For the past 50 years, the Standard Model of particle physics has given us a complete mathematical description of the particles and forces that shape our world.  It predicts with so much accuracy the microscopic properties of particles and the macroscopic ones of stars and galaxies that many physicists feel that it is the ultimate theory of matter and energy.

However as the table on the left shows most of its predictions regarding the particle nature of forces have been confirmed by observations with two notable exceptions: the Higgs boson and the graviton.

The reason given by its proponents for the fact that the first of these or the Higgs boson which mediates or defines a particles mass has not yet been observe is that we have been unable to attain the high energy environment that supports it.  This is true even though the LCH (Large Hadron Collider) has been able to attain energies close to those that existed just microseconds before the big bang.

However the idea it only exist at these very high energies does not fit in with the fact that particles have mass even thought they do not exist in those environments.   In other words how can the Higgs boson mediate or be the causality of mass in the relativity low energy particle environments humans occupy if it only exists in the high energy environments associated with the big bang.

It just does not make any sense.

However, they face a similar problem trying to explain why they have not yet observed the graviton.

Many say that they have not been able to detect it because it interacts very weakly with mass.  In other words their instruments are not sensitive enough to detect the passage of a graviton.

However if gravitational force is quantized in the form of gravitons then the movement of particles in space should be effected by the random variations in the gravitational fields associated with its quantum properties.   In other words one would not have to observe the graviton to verify that gravity was quantized if one can observe the effects it has on the movement of particles moving through it.

The fact that this has never been observe is bit hard to explain given the amazing precision by which space and land based sensors can monitor the movement of particles.

The fact that the graviton and Higgs boson have not been observed even when the technology exists to do so means that maybe we should begin hunting for alternative explanation for gravity based not on the Standard Models assumption that it is quantized but on its observed continuous field properties of space.

For example in 1924 Louis de Broglie’s theory that all particles have a wave component was verified 1927 by Davisson and Germer when they observed that electrons were diffracted by crystals.  This served as the basis for developing the general theory known by the name of wave mechanics.  However it also demonstrated that because of the continuous properties of waves there must exist a continuous non-quantized substance or field to support their matter wave component.

In the article "Why is energy/mass quantized?" Oct. 4, 2007 it was shown one can derive the quantum mechanical properties of energy/mass in terms of the continuous properties of three dimensional space by extrapolating the classical laws of resonance in a three-dimensional environment to four *spatial* dimensions.

Briefly it showed the four conditions required for resonance to occur in a classical Newtonian 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 of consisting of only four *spatial* dimensions.

The existence of four *spatial* dimensions would give a "surface" of a three-dimension space manifold (the substance) the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force a "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 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 systems 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 would be responsible for the incremental or discreet energy associated with quantum mechanical systems.

(This cannot be done in terms four dimensional space-time because time is only observed to move in one direction forward and there could not support the bi directional movement required for resonance to occur.)

Latter the article "Embedded Dimensions" Oct. 22, 2007 showed all forms of energy, including gravitational are derivable in terms of a curvature or displacement in a continuous "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

One can understand how a displacement in a "surface" of three-dimensional space is responsible for gravity by comparing it to one caused by a rod pushing down on the continuous surface of a rubber diaphragm that has on marble on it.

The surface of the rubber diaphragm will represent the "surface" of a three dimensional space manifold, the marble on the diaphragm, the resonant system the article "Why is energy/mass quantized?" showed was responsible for the quantum mechanical properties of energy/mass while the rod will represent the “W” axis of a fourth *spatial* dimension.

(The "W" axis of a fourth *spatial* dimension was also defined in the article "Embedded Dimensions" Oct 27, 2007)

If the end of the rod is orientated perpendicular to the "surface" of the diaphragm and is allowed to touch it without putting any pressure on it, the surface of the diaphragm will remain flat. The marble on the flat diaphragm would not move.

However, if pressure is applied to the rod, the "surface" of the diaphragm will become displaced and will no longer be perpendicular to the rod.

Gravitational forces will then have a tangential component along the "surface" of the rubber diaphragm. The tangential component of the gravitational force directed along the "surface" of the diaphragm will cause the marble to move towards the apex of the depression.

However, the article mentioned earlier "Embedded Dimensions" also derived all forms of energy in terms of a curvature or displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, because mass is a form of energy it should, according to the concepts contained in that article cause space to curve and the resonant systems defined in the article "Why is energy/mass quantized?" and the objects made up of them will experience a differential force directed towards the apex of that curvature when interacting with it. This force is called gravity.

Yet this means because of the continuous field properties of three-dimensional space that must be associated of with Louis de Broglie’s wave theory of matter one does not have to assume the existence of a graviton to understand how the force of gravity is propagated because similar to the marble on the rubber diaphragm the force causing gravitational acceleration can be derived in terms of a slope in a continuous "surface" of a three dimensional space manifold with respect to a fourth *spatial* dimension.

Some would disagree because of the fact that experiments show that the other three forces of nature are propagated by particles and why they might ask should gravity be different from them.

Classical wave mechanics tell us that a minimum quantity of energy is required to establish a resonance any given medium.  Gravity is the weakest of the four forces.  If the energy associated with its wave component is not energetic enough to cause space to resonant, its energy will be propagated by the continuous properties of three-dimensional space defined in the article "Embedded Dimensions".  However, if as in the cases of the other three forces of nature there is enough energy concentrated in a small enough volume it will propagated along the "surface’ of three-dimensional space in the resonant systems the article "Why is energy/mass quantized?" showed is responsible for their quantized or particle properties.

The article "The geometry of particle stability" derived the mechanism responsible for this by again extrapolating the laws of classical physics to a fourth *spatial* dimension.

Briefly in a three dimensional environment, 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 particle in the article "Why is energy/mass quantized?"

Gravity is by far the weakest of the four forces and therefore has an extremely long wave length.  This means the volume necessary to contain its resonant properties must also be very large.  Therefore one reason why we cannot observe the graviton is because we do not have any instruments with a detection system large enough to contain the volume associated with its resonant system.  The other three forces of nature have higher energies therefore their resonant volumes would be significantly smaller and therefore observable.  This means we should expect their energy to be propagated through space in quantized units whose volume would be inversely proportional to their energies.

This defines a method of experimentally verify or falsifying this scenario.  If one observers the three dimensional energy "volume" of the four forces inversely correlates with their energy it would have a tendency to support it however if it did not it would unequivocally falsify it.

Later Jeff

Copyright Jeffrey O’Callaghan 2012

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 space is composed of four *spatial* dimensions instead of four dimensional space-time.

One is that it would allow one to merge the observations associated with quantum or photonic properties of light such as Compton scattering with its wave properties by extrapolating the laws of a Classical three-dimensional environment to fourth *spatial* dimension.

Compton scattering is a type of scattering that X-rays and gamma rays undergo in matter.  The inelastic scattering of photons in matter results in a decrease in energy (increase in wavelength) of an X-ray or gamma ray photon, called the Compton Effect.  Part of the energy of the X/gamma ray is transferred to a scattering electron, which recoils and is ejected from its atom (which becomes ionized), and the rest of the energy is taken by the scattered, "degraded" photon.

Inverse Compton scattering also exists, where the photon gains energy (decreasing in wavelength) upon interaction with matter. Since the wavelength of the scattered light is different from the incident radiation, Compton scattering is an example of inelastic scattering, but the origin of the effect can be considered as an elastic collision between a photon and an electron.  The amount the wavelength changes by is called the Compton shift. Although nuclear Compton scattering exists Compton scattering usually refers to the interaction involving only the electrons of an atom.  The Compton Effect was observed by Arthur Holly Compton in 1923 at Washington University in St. Louis and further verified by his graduate student Y. H. Woo in the years following. Compton earned the 1927 Nobel Prize in Physics for the discovery.

The effect is important because it demonstrates that light cannot be explained purely as a wave phenomenon.  Thomson scattering, the classical theory of an electromagnetic wave scattered by charged particles, cannot explain low intensity shifts in wavelength (Classically, light of sufficient intensity for the electric field to accelerate a charged particle to a relativistic speed will cause radiation-pressure recoil and an associated Doppler shift of the scattered light, but the effect would become arbitrarily small at sufficiently low light intensities regardless of wavelength.)  Light must behave as if it consists of particles to explain the low-intensity Compton scattering. Compton’s experiment convinced physicists that light can behave as a stream of particle-like objects (quanta) whose energy is proportional to the frequency.

In the article "Why is energy/mass quantized?" Oct. 4, 2007 it was shown one can derive the quantum mechanical properties of energy/mass and a photon in terms of a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension by extrapolating the classical laws of resonance in a three-dimensional environment to one of four.

Briefly it showed the existence of four *spatial* dimensions would give three-dimensional space (the substance) the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or a photon interacting with an electron.  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 space, would meet the requirements mentioned above for the formation of a resonant system or "structure" in it. 

The energy associated with resonant system in three-dimensional space 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 energies associated with photon and all other quantum mechanical systems.

The electromagnetic wave properties of a photon were     derived, in the article "Electromagnetism in four *spatial* dimensions" Sept. 27, 2007 by extrapolating the laws of classical wave mechanics to a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly 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. Classical wave mechanics tells us 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.

However, as just mentioned 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 similar charges than it would be for a single charge.

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

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

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

However as mentioned earlier the quantum mechanical or particle properties of an electromagnetic wave can also be derived by extrapolating the laws of classical resonance to a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore the articles "Why is energy/mass quantized?" and "Electromagnetism in four *spatial* dimensions" explain both the electromagnetic and wave properties of a photon and electron because it defines one in terms of the other.

Yet it also allows one to explain how the low intensity shifts in wavelength of X and gamma rays occur when they interact with charged particles in terms of Classical wave mechanics because if the causality of their electromagnetic and particle properties are as suggested above related to the resonant properties of a matter wave then it tells us that interference will occur no matter how small the intensity of their interaction is.

This is because the velocity of all forms of electromagnetic energy including gamma and X rays is constant and therefore it cannot change after an interaction occurs with particles such as an electron while an electron’s can be altered by a change in its velocity.   Therefore, the only way to alter the energy, direction or momentum of a gamma or x-ray is by "degrading" or changing their wavelength.  Yet, if the electromagnetic and particle properties of both a photon and electron are a result of a matter wave is as suggested above then classical wave mechanics could define their interaction in terms of the interference of their electromagnetic wave properties.  However this also tells us their scattering at very low light intensities could take on any arbitrarily small value regardless of wavelength. 

In other words if one assumes the electromagnetic and particle characteristics of both a photon and electron is a property of a physical displacement created by a matter wave on in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension as is done here then one can Classically explain why it is not necessary to accelerate a charged particle to a relativistic speed to cause the low intensity shifts in wavelength associated with the Compton effect.

This shows how one can explain the inelastic scattering of photons in matter which results in the decrease in energy (increase in wavelength) of an X-ray or gamma ray photon, called the Compton Effect by extrapolating the laws of classical wave mechanics to a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Later Jeff

Copyright Jeffrey O’Callaghan 2012

As Michael D Fayer explains in Chapter two of his book "Absolutely Small How Quantum Theory Explains Our Everyday World" the difference between classical and quantum phenomena depend on the definition of size.

Classical mechanics assumes size is relative.  In other words we determine if something is big or small by comparing it to something else and we can always finding something smaller.  However quantum mechanics says their is limit to the smallness or size of an object.  In other words in a quantum mechanical world size is absolute.

But why does quantum mechanics assume that there is an absolute size that can not be compare to others.

The reason is that to observe the size of something we must interact with it.  However, we cannot do that without changing it.  For example one cannot observe a book in a totally dark room.  Yet turning a light on allows one to see and compare it to other books because some of the photons emanating from it will be absorbed and some will bounce off.  However, the absorbed photons will cause it to heat up and change.

In Classical mechanics is it important that act of observing a system does change it.  This is because one of its basic assumptions is that the characteristics of a system are caused by earlier events and if one knows their history one can predict their future to any degree of accuracy.   However, if the act of observing a system makes a noticeable change in it one can not predict its future with complete accuracy because that act is not reflected in its history. Therefore their must exist something relative smaller than what is being observed so that it will not make a noticeable change in the characteristics of a system when used to make a measurement.

This is why Classical mechanics assumes that when making an observation it is always possible to find something small enough so that can interact with a system without making a noticeable  change in the system being observed.      

Yet as mentioned earlier Quantum Theory is fundamentally different from classical mechanics in that it assumes that everything is quantized and that its smallest possible unit is defined by Planck’s constant or 6.62606957×10^−34.   How we arrive at that number is unimportant to this discussion however what is important is that it defines the degree by which we can determine smallness because there can be absolutely no disturbance, or anything else relatively smaller than it.

Dirac one of founders of modern quantum mechanics defined why this is so important in determining size when he said.

"(Quantun Mechanics assumes) There is a limit to the fineness of our powers of observation and the smallest of the accompanying disturbance, a limit that is inherent in the nature of things and can never be surpassed by improve technique or increased skill on the part of the observer.

In other words if there is an absolute limit to the smallness of a disturbance associated with a measurement as quantum theory suggests then there is also an absolute limit to the smallness of a entity that can be measured without creating a noticeable difference in its future.

Earlier it was mentioned that Classical mechanics requires the interaction of an observer with a system being measured must be small enough so that does not make a noticeable difference in its future.  Therefore, it assumes that one can always make the size of an observing system small relative to the one being observed.

However, the quantum mechanical assumption that there is an absolute limit to the smallest of a disturbance means that also is a limit to the "size" of a system that can be measure without making a noticeable difference in its future.  In other words there is a limit to the "smallness" of an our ability to make a measurement and therefore an absolute limit to "smallness" .

This is how one can justified saying one of the fundamental difference between quantum and classical Newtonian physics is size.

Later Jeff

Copyright Jeffrey O’Callaghan 2011

Articles posted 2011, 2010, 2009, 2008, and 2007

Preface

The purpose of "The Imagineer’s Chronicles" is to elaborate on the theoretical ideas contained in its companion book "The Reality of Four Spatial Dimensions".

In Thomas S. Kuhn’s book "The Structure of Scientific Revolution" he documents the doubts that precipitate a paradigm change in scientific thought.

For example, even though one could still make accurate predictions of planetary motions using the 15 century geocentric models it became increasing more difficult to integrate that concept with the more accurate observational data provided by the new technologies of that day. This resulted in some scientists questioning their validity.

He suggests the doubt generated by its persistent inability of to explain new data lead many scientists of that period to adopt the simpler rules of the revolutionary heliocentric model.

Modern physics appears to be on the verge of a similar revolution because the discoveries of dark matter and dark energy are extremely difficult to integrate into its current theoretical models.

As Thomas S. Kuhn points out failure of an existing paradigm is a prelude to the search for a new one.

The Imagineer’s Chronicles continues the search, began in its companion book the "The Reality of Four Spatial Dimensions" to not only explain how one can seamlessly integrate the observations of dark matter and dark energy into a theoretical model based on the existence of four *spatial* dimensions but to provide a unifying mechanism responsible for the four forces of nature (gravity, electromagnetism, the weak, and strong) governing the interactions of matter, energy, space, and time.

Each article covers one aspect of a search for the "reality" it defines. For example, the article "What is dark energy" defines its casually in terms of an interaction of three-dimensional space with a fourth while others derive the quantum mechanical properties of energy/mass in terms of a resonant system formed by a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

The Imagineer’s Chronicles is not meant to verify the many answers found in the book "The Reality of Four Spatial Dimensions". Instead it is meant to give the scientific community the specific information and experiment techniques required to either verify or falsify it contents. It relies less on mathematics and more on conceptual logic and thought experiments (much like Albert Einstein did) to show how one can explain and predict all modern observations by extrapolating the rules defining classical three-dimensional space to a fourth *spatial* dimension.

Copyright Jeffrey O’Callaghan 2011

"The universe’s most powerful enabling tool is not
knowledge or understanding but imagination
because it extends the reality of
one’s environment."

Articles posted 2011, 2010, 2009, 2008, and 2007

Before we can distinguish between objective reality and illusions we must first understand how human beings use knowledge to create the ideas or concepts associated with them. 

For the mind to create an illusion it first must obtain knowledge from a reality or environment outside of it because it cannot create something out of nothing.   In other words before one can have an illusion their must exist a reality upon which to based it.

This means there must be an objective reality outside of the mind which must be the same for all individuals because if each illusion was supported by a different physical reality it would take an infinite amount of energy to support the infinite number of realities that can be created by the human mind.

In other words a single objective reality must exist. The problem them becomes how can we identify it.

As mentioned earlier to create an illusion the mind requires an input form an external environment.

For example many people in the middle ages had the illusion that the earth was flat based on the observation that they could not see a physical curvature in its surface. 

However by the 15 hundreds many had the illusion that the earth was round based in part on the fact that Magellan had circumnavigated it.

More recently we have what many believe is the objective reality that the earth is pare shaped because it is the only way one can explain the knowledge we have gained from modern technology.

Yet we cannot be sure that that our understanding of its shape will not be altered in the future by new knowledge making us realize that what we now believe is an objective reality is only an illusion.

This suggests that one can only define or derive objective reality in terms of the knowledge associate with it.  However, because knowledge changes so can the reality we associate with it.

For this reason scientists have what appears to be an insurmountable paradox because they are tasked with finding the single objective reality for the environments containing it.   However this can only be done in terms of knowledge.   Yet as was just shown the knowledge of an environment can charge.  Therefore, our understanding of the "objective reality" we associated with an environment can also change which would seem to contract the earlier statement that there can only be one objective reality.

However we may be able to find solution to this conundrum by examining how we as humans use knowledge of our environment to create the ideas or concepts associated with its reality.

Humans build realties by first looking outward towards an environment and integrate any new knowledge gained from that into them.

For example the illusion that the earth was flat was created when the mind extrapolated the observation that locally the surface of the earth appeared to flat to its entire surface.  However, this reality was replaced by one that involves a spherical earth in part when the knowledge the one could sail around it became available.

In other words science is the process of creating new "more perfect realities" by integrating new knowledge gained though observation into the illusions that existed before those observations were made.

This defines how we can distinguish objective reality from illusions because as mentioned earlier there can only one.  As each new observation integrated into the current illusion that we have about our environment brings us a bit close to defining its true "reality".  We can be sure that we have found it only when we look out at it and do not observe anything that disagrees with the ideas and concepts we have about it. 

There can be no doubt of the existence of a single objective reality.  Our job as scientists is to use knowledge to create the illusions that will eventfully identify it.

Later Jeff

Copyright Jeffrey O’Callaghan 2011