with most people’s perception of reality. The first thing to notice is that Einstein was not trying to disprove Quantum Mechanics in any way. In fact, he was well aware of its power to predict the outcomes of various experiments. What he was trying to show was that there must be a "hidden variable" that would allow Quantum Mechanics to become a complete theory of nature
The argument begins by assuming that there are two systems, A and B (which might be two free particles), whose wave functions are known. Then, if A and B interact for a short period of time, one can determine the wave function which results after this interaction via the Schrödinger equation or some other Quantum Mechanical equation of state. Now, let us assume that A and B move far apart, so far apart that they can no longer interact in any fashion. In other words, A and B have moved outside of each other’s light cones and therefore are spacelike separated.
With this situation in mind, Einstein asked the question: what happens if one makes a measurement on system A? Say, for example, one measures the momentum value for it. Then, using the conservation of momentum and our knowledge of the system before the interaction, one can infer the momentum of system B. Thus, by making a momentum measurement of A, one can also measure the momentum of B. Recall now that A and B are spacelike separated, and thus they cannot communicate in any way. This separation means that B must have had the inferred value of momentum not only in the instant after one makes a measurement at A, but also in the few moments before the measurement was made. If, on the other hand, it were the case that the measurement at A had somehow caused B to enter into a particular momentum state, then there would need to be a way for A to signal B and tell it that a measurement took place. However, the two systems cannot communicate in any way!
If one examines the wave function at the moment just before the measurement at A is made, one finds that there is no certainty as to the momentum of B because the combined system is in a superposition of multiple momentum eigenstates of A and B. So, even though system B must be in a definite state before the measurement at A takes place, the wave function description of this system cannot tell us what that momentum is! Therefore, since system B has a definite momentum and since Quantum Mechanics cannot predict this momentum, Quantum Mechanics must be incomplete.
In response to Einstein’s argument about incompleteness of Quantum Mechanics, John Bell derived a mathematical formula that quantified what you would get if you made measurements of the superposition of the multiple momentum eigenstates of two particles. If local realism was correct, the correlation between measurements made on one of the pair and those made on its partner could not exceed a certain amount, because of each particle’s limited influence on the other.
In other words he showed there must exist inequities in the measurements made on pairs of particles that cannot be violated in any world that included both their physical reality and their separability because of the limited influence they can have on each other when they are "spacelike" separated.
When Bell published his theorem in1964 the technology to verify or reject it did not exist. However in the early 1980s, Allen Aspect performed an experiment with polarized photons that showed that the inequities it contained were violated.
This meant that science has to accept that either the reality of our physical world or the concept of entanglement does not exist because they are mutually excessive.
However Einstein himself predicted the entanglement of particles that are moving at the velocity of light no matter how far apart they are in his Special Theory of Relativity because he showed us that the separability or the distance between two points is dependent on the velocity of the observer with respect to what is being observed.
For example his theory tells the distance between the two objects A and B would be defined by their relative speed with respect to an observer.
Specifically he told us that it would be defined by
However this tell us the distance or length between observations measured between two photons or any particle moving at the speed of light from the perspective a photon would be zero no matter how far those observation might from the perspective of the observers making them because according to the concepts of relativity one could view the photons as being stationary and the observers as moving at the velocity of light. This is true even if they are moving in opposite directions.
Therefore according to Einstein’s theory all photons which are traveling at the speed of light are physical entangled with all other photons that originated within a common system no matter how far apart or "spacelike" separated they may appear to be to all observers who are not traveling at the speed of light.
In other words inequities in the measurements made on pairs of photons should be violated in a world containing the physical reality of Einstein’s theory and separability because they are not "spacelike" separated when viewed from all reference frames which is not traveling at the speed of light.
This tells us that the hidden variable that would allow Quantum Mechanics to become a complete theory of nature is Einstein Theory of Relativity or the Relativistic properties of motion.
Additionally if quantum entanglement did not occur for photons that were space like separated then the physical reality of Einstein spacetime universe as defined by his theory of Relativity must be discarded
One method for determining if this is the reason why Allen Aspect observed polarized photons violated Bells inequities would be to see if they are also violated by particles that were traveling slower that the speed of light because they would according to the Theory of Relativity could be "spacelike" separated.
In others words if it was observed that particles which were not traveling at the speed of light did not violate Bell’s inequity then it would support Einstein perception of reality and provide a physical verification for the causality in terms of the existence of spacetime for one of the most puzzling aspects of quantum mechanics; that of quantum entanglement.
However if it is found that bell’s inequity is violated by particles moving slower than the speed of light then Einstein’s perception of reality would be invalidated because it demands that things which are "spacelike" separated can only have a limited influence one each other.
Yet one must be careful when performing the calculations because the distance separating the particles would not be determined by the distance between the end points as viewed by the experimenter but by relativistic distance as viewed from the particles,
Later Jeff
Copyright Jeffrey O’Callaghan 2016
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However this may just be an illusion resulting from a lack of understanding of the quantum environment.
One of the fundament areas where this disconnect appears is in the probabilistic interpretation Schrödinger wave equation
However one could eliminate this disconnect if one could explain the causality of those probabilities in terms of a physical image based on the laws of classical physics similar to how we explain the causality of the movement of the planets around the sun in terms of a physical image of a curvature in spacetime.
Granted this will not change the fact that one cannot use quantum mechanics to make precise predictions of future events but it would give us a physical reason why we cannot in terms of our classical understanding of causality.
One way of accomplishing this would be look at the physically observable properties of all quantum systems and determine if by applying the laws of causality in a classical environment one can explain the reason for the probabilities associated with Schrödinger’s equation.
For example in 1924 Louis de Broglie theorized that all quantum objects are physically composed of a wave as was verified by 1927 by Davisson and Germer) when he observed electrons diffracted by crystals.
However, the fact that no one has been able to physically connect the causality of those observable properties to the probabilities of all quantum systems does not change the fact that there must be one because if there wasn’t they could not interact with our environment to create the physically observable properties of the world upon which those probabilities are determined.
One reason for this failure may be due to the fact that those probability are related to the spatial not time dependent properties of the wave function.
If so one may be able to establish the connection by looking at it in terms of its spatial properties instead of the spacetime ones associated with Einstein’s theories.
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 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 doing so would have allowed Louis de Broglie to physically define the casualty of the quantum properties associated with Schrödinger equation in terms of a physical or spatial displacement in a "surface" of a 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 the quantized properties of energy/mass are the result of a resonant system formed by a matter "wave" 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.
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 units of the universe.
However, these are the similar to the quantum mechanical properties of energy/mass in that they can only take on the discontinuous or discreet energies associated with the formula E=hv where "E" equals the energy of a particle "h" equal Planck’s constant "v" equals the frequency of its wave component.
In other words Louis de Broglie would have been able to physicality connect the properties of his particle waves to the quantum mechanical properties of Schrödinger equation in terms of the discrete incremental energies associated with a resonant system in four *spatial* dimensions if he had assume space was composed of it instead of four dimensional 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 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 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 would allow one to define a classical causality for quantum probabilities in terms the observable environment we inhabit.
Classical mechanics tell us that due to the continuous properties of waves the energy the article "Why is energy/mass quantized?" Oct. 4, 2007 associated with a quantum system would be distributed throughout the entire "surface" a threedimensional space manifold with respect to a fourth *spatial* dimension.
For example Classical mechanics tells us the energy of a vibrating or oscillating ball on a rubber diaphragm would be disturbed over its entire surface while the magnitude of those vibrations would decrease as one move away from the focal point of the oscillations.
Similarly if the assumption that quantum properties of energy/mass are a result of vibrations or oscillations in a "surface" of 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 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.
This shows that one can define the causality of the probabilities associated Schrödinger wave equation in terms of the laws of causality associated with our observable environment by redefining them in terms of four *spatial* dimensions.
In other words one can eliminate the disconnect between the probabilities associated his equation and a classical environment by defining their causality in terms of the laws of classical physics.
It should be remember 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 2016
Anthology of 

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