We are reposting this article, first published in 2012 because we do not want its message to become lost in time.

Many think the quantum mechanical world of probabilities define our reality.  However, the Greek philosopher, Plato around 375 BC would disagree.

In Plato’s allegory "The cave" he describes how people who have been chained to a cave wall view the world outside of it.  "The people watch shadows projected on the wall by things passing in front of a fire behind them, and begin to ascribe forms to these shadows. According to Plato’s Socrates, the shadows are as close as the prisoners get to viewing reality. He then explains how the philosopher is like a prisoner who is freed from the cave and comes to understand that the shadows on the wall do not make up reality at all, as he can perceive the true form of reality rather than the mere shadows seen by the prisoners.

However, he could have been talking about today’s scientists who are locked into a worldview that projects shadows that cannot be made to agree with the reality of the world they are living in.

For example, Quantum theory defines the existence of particles in terms of a mathematically generated probability function and that they do not exist until a conscience observer looks at it.  In other words, it assumes the act of observation or measurement creates the physical reality of our particle world.  However, because only conscience beings can be observers it implies that it cannot exist without them being there to observe it.

However, if one assumes reality exist only after someone observes it one must also assume that we humans evolved out of something that did not exist.

This seems to contradict the most common definition of reality: that it is an environment with a set of physical properties that exists even when there are no observers present.  In other words, most believe the world exist in even when no one is there to observe it.

Plato’s in his allegory "The Cave" he tells us that one should base his or her interpretation of reality on direct physical observations of the "shadows" they cast on the cave walls because he feels it is the only way to connect their existence to the reality of the world outside of it.

However, the  proponents of quantum mechanics face an even greater problem than those who reside in Plato’s cave because they assume that reality and existence is defined in terms of abstract mathematical probabilities which by definition do not have physical properties; Therefore, they are unable to cast shadows on the reality of the non-abstract environment that exists all around us.

In other words, the reality defined by quantum mechanics cannot create or define the physicality of the shadows projected on the walls of our world or cave as Plato calls it because they themselves do not have any.

Some would argue the fact that quantum mechanics can accurately predict what we observe in the world in terms of the abstract nature of probability functions means that what we perceive as the reality does not exist.

However, as Plato pointed out our only connection to reality is though the observation of the "shadows" it displays on our physical or material world.  Yet because of the abstract nature of probability functions of quantum mechanics they, by definition can never be part or interact with that world.  Therefore, because we can physicality observe of the "shadows" of the quantum mechanical world in our environment isn’t it more likely the abstract one defined by quantum mechanics does not exist while those of the world that we can see and touch do.

Einstein was often quoted as saying "If a new theory was not based on a physical image simple enough for a child to understand, it was probably worthless."

He realized as Plato did that reality can only be discovered by forming a physical image of what its shadows are telling us.

For example, Newton in a letter to Bentley in 1693, talks about a conceptual problem he has with his gravity theory by rejecting the action at a distance that it requires.

"It is inconceivable that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact…That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it."

Einstein looked at the shadows of reality cast by gravity and realized they could be created by a universe made up of four-dimensional space-time.  He extrapolated the physical image of how objects move on a curve surface in a three-dimensional environment to a curved four-dimensional space-time manifold to show that it can explain and predict how gravity "may act upon another at a distance through a vacuum" in terms of a curvature in space and time.  This allowed him to understand the reality behind the shadows we can see in our three-dimension world in terms of a physical image based on the existence of four-dimensional space-time.

In other words, he was able to explain the gravitational shadows on the Newtonian cave walls in terms of a physical image cast by four-dimensional space-time on them.

As Plato would say he perceived the true form of reality based on a physical image of the shadows seen by its prisoners.

Unfortunately, many of today scientists seem to be ignoring the lessons taught to us by Plato and Einstein.  They chose to look for reality in terms of abstract mathematics instead of the physical imagery given to us by its shadows.

The reason may be because it is easier to alter an abstract environment based on mathematics to conform to an observational inconsistency that it is to alter one based on physical imagery.

For example, Quantum theory makes predictions based on the random properties of a probability function.  However, because its abstract properties are not connected to any physical images of our world all observations no matter how inconsistent they are with the physical world it is describing can be incorporate into it.

This is in sharp contrast to the space-time environment defined by Einstein in that projecting the physical image of objects moving on a curve surface in a four-dimensional environment directly connects it to the physicality of the shadows it casts on our three-dimensional environment.

For example, a mass that was repelled by gravity instead of begin attracted would contradict the physical model define by Einstein and would be extremely if not impossible to explain according to that model because that would mean that we should observe objects rolling up hill in our three-dimensional environment.  In other words, because he defined gravity in terms of a physical image based on how objects move on a curve surface in a three-dimensional environment it makes observations like two masses repelling gravitational each other impossible to incorporate into it.

If However, if some observation happened to contradict complimentary principal of quantum mechanics such as simultaneously observing both the particle and wave properties mass it could easily explained in terms of the fact that its probability functions tell us that anything that can happen eventually will  This makes it impossible to find an observation that would contradict it because it tells us the even the impossible is possible if we wait long enough.  However, this can only happen in an abstract environment which is not bound by the physicality of our observational world because in that world we observe that some things just cannot happen.

But why should science put in the effort to understand the physical reality behind the shadows of our world when both the abstract mathematical foundation of quantum mechanics and the physics imagery of Einstein’s theories make very accurate predictions of future events based on the past.  Review Unifying Quantum and Relativistic Theories at Blogging Fusion Blog Directory

Because the mission of a science is to define reality in terms of what we perceive in the world around us which by definition is not abstract.

Later Jeff

Original Copyright Jeffrey O’Callaghan 2012

Can anything exist without time constituting at LEAST part of our observable existence?  Is it eternal because it defines the order of occurrence?  In other words because it defines that order there must always be a something before the after.

Yet if true it means it has a physical presence because it would be part of that observable existence.

However it can also be represented in the abstract as an invention of the human consciousness that gives us a sense of order, a before and after so to speak.  But this would not explain how the before and after can into being.

Even physicists who study time agree these questions are very difficult to answer even though many believe it is an ontologically “basic” or primary concept, of our existence and not made up of, or dependent on, anything else.

Yet if it is part of our physical existence we should be able to answer some of these questions by examining our existence.

For example we can directly observe or perceived matter or space however time can be perceived only in the abstract as an irreversible physical, chemical, and biological change in our existence which does not agree with the physicists who assume that it is basic part or our existence.

This is especially problematic for those who use Einstein’s theories to define gravity because they believe that it is the result of a physical curvature in a space-time dimension is responsible for it, the evolution of the universe and our existence.

This belief is bolstered by the fact that to this date his theoretical predictions are in complete agreement with observations.

However, there is another interpretation of his theories that would not be dependent on the physical existence of time making it possible for life to exist for these physicists without time.

The standard interpretation of his mathematics suggests that gravity is cause by a displacement in a three-dimensional space manifold with respect to time.

However an equally valid one defines gravity in terms of an environment consisting of only four *spatial* dimensions because by defining its properties in terms of the equation E=mc^2 and the constant velocity of light gives one the ability to redefine a unit of time he associated with the casualty of gravity in his space-time universe to unit of space in one consisting of only four *spatial* dimensions.

In other words one could explain gravity by assuming that it is a force created by a spatial displacement in a “surface” of three-dimensional space with respect to fourth *spatial* dimension as well as one in a space-time dimension.

This allows one to define gravity and evolution of the universe not in terms of physical properties of time but those of space which as mentioned earlier we are more familiar with.

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

Because understand the true nature how forces interact to create our environment may 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.

Similarly many physicists assume Einstein’s mathematics defines the forces that control the evolution of the universe depend on the physical existence of time in conjunction three-spatial dimensions.

However as was mentioned earlier an equally valid interpretation of his mathematics would be to assume that it is a result of the interaction of a higher or fourth *spatial* dimension with three-dimensional space. 

Granted we may never be able to directly observe a time or a fourth *spatial* dimensions but that does not mean we cannot use those concepts to help us understand the world around us.

For example changing our perspective on the casuistry of the forces causing gravity and the evolution of the universe such as reinterpreting Einstein’s equations in such a manner, may allow us to answer some unanswered questions in modern physicists such as the true nature of Dark Energy that is causing the accelerated expansion of the universe.

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 if we reinterpret Einstein’s mathematics in terms of their spatial properties gravitational energy would be defined by a depression in the three-dimensional “surface” of our universe with respect to a four spatial dimension while the potential energy component of 3.7 degree Kelvin of the cosmic background radiation could be defined as an elevation in that surface with respect to a fourth *spatial* dimension.

Similarly to the water in a pool 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 a four spatial dimensions then it would be accelerated outward for the same reason as the water in a pool whose sides had collapsed.

Changing one’s perspective on the physical structure of our environment can have far reaching consequents for our understanding of it   For example 1543 Nicolaus Copernicus proposed that the sun not the earth was the center of the universe.  That change in perspective enable Johannes Kepler to formulate his laws of planetary motion which then gave Issac Newton the ability to derive the laws of gravity.   Without that change in perspective none of that would have happened.

 Maybe physicists should try to live without time at least for a while.

 Later Jeff

Copyright 2019 Jeffrey O’Callaghan

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In Neil deGrasse Tyson book Death by Black Hole: And Other Cosmic Quandaries (Kindle Edition Locations 258-262) he tells us “the homing of our senses from birth through childhood allows us, as adults, to pass judgment on events and phenomena in our lives, declaring whether they “make sense.” Problem is, hardly any scientific discoveries of the past century flowed from the direct application of our five senses.  They flowed instead from the direct application of sense-transcendent mathematics and hardware.  This simple fact is entirely responsible for why, to the average person, relativity, particle physics, and 10-dimensional string theory make no sense.

However I disagree with his statement that only a direct application of “sense-transcendent mathematics and hardware” is the only way for us to make sense of the world around us because one advantage human beings have over them is that we can change our perspective on what our senses are telling us whereas they cannot.

For example an artist can “direct the mind” to perceive three-dimensional objects on a two dimensional canvas by using techniques that give one the perspective of three-dimension space.

Similarly scientists can and should direct the mind of the “average person” to see the four-dimensional aspects of Relativity by using techniques that would allow them to perceive them in our three-dimensional universe.

For example in Einstein’s General Theory of Relativity he derived gravity in terms of a curvature in the geometry of four dimensional space-time which one can connect to the “real world” by showing how that a planet to revolve around the sun for the same reason a marble revolves around a curvature in a rubber diaphragm.

However he was unable to do the same for electrical forces as was documented by the American Institute of Physics even though he felt “that electromagnetism and gravity could both be explained as aspects of some broader mathematical structure” .

“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 he could not define a common mathematical structure for electromagnetism and gravity may have been because human beings do not have the ability to perceive or sense the physical properties of time or a time dimension.  However they can perceive the physical properties of three-dimensional space.

In other words he may have been able to make the connection between gravity and electromagnetism by mathematically viewing their associated forces in terms of how our senses perceive the properties of three-dimensional space.

Einstein gave us the ability to do this when he used the velocity of light and the equation E=mc^2 to define relativistic properties of space-time because it allows one to convert a unit of time in his four dimensional space-time universe to a unit of space in a one consisting of only four *spatial* dimensions.  Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by mathematically defining the relativistic properties of a space-time universe in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining those properties in terms of the geometry of four *spatial* dimensions thereby giving one the ability to define electrical forces in terms our sense perception of the multi directional properties of the spatial dimensions while maintaining those relativistic properties.

The fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the curvature in space-time 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 forms of energy including gravitational and electromagnetism can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This would have allowed him to direct his and the mind of the “average person” to define electrical force in terms of our real world perception of a wave by extrapolating that perception to the movement of a wave in an environment consisting of four spatial dimensions.

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, as was shown in the article “What is electromagnetism?” Sept, 27 2007 an electromagnetic wave on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension would cause a point on that “surface” to become displaced or rise above and below the equilibrium point that existed before the wave was present.

Therefore, our sensory perceptions of three-dimensional space, 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 three-dimensional 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 would allow the “average person” to understand the causality of the attractive forces of unlike charges associated with the electromagnetism 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 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 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, our sensory perception of three-dimensional space also 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.

This shows how one can explain electrical forces by extrapolating our perception of a three-dimensional environment to one consisting of four *spatial* dimensions and would have allowed him to mathematically integrate them into his space-time model of the universe because, as was shown above they are mathematically identical.

However another advantage to viewing the relativistic properties of our universe in terms of its spatial instead of its time component is that it would allow one to integrate the quantum mechanical properties of electromagnetic energy into the mathematics of General Relativity in a manner that is consistent with our sense perceptions of three-dimensional space.

For example the article “Why is energy/mass quantized?” Oct  4, 2007 showed one can derive the quantized wave properties of electromagnetism by extrapolating our understanding of a resonant structure and perception of a wave in a three-dimensional environment to a electromagnetic 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 three-dimensional environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in one consisting of four spatial dimensions.

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

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

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

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

In our three-dimensional environment 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 the quantum mechanical properties of a photon or an electromagnetic field.

Yet one can also define its boundary conditions of its resonate structure in the terms of our perceptions of a three dimensional environment.

For example in our three-dimensional world, 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 an electromagnetic wave 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.

Additionally one of the most advantageous results of viewing the relativistic properties of Einstein’s theories in terms of their spatial instead of its time components is that it allow for the integration of one of most perplexing aspects of quantum mechanics; that of how and why a particle position when observed is based only on probabilities.

The physics of wave mechanics tell us that due to their continuous properties the energy waves the article “Why is energy/mass quantized?” Oct. 4, 2007 associated with a quantum system would be distributed throughout the entire “surface” a three-dimensional space manifold with respect to a fourth *spatial* dimension.

For example 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 are a result of vibrations or oscillations in a “surface” of three-dimensional space is correct those oscillations would be distributed over the entire “surface” three-dimensional space while the magnitude of those vibrations would be greatest at the focal point of the oscillations and decreases as one moves away from it.

As mentioned earlier the article “Why is energy/mass quantized?” shown a quantum particle is a result of a resonant structure formed on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Yet the science of Wave Mechanics tells us resonance would most probably occur on the surface of the rubber sheet were the magnitude of the vibrations is greatest and would diminish as one move away from that point,

Similarly a particle would most probably be found were the magnitude of the vibrations in a “surface” of a three-dimensional space manifold is greatest and would diminish as one move away from that point.

This shows how one can physically connect the probabilities associated quantum mechanics to our observable environment by redefining them in terms of the relativistic properties of Einstein’s space-time universe in terms of four *spatial* dimensions.

In other words by changing our perspective on fundamental make up of our universe from one of quantized parts to the relativistic properties of four *spatial* dimensions or four dimensional space time may allow us to ingrate the world of quantum mechanics into the space-time-universe of gravity defined by Einstein because as was shown above his mathematics tell us they are interchangeable.

Additionally as mentioned earlier Einstein felt “that electromagnetism and gravity could both be explained as aspects of some broader mathematical structure”.

The above discussion vindicates that belief because it shows that one can not only incorporate gravity and electromagnetism but also its quantum properties into a broader mathematical structure by rewriting the mathematics of space-time in terms of the relativistic properties of four *spatial* dimensions.

It also shows the advantages of “directing the mind” to perceive how three-dimensional space would interact with four by using techniques such as those outlined above to understand how they are responsible for the reality we all see around us.

It should be remember that Einstein’s genius allows us to choose whether to create physical images of an unseen “reality” in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of the constant velocity of light.

Later Jeff

 Copyright Jeffrey O’Callaghan 2019Anthology of  The Road to Unification  2007 thru 2015    Ebook

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One of the primary purposes of the physical sciences is help us understand how the different components of our universe physically interact to create its observable properties.  However many scientist’s use the abstract properties of mathematics to extract, by quantification the underlying rules governing them.  In other words they define those rules not in terms of the physical objects that they are studying but in terms of non physical or abstract properties of mathematical equations.

Granted many of our most successful theories began as a mathematical study of “real world” problems. In other words scientists attempt to use mathematics to quantify “real world” environments and to establish the underlying rules that govern them.

However the fact that one can mathematically quantify an environment does not mean that they accurately defined the “reality” of the rules that govern it.

For example, Isaac Newton made qualitative observations of how objects in a “real world” environment interacted with the earth’s gravitational field. He then used the understanding develop form those observations and his knowledge of mathematics to derive a theoretical model that could not only quantity them but also explain why they interacted the way they did in terms of those observations.

In other words he was able to provide a direct physical connection between the abstract properties of his mathematics and a “real world” perception of those interactions based on observable components of his environment.

However, with the advent of higher mathematics and advance computing technology physicists now feel they have to ability to define the “reality” of what we observe in purely abstract mathematical terms

For example, String Theory is based purely on mathematically analyzing the quantitative observation of the “real world” and then, using only that information defines its reality. In others words they not only define the observable properties of the environment but also the rules governing the interaction of its components in terms of abstract mathematics without physically connecting them to the “real world” perception of how those components interact.

Therefore, String Theory does not and cannot provide a physical connection to the observable universe because its description is based purely on abstract properties of mathematics and not on the physical observations as Isaacs Newton’s were, of how its components interacted to form the environment they are describing.

These two different approaches to theoretical philosophies are called Empiricism and Realism.

On the surface they both to be appear to equally viable methods for defining the rules that governing our observable environment even though their methodologies are very different.

Empiricists say that our theoretical models should only be concerned with the quantifiable properties of observations while the Realist tell us that our theories should not only make accurate quantitative predictions of an environment but also allow us to understand why nature behaves the way it does based on the observable properties of the environments they are describing.

For example empiricists feel that, as mentioned earlier science should only be concerned with quantifying observations and that they should not be tested against the observable properties of the “real world”.  In other words they are not interested in or feel that it is important to integrate the observations of how objects interact in the “real world” to create our observable environment. This is the attitude most string theorist take because they attempt to define not only observations but how the “real world” behaves the way is does in terms of the abstract properties of mathematics.

Realists, on the other hand believe that science should not only be concerned with quantifying experiences but also explaining why the real world behaves the way it does based on observations. In other words they feel that mathematics should not only be used to quantify an environment but also should explain why objects in the “real world” interact the way we do in terms of the observable properties of that environment. This, they feel would give the underlying essence of a physical environment developed by mathematics a stronger tie to its reality.

For example, Einstein who some would call a realist first developed a conceptual understanding of space-time, based, in part on the assumption that the speed of light was constant in all reference frames. However unlike the Empiricists he then developed the theoretical structure of Special Relativity by forming a physical image of what it would be like to chase after a beam of light based on observable properties of the “real world” and then translated or transposed that understanding to define how and why matter and energy in motion would interact in a space-time environment. Later he developed the equations that quantified and verified the accuracy of his conceptual model based on observations of speed of light in the “real world”.

However, the proponents of Empiricism take the opposite approach to science. They observe the quantitative results of observations and then, through trial and error define a series of abstract equations, which can accurately predict them. They then use those equations to define a theoretical structure which then predicts the reality or rules governing the underlying essence of that environment.

For example, Quantum Theories, which espouses the empiricist approach because defines the observations of the quantum mechanical environment of energy/mass based solely on mathematical probability functions or equations. They then use those abstract equations to not only quantify those observations but to define the rules which govern the environment they occupy.

However this circular method of predicting both observations and the operating environments based on only on mathematics does not allow one to determine the physical reality of the environments they define because those mathematically created environments are by definition abstract and therefore are independent of the physical world they are defining.

But is there a way science can verify when a mathematical created environment which defines the underlying essence of the “real world” does not have a direct “physical connection” to it.

The realist answer to this is that it is possible connect them, as Newton and Einstein did to the physical environment they are defining though observations.

For example Quantum theory makes predictions based on the abstract mathematical environment of probability functions. However because its abstract properties are not connected to any physical images of the “real world” all observations, no matter how inconsistent or bazaar they are can be incorporated into it.

This is in sharp contrast to the space-time environment defined by Einstein because he, as mentioned earlier developed the theoretical structure of a space-time environment based on a physical image of what it would be like to chase a beam of light in the “real world”. This not only gives the abstract properties of his mathematics a physical connection to the “real world” it also give science a way of checking its conceptual validity.

For example Einstein’s theory would be invalidated if it was found that something could travel faster than the speed of light because that would contradict the physical model he define.

If however if some observation happened to contradict principals of quantum mechanics such as simultaneously observing of both the particle and wave properties of mass it could easily explained by the fact that its probability functions tells us that anything that can happen will eventually happen. Therefore it is impossible to find any observation that would contradict its basics assumption in a “real world” that is based on probabilities because it tells us that anything can, will and must happen at some time in the future even if it is direct contraction to its basic theoretical concepts.

Yet this can only happen in an abstract environment which is not bound by the physicality our observational world because in the “real world” we observe that some things just do not happen.

But why should science put in the effort to understand the observational reality of our world when both the abstract mathematical foundation of quantum mechanics and the physical imagery of Einstein’s theories make very accurate predictions of future events based on the past.

Because the only way to determine if the rules provided by abstract mathematical equations apply to our observable world is through observations.

For example with powerful enough computers one could still use the geocentric or earth centered model of planetary motion to accurately quantify their relative motions.  However it could not explain the observation that objects such as the orbits of moon of Jupiter are centered on a different objects other that the earth.   If we were unable to make those observations then we may still incorrectly think that the earth is the center of planetary motion.

We as educators must make sure that our students are aware of the difference between defining and describing our observable universe and the importance of having those definitions correlate with the observations they are defining. Later Jeff

Copyright Jeffrey O’Callaghan 2019Anthology of  The Road to Unification  2007 thru 2015    Ebook

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In 1687 Isaac Newton proposed what has come to be called Newton’s Bucket which was an attempt to understand the nature of accelerated motion. It has been accepted for centuries that motion is relative. In other words, if two freely moving objects are each moving at constant but different velocities, neither object has a special status with respect to their motion.

 

Newton’s Bucket

His experiment was meant to show that accelerated motion is different in that it is not relative. However, since velocity is relative, this raises the question of why changes in velocity (acceleration) not. The Newton’s Bucket experiment is designed to clarify the question and provide an answer.

Briefly his experiment involved hanging a bucket of water from a rope and rotating it until the rope is tightly twisted and then releasing it so it can spin. Initially, the bucket will spin but the water will remain stationary; its surface flat. As the bucket continues to spin, friction between the bucket and the water will cause the water to spin. The water’s surface will become concave. When the rope has completely untwisted, the angular momentum of the bucket and water will cause the bucket to continue to spin, the water to spin, and the rope to twist in the other direction. Finally, the twist of the rope will cause the bucket to stop spinning. However, for a time, the water will continue to spin; rope stationary, bucket stationary, and water spinning (with a concave surface).

The question Newton was trying to answer is how is rotation and its associated acceleration defined, in nature? If all motion is relative, then changes in motion can only exist as relative quantities. Could an object be said to spin, even if it were the only thing in the universe? Newton concluded that it cannot be the motion of the water relative to the bucket, because the water’s surface is most distorted when the water is spinning most rapidly at the same speed as the bucket. For him, the only explanation was that the water was spinning with respect to absolute space.

 However in1905 Einstein in his Special Theory of Relativity came along and clearly showed that all motion is relative is because of the flexibility of space and time. In other words space or more correctly space-time is not absolute.  However he did attempt to explain Newton’s Bucket in terms absolute space-time as described below.

“To deny the ether is ultimately to assume that empty space has no physical qualities whatever. The fundamental facts of mechanics do not harmonize with this view. For the mechanical behavior of a corporeal system hovering freely in empty space depends not only on relative positions (distances) and relative velocities, but also on its state of rotation, which physically may be taken as a characteristic not appertaining to the system in itself. In order to be able to look upon the rotation of the system, at least formally, as something real, Newton objectiveness space. Since he classes his absolute space together with real things, for him rotation relative to an absolute space is also something real. Newton might no less well have called his absolute space “Ether”; what is essential is merely that besides observable objects, another thing, which is not perceptible, must be looked upon as real, to enable acceleration or rotation to be looked upon as something real”., Einstein, Albert: “Ether and the Theory of Relativity” (1920), Sidelights on Relativity (Methuen, London, 1922)

Later writing “Because it was no longer possible to speak, in any absolute sense, of simultaneous states at different locations in the aether, the aether became, as it were, four-dimensional, since there was no objective way of ordering its states by time alone.”  A. Einstein (1924), “Ãœber den Äther”, Verhandlungen der Schweizerischen naturforschenden Gesellschaft, 105

However a more straight forward way of explaining why the surface of the water in Newton’s experiment becomes concave would be to use absolute zero or the absolute properties of energy instead of the physical properties of four dimension space-time.

Einstein told us the energy content of an object in motion is not only depended on its rest mass but also on its relative velocity with respect to an observer.

However, if one measures the energy content of two objects in motion with respect to absolute zero (a point in space where its energy is zero) and subtracts the energy component contributed to each by their rest mass; then what is left must be a function of their velocities. Therefore, their energy of motion would be relative to each other because the difference after their rest mass component has been removed will be constant  unchanging and relative when measured with respect to each other.

Acceleration is not a relative quantity because the energy content of object undergoing it does not remain constant.

For example if you know the energy component of an objects mass with respect to absolute zero and how much energy you impart to it you can calculate the magnitude of acceleration it will undergo.

In other words all acceleration can be defined with respect to absolute zero even that experienced by the water in Newton’s bucket.

For example its rotational energy with respect to energy associated with absolute zero is constantly changing because of the energy imparted to it by the rotating bucket. This would be true even for someone sitting on the edge of the bucket because radius of its circular motion is smaller near its center. Therefore its surface will become concave because, its radius increases as it approaches the sides of the bucket the energy imparted to it by its rotation will decrease.

In other words Newton was right when concluded that it cannot be the motion of the water relative to the bucket because it is moving at the same speed.  Instead one could say that it was moving relation to the energy field of the bucket.

Einstein told us field properties of space and time interact to create the mass and energy that make up our physical universe. However the equation E=mc^2 also tells us energy is equivalent to mass. Therefore, one can derive the rotational properties objects with respect to the properties of their energy components for the same reason as we can do so any of its other properties.

In other words the answer the question as to how an object can be said to spin, even if it were the only thing in the universe is that one can explain the concave surface of the water in the bucket with respect to the absolute field properties of the energy component space.

Additionally one can also understand the accelerations associated with gravity in the same terms because the curvature in space-time Einstein associated with it would correspond to an object moving though an energy field with increasing magnitude as it approached an object while following the contour of the that field. 

In other words using absolute zero, (a point in space where is energy is zero) as reference point gives a universal, measurable and observable point of reference for all motion both constant and accelerated.            

Latter Jeff

Copyright 2019 Jeffrey O’Callaghan

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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

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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