We have shown throughout "The Imagineer’s Chronicle’s" that observations of our environment suggest that space is composed of four *spatial* dimensions instead of four-dimensional space-time.

If true we should be able to define the wave / particle properties of particles as observed in the "The double-slit experiment in terms of the geometry of four *spatial* dimensions. 

Wikipedia, describes the double slit experiment as being made up of

A coherent source of photons illuminating a screen after passing through a thin plate with two parallel slits cut in it.  The wave nature of light causes the light waves passing through both slits to interfere, creating an interference pattern of bright and dark bands on the screen.  However, at the screen, the light is always found to be absorbed as discrete particles, called photons.

When only one slit is open, the pattern on the screen is a diffraction pattern however, when both slits are open, the pattern is similar but with much more detailed.  These facts were elucidated by Thomas Young in a paper entitled "Experiments and Calculations Relative to Physical Optics," published in 1803.  To a very high degree of success, these results could be explained by the method of Huygens–Fresnel principle that is based on the hypothesis that light consists of waves propagated through some medium.  However, discovery of the photoelectric effect made it necessary to go beyond classical physics and take the quantum nature of light into account.

It is a widespread misunderstanding that, when two slits are open but a detector is added to determine which slit a photon has passed through, the interference pattern no longer forms and it yields two simple patterns, one from each slit, without interference.  However, there ways to determine which slit a photon passed through in which the interference pattern will be changed but not be completely wiped out.  For instance, by placing an atom at the position of each slit and monitoring whether one of these atoms is influenced by a photon passing the interference pattern will be changed but not be completely wiped out.

The most baffling part of this experiment comes when only one photon at a time impacts a barrier with two opened slits because an interference pattern forms which is similar to what it was when multiple photons were impacting the barrier.  This is a clear implication the particle called a photon has a wave component, which simultaneously passes through both slits and interferes with itself.  (The experiment works with electrons, atoms, and even some molecules too.)"

However, one can understand the "The most baffling part of this experiment" or why the interference pattern remains when only one photon at a time impacts a screen with two opened slits in terms of the laws of classical physics if one assumes (as is done in the "The Imagineer’s Chronicle’s") the universe is made up of four *spatial* dimensions instead of four dimensional space-time

The article, "Why is mass and energy quantized?" Oct. 4, 2007 showed it is possible to explain and predict the duality or particle / wave properties of matter and energy in terms of a classically resonating system or "structure" generated by a wave moving on “surface” of a three dimensional  space manifold with respect to a fourth *spatial* dimension.  It also explains why all energy must be quantized or exists in these discrete resonant systems when observed.

The reason why the interference patterns remains when one photon at a time is fired at the barrier with both slits open or "the most baffling part of this experiment" is because, as mentioned earlier it is made up of a resonant system or  "structure" who’s volume would be directly related to the wavelength of that system.

This means a portion of a photon’s energy could simultaneously pass both slits, if the diameter of its volume exceeds the separation of the slits and recombine on the other side to generate an interference pattern. 

However, according to the laws of classical wave mechanics the "concentration" of a wave’s energy is maximum at its peaks and troughs.  Therefore, one could only observe or "drain" the energy continued in a particle’s wave function at points corresponding to its peaks and valleys because those would be the only points where its energy would be “concentrated” enough to be redirected as a resonant system to the observing instrument.  However, as was shown in the article "Why is mass and energy quantized?" its wave properties, which define its energy, can only be observed in terms of its quantized resonant "particle" structure.  Additionally, this means when one looks at the interference pattern generated by the wave function of a single or multiple particles, there would be a higher probability observing it at the places where the peaks and trough reinforced and less where they cancelled.

This is analogous to how the energy of water in a sink is release by allowing it to go down the drain.  If all we could observe is the water coming out of the drain we would have to assume that it was concentrated in the region of space defined by the diameter of the drain.  However, in reality the water occupies a much larger region. 

It also explains why the interference pattern disappears, in most cases when a detector is added to determine which slit a photon has passed through.  The energy required to measure the portion of its energy that passes through one of the two slits interacts with it causing the wavelength of that portion change so that it will not have the same resonant characteristics as one that passed through the slit were no measurement was taken.  Therefore, the energy passing thought each slit will not be able to interact to form an interference pattern on the screen.

However it also explains why, as was mentioned in the Wikipedia article "there are ways to determine which slit a photon passed through in which the interference pattern will be changed but not be completely wiped out"; a direct contraction of the Copenhagen interpretation of quantum mechanics.  It demands when a detector is added to the experiment to determine which slit a photon has passed through the interference pattern can no longer form.  The experimental apparatus should then yield two simple patterns, one from each slit, without interference.

The fact that the interference pattern can occur even if a measurement is made is because if the energy passing through one of the two slits is altered by a relatively small amount compared to what it was originally classical wave mechanics tells us it will be able to interact to form a slightly different resonant system with a slightly different interference pattern on the other side than would be the case if no measurement was taken.

Therefore, there should be a quantifiable minimum value of interaction between a measuring device and a photon that will permit the interference pattern to be reestablished on the other side after measuring which slit the photon passes through.

Additionally there should be a direct relationship between the energy of a particle and when and if an interference pattern is generated when one tries to measure which slit it moves through in the double slit experiment.

One can also define the reason, in terms classical wave mechanics why the results of this experiment are always in the form of discrete particles such as a photon or electron.

As mentioned earlier, all energy must be quantized so therefore the energy impacting the screen will be observed as having the discrete non-wavelike characteristics of a photon whether or not interference occurs.

However, as mentioned earlier, according to the laws of classical wave mechanics the "concentration" of a wave’s energy is maximum at its peaks and troughs.  Therefore, one could only observe or "drain" the energy continued in wave function associated with its resonant system at points corresponding to its peaks and valleys because those would be the only points where its energy would be “concentrated” enough to be redirected to the observing instrument.  This means when the wave function of single or multiple particles interact, there would be a higher probability observing it at the places where the peaks and trough reinforced and less where they cancelled.

Richard Feynman the farther of Quantum Electrodynamics or "OED" realized the significance of this experiment because it demonstrates the inseparability of the wave and particle properties of particles and felt a complete understanding of quantum mechanics could be gleaned from carefully thinking through its implications.

The above article demonstrates why.

It shows the quantum and wave properties of mass and energy displayed by the double slit experiment can be understood if one assumes they are made up of a classical resonant system in a moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This cannot be done if one define the universe in terms of four dimensional space-time because as was shown in the article “Why is mass and energy quantized?" time is only observed to move in one direction forward and therefore could not support the bi-directional movement required to derive classical resonance.

Later Jeff

The "Shadows" of four spatial dimensions

Copyright 2009 Jeffrey O’Callaghan

(In a PDF format)

We may soon know because the scientists at CERN have been given the go-ahead to perform an experiment that will determine if it does.  As describe in the NewScientist article "Antimatter mysteries 3: Does antimatter fall up?" Apr 29, 2009, the AEGIS team will use uncharged particles to prevent electromagnetic forces from drowning out gravitational effects.  It will first build highly unstable pairings of electrons and positrons, known as positronium, then excite them with lasers to prevent them annihilating too quickly.  Clouds of antiprotons will rip these pairs apart, stealing their positrons to create neutral antihydrogen atoms.

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

WE PREDICT that anti-matter posses a negative gravitational potential and will “fall up” based on the theoretical model presented in  “The Imagineer’s Chronicles" and the paper "The Shadows of four *spatial* dimensions"

In the article "Defining gravity" Dec. 15, 2007, we derived mass and its 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 also 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

(In a PDF format)

We have shown throughout "The Imagineer’s Chronicles" observations of our environment indicate the universe is composed of four *spatial* dimensions rather than four-dimensional space-time as is suggested by Einstein’s theories.

The recent discovery of Dark energy is one of those observations.

As Alexey Vikhlinin of the Smithsonian Astrophysical Observatory in Cambridge, Mass. wrote in the Scientific Frontline article Dark Energy Found Stifling Growth in Universe Dec 16, 2008:

This "study strengthens the evidence that dark energy is the cosmological constant.  Although it is the leading candidate to explain dark energy, theoretical work suggests it should be about 10 raised to the power of 120 times larger than observed. 

Putting all of this data together gives us the strongest evidence yet that dark energy is the cosmological constant, or in other words, that ‘nothing weighs something’," said Vikhlinin.  "A lot more testing is needed, but so far Einstein’s theory is looking as good as ever."

But the fact that Dark Energy or a Cosmological constant was discovered does not alter the fact Einstein introduced it because he was trying to make or "force" the universe conform to his expectations, rather than using his theory to guide him to an understanding of its properties.

However, it can be shown that its existence can be seamlessly integrated into a relativistic theory based on four *spatial* dimensions.

In the article "Why Space-time?" Sept. 27, 2007 it was shown it is possible to explain and predict the observed relativistic properties space, time, mass and energy in terms of the geometry of four *spatial* dimensions.

Additionally it was show in the article “Gravity” Dec 15, 2007 it is possible to consistently define all the observed properties of gravity including its equivalence to an accelerated reference frame in terms of a curvature in "surface" of a three-dimensional space manifold with respect to a fourth *spatial *dimension.

However, theoretically defining the universe in terms of four *spatial* dimensions as we have done in "The Imagineer’s Chronicles" and the paper The "Shadows" of four *spatial* dimensions means one does not have to "force" the integration of Dark energy or a cosmological constant into its theoretical structure as Einstein had to do to integrate it into Relativity.

If a gravity is a result of a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension, as we are suggesting then when stars convert mass to energy in nuclear reactions the magnitude of that curvature would decrease.  However, this would result in the expansion of a "surface" three-dimensional space with respect to a fourth *spatial* dimension analogous to how removing the coils or curvature in a rope causes a physical expansion of its two dimensional length when measured with respect to three-dimensional space.

But this expansion would be in addition to the expansion associated with the big bang therefore, it would be perceived as acceleration.

Additionally the article “Defining energy“ Jan. 15, 2009 showed one could also derive the temperature or kinetic energy of particles in terms of a curvature in "surface" of a three-dimensional space manifold.  Therefore, a second component of dark energy would be related to an energy reduction related to the cooling of the universe because it would also cause a decrease the magnitude of that curvature and an expansion of a three-dimensional volume.  Again, this expansion would be perceived as acceleration because it would be viewed in addition to the expansion associated with the big bang.

In other words, one can use a relativistic theory on based on the existence of four *spatial* dimensions to guide them to an understanding of the properties of Dark Energy or a cosmological constant rather than basing it on expectations as Einstein had to.

The reason he could not is that a reduction in a curvature of three-dimensional space with respect to time does not have spatial expansive properties associated with Dark Energy.  Therefore, a reduction of mass by its conversion to energy could not account for the observed spatial properties of dark energy.

One could quantify the magnitude of dark energy by calculating the magnitude of the reduction in the curvature of space based on the reduction in mass by the nuclear reactions in stars and the loss of kinetic energy due to the cooling due to the expansion of the universe.

This is because, according to this theoretical model its magnitude would be proportional to the quantity of mass/energy the universe losses due to the nuclear reactions and the cooling due to its expansion.

However, the "concentration" of Dark Energy relative to gravitational energy would be defined by the experimentally confirmed equation E=mc^2.  This means its strength should be 1/c^2 weaker than gravitational forces.  Therefore, because gravitational forces are much stronger than those of dark energy, the space between gravitationally bound objects would not appear to be expanding.

Additionally, this is the reason its magnitude, as mentioned in the article "Dark Energy Found Stifling Growth in Universe" is about 10 raised to the power of 120 times smaller than predicted by many theories. 

Therefore, because of the relative weakness of dark energy relative to gravitational, its force would not affect objects that have relatively strong gravitational bonds such as galaxies or planetary systems.  However, it would affect the overall expansion of space between ones in which the gravitational bonds are not as strong, such as the void between galaxies.

Additionally it would also explain why the rate of acceleration appears to be increasing and predicts there should be a crossover point where it exceeds the gravitational deceleration caused by the mass density of the universe.  As the universe expands due to the energy of the big bang it mass density decreases and therefore the accelerative properties associated with mass being converted to energy would be a larger in proportion to the decelerative gravitational forces. 

Therefore, this mechanism predicts there should be a point in time where the accelerations due to a conversion of mass to energy should exceed the decelerative influence of the mass of the universe.

However, contrary to what Alexey Vikhlinin said in the article Dark Energy Found Stifling Growth in Universe, this means that "so far Einstein’s theory" Not "is looking as good as ever" because there is a alternative theory that can, as mentioned earlier explain and predict all previous predictions made by his theories regarding relative motion and accelerated reference frames while at the same time incorporating the new observation regarding Dark Energy which his theories cannot.

Later Jeff

The "Shadows" of four spatial dimensions

Copyright 2009 Jeffrey O’Callaghan

(In a PDF format)

Many physicists assume based on the General Theory of Relativity the mass of larger stars that have used up their nuclear fuel will implode to form a singularity or black hole.  (A singularity is defined as region of space in which mass is concentrated in a one-dimensional point in space and whose gravitational field is so great that neither light nor time can escape.)

However, the time dilatation it predicts would be caused by a gravitational field indicates mass must maintain a quantifiably finite volume which is greater that a one-dimensional point.

Einstein in his General Theory of Relativity predicted time is dilated or moves slower when exposed to gravitational field than when it is not.  Therefore, according to Einstein’s theory a gravitational field, if strong enough it would stop time.

In 1915, Karl Schwarzschild discovered that according to Einstein’s General Theory of Relativity the gravitational field associated with the mass of a star greater than approximately 2.0 times a solar mass would stop the movement of time if it collapsed to a singularity.  He also defined the critical circumference or boundary in space around a singularity where the strength of a gravitational field will result in time being infinitely dilated or slowing to a stop.

In other words as a star contacts and its circumference decreases, the time dilation on the surface of the mass associated with that stars gravitational field will increase.  At a certain point the contraction of that mass will produce a gravitational field strong enough to stop the movement of time.  Therefore, the critical circumference defined by Karl Schwarzschild is a boundary in space where time stops relative to the space outside of that boundary.

This critical circumference is called the event horizon because an event that occurs on the inside of it cannot have any effect on the environment outside of it.

Many physicists believe the existence of a singularity is an inevitable outcome of Einstein’s General Theory of Relativity.

However, it can be shown using the concepts developed by Einstein; this is not true.

In Kip S. Thorne book "Black Holes and Time Warps", he describes how in the winter of 1938-39 Robert Oppenheimer and Hartland Snyder computed the details of a stars collapse into a black hole using the concepts of General Relativity.  On page 217 he describes what the collapse of a star would look like, form the viewpoint of an external observer who remains at a fixed circumference instead of riding inward with the collapsing stars matter.  They realized the collapse of a star as seen from that reference frame would begin just the way every one would expect.  "Like a rock dropped from a rooftop the stars surface falls downward (shrinks inward) slowly at first then more and more rapidly.  However, according to the relativistic formulas developed by Oppenheimer and Snyder as the star nears its critical circumference the shrinkage would slow to a crawl to an external observer because of the time dilatation associated with the relative velocity of the star’s surface.  The smaller the circumference of a star gets the more slowly it appears to collapse because the time dilation predicted by Einstein increases as the speed of the contraction increases until it becomes frozen at the critical circumference.

However, the time measured by the observer who is riding on the surface of a collapsing star will not be dilated because he or she is moving at the same velocity as the surface of that star.

Therefore, the proponents of singularities say the contraction of a star can continue until it becomes a singularity because time has not stopped on its surface even though it has stopped to an observer who in remains at fixed circumference to that star.

But one would have to draw a different conclusion if one viewed time dilation in terms of the gravitational field of a collapsing star instead of in terms of the velocity of the contraction.

Einstein showed that time is dilated by a gravitational field.  Therefore, the time dilation on the surface of a star will increase relative to an external observer as it collapses because, as mentioned earlier gravitational forces at its surface increase as its circumference decrease.

This means, as a star nears its critical circumference its shrinkage slows with respect to an external observer who is outside of the gravitation field because the increasing strength of its gravitational field causes a slowing of time on its surface.  The smaller the star gets the more slowly it appears to collapse because the gravitational field at its surface increase until time becomes frozen for the external observer at the critical circumference.

Therefore, the observations an external observer would make using conceptual concepts of Einstein’s theory regarding time dilation caused by the gravitational field of a collapsing star would be identical to those predicted by Robert Oppenheimer and Hartland Snyder in terms of the velocity of its contraction.

However, Einstein developed his Special Theory of Relativity based on the equivalence of all inertial reframes which he defined as frames that move freely under their own inertia neither "pushed not pulled by any force and therefore continue to move always onward in the same uniform motion as they began".

This means that one can view the contraction of a star with respect to the inertial reference frame that, according to Einstein exists in the exact center of the gravitational field of a collapsing star.

(Einstein would consider this point an inertial reference frame with respect to the gravitational field of a collapsing star because at that point the gravitational field on one side will be offset by the one on the other side.  Therefore, a reference frame that existed at that point would not be pushed or pulled relative to the gravitational field and would move onward with the same motion as that gravitational field.)

The surface of collapsing star from the view point of an observer who is at its center would look according to the field equations developed by Einstein as if the shrinkage slowed to a crawl as the star near its critical circumference because of the increasing strength of the gravitation field at the surface of the star relative to its center.  The smaller the star gets the more slowly it appears to collapse because the gravitational field at its surface increases until time becomes frozen at the critical circumference.

Therefore, because time stops or becomes frozen at the critical circumference for both an observer who is at the center of the clasping mass and one who is at a fixed distance from its surface the contraction cannot continue from either of their perspectives.

However, Einstein in his general theory showed that a reference frame that was free falling in a gravitational field could also be considered an inertial reference frame.

As mentioned earlier many physicists assume that the mass of a star implodes when it reach the critical circumference.  Therefore, the surface of a star and an observer on that surface will be in free fall with respect to the gravitational field of that star when as it passes through its critical circumference.

This indicates that point on the surface of an imploding star, according to Einstein’s theories could also be considered an inertial reference frame because an observer who is on the riding on its surface will not experience the gravitational forces of the collapsing star.

However, according to the Einstein theory of relativity, as a star nears its critical circumference an observer who is on the stars surface will perceive the differential magnitude of the gravitational field relative to an observer who is in an external reference frame to be increasing.  Therefore, he or she will perceive time in those reference frames that are not on its surface slowing to a crawl as it approaches the critical circumference.  The smaller the star gets the more slowly time appears to move with respect to an external reference frame until it becomes frozen at the critical circumference.

However, the contraction of a stars surface must be measured with respect to the external reference frames in which it is contracting.  But as mentioned earlier Einstein’s theories indicate time on its surface would become infinitely dilated or stop in with respect to reference frames that were not on its as it nears its critical circumference. 

Therefore, if time stops on the surface of a collapsing star from the perspective of all observers when viewed in terms of the gravitational forces it cannot move beyond the critical circumference because motion cannot occur in an environment where time has stopped.

This contradicts the assumption made by many that the implosion would continue for an observer who was riding on its surface.

Therefore, based on the conceptual principles of Einstein’s theories relating to time dilation caused by a gravitational field a collapsing star it cannot implode to a singularity as many physicists believe and must maintain a quantifiable minimum volume which is equal to or greater than the critical circumference defined by Karl Schwarzschild.

This means either the conceptual ideas developed by Einstein are incorrect or there must be an alternative solution to the field equations based on the general theory of Relativity that many physicists used to predict the existence of a singularity because the theoretical predications made by them regarding its existence are contradictory to the concepts contained in Special Relativity.

We are not saying that black holes do not exist however we are saying that according to the concepts of Relativity a singularity is NOT an inevitable outcome of Einstein’s General Theory of Relativity.  In otherwords the mass of a star greater than approximately 2.0 times a solar mass may not collapse to a singularity but only to a finite volume equal to its event horizon.

Only observations can determine which one is correct because both are based on the validity of the concepts presented in Einstein’s theories and the mathematical equations he developed.

Later Jeff

The "Shadows" of four spatial dimensions

Copyright 2008 Jeffrey O’Callaghan

(In a PDF format)