Can the arrow of time be reversed?  Some like Richard Feynman, the architect of quantum electrodynamics suggest that it can because he defined antiparticles as particles traveling backwards in time. However even though it may allow one to define a very accurate quantitative description of their properties it may not reflect how and why they interact with their environment

The reason he found it necessary to make this assumption is because when Paul Dirac used his mathematical calculations to integrated quantum mechanics with Einstein’s theories, he realized his equations not only worked for an electron with negative charge it also worked for a particle that behaves like an electron with positive charge.
In other words, they predicted something entirely new to science – antiparticles.

However, the only way to define how they interact with normal matter with the present interoperation of Einstein’s theories was to assume they move backwards in time even though no has ever observed it to move that way. 

Yet Einstein gave us another way to understand the interaction between matter and antimatter when he defined the geometric properties of space-time in terms of the constant velocity of light because that provided a method of converting a unit of time in a space-time environment of unit of space in four *spatial* dimensions. In other words it gives us mathematical way to convert a universe composed of four dimensional space-time to one made up 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 space-time universe and one made up of four *spatial* dimensions.

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

Additionally it provides another possible way that antiparticle can interact with normal matter that is related to the spatial not of the time properties of the universe.

But why should we care if they give us the same numerical results.

Because understanding the true nature of interactions opens doors to new and more accurate understanding of how our universe works.

For example the caloric theory of heat assumed that it was an interaction of a self-repellent fluid called caloric that flows from hotter bodies to colder bodies. Caloric was also thought of as a weightless gas that could pass in and out of pores in solids and liquids.

However the realization heat is transferred by the interactions of particles allowed for the development of thermodynamics and for our modern understanding of entropy which serves one of the physical foundations of our modern understanding of the evolution of our universe.

In others words if we had held on to the caloric interpretation we would not have the in depth understanding of its physical evolution as we now have.

Similarly a correct interpretation of the interaction between matter and antimatter may provide us with a more in-depth understanding of the processes involved in the evolution of the subatomic world.

As mentioned earlier the article “Defining energy?” Nov 27, 2007 showed that all forms of energy can be derived in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension However this means because Einstein’s mathematics allow one to qualitatively and quantitatively define energy associated with matter and antimatter in terms of four *spatial* dimensions as well one made up of four dimensional space-time.   In other words a particle of antimatter could be defined as being the result of an oppositely directed spatial displacement with respect to a four *spatial* dimension in a "surface" of a three dimensional space manifold as well as one that was traveling in backwards in a space-time.

Unfortunately as mentioned earlier there is no way using Einstein’s mathematics to determine which one of them defines the true nature of their interactions because as mentioned earlier both interpretations yield the identical quantitative results.

However there is an experiment as describe in the New Scientist article "Antimatter mysteries 3: Does antimatter fall up?" Apr 29, 2009, that will verify which one of these different interpretations actually defines the physical interactions between matter and antimatter.

First it would require the building of highly unstable pairings of electrons and positrons, known as positronium, then excite them with lasers to prevent them annihilating too quickly. Clouds of antiprotons will rip these pairs apart, stealing their positrons to create neutral antihydrogen atoms.

Pulses of these anti-atoms shot horizontally through two grids of slits will create a fine pattern of impact and shadow on a detector screen. By measuring how the position of this pattern is displaced, the strength – and direction – of the gravitational force on antimatter can be measured.

However, if it is found that an antiparticle does posses negative gravitational energy Einstein’s mathematics tells us the reversal of time cannot be the explanation of its properties because all of his equations that define energy of mass such as E=mc^2, the time component is squared.  There can be no other interpretation if one accepts the present interpretation of Einstein’s theories.

Yet, as mentioned earlier the fact that one can use Einstein”s equations to qualitatively and quantitatively redefine his space-time environment in terms of four *spatial* dimensions allows for an alternate explanation for the interaction between matter and antimatter in terms of a oppositely directed spatial displacements in a "surface" of a three-dimensional space manifold with respect to a fourth "spatial" dimension that is consistent with his theories, without involving reversing the arrow of time.

In other words if it is found that antimatter possess negative gravitational potential one may be able to integrated its quantum mechanical properties with Einstein’s mathematics by assuming that our universe is made up of four *spatial* dimensions instead of four dimensional space-time which as mentioned earlier makes it more consistent with the observed properties of time.

It should be remember Einstein’s genius allows us to choose to define our universe in either a space-time environment or one consisting of 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 the how matter and energy interact.

Later Jeff

Copyright 2018 Jeffrey O’Callaghan

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Should we let imagination define our reality?  If so how much should we allow science to dependent on it?

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 space-time dimension to define gravity.  However no one has ever directly observed a space-time dimension.

Similarly quantum mechanics describes the interactions of particles in terms of the mathematical probabilities associated with a wavefunction which like a space-time 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 three-dimension environment to define a four-dimensional space-time universe.

In other words even though its explanatory mechanism is based the existence of a space-time 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 The Road to Unification 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 three-dimension environment using Riemannian geometry to define a four-dimensional space-time 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 The Road to Unification 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 three-dimension environment to define a four-dimensional space-time 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.

One of the most difficult question one can ask a physicists or anyone for that matter is what is time because it does not have a physical presence. This may be the reasons 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 physicists are not afforded the option of an abstract definition because they have defined gravity in terms of the physical curvature in a space-time dimension. For example, a physical curvature in space-time 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 space-time 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 space-time 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 [space-time] 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 three-dimensional existence.”

In other words according to Einstein the structure of space-time 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 three-dimensional 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 three-dimensional 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 space-time 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 space-time universe and one made up of four *spatial* dimensions.

In other words he tells the physical properties of a space-time 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 space-time 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 space-time 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 three-dimensional space manifold with respect to a fourth *spatial* dimension instead of one in a space-time 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 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.

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 three-dimensional 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 space-time 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 

Ockham’s razor is the idea that, in trying to understand something, getting unnecessary information out of the way is the fastest way to the truth or to the best explanation.

For example Einstein’s General Theory of Relativity is based on the relative simple concept of a curvature in a space-time metric.  Granted the math required to determine the gravitational forces on an object can be very complicated and not easy for many to understand however understanding or visualizing how a curvature in space-time can cause objects to accelerate is relative easy to do.  This is because one can form a relatively simple physical image of it based on how objects such as a ball is accelerated on a curved two dimensional surface on the earth and them extrapolating that to a curvature in a space-time metric. 

However, even though in 1917, he added a cosmological constant to his equations which some fell would provide one of simplest mathematical explanations for Dark energy it is difficult for many to conceptually integrate it with the physical imagery that is provided by his theory. 

Yet, this may be due to the fact that Einstein chose to define gravity in terms of time or a space-time dimension while the accelerative forces of Dark Energy are related to the spatial properties of an expanding universe.

In other words, as Ockham pointed out the best way to understand it would be to eliminate time or the space-time dimension from his general theory of gravity and replace it with spatial one because as was just mentioned our universe is not expanding through time dimension therefore it is not necessary to our understanding of its spatial expansion.

Einstein gave us the ability to do this he derived the physical properties of a gravity in a space-time environment in terms mass and energy and the constant velocity of light because that  provided a method of converting a unit of time in a space-time environment with unit of space in four *spatial* dimensions.   Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.
This fact that one can use Einstein’s theories to qualitatively and quantitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions is one the bases of assuming as was done in the article “Defining energy” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

In other words one can not only use Einstein’s equations to quantitatively and qualitatively derive how energy interacts with time in a space-time dimension but also how it would interact with its spatial equivalent in four spatial dimensions.

We know from the study of thermodynamics that energy flows from areas of high to ones with low density very similar to how water flows form an elevated or “high density” point to a lower one.

For example if the walls of an above ground pool filled with water collapse the elevated two-dimensional surface of the water will flow or expand and accelerate outward towards the three-dimensional environment sounding it.

Yet we know from observations of the cosmic background radiation that presently our three-dimensional universe has an average energy component equal to about 3.7 degrees Kelvin. 

However this means that according to concepts developed in the article “Defining energy” (mentioned earlier) the three-dimensional “surface” of our universe which has an average energy component of 3.7 degree Kelvin would be elevated with respect to a fourth *spatial* dimension.

Similarly if the “surface” of a three-dimensional manifold was elevated with respect to a fourth *spatial* dimension as Einstein tell us as it would be if one redefined his space-time  universe in terms of four spatial dimension then it would be accelerated outward for the same reason as how the water in a pool whose sides had collapsed.

In other words one qualitatively understand the casually of the accelerated expansion of our universe in term of the physical image of water accelerating out of collapsed pool.

Some may feel that this is an over simplification of what appears on the surface to be a rather complex phenomena such as Dark Energy but is no more simplistic that the one use to help us understand how gravity works in a space-time environment.  Granted the math behind this concept may be complex and difficult to understand as it is with the gravitational curvature in space-time however that does not mean that we cannot use it to understand its causality.

It should be remember that Einstein’s genius and the symmetry of his mathematics allows us to choose whether to define the forces associated with gravity and dark energy in either four *spatial* dimensions or four dimensional space-time.

Later Jeff

Copyright 2016 Jeffrey O’Callaghan

Can one integrate the quantum mechanical interpretation of electromagnetism with the classical concepts of a particle and wave?  We think so.

One of the most troubling aspects of its interpretation at least to classical or relativistic physicists is how the role of an observer defines the system under observation.
For example many of the proponents quantum mechanics assume that light and all other objects in our universe simultaneously exist as a particle and wave and only decides which one it want to be when an conscience being measures or observer it. 

The standard interpretation of quantum mechanics explains this paradox as a fundamental property of the Universe, while alternative interpretations explain the duality as an emergent or a second-order consequence of various limitations of the observer. This treatment focuses on explaining the behavior from the perspective of the widely used Copenhagen interpretation, in which wave–particle duality serves as one aspect of the concept of complementarily, that one can view phenomena in one way or in another, but not both simultaneously.

Some have even gone so far as to say that some form of intelligent being must observe light before it makes a decision as to whether or not it what’s to be a particle or a wave.

However, assuming that a light has the ability or intellectual capability to decide what it wants to be is, at least in my opinion is a bit bizarre.  

Even so one could find a solution to how quantum systems “decides” if they want to be a particle or wave by looking at the effects an observation has on them in classical terms.

But first, we must first show how and why we can apply the laws of a classical environment to them.

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

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

However, redefining the physical properties of quantum system in terms of its spatial instead of its time components would allow understand how quantum system “decides” if  wants to be a particle or wave in terms of the currently accepts classical laws of our observable environment.

For example in the article “Why is energy/mass quantized?” it was shown one can predict the quantum properties of a photon of electromagnetic energy by extrapolating the laws of classical resonance in three-dimensional space to a wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

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

The existence of four *spatial* dimensions would give a continuous non-quantized field of energy/mass (the substance) the ability to oscillate spatially on a “surface” between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

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

Therefore, these oscillations in a continuous non-quantized field of energy/mass, would meet the requirements mentioned above for the formation of a resonant system in space.

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

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

Additionally it also tells us why in terms of the physical properties four dimensional space-time or four *spatial* dimensions an electron cannot fall into the nucleus is because, as was shown in that article all energy is contained in four dimensional resonant systems. In other words the energy released by an electron “falling” into it would have to manifest itself in terms of a resonate system. Since the fundamental or lowest frequency available for a stable resonate system in either four dimensional space-time or four spatial dimension corresponds to the energy of an electron it becomes one of the fundamental energy units of the universe.

Yet it also allowed one to derive the physical boundaries responsible for a particle in terms of the geometric properties of four *spatial* dimensions.

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

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

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

In other words, what determines if one observes a wave or particle would be dependent on if its wave component was allowed to move freely, or if it was confined to a specific volume.

This also explains in terms of the classical laws of our observable environment why particles and waves simultaneously exist and only “decide” which one it wants to be when it is observed. 

For example a system always present its particle properties when being observed because the act of observing it restricts its energy to a specific volume and as was shown in the article “Why is energy/mass quantized?the act of confining its wave component to specific volume results in it presenting its particle properties.

However, when a quantum system it is allowed to move freely though space as when it moves unobserved through the slits in the Thompson double slit experiment its wave properties to become predominate as is demonstrated by a diffraction pattern on a screen placed behind the slits because its energy has not restricted to a specific volume.

Yet one can also use those same concepts to explain the electromagnetic properties of both its wave and particle or photonic components.

For example one could explain and predict that the incremental or discrete energies associated with a photon as was done in the article “Why is energy/mass quantized?“ in terms of the resonant properties of  wave on a “surface” of a three dimensional space manifold or with respect to a fourth spatial dimension.

Yet one can also use the wave properties of a quantum system to explain its electromagnetic characteristics if one views them in terms of four spatial dimensions instead of four dimensional space-time because as was shown in the article “Defining energy?” Nov 27, 2007 its energy can be derived terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

For example, a wave on the two-dimensional surface of water causes a point on that surface to be become displaced or rise above or below the equilibrium point that existed before the wave was present.  A force will be developed by the differential displacement of the surfaces, which will result in the elevated and depressed portions of the water moving towards or become “attracted” to each other and the surface of the water.

Similarly a wave on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension would cause a point on that “surface” to become displaced or rise above and below the equilibrium point that existed before the wave was present.

However, as just mentioned classical wave mechanics, if extrapolated to four *spatial* dimensions tells us the force developed by the differential displacements caused by it will result in its elevated and depressed portions moving towards or become “attracted” to each other.

This defines the causality of the attractive forces of unlike charges associated with the electromagnetic wave component of a photon in terms of a force developed by a differential displacement of a point on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, it also provides a classical mechanism for understanding why similar charges repel each other because observations of water show that there is a direct relationship between the magnitudes of a displacement in its surface to the magnitude of the force resisting that displacement.

Similarly the magnitude of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by two similar charges will be greater than that caused by a single one.  Therefore, similar charges will repel each other because the magnitude of the force resisting the displacement will be greater for two similar 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 from the apex of that displacement.

In other words the one can explain the electromagnetic prosperities wave and quantum properties of light by assuming it is a wave moving on a “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension.

However, also explains how and why the reality of a quantum system is determined by observation because as was shown above one can use classical understanding of waves to explain why when no one is looking it has the properties of wave however when they are observed they always are appear as a particles.

In other words one of  the most troubling aspects of quantum mechanics that of how an observer defines the reality of all systems including electromagnetic energy can be easily understood by redefining Einstein’s space-time universe in terms of four spatial dimensional and applying the laws of a classical environment to it.

It should be remember that Einstein’s genius allows us to choose whether to define the reality of a quantum system in either a space-time environment or one consisting of four *spatial* dimension when he derived its physical geometry in terms of the constant velocity of light.

Later Jeff

Copyright Jeffrey O’Callaghan 2016

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