One is that it allows for the defining a common mechanism responsible for both dark and gravitational energy

On May 30, 2004, physicsworld.com reported, in the article Dark Energy "New evidence has confirmed that the expansion of the universe is accelerating under the influence of a gravitationally repulsive form of energy that makes up two-thirds of the cosmos.

However, since its discovery no one has been able to define a mechanism that can account for its existence.

In the article “Defining energy” Nov. 26, 2007 it was shown it is possible to derive all forms of energy including gravitational in terms of the geometry of four *spatial* dimensions. 

The mechanism which defined gravity in that article is very similar the one General Relativity uses in that they both derive it in terms of a geometric property of dimensions.  It was shown that gravity could be derived in terms of a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth spatial dimensions as well as the space time curvature of General Relativity.

However, if it were true that all forms of energy are related to a geometric property of four *spatial* dimensions one should be able to define a causal link between dark and gravity energy in terms of four *spatial dimensions

If gravity, as mentioned earlier is a result of a curvature in a three-dimensional space manifold with respect to a fourth *spatial* dimension, then reducing the mass of an object would reduce the magnitude of that curvature.  This would result in a physical expansion of that three-dimensional space manifold with respect to a fourth *spatial* dimension and thereby increasing the volume of the universe.  This is analogous to how removing the coils or curvature in a rope causes a physical expansion of its length with respect to three-dimensional space.

However, this is one of the properties of Dark Energy in that it causes a physical expansion of space and since this expansion occurs in addition to any resulting from the expansive energy associated with the Big Bang it will be viewed as an acceleration.

This means that one can explain the causality of Dark and gravitational energy in terms of a common mechanism related to the existence of four *spatial* dimensions.

This is extremely difficult to do in terms of four-dimensional space-time because the expansion of a time or a space time-dimension cannot explain the spatially expansive properties of Dark Energy.

The fact that the effects of Dark Energy are only observable between bodies that are not gravitational bound can also be explained by assuming it’s causality is a result of the geometry of four *spatial* dimensions. 

If both dark and gravitational energy are related to the existence of four *spatial* dimensions then, as will be shown in a latter article "Why E=mc^2" the "concentration" of Dark relative to gravitational energy would be defined by the experimentally confirmed equation E=mc^2".  Therefore, because the expansive effects it has on space are considerably less "concentrated" by factor of c^2 than the contractive forces associated with mass it would be extremely difficult to observe it between gravitationally bound objects.

This shows that one of the advantages to defining the universe in terms of four *spatial* dimensions instead of four dimension space-time is that it allow one to establish a logical and consistent theoretical link between the observed properties of both dark and gravitational energy

Later Jeff

The "Shadows" of four spatial dimensions

Copyright 2009 Jeffrey O’Callaghan

One of these observations involves the theoretical existence of quantum fluctuations.

Quantum fluctuations are a theoretical construct based on the Uncertainty Principal.  It states one cannot know the precise amount of energy contained in a microscopic volume of space. Therefore, over a short enough time intervals the energy levels in an empty volume of space can fluctuate.  Some physicist believe these fluctuations can provide enough energy to generate virtual particle antiparticle pairs so long as they annihilate each other within the interval of time specified by the uncertainty principal so there is no net creation of matter.

Even though the existence of quantum fluctuations is based solely on theoretical arguments, it may be beneficial to examine the consequence to our understanding of physical structure of the universe if they do exist.

Presently the only viable theory that defines energy is based on Einstein’s concept of a space-time manifold. 

However, it is difficult to understand how the "surface" of a space-time manifold can produce the energy theorists associated with quantum fluctuations.

This is because Einstein defined the rate at which time "moves" in terms of the energy content of a volume and according to his space-time concepts time must always move slower in an environment with a different energy content relative to another.

However, this presents a problem for those who define quantum fluctuations in terms of symmetrical energy distortions in the space-time manifold defined by Einstein. 

As mentioned earlier, according to Einstein’s space-time concepts time is dilated or always "moves" slower in volumes that contain a different energy content than the ones from which they are observed.  This means the time dilation associated with quantum fluctuations will be cumulative even though the energy associated with the particle antiparticle pairs is not.  Therefore, because of the random nature of these fluctuations we should observe random time dilations in volumes were they occur relative to others throughout the universe.  However, this means the velocity of light will not appear to be constant because time would not "move" at constant speed in all volumes.

Since the velocity of light is constant in all volumes we must conclude that either quantum fluctuations do not occur or the space-time concepts of Relativity are invalid.

Additionally according to Einstein’s concepts the high energy density associated with quantum fluctuations means time in volumes were they occur would "move" significantly slower than in the adjacent volumes.  This means the time interval specified by the uncertainty principal to assure that no net creation of matter occurs would be different inside of the volume where they occur relative to the adjacent volumes.  This sets an upper limit on the magnitude of the energy of particle antiparticle creation because higher energy means it would take longer for them to annihilate each other relative to the adjacent volume.  Therefore, to satisfy the time requirement of the uncertainty principal of no net creation of matter relative to the adjunct volumes means, that according to Einstein’s concepts there must be an upper limit to the magnitude of their energy.

However, as was done in the article “Defining energy” Nov 26, 2007 defining energy in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would allow one to define the particle antiparticle pairs associated with quantum fluctuations in terms a symmetrical spatial displacement in that manifold and their annihilation in terms of the canceling out of those spatial displacements.

Additionally defining time dilation in terms of a spatial displacement as was done in the article "The relativity of four spatial dimensions"  Dec 1, 2007 eliminates the problem associated with the cumulative effects causes by defining it in terms of the properties of a space-time manifold because the spatial displacements are oppositely directed, the time differentials associated with them will cancel out.

Later Jeff

The "Shadows" of four spatial dimensions

Copyright Jeffrey O’Callaghan 2009

The observations supporting the existence of a continuous non-quantized form of mass were presented in the article "What is Dark Matter?" Sept 10, 2007.

Dark Matter is a substance that posse’s gravitational energy but does not have an observable particle component.  This would be the properties of a continuous non-quantized form of mass.  It would posse gravitational energy because it is mass and it would not have an observable particle component because it is not made up of them.

However, many in the scientific community have assumed the reason they have not discovered its particle component is that, even with the recent advancements in instrumentation technology they are not yet sensitive enough to resolve them.  However, another possibility is that it is not made up of particles as we are suggesting.

One of the many observations presented in this blog supporting the existence of four *spatial* dimensions instead of four-dimensional space-time is that combining it with a continuous non-quantized form of mass would enable one to define a quantum theory of gravity in terms of the classical laws of physics.

The article "Why is energy quantized?" Oct, 4 2007 showed the properties of a particle could derived in terms of a classically resonating system made up oscillations in a continuous non-quantized form of mass on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimensions.

While the article "Defining energy?" Nov. 26, 2007 shown one can explain and predict gravitational forces in terms of a displacement or curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, both of these mechanisms have a common element in that they cause a compression in a volume were they are located.

As mentioned earlier a particle’s properties can be derived terms of a resonant or "standing" matter wave in a continuous non-quantized form of mass on a "surface" of a three-dimensional space manifold. 

This means it may be possible to derive its mass in terms of a geometric compression of three-dimensional space caused by that matter wave.

This is because a wave on a "surface" of a three-dimensional space manifold would compress the three-dimensional volume with respect to a fourth *spatial* dimension between two points on that "surface" analogous to how a wave on a surface of water compress the two-dimensional distance between two water molecules on its surface.

However, if a volume, without any particles present contains a continuous non-quantized form of mass, a matter wave moving on its three-dimensional "surface" would compress it, making its continuous non-quantized mass component denser relative to the adjacent regions of space.  Therefore, if a particle is a result of a standing matter wave, on a "surface" of a three-dimensional space manifold, as suggested in the article “The geometry of a photon / particle” June 15, 2009 one could derive its mass in terms an increase in the density of a continuous non-quantized component of space caused by a geometric compression of a volume. 

If, as suggested in the article "Defining energy?" a curvature in a "surface" of a three-dimensional space manifold is responsible for gravitational energy then one could define the mass associated with that energy in terms of a compression of a three-dimension space manifold associated with that curvature.  This would be analogous how the material in a mattress is compressed due to a curvature in its surface caused by someone laying on it. 

This defines Quantum Theory of Gravity and link between gravity and quantum mechanics because it derives both the quantum and gravitational properties of mass in terms a common mechanism related to the existence of a continuous non-quantized form of mass and four *spatial* dimensions in terms of classical mechanics.

This cannot be done in terms of four-dimensional space-time because a curvature in it will not result in a compression of a three-dimensional volume.  Therefore, it is extremely difficult to define a connection between them in terms of classical mechanisms associated with their masses as we have done here and throughout this blog.

Later Jeff

The "Shadows" of four spatial dimensions

Copyright 2009 Jeffrey O’Callaghan

However, if this were true one would think that black body radiation should be continuous over its entire range of values.

The reason it is not can be found in the article "The Photon: a matter wave?" Oct. 1, 2007 where it was shown the quantum properties of energy are a result of a resonant system or "structure" generated by a matter wave moving on  "surface" of a three-dimensional space manifold.

Additionally, the article "Why is energy quantized?" Oct. 4 2007 showed the environment occupied by this matter wave would met the requirements for resonance to occur in a classical Newtonian world, an object, or substance (a continuous non-quantized form of mass) 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 fourth *spatial* dimension).

However, the resonant properties of a continuous non-quantized form of mass cannot only explain in terms of classical mechanics why energy is quantized but can predict the observed properties of black body radiation.

A black body is an idealized object that absorbs all electromagnetic radiation that falls on it.  No electromagnetic radiation passes through it or is reflected from it.  Because no light is reflected or transmitted, the object appears black when it is cold.  However, a black body emits a temperature-dependent spectrum of light.  This thermal radiation from a black body is termed black body radiation.

At room temperature, black bodies emit mostly infrared wavelengths, but as the temperature increases past a few hundred degrees Celsius, black bodies start to emit visible wavelengths, appearing red, orange, yellow, white, and blue with increasing temperature.  By the time an object is white, it is emitting substantial ultraviolet radiation.

The problem is that the laws of classical mechanics, specifically the equipartition theorem, states that black-bodies which have achieved thermodynamic equilibrium are mathematically obligated (by classical, pre-quantum, laws) to radiate energy in the form of ultraviolet light, gamma rays and x-rays at a certain level, depending on the frequency of emitted light.

Unfortunately, for classical laws, when a black body gets hot enough, the amount of radiation, which should theoretically be given off, according to the equipartition theorem, should begin to approach infinity.

However, observations of black body radiation indicate that there was less and less energy given off at high end of the spectrum.

The conflict between the predictions of classical laws and observations came to be known as the Ultraviolet Catastrophe.

Einstein pointed out that the difficulty could be avoided by making use of a hypothesis put forward five years earlier by Max Planck.  Planck postulated that electromagnetic energy did not follow classical laws, but could only oscillate or be emitted only in discrete packets of energy proportional to the frequency, as given by Planck’s law.  In other words, the light waves of each frequency in a black body could not have any energy but are limited to a few discrete values.

However, as was shown in the article "The Photon: a matter wave?" the energy of light at each frequency is determined by a resonant system which is, in turn determined by the physical perimeters of the environment it is occupying.  Environments will only support the discrete energies or frequencies of light that have a fundamental or a harmonic of the resonant system associated with the environments where they are found.  According to classical mechanics, any frequency other than that would be irregular and non-repeating and therefore the energy associated with it would be absorbed into the fundamental frequency of the environment.

Therefore, the energy contain in a black body should be limited to a few discrete values based on classical mechanics if the causality of energy quantization is a resonant system formed by a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This shows one can derive a mechanism that can explain and predict the observe properties of black body radiation in terms of classical laws if one assumes space is composed of a continuous non-quantized form of mass and four *spatial* dimensions as we have done in this blog.

This is not possible if one defines space in terms of four-dimensional space-time because time is only observed to move in one direction forward while one can move bidirectionally in a spatial dimension.  Therefore, it is not possible to define the spatial oscillations or bidirectional movements in a space-time manifold that is required to define a classically resonating system.

Later Jeff

The "Shadows" of four spatial dimensions

Copyright 2009 Jeffrey O’Callaghan

Karl Poppers answers this in his book "The Logic of Scientific Discovery" by explaining how and why only those theories that are testable and falsifiable by observations add value to a scientific community. 

Theories are a result of creative imagination.  Therefore, the growth of scientific knowledge rests on the ability to distinguish the reality of the "real world" from one created by imagination.  Therefore, only theories, which are testable and falsifiable by observations of the "real world" add to science since they are the only ones distinguishable from an imaginary one.

In the earlier article Causality, explanation, and deductions of predictions Nov-01-08 we discussed the two basic components or statements Karl feels all theories must have to be falsifiable and therefore add value to a scientific community.

The first or as he calls it the "universal statement of laws" apply to the entire universe.  These are more commonly called laws of nature.  Newton’s law of gravity would be an example of a universal statement because it can be applied throughout the universe.

The second or singular statement is defined as statements that apply only to specific events.  A bird striking Flight 1549 caused it to crash land in the Hudson River on January 15, 2009 is an example of a singular statement because the bird strike applies only to that event.

In this article, we will discuss why adopting Karl’s definition of falsifiability is important for the advancement of science.

The primary reason the value of a scientific system should be dependent on its ability to be falsified and not on its ability to be verified is that it is possible to logically proceed from one true singular statement to the falsity of a universal statement even though all other singular statements may verify it.

However, determining which singular statement can result in the downfall of a scientific system is not easy as Karl points out because it is almost always possible to introduce an ad hoc or auxiliary hypotheses to successfully integrate a singular statement into almost any scientific system.

Therefore, Karl proposes that we adopt certain rules regarding how we define falsifiability with respect to theoretical statements.

The first is all ad hoc or auxiliary hypothesis added to a theory to explain a specific observation must not decrease the falsifiability or testability of the system in question.  Putting it another way, its introduction must be regarded as an attempt to develop a new system which if adopted would represent a real advancement in our understanding our world.

An example of an acceptable auxiliary hypothesis is Pauli’s exclusion because it increased the precision and the testability of older quantum theories.

An example of an unacceptable one would be the contraction hypotheses proposed by Fitzgerald and Lorentz to explain the experimental findings of Michelson and Morley because it had no falsifiable consequences but only served to restore agreement between theory and experiment.  Therefore, it did little to advance our understanding of the "real world".  However, advancement was achieved by Relativity because it explained and predicted Michelson and Morley’s observations along with providing new consequences and testable physical effects thereby opening up new avenues for testing and falsification of the theory.

Recently modern physicists have attempted to develop new explanations of experimental findings that appear to contradict current theories by hypothesizing structures which according the above criteria are unfalsifiable and therefore do not add value to the scientific community. 

For example, string theorist have hypothesized the universe is composed of one-dimensional strings in an attempt to unify gravity with the other forces of nature.  However, the existence of strings is not falsifiable by observations of the "real world" because by definition they are too small to be observed.  Additionally, the mathematical arguments used to support their existence have no falsifiable consequences because in most cases they can modified to restore agreement between them and experimental findings.  Therefore, there is no way to verify if the mathematical worlds created in the minds of string theorists exist in the real world.

Physics is by definition an observational science.  Imagination is a very important component in its advancement however; it must be tempered with the "reality" of the observable world.

Later Jeff

‘A nice adaptation of conditions will make almost any
hypothesis agree with the phenomena.  This will please the imagination,
but does not advance our knowledge.’
J Black,

Copyright 2009 Jeffery O’Callaghan

(This article is a collaboration between Israel Sadovnik and Jeff.)

We have shown through out this blog observations of our environment suggest space may be composed of four *spatial* dimensions instead of four-dimensional space-time.

The inertial property of objects is one of those observations.

Newton, in his laws of motion defined how the inertia of an object interacted with its environment and the effects gravity has on them.  However, he was unable to define the causality of gravity or inertia.

Einstein was able to define the causality of gravitational accelerations on objects and the relative properties of their movements in terms of a curvature in a four-dimensional space-time manifold but he was unable to define the causality of inertia. 

However, one can define a casual relationship between the inertial properties of objects and gravity if one defines them in terms of four *spatial* dimensions instead of four-dimensional space time. 

In the article "Defining energy" Nov. 26, 2007 it was shown all forms of energy including the inertia or momentum of an object can be derived in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  While the article "Why Space-time?" Sept 27, 2007 showed one could derive gravitational accelerations in terms of a curvature in a four-dimensional space metric as well as one in four-dimensional space-time.

However, defining them in terms of four *spatial* dimensions gives one the ability to define the causality of both gravity and inertia in terms of a displacement in a "surface" of three-dimensional space.

As was shown in article "Defining energy" a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is the causality of the gravitational accelerations.  While a gravitational potential was derived in terms of a displacement in the "surface" of that manifold caused by that curvature.   (This curvature is analogous to a curvature in a four-dimensional space-time manifold Einstein theorized was the causality of gravitational accelerations.)

However, according to the concepts presented in that article the causality of inertia, momentum or "potential energy" of an object due to its motion would be defined by a displacement in the entire "surface" of a three-dimensional manifold.  Therefore, the displacement associated with its inertia would be the sum of two components.  The first would be caused by the gravitational curvature associated with the mass of the object and second would be a displacement of the "surface" of the three-dimensional space manifold with respect to a fourth *spatial* dimension where that curvature is located.  (The momentum of an object at rest with respect to other objects is zero so the displacement of three-dimensional space with respect to those objects would also be zero.)

That article showed forces or the ability to change the momentum of an object is caused by it interacting with a curved "surface" of a three-dimensional space manifold.  However, if, as mentioned earlier the momentum of objects is caused by a constant or flat displacement of a "surface" of a three-dimension space manifold they would tent to stay rest or ones in motion would tend to stay in motion is because they are occupying a "surface" of a three-dimensional plane that is not curved with respect to a fourth *spatial* dimension and therefore would not experience any forces.

This defines a causal link between the inertial properties of objects and gravity in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Einstein could define the casualty of gravity but not inertia in terms of a four-dimensional space-time manifold because its "surface" can be curved but cannot be displaced as is possible for a three-dimensional manifold contained in four-dimensional space.

Later Jeff

The "Shadows" of four spatial dimensions

Copyright 2009 Jeffrey O’Callaghan

A few physicists led by George Gamow showed an expanding universe meant that it might have had its beginning in a very hot infinitely dense environment, which then expanded to generate the one we live in today.

They were able to show the radiation emitted approximately 300,000 years after the beginnings of the expansion should be visible today because before that time space was so hot that protons and electrons existed only as free ions making the universe opaque to radiation.  This period is referred as the age of "recombination". 

Additionally they predicted this Cosmic Background Radiation or radiation left over from the age of recombination would have cooled form several thousand K back when it was generated to 2.7 K today due to the expansion of the universe.

The conflict between the Steady State and Big Bang Theory was resolved when this radiation was discovered by Penzias and Wilson in1965 because it showed the temperature of the universe had changed through time, which was a direct contradiction to the Steady State Model". 

However, if the universe began as an expansion of in an infinitely dense hot environment one would expect the universe and Cosmic Background Radiation to be homogeneous because an infinitely dense environment must be, by definition homogeneous.  Therefore, if there the universe was homogeneous when it began it should still be.

But the existence of galactic clusters and the variations in the intensity of the cosmic background radiation discovered by NASA’s WMAP satellite show the universe is not and were not homogeneous either now or at the time of recombination.

Many proponents of the big bang model assume that these "anisotropy" in the universe are caused by quantum fluctuations in the energy density of space.  They define quantum fluctuations as a temporary change in the energy of space caused by the uncertainty principle.

They have been able to mathematically show that very small quantum fluctuations in the energy content of the universe back when it first formed would have expanded enough to not only the create the observed variations in the intensity of the CBR but also the existence of galactic clusters.

However, there is an equally valid alternative interpretation of the existence of galactic clusters and the variations in the intensity of the CBR that has not been given serious consideration by modern science.

Science has yet not determined if the total attractive gravitational energy in the universe exceeds the total expansive energy generated by the big bang.  Therefore, they cannot tell if the universe will continue to expand or at some point enter a contraction phase.

(In a later article, it will be shown why using the currently accepted physical laws the universe must enter a contraction phase.)

But by definition, the universe is a closed system therefore, according to the first law of thermodynamics, all the energy, or heat dissipated by its expansion would be returned to it if it did enter a contraction phase.  However, this means that at some point in the contractive phase the universe will heat up enough to cause the disassociation of protons and electrons into free ions again making the universe opaque to radiation.  However, the expansive forces generated by the heat of its contraction would eventually become greater than the momentum of its contraction and cause the universe to expand again and generate another age of recombination.

If this were true, it would mean that the expansion of the universe did not begin from an infinitely dense environment but from an extended less dense spatial environment.  This also means that the variations in the intensity for the CBR and the formation of galactic clusters could be explained in terms of variations in the energy density of the universe cause by the non-uniformity of its contraction.

This scenario could be analytically verified by developing equations based on observing the thermodynamic "anisotropy" of our present universe and extrapolating them back in time to a point where the contraction stopped and its expansion began.  This would give an observational basis for defining the "anisotropy" in found in the universe and Cosmic Background Radiation based on what came before the big bang.

This conclusion is supported by Marc Kamionkowski, Caltech’s Robinson Professor of Theoretical Physics and Astrophysics in the Scientific Frontline article "Researchers Interpret Asymmetry in Early Universe" Tuesday, December 16, 2008.  In that article he suggests that today’s computer technology give researchers the ability to extrapolate perturbations in a cyclical universe back in time to a point where the contraction reverses and its expansion begins.  This, as the article points out would allow researchers the first glimpse at what came before the Big Bang"

This alternative explanation of the observed "anisotropy" of the Cosmic Background Radiation, if verifiable as Marc Kamionkowski suggests should have more creditability than one derived from quantum fluctuations because it would be based on direct real time observations of our present environment instead of an unobservable environment of quantum fluctuation at the time of a "Big Bang"

Later Jeff

The "Shadows" of four spatial dimensions

Copyright 2009 Jeffrey O’Callaghan

The properties of a quantum "field" is one of those observations.

On page 23 of Gordon Kane’s book "Supersymmetry" he explains how physicists learned that they could simplify the calculations of the forces involved in planetary motion by assuming or imagining the existence of a continuous gravitational field.  They defined this field in such a way that if another planet were put at any point in that field the resulting force between the any other planet would be exactly the Newtonian one.  This simplified the calculations of planetary motion because it allowed them to isolate and analyze the forces of one planet on another instead of trying to analyze the forces exerted on a planet by all of the others at the same time.

Originally, many thought this was just a trick to simplify calculations.

However, as Gordon points out in his book Michael Faraday, while researching electromagnetism discovered that a field has real physical properties and therefore was able to convince others that is was more the just a calculating device.

But Quantum Field Theory and the Standard Model of Particle Physics defines the force of electromagnetism in terms of the exchange of a photon between charged particles. However, according to Wikipedia these photons should not be thought of particles but as quantum fields, a position-space wave function or "chunked ripples" in a field that "look like" particles.

Therefore, as the name implies Quantum Field Theory assumes that a particle’s properties are a result of "chucked ripples" in a continuous medium or field.

But this presents particle physicists and proponents of Standard Model and Quantum Field Theory with a very real problem because they assume all forces are transmitted by particles while at the same time they define the properties of those particles in terms of "ripples" in the continuous medium of a field.  Therefore, the force they associate with particles is actually mediated by "ripples" in a continuous field, which contradicts their assumption that all forces are mediated by particles.

However, we may be able to develop a better understanding of the makeup of a volume containing this field by examining the physical environment required to generate it instead of looking at the mathematical explanations provided by both the Standard Model and Quantum Field Theory of particle interaction.

Its most obvious physical property is that it is continuous because both the Standard Model and Quantum Field Theory define particle interaction term of "ripples" or a "position-space wave function" moving in space.  This means that each point in a volume containing them must be connected to every other point in a volume to allow the "ripples" Quantum Field Theories associated with a particle to propagate in it.  

In the article "Why is mass and energy quantized?" Oct. 4, 2007 it was shown that one could derive the quantum properties of energy in terms of a resonant system formed by "ripples" in a continuous non-quantized field of mass.

However, the physical properties associated with a continuous non-quantized field of mass appears to have the characteristics required by Quantum Field Theories and the Standard Model of particle physics to support the exchange of a photon between particles.  

Its continuous or field like nature would support propagation of ripples in a volume and the fact that it has mass means, as was shown in the article mentioned earlier "Why is mass and energy quantized?" it could support resonance.  Therefore, its existence predicts the particle nature of the ripples in a continuous non-quantized field of mass defined in Quantum Field Theories and the Standard Model of Particle Physics.  Additionally, this continuous non-quantized field of mass must be present at every point in a volume even though there are no particles or baryonic matter in it.

Therefore, the experimental verification of the existence of a quantum field also provides experimental verification of the existence of a continuous non-quantized form of mass.

Later Jeff

The "Shadows" of four spatial dimensions

Copyright 2009 Jeffrey O’Callaghan

A two-dimensional animation showing how three-dimensional space can be compressed with respect to a fourth *spatial* dimension

Credit: John Eden

For the past 25 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 properties stars and galaxies that many physicists feel that it is the ultimate theory of matter and energy.

But as Charles Seife mentions on page 142 of his book Alpha & Omega "Taken literally the plain vanilla form of the Standard model of particle physics does not say anything about particle mass at all: in fact if theorists try to put mass in to the equations of that model the equations blowup and become meaningless."

However, one of the most observable properties of particles is that they have mass.  Therefore, if the Standard Model is the ultimate theory of particles, as many physicists believe you would think that it should be able to define or at least incorporate that observation into its theoretical structure.  The fact it can’t, as mentioned in Charles book, is a reason to look beyond it for a deeper understand of our universe.

In the article "The “gravity” of four *spatial* dimensions" Jun. 1, 2009 it was shown a gravitational potential can be defined in terms of curvature in a "surface" of a three-dimensional space manifold with respect to a fourth "spatial" dimension and that mass is derivable in terms of a geometric compression caused by a curvature in that "surface".

This concept is similar to one presented in the General Theory of Relativity which defines a gravitational potential and mass in terms of a geometric curvature in a four-dimensional space-time manifold.

However, even though these two concepts are based on different geometries they make identical predictions, as we have shown throughout this blog regarding the relativistic properties of space, time, mass, and energy.

One advantage to defining mass in this way is that it permits  the microscopic mass of a particle to derive be in a manner that is consistent with those of planets and stars.

In 1924, Louis de Broglie theorized that all particles have a transverse wave component.  (His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.)  But he abandon the attempt made in his paper "The Theory of the double solution" to interpret their wave properties in terms of classical space and time because of the almost universal adherence of physicists to the purely probabilistic interpretation of Born, Bohr, and Heisenberg.

This was unfortunate because as was shown in the article "Why is mass quantized?" May 1 2008 one can define both the probabilistic interpretation of a particle made by Born, Bohr, and Heisenberg and its transverse wave properties theorized by Louis de Broglie in terms of a resonant system formed by a matterwave moving on a continuous "surface" of a three-dimensional space manifold respect to a fourth *spatial* dimension.

However, defining the quantum characteristics of a particle in terms of a resonant system generated by a matterwave also allows one to derive its mass in terms of a mechanism similar to the one that defined the mass of star or planet in the article, mentioned earlier "The “gravity” of four *spatial* dimensions".

This is because a transverse wave on a "surface" of a three-dimensional space manifold responsible for generating the resonant structure associated with a particle would compress or shorten the three-dimensional distance between two points on that manifold. 

This would be analogous to the how a transverse wave on the "surface" of water shortens or compress the two-dimensional distance between two water molecules on its surface.

Therefore, one could derive the mass and gravitation potential of both macroscopic and microscopic objects such as stars planets or particles terms of a common mechanism related to a geometric compression in a "surface" of a three-dimensional space manifold with respect to a four *spatial* dimension. 

The concept of deriving  gravitational potential and the quantum properties of mass in terms of a compression in three-dimensional space manifold with respect to a fourth *spatial* dimension can also can serve as the basis for defining a theory of quantum gravitation.

However, this cannot be done if one tries to define them in terms of a space-time geometry because time is only observe to move in one direction forward and therefore cannot support the up and down movement of the transverse wave that de Broglie theorized was responsible for its quantum properties.

This suggests if one assumes mass and gravitational potential is result of the geometric properties of four *spatial* dimensions instead of four-dimensional space-time it may be possible to incorporate the observation that particles have mass into the theoretical structure of the Standard Model and define a quantum gravity.

Later Jeff

The "Shadows" of four spatial dimensions

Copyright 2009 Jeffrey O’Callaghan

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

WE PREDICT that anti-matter posses a negative gravitational potential and will fall up based on the theoretical model presented in this blog and the paper "The Shadows of four *spatial* dimensions"

In the article "The causality of gravity" Dec. 15, 2007, we defined gravitational force in terms of a "depression" caused by a displacement in a "surface" of a three-dimensional space manifold with respect to fourth *spatial* dimension instead of a curvature or "depression" in a four-dimensional space-time manifold. 

In the article "Matter verses antimatter" May 15 2009, we derived the mass or energy associated with anti-matter in terms of an oppositely directed "displacement" in a "surface" of a three-dimensional space manifold. 

Therefore, the gravitational forces associated with matter and anti-matter should be oppositely directed and if this theoretical model is correct anti-matter will fall up.

This provides an experimental verifiable distinction between its predictions and those of Relativity and the Standard Model of Particle Physics because they do not and cannot support the existence of a negative gravitational potential.

Therefore, if the scientists at CERN find that anti-matter particles fall up they would be required to not only rethink the relationship between matter and antimatter but completely revamp our understanding of the mechanism responsible for gravitational forces and the geometry of the universe as we have done.

Later Jeff

Copyright 2009 Jeffrey O’Callaghan