Both Einstein’s General and Special Theories of Relativity define macroscopic properties of energy/mass in terms of the continuous properties of four dimensional space-time while quantum mechanics defines its microscopic properties in terms of its discontinuous properties of three-dimensional space. 

This fact makes it extremely difficult to conceptually integrate them because something that is discontinuous cannot by definition be continuous.

However it is possible to define a mechanism responsible for creating a discontinuous or quantum unit of space-time if one redefines Einstein’s space-time universe into one consisting of only four *spatial* dimensions.

Einstein gave us the ability to do this when he used he used the velocity of light to defined the geometric properties of space-time and energy/mass because it allows one to convert a unit of time in his space-time universe to a unit of space.  Additionally because the velocity of light is constant means 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 defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

However as mentioned earlier doing so would also allow one to define a physical mechanism responsible for creating a quantum of space-time in terms of the existence of four *spatial* dimensions.

For example the article "Why is energy/mass quantized?" Oct. 4, 2007 showed it is possible to explain the quantum properties of energy/mass by extrapolating the laws of classical resonance in a three-dimensional environment to a matter wave on the continuous "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

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

The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a continuous "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.

The oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established in four *spatial* dimensions.

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

Therefore the discrete or quantized energy of resonant systems in a continuous four dimensional environment would be responsible for the discrete quantized energy quantum mechanics associated with energy/mass.

However, it did not explain the mechanism responsible for quantizing the space containing energy/mass

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 responsible for the quantization of four-dimensional space because it would result in the formation of discrete or quantized volumes associated with the observed quantum properties of energy/mass.

In other words defining space in terms of four *spatial* dimensions allows one to conceptually the integrate the discontinuous quantum mechanical properties of energy/mass into the continuous field properties four-dimensional space in terms of a resonant system created by the wave properties of energy/mass.

However also allows one to integrate the quantum mechanical properties of energy/mass into the continuous field properties of Einstein’s space-time universe because as mentioned earlier by defining those properties in terms of energy/mass and the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of four *spatial* dimensions. 

Additionally it demonstrates it is not necessary to assume the fundamental component of energy/mass is composed of a quantum of space-time or any other field as is assumed quantum field theory because it provides a valid and verifiable mechanism for creating it out of the field properties of space-time.

Physicists should remember it is impossible to derive a mechanism to explain and predict the continuous properties of four dimensional space-time in terms of quantum mechanics because something that is discontinuous cannot by definition be continuous.  However one can understand the quantum in terms of the continuous properties of space-time because something that is continuous by definition can be divided  into smaller units.

Copyright Jeffrey O’Callaghan 2013

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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.

This presents a problem for the proponents of quantum mechanics because it assumes 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 we see 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 material 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 reality in our environment isn’t it more likely the world defined by quantum mechanics does not exist instead of our material world that we can see and touch.

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 dimension 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. 

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

Copyright Jeffrey O’Callaghan 2012

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Albert Einstein in the address "Aether and the theory of Relativity" delivered on May 5th 1920 at the University of Leyden Germany indicated that The General Theory of Relativity predicts, "space is endowed with physical qualities".

"Recapitulating, we may say that according to the General Theory of Relativity space is endowed with physical qualities; in this sense, therefore, there exists Aether.  According to the General Theory of Relativity space without Aether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense.  But this Aether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts, which may be tracked through time.  The idea of motion may not be applied to it."

But why have the best minds in the scientific community been unable devise an experiment to detect the physical properties of space that Einstein was so sure must exist to support the propagation of light.

The reason may be because they are not looking in the right direction.

For example 1887 Albert Michelson and Edward Morley devised an experiment to detect the relative motion of matter through the stationary Aether ("Aether wind") by creating a device that sent yellow light from a sodium flame through a half-silvered mirror that was used to split it into two beams traveling at right angles to one another. After leaving the splitter, the beams traveled out to the ends of long arms where they were reflected back into the middle by small mirrors. They then recombined on the far side of the splitter in an eyepiece, producing a pattern of constructive and destructive interference. If the Earth is traveling through an Aether medium, a beam reflecting back and forth parallel to the flow of Aether would take longer than a beam reflecting perpendicular to the Aether because the time gained from traveling downwind is less than that lost traveling upwind.

However they did not observe a fringe shift and therefore conclude that space did not contain the "physical medium" called Aether. This negative result is generally considered to be the first strong evidence against the then prevalent Aether theory, and initiated a line of research that eventually led to special relativity, in which the stationary Aether concept has no role.  The experiment has been referred to as "the moving-off point for the theoretical aspects of the Second Scientific Revolution".

However Einstein in his General Theory of Relativity did not endow space with the physical qualities of mass, he endowed it with the geometric properties of a space-time dimension.  Therefore, when Einstein referred to space as having physical properties he may not have been referring to the physical properties of a medium made up of mass such as the "Aether" but those imparted to it by the geometry of space-time.

The significance of changing one perspective form space having the physical properties associated with mass to one of the geometric properties of space or a space-time dimension can be best understood if, as has been done many times in the Imagineer’s Chronicles one transposes Einstein’s space-time universe to one of four *spatial* dimensions.  This is because one could use the physicality of the spatial dimensions instead of the non physical properties of a time or space-time dimension to derive the physical properties of Einstein’s space. 

Einstein made this possible when he derived the geometric properties space-time, energy and the dynamic balance between it and mass in terms of the constant velocity of light and the equation E=mc^2. 

For example he told us the energy associated with mass causes a curvature or contraction in the "surface" of space-time and when mass is converted to energy it causes the three-dimensional properties of space-time to expand because of a decrease in its curvature he associated with that event.  This spatial expansion and contraction would be analogous to how the two-dimensional surface of a balloon either expands of contract when air (energy) is added or taken away from it.

Observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence defined by Einstein one must assume that energy also has a spatial component.  However, one can use the fact that the equation E=mc^2 uniquely defines the geometric properties of a space-time universe in terms of both energy and mass to convert or transpose the curvature in space-time Einstein’s equations associated with energy to one that would define it in terms of a curvature in a four *spatial* dimensions associated with the *spatial* properties of mass.

Additionally because the velocity of light is constant it allows for the defining of a one to one qualitative and quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

This was the bases for assuming as was done in the article “Defining energy” Nov 27, 2007 that one can derive all forms of energy in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension.

Additionally it tells us the medium Einstein referred to in his address at the University of Leyden was most likely the geometry of three-dimensional space because his theories show that space it in itself has physical properties in that it can cause changes in its environment similar to how the geometric expansion and contraction of the two dimension surface of a balloon can cause physical changes in its environment.

If it is true that the physical medium Einstein was referring to was related to the geometric properties space and not a properties of mass as we are suggesting one should be able to explain why Albert Michelson and Edward Morley were unable to detect it in terms of the concepts contained in that article.

Part of the answer can be found in the article "The causality of motion" May 1, 2013 which derived the causality of an inertial reference frame in terms of the relative separation the "surfaces" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly it showed the causality of all accelerated motion including gravitational was a result of the interaction of an inertial reference frame with the slope of a curvature in the "surface" of three-dimensional space while deriving the causality of its inertial properties in terms of a constant linear displacement of two different "surfaces" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

(This curvature is analogous to a curvature in a four-dimensional space-time manifold Einstein theorized was the causality of all accelerated reference frames.)

In other words it showed the energy of relative motion was not imparted to it by its motion through space but by a displacement of its three-dimensional geometry with respect to fourth *spatial* dimension.

However this means the casualty of the forces experience by the components of an inertial reference frame in constant motion are an integral part of the geometry of their moving environment and therefore would not be dependent of their relative motion.

The theoretical significance of defining the causality of constant motion in terms of the geometry of four *spatial dimensions is that it allows one to understand why the propagation of light or electromagnetic energy is independent of the motion of an inertial reference frame.

As mentioned the article “Defining energy” Nov 27, 2007 derive all forms of energy in terms of a geometric displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This was the basis for defining the causality of electromagnetic energy in the article "What is electromagnetism?" Sept, 27 2007 in terms of the differential force caused by the "peaks" and "toughs" of a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly it showed it is possible to derive the electromagnetic properties of electromagnetism by extrapolating the geometric properties of a three-dimensional environment to a matter wave moving on a "surface" of three-dimensional space manifold with respect to a fourth *spatial* dimension.

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

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

Therefore, classical wave mechanics, if extrapolated  to four *spatial* dimensions tells us a force will be developed by the differential displacements caused by a matter wave moving on a "surface" of 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 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 charges than it would be for a single charge.

One can define the causality of electrical component of electromagnetic radiation in terms of the energy associated with its "peaks" and "troughs" that is directed perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that perpendicular displacement.

However, Classical Mechanics tells us a horizontal force will be developed by that perpendicular or vertical displacement which will always be 90 degrees out of phase with it.  This force is called magnetism.

This is analogous to how the vertical force pushing up of on mountain also generates a horizontal force, which pulls matter horizontally towards the apex of that displacement.

However this also defines the causality of the electromagnetic properties of light and its propagation in terms of the physicality of the dimensional properties of space.

Yet this also means that the propagation of light would not be depend on the existence of the physical properties of mass as most including Albert Michelson and Edward Morley associated with the aether but only on the physicality of of the geometric properties of space.

This also means the velocity of light would not be influenced by the relative motion of an inertial reference frame because as mentioned earlier all of its components including light share the same geometry and therefore the same relative velocity.

This suggests that the "Aether" or the medium Einstein said must exist to support the propagation of light, and the existence for standards of space and time is a physical property of the geometry of space and not that of an independent element as is suggested by the modern interpretation of the Albert Michelson and Edward Morley.

However it also means that according to Einstein space-time concepts no experiment no matter how sensitive to motion will be able to detect any change in the velocity light due to the relative motion of an inertial reference frame.

Latter Jeff

Copyright Jeffrey O’Callaghan 2013

 

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According to Newton’s view, force does not the cause motion but only a change in it and because a freely moving object continues to move inertia and motion in itself needs no causal explanation.

However as Gao, Shan points out in on page 29 of his book "God Does Play Dice with the Universe" there is a problem with that concept of motion because:

"According to Newton, neither external force nor internal force is the cause of constant motion. So there is only one possibility left , i.e., that motion has no cause.  In other words the change in position or state of an object due to a constant velocity does not have cause.

However modern science is based on the assumption that all changes in the state of a system require a cause.  In other words one cannot integrate the Newtonian concept of motion or the change in position associated with it into our current scientific paradigms which are based almost entirely on causality".

Granted Einstein was able to define the causality of gravity and accelerated motion in terms of curvature in four dimensional space-time and the relativistic properties of motion in terms of that same four dimensional model however he was unable or did not chose to address the causality of that motion and the inertia Newton associated with it. 

However he did provide us with the conceptual foundations for the deriving the causality of inertia and constant motion when he define the dynamic relationship between space, time, energy, and mass in terms of the constant velocity of light and the equation E=mc^2.

Einstein defined accelerate motion in terms of a curvature in space-time and a dynamic balance between mass and energy defined by the equation E=mc^2.  However when he used the constant velocity of light in that equation to define that balance he provided a method of converting a unit of space he associated with mass to a unit of acceleration he associated with energy.   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.

In other words by defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

As mentioned earlier Einstein’s equation E=mc^2 tells us there is a dynamic relationship between the geometric properties of our universe and mass/energy in that when one coverts mass to energy in a closed three-dimensional *spatial* environment, the space it is made up of expands while if one coverts energy to mass that environment contracts.

This is analogous to how the two-dimensional surface of a balloon either expands or contracts with respect to three-dimensional space when air (energy) is either added or removed from it.

Observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence defined by Einstein one must assume that energy also has a spatial component.  However, because the equation E=mc^2 uniquely defines the geometric properties of a space-time universe in terms of both energy and mass one can use it to convert or transpose the curvature in space-time Einstein’s associated with gravity and accelerated reference frames to a curvature or displacement in "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimensions

This fact that one can quantitatively derive the spatial properties of all forms of energy including that associated with constant motion in a space-time universe in terms of four *spatial* dimensions is one of 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.

One of the theoretical advantages to transposing Einstein space-time concepts to four *spatial* dimensions is that it allowsone define a common mechanism for the causality of gravity, acceleration, inertia and constant motion.

For example the article "Why Space-time?" Sept. 27, 2007 showed the energy associated with rest mass is directly proportional to the magnitude of a curvature or "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  Additionally it was shown that one can derive the causality of all accelerations including gravitational in terms of an interaction of rest mass with the slope of a curvature in the "surface" of three-dimensional space caused by that displacement.

(This curvature is analogous to a curvature in a four-dimensional space-time manifold Einstein theorized was the causality of all accelerations.)

However as was shown in the article "Defining energy" there will be a 1 to 1 correspondence between an objects rest mass and the curvature in space associated with the energy required to make a unit change in its displacement with respect to a fourth *spatial* dimension.  Therefore the inertia of an object, as is confirmed by observations would be directly proportional to its rest mass if one assumes as was done in that article that causality of both is related to a displacement caused by a curvature in "surface" of a three-dimensional space manifold with respect to fourth *spatial* dimension.  This allows one to define the causality of inertia in terms of an interaction of the rest mass of an object with a curvature in a three-dimensional space manifold with respect to a four *spatial* dimensions.

This also to defines the causality of constant motion because according to the theoretical concepts presented in that articlethe energy associated with its momentum would be defined by a constant linear displacement of the depression associated with its rest mass in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore motion will continue unchanged unless it interacts with the curved "surface" of three-dimensional space that article associated with accelerations. This allows one to define the casualty constant motion in terms of a linear or constant displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However it also enables one to define causality of the relative properties of constant motion because according to the concepts develop in that article the momentum of an object in motion would be determined by the relative separation its three-dimensional "surface" has with respect to the three-dimensional "surface" of the object or measuring device used to determine its velocity.  In other words all motion is relative because its causality is directly related to the relative separation of its three-dimensional "surface" with respect to the three-dimension "surface" of another object or measuring device.

This defines a causal link between constant motion inertia, rest mass gravity and all accelerations in terms of an interaction of the "surfaces" of a three-dimensional space manifold and a fourth *spatial* dimension.

This cannot be done in terms of four dimensional space-time because it does not allow for the linear displacement of a "surface" of three-dimensional space with respect to a time dimension.

This shows how one can integrate the causality of a change in position associated with constant motion into our current scientific paradigms which are based almost entirely on causality and conceptually link it with Einstein’s concept of gravity and accelerate motion in terms of four *spatial* dimensions.

Additionally it allows one to fully integrate the Newtonian concept of motion or the change in position associated with it into our current scientific paradigms which are based almost entirely on causality

Later Jeff

Copyright Jeffrey O’Callaghan 2013

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Is it possible to define the physical "reality" of a Quantum field?

We think so.

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

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

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

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

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

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

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

Therefore because they share a common connection to the observable "reality" of our three-dimensional spatial environment one should be able to define the physical "reality" of both Einstein space-time dimension and the field properties of quantum mechanics in terms of their non-abstract spatial components.

Einstein gave us the ability to do this when he used the constant velocity of light in the equation E=mc^2 to define how energy/mass effects a space-time environment.  Additionally because the velocity of light is constant it also allows one to defined a one to one qualitative and quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

For example he told us the energy associated with mass causes a curvature or contraction in the "surface" of space-time and when mass is converted to energy it causes the three-dimensional properties of space-time to expand because of a decrease in its curvature he associated with that event.

This expansion and contraction would be analogous to how the two dimensional "surface" of a balloon either expands of contract when air (energy) is added or taken away from it.

However observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence defined by Einstein one must assume that energy also has a spatial component.  However, because the equation E=mc^2 uniquely defines the geometric properties of a space-time universe in terms of both energy and mass one can use it to convert or transpose the space-time curvature Einstein’s associated with energy to one that would define it terms of a spatial curvature in a four *spatial* dimensions.

Additionally because the velocity of light is constant it allows for the defining of a one to one qualitative and quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

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

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

The physical "reality" of the field properties energy/mass in four *spatial* dimension was developed in the article “Electromagnetism in four *spatial* dimensions” Sept 27, 2007 where it was shown the forces associated with an electromagnetic field can be explained and predicted in terms of matter wave on field consisting of four *spatial* dimensions.

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

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

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

Therefore observations  of our three dimensional "reality", if extrapolated  to four *spatial* dimensions tells us the force developed by the differential displacements caused by a matter wave moving on a "surface" of three-dimensional space with respect to a fourth *spatial* dimension will result in its elevated and depressed portions moving towards or become "attracted" to each other.

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

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

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

One can define the causality of electrical component of electromagnetic radiation in terms of the energy associated with its "peaks" and "troughs" that is directed perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that perpendicular displacement.

However, observations of our three dimensional environment tell us a horizontal force will be developed by that perpendicular or vertical displacement which will always be 90 degrees out of phase with it.  This force is called magnetism.

This is analogous to how the vertical force pushing up of on mountain also generates a horizontal force, which pulls matter horizontally towards the apex of that displacement.

This shows how one can explain and predict the continuous field properties of electromagnetism by extrapolating the observable non-abstract properties of our three dimensional environment to a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, as was shown in the article “The Photon: a matter wave?” Oct. 1, 2007 the quantum field properties of four *spatial* dimension can also be derived by extrapolating the observable non-abstract resonant properties of a three-dimensional environment to one consisting of four *spatial* dimension.

There are four conditions required for resonance to occur in a three-dimensional environment an object or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial.

The existence of four *spatial* dimensions would give the continuous surface or field of three-dimensional space manifold (the substance) the ability to oscillate spatially with respect to a fourth *spatial* dimension thereby fulfilling one of the requirements for classical resonance to occur.

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

Therefore, these oscillations in four *spatial* dimensions, would meet the requirements mentioned above for the formation of a resonant system or "structure" in space. 

Observations of a three-dimensional environment show the energy associated with resonant system can only take on the incremental or discreet values associated with a fundamental or a harmonic of the fundamental frequency of its environment.

Similarly the energy associated with resonant systems in four *spatial* dimensions could only take on the incremental or discreet values associated a fundamental or a harmonic of the fundamental frequency of its environment.

These resonant systems in four *spatial* dimensions are responsible for the incremental or discreet field energies associated quantum and electromagnetic field theories

This shows how one can define the "reality" of the continuous field associated with Schrödinger’s wave equation and a physical mechanism responsible for the creation of particles in that field in terms of the observable non-abstract "reality" of our three-dimensional environment.

Latter Jeff

Copyright 2013 Jeffrey O’Callaghan

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By the early 19 hundreds many felt the sum total of all human knowledge about the physical universe could be found in two theories.  The first, Einstein’s Theories of Relativity gave us an understanding of the very large while the other, quantum theory gave us a theory of the very small, the bizarre world of the atom.

However there was considerable disagreement as to how one should interpret the quantum mechanical world.

Some like Bohr thought that one should not attempt to define it in terms of causality but only in terms of the probabilities associated with Schrödinger’s wave equation

However Einstein disagreed.  He thought the quantum mechanical properties of energy/mass could be a subset of a larger theory based on the causality he had associated with the geometric properties of space-time.

As Michio Kaku pointed out in his book Einstein’s Cosmos: “How Albert Einstein’s Vision Transformed Our Understanding of Space and Time, “Einstein used an analogy drawn from his own work to explain why he felt that way.”

Einstein pointed out that Relativity did not prove the Newtonian theory was completely wrong; it only showed that it was incomplete, that it could be subsumed into a larger theory.  Thus, Newtonian mechanics is quite valid in its own particular domain: the realm of small velocities and large objects. Similarly, Einstein believed that the quantum theory’s bizarre assumptions about the lack of causality could be explained in a higher theory.”

However he was unable to do so.

One reason may be because they do not have a common parameter that can be used for their integration.

For example Einstein’s theories defined the domain of energy/mass in terms of a continuous property of time or a space-time dimension whereas quantum mechanics defines its domain in terms of the discontinuous spatial properties associated with particles.

Additionally Schrödinger’s wave equation that is used to define a quantum system, only defines the probability a particle will be located in a given volume of space without giving reference to causality while Einstein defined the casualty he associated with the geometric properties of space-time in terms of a dynamic balance between mass and energy defined by the equation E=mc^2 without giving reference to its probabilistic non-casual properties.

This suggests that the inability to merge these two theories is due to the incompatibility of the probabilistic, discontinuous based explanations and predictions of quantum mechanics and the continuous, casual or deterministic ones of Relativity.

However Einstein gave us an opportunity to resolve this conundrum when he derived the geometric properties space-time, a particles energy and the dynamic balance between it and mass in terms of the constant velocity of light and the equation E=mc^2. 

For example he told us the energy associated with mass causes a curvature or contraction in the “surface” of space-time and when mass is converted to energy it causes the three-dimensional properties of space-time to expand because of a decrease in its curvature he associated with that event.

This expansion and contraction would be analogous to how the two dimensional “surface” of a balloon either expands of contract when air (energy) is added or taken away from it.

However observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence defined by Einstein one must assume that energy also has a spatial component.  However, because the equation E=mc^2 uniquely defines the geometric properties of a space-time universe in terms of both energy and mass one can use it to convert or transpose the space-time curvature Einstein’s associated with energy to one that would define it terms of a spatial curvature in a four *spatial* dimensions.

Additionally because the velocity of light is constant it allows for the defining of a one to one qualitative and quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

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

One of the theoretical advantages of a model based on four *spatial* dimensions is that it provides a common parameter for comparing or integrating the discontinuous properties energy/mass associated with quantum mechanics with the continuous ones associated with Einstein’s theories in terms of its spatial properties.

For example the fact that one can define energy/mass in terms of a spatial displacement on a “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension means that one should be able to, as was done in the  article “Why is energy/mass quantized?” Oct. 4, 2007 derive its quantum mechanical properties in terms of those spatial properties.

Briefly that article showed that one can derive the quantum mechanical properties of energy/mass in terms of the four conditions required for resonance to occur in a spatial, 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 the “surface” of a three-dimensional space manifold (the substance) the ability to oscillate spatially with respect to it thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the “surface” of a 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 on a “surface” of three-dimensional space, would meet the requirements mentioned above for the formation of a resonant system or “structure” in space.

Observations of a three-dimensional environment show the energy associated with resonant system can only take on the incremental or discreet discontinuous values associated with a fundamental or a harmonic of the fundamental frequency of its environment.

Similarly the energy associated with resonant systems in four *spatial* dimensions could only take on the incremental or discreet values associated a fundamental or a harmonic of the fundamental frequency of its environment.

Therefore these resonant systems in four *spatial* dimensions define the discreet discontinuous energy associated with the quantum mechanical wave function in terms of a causal mechanism based on the existence of four *spatial* dimensions.

One cannot accomplish this in an environment consisting of four dimensional space-time because time or a space-time dimension is only observed to move in one direction forward therefore it cannot support the bidirectional spatial movement required for classical resonance to occur.

As mentioned earlier Einstein was convinced that quantum mechanics was an incomplete theory.

He used the analogy that Relativity did not prove that Newtonian theory was completely wrong; it only showed that it was incomplete, that it could be subsumed into a larger theory.  Similarly Einstein believed that quantum mechanics could be subsumed in a larger theory.

However to understand how quantum theory could be integrated or subsumed into a larger theory of four *spatial* dimensions one must not only show why the energy/mass associated with the quantum mechanical wave function would be discontinues in four *spatial* dimension as was done in the article “Why is energy/mass quantized?” one must also explain the physical significance of Planck’s length one of its fundamental components and how it is related to the uncertainties associated with quantum mechanics in terms of four *spatial* dimensions. 

In quantum physics Planck’s length is the scale at which classical ideas about gravity and space-time cease to be valid, and quantum effects dominate.  In other words Planck’s length the smallest measurement of length with any meaning in relativistic theories.

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 geometric boundaries of the resonant system associated with a the wave function in the article “Why is energy/mass quantized?“  However, it also allows one define the physical significance of Planck’s length in terms of the size or length of one side of the quantum mechanical “box” in four *spatial* dimensions containing the wave function of a quanta.

Another fundamental component of quantum theory, Planck’s constant which can be derived from Planck’s length is related to Heisenberg’s Uncertainty Principle which asserts that there a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position x and momentum p, can be simultaneously known.  For example attempting to measure an elementary particle’s position (▲x) to the highest degree of accuracy leads to an increasing uncertainty in being able to measure the particle’s momentum (▲p) to an equally high degree of accuracy.  Heisenberg’s Principle is typically written mathematically as ▲x▲p ≥h / 2    where h represents Planck constant

As mentioned earlier the resonant wave that corresponds to the quantum mechanical wave function defined in the article “Why is energy/mass quantized?” predicts that a particle will most likely be found in the quantum mechanical “box” whose dimensions would be defined by integral number of Planck’s lengths.  However quantum mechanics treats particles as one dimensional points and because it could be anywhere in that “box” there would be an inherent uncertainty involved in determining its exact position

For example the formula give above ( ▲x▲p ≥h / 2  ) tells us that uncertainty of measuring the exact position of the point in that “box” defined by its resonant wavefunction would be equal to ▲x▲p ≥h / 2 .   However because we are only interested in determining its exact position we can eliminate all references to its momentum.

However one cannot measure a particles position to an accuracy greater than 6.626068 × 10^-34 meters or the equivalent of Planck’s constant expressed in meters because as mentioned earlier it is impossible to determine were in the “box” the quantum mechanical point representing it is located.

This shows how one can define the physical mechanism responsible for the uncertainty principal and why at Planck’s scale the classical ideas about gravity and space-time cease to be valid, in terms of the existence four *spatial* dimensions because it defines the maximum degree of accuracy one can measure the position or momentum of a particle.

However it also defines a physical mechanism responsible for the lack of causality the quantum world because if one cannot make an exact measurement of the initial conditions of a system one cannot use it to predict its future evolution.  Therefore one cannot define a casual or deterministic relationship between its past and future.

Yet the above discussion also shows that Einstein’s theories were not completely wrong because it is still valid in own particular domain: the realm of macroscopic space and time while demonstrating how his relativistic concepts of a space-time environment and quantum theory’s bizarre assumptions about the lack of causality could be a subset of a higher theory based on the existence of four *spatial* dimensions.

Later Jeff

Copyright Jeffrey O’Callaghan 2013

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Does time have an end?  If so when and where will it happen?

This question is a difficult to answer definitively because if time does end no one would have the time to tell us it had.

How then can we determine if it will?

One was is by analyzing what we know about the present time and project it into the future.

For example cosmologists believe that time will come to an end because our universe is expanding and will experience heat death or a state were no thermodynamic process occur.  This conclusion is base in part on the observation that the expansion of the universe is accelerating and therefore they feel it will continue until it reaches thermodynamic equilibrium.

However they make this prediction even though they do not have a theoretical model defining what is causing its expansion to accelerate or how long it will continue.

Yet one can look at those same observations regarding an expanding universe and come to a completely different conclusion using Einstein concepts of space-time and observations of our three dimensional environment.

For example Einstein defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2.

He told us the energy associated with mass causes a curvature or a contraction in the "surface" of space time and when mass is converted to energy it causes space-time to expand because of a decrease in its curvature he associated with that event. This expansion and contraction would be analogous to how the two dimensional "surface" of a balloon either expands of contract when air (energy) is added or taken away from it.

However one of the difficulties in integrating an accelerating universe into Einstein’s space-time concepts is that observations tell us that three-dimensional space is expanding towards a higher spatial dimension not a time or space-time dimension.  

Therefore to explain the observed spatial expansion of the universe one would have to assume the existence of a fourth *spatial* dimension in addition to the three spatial dimensions and one time dimension that Einstein’s theories contain.

This would be true if Einstein had not given us a means of qualitatively and quantitatively converting the geometric properties of his space-time universe to one consisting of only four *spatial* dimensions.

As mentioned earlier Einstein defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2.  However when he used the constant velocity of light in the equation E=mc^2 to define that balance he provided a method of converting a unit of space he associated with mass to a unit of space-time he associated with energy.   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.

In other words by defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of geometry of four *spatial* dimensions.

Observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence defined by Einstein’s one must  also assume that energy must have spatial properties because Einstein equation E=mc^2 tell us there is a dynamic relationship between the geometric properties of our universe and mass/energy in that when one coverts mass to energy in a closed three-dimensional *spatial* environment, the space it is made up of expands while if one coverts energy to mass that environment contracts. 

Yet as mentioned earlier it is difficult to understand how three-dimensional space can both expand and contract in a space-time universe because our experiences tell with time tells us that it only moves in one direction forward.

However it is easy to understand how it could in one consisting of four *spatial* dimension because our experiences it tell us that we can move in two direction in a spatial environment up down forwards of backwards.

The fact that one can use the equation E=mc^2 to quantitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions is one the 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.

In other words one can use Einstein’s equations to define energy in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimensions.

We know from the study of thermodynamics that energy flows from areas of high density to area of 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 and that the force associated with that expansion will decline as its surface spread out.

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" or "displaced" with respect to a fourth *spatial* dimension,

Yet this means similar to the two dimensional surface of the water in the pool three-dimensional space will accelerate and flow or expand outward in the four dimensional environment surround it and that the force associated with that it will decline as it expands. 

This shows how one can use Einstein experimental verified relationship between mass and energy defined by the equation of E=mc^2 to explain the casualty of the force called dark energy and why it is causing the accelerated expansion of the universe in terms of the geometry of four *spatial* dimension.

However it should be remembered this solution was derived directly from Einstein’s General Theory of Relativity and the observable and therefore verifiable properties of three-dimensional space.

Yet the equation E=mc^2 also tells us the ratio of the attractive gravitational mass component of a three-dimensional environment with respect to the expansive component of dark energy must increase as space expands because it tells that each unit of space that undergoes cooling or reduction in energy must be accompany by an increase in its mass component.  Granted this mass would be spread out over a very large volume however it would still exert a gravitational influence on its environment that would counter act the expansive properties of Dark Energy. 

(Some may try to dismiss this by saying that as the universe expands its energy is spread out over a larger volume so after a while it just vanishes so to speak or as some like to say that the universe experiences a heat death.  However Einstein theories do not permit energy to just disappear or "die".  It unequivocally tells us that if the energy content in a closed environment decreases the mass content of that environment must increase irrespective of the volume of that environment.  Therefore because by definition the universe is a closed system one must assume that any reduction in its overall energy content of the universe including its heat energy must be must be compensated for by an increase in its total attractive gravitational mass content.)

Yet this also tells us the evolution of time would be defined by a dynamic interaction between the spatial components of mass and energy because it tells the forces associated with them diametrically oppose each other.

Current observations of our universe tell us, if the above theoretical model is correct that it is undergoing an accelerated expansion with respect to a fourth *spatial* dimension because as mentioned earlier the expansive energy due to the elevated "surface" of three-dimensional space exceeds the contractive gravitational forces associated with its energy/mass component.  However as time goes by the power of its expansive component will decrease for the same reason as the expansive power of the water in a pool whose walls have collapsed decrease as it expands.  This means the contractive gravitational forces Einstein associated with energy/mass created by the decrease in its energy content will become predominate.  This will result in the entering a contraction phase.

(For a more detailed explanation of causality this process please review the article "The Return of the Big Bang" Jan 15, 2008)

This contraction will continue until the heat generated by its collapse elevates the "surface" of three dimensional space with respect to a fourth *spatial*enough to counter act the contractive forces caused the gravitational component of its energy/mass thereby causing it to enter a period of expansion.

However after a given period the power of its expansive forces will decrease because as mentioned the elevation in the "surface" of three dimensional space with respect to a fourth *spatial* dimensions decreases as it expands in a four dimension environment and the contractive force Einstein’s equation E=mc^2 associates with mass will again take over.

As mentioned earlier it should be remember this theoretical model was derived directly from Einstein experimentally verified equation of E=mc^2 and the observable and therefore verifiable properties of three-dimensional space. .

This suggests that there may not be and end of time because our universe would not experience heat death or thermodynamic equilibrium and therefore it would continue uninterrupted through dynamic cyclic interchange of mass and energy brought on by contraction and expansion of our universe.

Later Jeff

Copyright Jeffrey O’Callaghan 2013

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Einstein in the address "Aether and the theory of Relativity" delivered on May 5th 1920 at the University of Leyden Germany he indicated that The General Theory of Relativity predicts, "space is endowed with physical qualities".

"Recapitulating, we may say that according to the General Theory of Relativity space is endowed with physical qualities; in this sense, therefore, there exists Aether.  According to the General Theory of Relativity space without Aether is unthinkable; for in such space there not only would be no propagation of light, but also no

possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense.  But this Aether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts, which may be tracked through time.  The idea of motion may not be applied to it."

But why have the best minds in the scientific community been unable devise an experiment to detect the physical properties of space that Einstein was so sure must exist.

The reason may be because they are not looking in the right direction. 

For example 1887 Albert Michelson and Edward Morley devised an experiment to detect the relative motion of matter through the stationary Aether ("Aether wind") by creating a device that  sent yellow light from a sodium flame through a half-silvered mirror that was used to split it into two beams traveling at right angles to one another. After leaving the splitter, the beams

traveled out to the ends of long arms where they were reflected back into the middle by small mirrors. They then recombined on the far side of the splitter in an eyepiece, producing a pattern of constructive and destructive interference. If the Earth is traveling through an Aether medium, a beam reflecting back and forth parallel to the flow of Aether would take longer than a beam reflecting perpendicular to the Aether because the time gained from traveling downwind is less than that lost traveling upwind., However they did not observe a fringe shift and therefore conclude that space did not contain the "medium" called Aether. The negative results are generally considered to be the first strong evidence against the then prevalent Aether theory, and initiated a line of research that eventually led to special relativity, in which the stationary Aether concept has no role.  The experiment has been referred to as "the moving-off point for the theoretical aspects of the Second Scientific Revolution".

However Einstein in his General Theory of Relativity did not endow space with the physical qualities of mass, he endowed it with the geometric properties of a space-time dimension.  Therefore when Einstein referred to space as having physical properties he was talking about the physical properties imparted to it by the geometry of space-time,

This suggests that the physical qualities Einstein was referring to in the statement "Recapitulating, we may say that according to the General Theory of Relativity space is endowed with physical qualities; in this sense, therefore, there exists Aether" was the geometric properties of space-time universe and not the physical properties of mass most including Albert Michelson and Edward Morley associated with the Aether.

The significance of changing one perspective form the Aether having the physical properties associated with mass to one of the geometric properties of space can be best understood if, as has been done many times in the Imagineer’s Chronicles one transposes Einstein’s space-time universe to one of four *spatial* dimensions. This is because one could use the physical properties of the spatial dimensions instead of the non physical properties of a time or space-time dimension to define the physical properties of Einstein’s Aether. 

Einstein made this possible when he derived the geometric properties space-time, energy and the dynamic balance between it and mass in terms of the constant velocity of light and the equation E=mc^2. 

For example he told us the energy associated with mass causes a curvature or contraction in the "surface" of space-time and when mass is converted to energy it causes the three dimensional properties of space-time to expand because of a decrease in its curvature he associated with that event. This expansion and contraction would be analogous to how the two dimensional "surface" of a balloon either expands of contract when air (energy) is added or taken away from it.

Observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence defined by Einstein one must assume that energy also has a spatial component.  However, because the equation E=mc^2 uniquely defines the geometric properties of a space-time universe in terms of both energy and mass one can use it to convert or transpose the curvature in space-time Einstein’s field equations associated with energy to one that would define the curvature in a four *spatial* dimensions he indirectly associated with the *spatial* properties of mass.

Additionally because the velocity of light is constant it allows for the defining of a one to one qualitative and quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

This was the bases for assuming as was done in the article “Defining energy” Nov 27, 2007 that one can derive all forms of energy including those associated with velocities, mass and the medium Einstein was referring to in his address mentioned earlier in terms of a curvature or displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of four dimensional space-time.

Einstein in his address he gave at the University of Leyden was careful to define the "quality characteristics" of the physical medium his General Theory of Relativity tells us space must be endowed with.  Specifically he said that it could not consist of parts, which could be tracked though time.  This would be true for both the geometric properties of space-time and four *spatial* dimension because by definition their geometry is continuous and therefore they do not have "parts which may be tracked through time".

As mentioned earlier Einstein’s General Theory of Relativity defined the physical of qualities of mass in terms of the geometry of space-time.  However because he defined an equivalence between all forms of energy and mass we must also assume the energy associated with velocity is also related to the geometric properties of space.

However as was shown above one can use Einstein’s equations to define a one to one qualitative and quantitative correspondence between his space-time universe and one consisting of four *spatial* dimensions.

Therefore according to the theoretical concepts presented in the article “Defining energy” which defined energy in terms of four *spatial* dimensions instead of four dimensional space-time, the energy associated with the "quality characteristic of ponderable media" Einstein referred to in his address and its motion through his space-time universe could also be defined by a geometric displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

Yet as was mentioned earlier defining energy in terms the of physical properties of a spatial dimension instead of a time or space-time dimension allows one to understand the physical properties of Einstein’s Aether because one can apply the rules of spatial geometry to it.

For example the *spatial* displacement associated with center of the inertial reference frame Albert Michelson and Edward Morley used to conduct their experiment would be centered on the point similar to the way geometry of a circle is centered on a point at its center.

However, this means the "idea of motion may not be applied to it" similar to how the idea of motion cannot be applied to the center of a circle with respect to its circumference because if was it could it would no longer be its center.

Additionally if one defines energy associated with medium Albert Michelson and Edward Morley were trying to detect in terms of the geometric properties of four *spatial* dimensions as was done in the article "Defining energy" it would be an integral part of that geometry and the idea of motion could not be applied to it for the same reason as one could not apply the idea of motion to the center of a circle with respect to its circumference.

This is not possible in a space-time environment because the linear progression or flow of time does not allow one to define energy of a point associated with the relative center of an inertial reference frame with respect to the spatial geometry of that reference frame.

This suggests that the Aether or the medium Einstein said must exist to support the propagation of light, and the existence for standards of space and time is a physical property of the geometry of space and not that of an independent element as is suggested by the modern interpretation of the Albert Michelson and Edward Morley.

Later Jeff

Copyright Jeffrey O’Callaghan 2013

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We have shown throughout "The Imagineer’s Chronicles" and its companion book "The Reality of the Fourth Spatial Dimension" there would be many theoretical advantages to assuming the universe is made up of four *spatial* dimensions instead of four-dimensional space-time.

For example it would allow one understand why the force called Dark Energy is causing the expansion of our universe to accelerate by extrapolating observations made in a three-dimensional environment to one consisting of four *spatial* dimensions.

Einstein defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2.

For example he told us the energy associated with mass causes a curvature or a contraction in the "surface" of space-time and when mass is converted to energy it causes space-time to expand because of a decrease in its curvature he associated with that event. This expansion and contraction would be analogous to how the two dimensional "surface" of a balloon either expands of contract with respect to three-dimensional space when air (energy) is added or taken away from it.

However one of the difficulties in integrating the expansive force called Dark Energy into Einstein’s space-time universe is that observations tell us that three-dimensional space is expanding towards a higher spatial dimension not a time or space-time dimension.  

Therefore, to explain the observed spatial expansion of the universe one would have to assume the existence of a another *spatial* or fourth *spatial* dimension in addition to the three-spatial dimensions and one time dimension that Einstein’s theories contain to account for the observation that three-dimensional space is undergoing a spatial expansion.

This would be true if Einstein had not given us a means of qualitatively and quantitatively converting the geometric properties of his space-time universe to one consisting of only four *spatial* dimensions.

Einstein defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2.  However when he used the constant velocity of light in that equation to define that balance he provided a method of converting a unit of space he associated with mass to a unit of space-time he associated with energy.   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.

In other words by defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

Observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence between mass and energy defined by Einstein’s one must assume that energy must also have spatial properties.

As mentioned earlier Einstein’s equation E=mc^2 tells us there is a dynamic relationship between the geometric properties of our universe and mass/energy in that when one coverts mass to energy in a closed three-dimensional *spatial* environment, the space it is made up of expands while if one coverts energy to mass that environment contracts.

Yet, as mentioned earlier it is difficult to understand how three-dimensional space can both expand and contract in a space-time universe because our experiences with time tells us that it only moves in one direction forward.

However it is easy to understand how it could in one consisting of four *spatial* dimension because our experiences it tell us that a spatial environment such as three-dimensional space can move in two directions, like the surface of a balloon in a higher spatial dimension allowing it to either expand or contract. 

The fact that the equation E=mc^2 allows us to 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 use Einstein’s equations to quantitatively define energy in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimensions instead of one in a space time environment.

We know from the study of thermodynamics that energy flows from areas of high density to area of 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.

Yet this means similar to the two dimensional surface of the water in the pool three-dimensional space will accelerate and flow or expand outward in the four dimensional environment surround it.

This show that one can understand and explain what the force called dark energy is and why it is causing the accelerated expansion of the universe in terms of the geometry of four *spatial* by extrapolating observations made in a three-dimensional environment to a fourth *spatial* dimension.

Later Jeff

Copyright Jeffrey O’Callaghan 2013

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Is our universe made up of particles or fields? 

On the one hand quantum physics tells that the universe is made up of discrete units of energy/mass while relativistic physics tells us it is composed of a continuous field of space-time

Unfortunately these two ideas do not work well together because a continuous field by definition cannot be made up of discrete parts as is suggested by quantum mechanics.

Some have tried to merge them by defining what is has come to be called a relativistic quantum field theory.  It assumes that particles can be understood as the quanta of some quantum field which in essence elevates fields to the most fundamental objects in nature and that each type of field generates its own particular type of particle.

However, you cannot have it both ways because by definition a field is continuous and saying they can be understood in terms of some quantum field does not mean that you have connected them to the continuous properties of a relativistic space-time field or any field for that matter.  All it does is elevate its size to that of the entire universe because by definition a field is continuous throughout its entire domain.  Therefore if the fundamental component of the universe is a quantum field as quantum field theory suggests then it could only contain one quantum entity because if it contained more the continuity of the field would be broken.  In words saying one can understand the continuous properties of a field in terms of a quantum field is like saying that one can understand why a circle is round is because it is a circle. 

Another reason why it is so difficult to conceptually to integrate Quantum field theory with the field properties of Einstein’s theories is because it defines space in terms of a field consisting of time or a space-time dimension while Quantum field theory defines itself in terms of its spatial properties of energy/mass.  

For example Schrödinger’s wave equation only defines the probability of a particle will be located in a given volume of space without giving a reference to time while Einstein defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2.

Yet one can overcome the difficultly in integrating a quantum of energy/mass into the continuous field of space-time by redefining the field properties of space-time Einstein associated with energy/mass to its spatial properties Quantum field theory associates with it. 

Einstein gave us the ability to do this when he used the constant velocity of light in the equation E=mc^2 to define how a quantum of energy/mass effects a space-time environment.  Additionally because the velocity of light is constant it  also allows us to defined a one to one qualitative and quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

Observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence defined by Einstein’s one must assume that energy also must have spatial properties.

Einstein’s equation E=mc^2 tells us there is a dynamic relationship between the geometric properties of our universe and mass/energy in that when one coverts mass to energy in a closed three-dimensional *spatial* environment, the space it is made up of expands while if one coverts energy to mass that environment contracts.  Yet it is difficult to understand how three-dimensional space can both expand and contract in a space-time universe because our experiences tell with time tells us that it only moves in one direction forward and therefore does not have the ability to both expand and contract.  However it is easy to understand how it could in one consisting of four *spatial* dimension because our experiences it tell us that spatial environments can more in two directions up or down, forwards or backwards and therefore three-dimensional space would have the ability to both expand and contract with respect to it.

One of the theoretical advantages to assuming that the universe is made up of four *spatial* dimensions instead of four dimensional space-time is that it allows one to derive the quantum mechanical properties of energy/mass in terms of the field properties of four *spatial* dimensions instead of defining the field properties of space in terms of its quantum mechanical properties as is done in quantum field theory.

The field properties of four *spatial* dimension was developed in the article “Electromagnetism in four *spatial* dimensions” Sept 27, 2007 where it was shown the forces associated with an electromagnetic field can be explained and predicted in terms of matter wave on a continuous field consisting of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly it showed that one can derive its properties by extrapolating the laws of Classical Wave Mechanics to a field consisting of fourth *spatial* dimensions.

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

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

Therefore, classical wave mechanics, if extrapolated  to four *spatial* dimensions tells us the force developed by the differential displacements caused by a matter wave moving on a "surface" of three-dimensional space with respect to a fourth *spatial* dimension will result in its elevated and depressed portions moving towards or become "attracted" to each other.

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

However, it also provides a 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 charges than it would be for a single charge.

One can define the causality of electrical component of electromagnetic radiation in terms of the energy associated with its "peaks" and "troughs" that is directed perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that perpendicular displacement.

However, Classical Mechanics tells us a horizontal force will be developed by that perpendicular or vertical displacement which will always be 90 degrees out of phase with it.  This force is called magnetism.

This is analogous to how the vertical force pushing up of on mountain also generates a horizontal force, which pulls matter horizontally towards the apex of that displacement.

This shows how one can explain and predict the electrical and magnetic field properties of an electromagnetic wave by extrapolate the laws of classical wave mechanics in a three dimensional environment to a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, as was shown in the article “The Photon: a matter wave?” Oct. 1, 2007 the quantum field properties of four *spatial* dimensions can be explained and predicted by extrapolating the resonant properties of field in a three-dimensional environment to one consisting of four *spatial* dimension.

There are four conditions required for resonance to occur in a classical environment an object or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial.

The existence of four *spatial* dimensions would give the continuous surface or field of three-dimensional space manifold (the substance) the ability to oscillate spatially with respect to a fourth *spatial* dimension thereby fulfilling one of the requirements for classical resonance to occur.

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

Therefore, these oscillations in four *spatial* dimensions, would meet the requirements mentioned above for the formation of a resonant system or "structure" in space. 

Observations of a three-dimensional environment show the energy associated with resonant system can only take on the incremental or discreet values associated with a fundamental or a harmonic of the fundamental frequency of its environment.

Similarly the energy associated with resonant systems in four *spatial* dimensions could only take on the incremental or discreet values associated a fundamental or a harmonic of the fundamental frequency of its environment.

These resonant systems in four *spatial* dimensions are responsible for the incremental or discreet field energies associated with relativistic quantum field theories.

This shows that it is possible to logically and consistently explain and predict the quantum mechanical field properties energy/mass in a microscopic environment by assuming by assuming that space is composed of four *spatial* dimensions instead of four dimensional space-time.

However it also shows it is more logical and consistent with observations to assume that our universe is fundamentally composed of fields not quanta of energy/mass as is assumed by quantum field theory.

These arguments would not be valid in a universe consisting of four dimensional space-time because as mentioned earlier time is only observed to move in one direction forward and therefore would not support the transverse or bi-directional oscillatory movement required to establish a resonant system

Latter Jeff

Copyright 2013 Jeffrey O’Callaghan

		The Reality of the Fourth Spatial Dimension Paperback $11.99 Ebook $2.99
	The Imagineer’s Chronicles Vol. 3 – 2012 Paperback $11.54 Ebook $2.99		The Imagineer’s Chronicles Vol. 2 – 2011 Paperback $9.24 Ebook $2.99
		The Imagineer’s Chronicles 2007 thru 2010 Paperback $15.43 Ebook $2.99