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  his attempt, made in the 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.

However, 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.

But 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 way 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 suggested in this blog 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 2008 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 Jeffrey O’Callaghan 2009

Source: Maths: Fourth Dimension Videos

(Louis de Broglie was the first to theorize that all particles have a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.)

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

It was shown those how those conditions define the stability or instability of a quantum particle in terms of the existence of four *spatial* dimensions but did not explain how they contribute to it.

However, one can understand how by comparing the geometry of four *spatial* dimensions to the two-dimensional of surface of paper.

A point on the two-dimensional surface of paper is confined to that surface.  However, it can move up or down with respect to three-dimensional space without it ever leaving it.

Summarily, energy in a three-dimensional volume would be confined to that volume.  However, it can move "up" or "down" with respect to a fourth *spatial* dimension without ever leaving three-dimensional space.  This also means that a matterwave moving on a "surface" of a three-dimensional space manifold would be confined to a specific volume or "resonant chamber" whose sides are the geometric edges of three-dimensional space.  Therefore, because the boundaries of this volume are the edges of space they could not absorb energy.

The article “Defining energy” Nov. 26, 2007 showed that all forms of energy are definable in terms of a displacement in a "surface" of a three dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, a stable particle would be definable in terms of the energy associated with the oscillations or displacements, with respect to a fourth *spatial* dimension of a volume containing a continuous non-quantized form of mass at the fundamental or harmonic of the resonant frequency of the volume it is occupying.

An unstable particle would be one in which the continuous non-quantized mass component of a volume is oscillating at frequencies that are not associated with ether the fundamental or harmonic of the resonant frequency of the volume it is occupying.  These particles will decay by losing or gaining energy from their environment until they have the stable resonant structure associated with either the fundamental or harmonic of the resonant frequency of that volume.

This shows that one can define the stability or instability of a particle in terms of a classically resonating system and the geometry of four *spatial* dimensions whereas one cannot in terms four-dimensional space-time because it cannot provide the geometric boundaries required to define a resonant volume.

Later Jeff

The "Shadows" of four *spatial* dimensions

Copyright Jeffrey O’Callaghan 2009

However, some believe that gravitational forces because of their spherical properties cannot be defined in terms of the existence of only four *spatial* dimensions.

This would be true if the movement of three-dimensional space is restricted orthogonally to a fourth *spatial* dimension.

Observations of our three-dimensional environment show us that we can move and rotate a two-dimensional surface independently with respect to each axis of three-dimensional space and the individual axis of that surface are not required to be orthogonal.

We know this because the curvature of the surface of a balloon shows us that it can be rotated in any direction with respect to three-dimensional space and that the angle of the individual axis of its surface are not required to be orthogonal to each other.  Additionally we observe that when a force is applied to it with respect to three-dimensional space every point on it either or contracts or expands while the angles the individual dimensional axis of that surface make with each other shift to conform to that curvature.

We have shown throughout this blog that observations suggest the existence of a fourth *spatial* dimension which has properties similar to those of the three-dimensions that make up our environment.  This means the axes of a three-dimensional sphere should interact with a fourth *spatial* dimension in manner similar to the way a two-dimensional surface interacts with three-dimensional space.

Therefore, based on observations of our three-dimensional environment we can assume the individual axes of four-dimensional space are not required to be orthogonal to each other.  Additionally they also show that every point on a "surface" of a three-dimensional manifold that defines a volume could either expand or contract with respect to a fourth *spatial* dimension while the orientation of the axis of that volume could shift to conform to the curvature associated with that expansion or contraction.

Therefore, it would be possible to define the spherical nature of a gravitational field in terms of a spherical curvature in a "surface" of three-dimensional space with respect to a fourth *spatial* dimension.

Later Jeff

The "Shadows" of four spatial dimensions

Copyright 2009 Jeffrey O’Callaghan

The Big Bang theory suggests that matter and antimatter should have been produced in equal quantities.  Since collisions between matter and antimatter result in their mutual annihilation there should not be any ordinary matter, and its antimatter equivalent left in the universe.  However, it is obvious this did not happen because no galaxies or intergalactic clouds of antimatter have yet been detected that have the ability to offset the observed quantity of matter in the universe.  Therefore, it looks as if matter won out over antimatter.

"Why is there more matter that anti-matter in the universe?" can be understood if one views the universe in terms of four *spatial* dimensions instead of four-dimensional space-time as is being done in this blog.

In the article "The causality of energy"  Sept. 27, 2007 it was shown that all forms of energy can be defined in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  Additionally it has been shown it is possible to derive the "quantity" of mass in an object or particle terms of the magnitude of a displacement in a "surface" of that three-dimensional space manifold. 

This would also allow particle antiparticle annihilation to be definable and understandable in terms of the "upward" displacement in a "surface" of a three-dimensional space manifold associated with an antiparticle "filling in" the equal but oppositely directed "downward" displacement associated with a particle.

This would not be possible if one defined the universe in terms of four-dimensional space-time because observations tell us that time can only be displaced or "moved" in one direction whereas it is possible to move a spatial dimension in two directions, up or down.

As mentioned earlier the article "The causality of energy"  Sept. 27, 2007 showed the energy of a system can be defined in terms of the magnitude of a spatial separation in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, this means that one could define the energy of particle antiparticle annihilation in terms of the absolute magnitude of the oppositely directed displacements their masses cause in a "surface" of a three-dimensional space manifold.  Therefore, the energy of their annihilation would be equal to the sum of the energy associated with their combined masses.

However, this definition also provides an explanation of the why there is more matter than antimatter in there universe.

As was mentioned earlier, mass can be defined in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  Therefore, the mass of a particle would be definable in terms of a "downward" displacement in that "surface" with respect to a fourth *spatial* dimension while the mass of an antiparticle would be definable in terms of an "upward" displacement in that same surface.

But this indicates on average it would require less energy to form a particle than an antiparticle for the same reason that it takes less energy to fill a bucket with water by pushing it down below the surface of the water than it does by lifting the water into a bucket that is above its surface.

Therefore, there should be more particles than antiparticles left over after the big bang because it would take less energy to maintain the integrity of matter particle than an antimatter particle.

Later Jeff

The "Shadows" of four spatial dimensions

Copyright Jeffrey O’Callaghan 2009

With the activation of the Large Hadron Collider (LHC) they will have the ability to probe the microscopic particle properties of mass to resolution approaching 2.17645 × 10⁻⁸ kg or Planck mass and energy to 1.22 × 10²⁸ eV or Planck’s energy. 

While the images from the Hubble and Spitzer Space Telescopes have given them ability to make detailed measurements of universe’s macroscopic properties back almost to its beginnings.

However, even with these advances in measurement technology science has been unable to define a common mechanism to explain how and why the microscopic properties of mass and energy probed by the Large Hadron Collider could have resulted in macroscopic properties of the universe as seen by the Hubble and Spitzer Space Telescope.

This may be because science defines the microscopic environment probed by the LHC in terms of quantum mechanics while defining the macroscopic environment observed by the Hubble and Spitzer Space Telescopes in terms of Einstein theories.

Einstein’s theories define mass and the gravitational forces associated with mass in terms of a curvature in a continuous space-time metric while quantum theories define mass in terms of the discontinuous properties of particles.  However, no one has been able to define a common mechanism that can account for the continuous properties of gravitational forces predicted by Einstein’s theories in terms of the discontinuous properties of mass defined by quantum theories.

Therefore, scientists must rely on two seemly incompatible theories to completely define the observations of our environment.

However, as Dr. Robert Hert shows in this NASA video advancements in technology have not only allowed science to make more detailed measurements of our environment but also has greatly improved our the ability to integrate them into a larger setting.

Einstein’s theories predicts the position of an object such as a star, planet or particle by assuming it is defined by the forces it experiences as it moves along a well defined trajectory whereas quantum theory predicts the position of a particle in terms of the probability it will be at a specific point at a specific point in time.  Therefore, quantum theories assume there are an infinite number of trajectories a particle can take while Einstein’s theories predict that there is only one for its movement from one point to another.

However, the assumption of quantum theory that particles take all possible trajectories to reach a specify point is not supported by experimentation.

This fact is evident because scientists use magnetic forces in particle accelerators, such as the Large Hadron Collider to direct them along a predetermined circular path to position them so they collide with other particles.  This provides experimental verification their positions are definable in terms of the forces they experience as they move through space.

This appears to contradict quantum theories assumption that a particles trajectory in undeterminable.

Granted there is an uncertainty in their trajectories before the particles are created due to the Uncertainty Principle but after the collision, their trajectories are observable and completely determinable down to the limits imposed by that principle.

However, it agrees with the assumption made by Einstein that the trajectory and position of a particle should be determinable by the forces it experiences as it moves through space.

The NASA video shows that we now have the ability to integrate many different types of databases to give a “Big Picture” of our environment.  For example, they were able to merge the invisible of inferred and ultraviolet light with the visible by assigning each a color in the visual spectrum.  This allowed them to integrate or overlay the images of the invisible inferred and ultraviolet environments into a visual one.  As Dr. Robert Hert suggests this “Big Picture” may improve our ability, to “see” how and why these environments interact.

Now for the first time in humankind’s history we can directly observe both the macroscopic and microscopic aspects of our environment in detail and have the technical and computing ability to integrate them in a “Big Picture” as NASA has done with spectral properties of light.

Perhaps we should try to directly overlay the data bases or images given to us by the LHC and Spitzer Space Telescope instead of indirectly using Quantum and Relativistic theories to explain them because, as video shows it may allow us to better understand or “see” how and why these environments interact. 

Later Jeff

The “Shadows” of four spatial dimensions

Copyright Jeffrey O’Callaghan

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Most if not all scientific advancements humankind has made have been based on concepts derived though observations of the environment.

For example, Isaac Newton discovered the laws of gravity first by developing a conceptual understanding of how objects interacted in an environment he could observe on the earth and then extrapolated them to unobservable environments beyond the earth.  He then used those concepts to define a mathematical language to quantify them.  His theory gained general acceptance because the language he derived from those concepts could make accurate quantitative predictions of planetary motion.

However, many modern physicists seem to have taken a different road to understanding the laws that govern our world. 

For example, the generally accepted modern theory of the origin of particles or, "The Standard Model of Particle Physics" was developed by defining a mathematical language directly from observing the quantitative results of particle interactions.  The proponents of this theory then attempt to understand the interactions of particles by analyzing that mathematical language and base its validity on the fact that it can accurately quantify the properties of particles.

Both these methods allow scientists to make accurate quantitative predictions of observations however; the methodology they use to derive those predictions is different.

Newton’s method used a conceptual understanding of why objects interact in an environment to derive a mathematical language to quantify the interaction of all objects while the Standard model uses one developed from the quantitative results of particle interactions to understand why they interact.

As mentioned earlier the validity of both these theories is based on their ability to make accurate quantitative predictions while the Standard Model uses quantitative observations of a particles environment to derive a mathematical language to validate those quantitative observations.  Therefore, it is self-validating and cannot be falsified. 

But the Newtonian method of conceptualizing a theory first through observations then developing a mathematical language to make quantitative predictions from those concepts can be falsified because that language is not based on those quantitative observations.

Some try to justify using only the quantitative properties of particle interactions to derive a mathematical language to define them because technology does not to allow direct observations of the environment where they take place.  Therefore, because they cannot directly observe the environment where those interactions take place, they feel it is the only way for them to develop a mathematically language to quantify them.

However, as mentioned earlier science has been able to extrapolate Newton’s conceptual understanding of gravity based on observations of the earth’s environment to make quantitative predictions of its effects in unobservable environments.

It has been shown throughout this blog that it is possible to derive not only the observed properties of particles but also the quantum and relativistic properties of mass, energy, space, and time by extrapolating a conceptual understand of our observable environment to one that is unobservable.

However, I have not been able to define a mathematical language to quantify those concepts.  But this does not mean that one cannot separate the conceptual validation of the ideas presented in this blog from the mathematical language required to quantitatively validate them.

A concept is like a language in that it comes in many different forms.  If someone does not speak English, he or she would not understand someone who is speaking in English.  However, English can be translated to French by those who have had linguistic training so that someone who only speaks French can understand concepts presented in English.

The reason I have not defined a language to quantify these ideas is that I received a head injury, which affects my short-term memory.  This makes it extremely difficult to use mathematical coding to explain concepts.

For example, a Wechsler memory scale test given by the Veteran’s Administration indicates my visual short-term memory has a raw score of 23, which translates to the 2-percentile range.

The doctors tell me that one of the reasons why mathematics may be so difficult for me is because I have trouble remembering what the visual mathematical symbols represent as my mind works through equations.

The reason I created this blog and wrote the "Shadows" paper is that I am hoping a few who have mathematical training may feel the conceptual ideas it presents are worth the effort to translate them into a more quantitative mathematical language.

Later Jeff

Copyright 2009 Jeffrey O’Callaghan

However one of the primary goals of science is to extend our knowledge of nature’s processes by "seeing" the invisible.

For example, Isaac Newton showed that one could determine the position of a planet if one assumed that mass generated an attractive gravitational force on all other objects that was directly proportional to their combined masses and inversely  proportional to the square of the distance between them.

However no one can "see" a gravitational force.  How then can scientists be sure that the "thing" called a "gravitational force" is real or exists.

The answer is they can not.  They can only assume that it does based on the fact that using it they can make accurate predictions of a planets position.

But history has shown, assuming the existence of something based only on its predicted powers is fraught with danger.

For example in the Ptolemaic or geocentric system of astronomy, the existence of epicycles were required to explain the retrograde motion of the Moon, Sun, and planets.

It was not until scientific investigations were stimulated by Copernicus’s publication of his heliocentric theory did scientists realize epicycles did not exist.

This is true even though many Greek, Indian and Muslim savants had published heliocentric hypotheses centuries before Copernicus.

However, why did it take almost two thousand years for science to realize that their ideas were correct.

One reason may have been because the existence of epicycles was based solely on their predictive powers and not on the observations of the environment.  If the scientists who assumed the existence of epicycles had taken the time to see or observe how objects moved on earth they would have realized that there was a problem with that concept because, at least on earth, objects do not "naturally" follow a curve path.

However, the scientific community assumed the existence of epicycles on their predicative powers. Therefore, they were able to justify suppressing the correct Greek and Muslim ideas for almost 2000 years because, using them, they were still able to make accurate predictions a planet’s position even though there was a more logical and accurate predicative methodology based on observations.

For the past 25 years the Standard Model of cosmology has assumed the macroscopic cosmologic properties universe are the result of the existence of four-dimensional space-time.

However, as scientists we must remember that one can never prove the existence of the invisible.

Later Jeff

The "Shadows" of four spatial dimensions

Copyright 2009 Jeffrey O’Callaghan

The electrical properties of quarks are one of those observations.

In the article "Why is mass quantized?" it was shown the properties of a particle could be derived in terms of a resonant system formed on "surface" a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, observations of particles indicate they are made up of distinct components called quarks of which there are six types, the UP/Down, Charm/Strange and Top/Bottom.  The Up, Charm and Top have a fractional charge of 2/3.  The Down, Strange and Bottom have a fractional charge of -1/3.  Scientists have also determined that quarks can take on one of three different configurations they have designated by the colors red, blue, and green.

But if space was made up of four *spatial* dimensions one should be able to explain why quarks have a fractional charge and how they interact to form particles in terms of the geometry four *spatial* dimension.

The article “Defining energy” Nov. 26, 2007 showed it is possible to define all forms of energy including electrical in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, we as three-dimensional beings can only observe three of the four spatial dimensions.  Therefore, the energy associated with a displacement in its "surface" with respect to a fourth *spatial* dimension will be observed by us as being directed along that "surface".  However, because two of the three-dimensions we can observe are parallel to that surface we will observe it to have 2/3 of the total energy associated with that displacement and we will observe the other 1/3 as being directed along the signal dimension that is perpendicular to that surface.

This means the 2/3 fractional charge of the Up, Charm and Top may be related to the energy directed along a "surface" of a displaced three-dimensional space manifold with respect to a four *spatial* dimension while the -1/3 charge of The Down, Strange and Bottom may be associated with the energy that is directed perpendicular to that "surface".

The reason why quarks come in three configurations or colors with a fractional charge of 1/3 or 2/3 may be because, as was shown in the article ”Embedded Dimensions” Nov. 22, 2007 there are three ways the individual axis of three-dimensional space can be oriented with respect to a fourth *spatial* dimension.  Therefore, the configuration or "colors" of each quark may be related to how its energy is distributed in three-dimensional space with respect to a fourth *spatial* dimension.

However, it may also explain why it takes three quarks of different "colors" to form a particle because, as mentioned earlier one can define a particle in terms of a resonant system on a "surface" a three-dimensional space manifold with respect to a fourth *spatial* dimension.  If the colors of each quark represent the central axis associated with its charge then to form a stable resonate system would require three quarks that have different central axis to balance its energy with respect to the axes of three-dimensional space.  A particle could not exist if two quarks have the same central axis or color because it would cause an energy imbalance along that axis.  Therefore, a particle consisting of anything but quarks of three different colors would not stable.

This shows that it may be possible to define the electrical properties of quarks and how they combine to form particles in terms of the geometry of four *spatial* dimensions.

Later Jeff

The "Shadows" of four spatial dimensions

Copyright 2009 Jeffrey O’Callaghan 

For example, many sci-fi writers use the fact that the gravitational force of a black hole is so intense that nothing can escape from its "clutches" to develop their story lines.  However, many of them fail to point out the other side of story, which is, in many cases they use gravity to escape from that very same black hole.

This episode of the Spaceship Spitzer is a classic example of this omission.

In the opening scenes, we find our heroin, Dr. Michelle Thaller tiring to escape the Evil Mines by hiding in the myriad of stars in the center of our galaxy

However, she explains to her robotic sidekick Erwin they must establish a stable orbit around the supper massive black hole at its center.  If they don’t they will fall below its event horizon were the gravitational force becomes so great that nothing can escape.

But unfortunately, the Mines find them and established a similar orbit in the opposite direction so they can intercept and destroy them.

Erwin suggests that they speed up and move away from the black hole but Dr. Michelle points out that is not an option because it will make them a target for the Mines’ plasma bolts.

However, Dr. Michelle remembers they have a tactical advantage over the Mines because the rotating gravitational field of a black hole drags space along with it.  This means because they are orbiting it in the same direction as its rotation their instruments would indicate that they traveling faster relative to its event horizon than the Mines’ would.

Dr. Michelle tells Erwin to reduce their orbital speed to the point where it places them just above the black hole’s event horizon because if the Mines want stay on an intercept course they will have to match it.  However, as mentioned earlier the Mines will be moving slower with respect to the event horizon than they are because they are orbiting it in the opposite direction. Since the distance above the event horizon is dependent on their orbital speed the Mines will be closer to the event horizon than they are and will fall below it never to be seen again.   After the Mines have disappeared below the event horizon, she tells Erwin to power up their engines and escape from both the Mines and the "clutches" of the black hole.

The lesson we can learn from this side of the story is that nothing not even an Evil Mine can escape the intense gravitational field of a black hole after crossing its event horizon.

However, were did the energy to power their engines come from.

Some would say that has its origins in the burning of their engine fuel.

But the observationally verified equation E=mc^2 tell us that all forms of energy are derived from mass.  In other words, the energy that allowed them to accelerate away from the gravitational forces associated with the mass of the black hole came from the mass of their engine fuel.  But the only forces we associated with mass are gravitational.  Therefore, one must conclude that what saved them from the "clutches" of the black hole was the generation of an oppositely directed gravitational force, with respect to that of the black hole generated by the conversion of the mass contained in their engine fuel.

As was shown in the article "What is Dark Energy?" the force causing the accelerated expansion of the universe may have a similar origin.  Stars emit energy by the conversion of its mass.  Since as mention earlier all energy is derived from mass,   we should expect because of its asymmetrical relationship to energy that its conversion will produce an oppositely directed force with respect to the gravitational force of the star’s mass where it is being converted.

This means that Dark Energy or the force causing the accelerated expansion of the universe may be caused by the conversion of gravitation forces associated with mass to the oppositely directed force associated with dark energy.

The lesson we should learn from this side of the story is that mass maybe the power source for everything in the universe including Starships Spitzer ability to escape, the "clutches" of a black hole and Dark Energy or the force that is accelerating the expansion of the universe.

The "Shadows" of four spatial dimensions

Copyright 2009 Jeffrey O’Callaghan