We have shown in "The Imagineer’s Chronicles" one can define a universe in terms of the existence of four *spatial* dimensions in a manner that makes predictions identical to those of both the General and Special Theories of Relativity while at the same time describing the theoretical advantages to doing so.

One of these is that it would allow for the development of a theoretical interpretation of the Heisenberg’s Uncertainty Principal in terms of the laws Classical of Physics.

The Heisenberg Uncertainty Principle states that certain pairs of physical properties, like position and momentum, cannot both be known to arbitrary precision. That is, the more precisely one property is known, the less precisely the other can be known. This is not a statement about the limitations of a researcher’s ability to measure particular quantities of a system; it is a statement about the nature of the system itself as described by the equations of quantum mechanics.  According to the uncertainty principle, it is, for instance, impossible to measure simultaneously both position and velocity of a microscopic particle with any degree of accuracy or certainty.

In the article "Why is mass and energy quantized?" Oct 4, 2007 it was shown one can theoretically derive the properties of a particle in terms of a classically resonating system if one assumes it is a result of matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  Additionally, it was showed why all energy exists in these resonant systems and therefore is quantized.

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

(In a latter article "The geometry of quarks" it will be shown how and why quarks join together to form these resonant systems in terms of the geometry of four *spatial* dimensions.)

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

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

However, these oscillations in a "surface" of a three-dimensional space manifold, according to classical mechanics would generate a resonant system or "structure" in space.  These resonant systems are known as particles.

The only way to dampen the frequency of a classically resonating system is to add or remove energy from it, which results in changing the characteristics of that system. 

Additionally the energy in a classically resonating system is discontinuous and can only take on the discrete values associated with its fundamental or harmonic of its fundamental frequency.

However, these properties of a classically resonating system are the same as those found in a particle in that they are made up of discreet or discontinuous packets of mass/energy and when energy is either added or removed from it, its characteristics change. 

The reason why we do not observe energy in its continuous wave form is that, as mentioned earlier all energy is propagated through space in the discrete components associated with its resonant structure. Therefore, when observing the energy of a wave function it would appear as though its energy was concentrated in a single point in space associated with the center of its resonant structure.

This is analogous to how the potential 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. 

However, this also defines a Classical reason for the validity of Heisenberg’s Uncertainty Principle, which states that certain pairs of physical properties, like position and momentum, cannot both be known to arbitrary precision.

Classical wave mechanics tells us a wave’s energy is instantaneously constant at its peaks and valleys or the 90 and 270-degree points as its slope changes from positive to negative while it changes most rapidly at the 180 and 360-degree points.

Therefore, the precise position of a particle could be only be defined at the peaks and valleys of the matter wave responsible for its resonant structure because those points are the only place where its energy or "position" is stationary with respect to a fourth *spatial* dimension.  Whereas its precise momentum would only be definable with respect to where the energy change or velocity is maximum at the 180 and 360-degree points of that wave.  All points in between would only be definable in terms of a combination of its momentum and position.

However, to measure the exact position of a particle one would have to divert or "drain" all of the energy at the 90 or 270-degree points to the observing instrument leaving no energy associated with its momentum left to be observed by another instrument.  Therefore, if one was able to determine precise position of a particle he could not determine anything about its momentum. Similarly, to measure its precise momentum one would have to divert all of the energy at the 180 or 360 point of the wave to the observing instrument leaving none of its position energy left to for an instrument trying to measure it position.  Therefore, if one was able to determine a panicles exact momentum one could not say anything about its position.

The reason we observe a particle as a point mass instead of an extended object is because, as mentioned earlier the article "Why is mass and energy quantized?" showed its energy must be packaged in terms of its resonant frequency.  Therefore, when we  observe or "drain" the potential energy continued in its wave function it will appear to come form a specific point in space similar how the potential energy of water flowing down a sink drain appears to be coming from a "point" source with respect the extended volume of water in the sink.

As mentioned earlier, all points in-between are a dynamic combination of both position and momentum.  Therefore, the degree of accuracy one chooses to measure one will affect the other.  For example, if one wants to measure the position of a particle to within a certain predefined distance "m" its wave energy or momentum within that distance will "move" or change by an amount defined by its wave function or the energy change within that distance or ("m"kg / s).  Summarily if one wants to measure the momentum ("m"kg / s) of a particle in a predefined volume or distance ”m" its position will change within that distance.

However, because of the dynamic interaction between the position and moment component of the matter wave responsible for generating the resonant system associated with a particle defined in the article  "Why is mass and energy quantized?" the change or uncertainty of one with respect would be defined by the product of those factors or m^2 kg / s

This defines the reason in terms of Classical Wave Mechanics for Heisenberg uncertainty principal and why it has the units of m^2 kg / s

Later Jeff

The "Shadows" of four spatial dimensions

Copyright Jeffrey O’Callaghan 2010

(In a PDF format)

or the discrepancy between the worldview implied by the accuracy of modern quantum mechanics and our Common sense (Sept. 1, 2008) understanding of reality is due to the incompleteness of its theoretical structure.  

The strangeness of the quantum mechanical worldview is exemplified by the fact that it defines reality only in terms of probabilities.

However, its absurdity arises from the fact, as Heisenberg one of the founding fathers of quantum mechanics put it "atoms or elementary particles themselves are not real but are forms of world probability or possibilities rather than things or facts".

Quantum mechanics defines the probability of finding a particle in given region in terms of Schrödinger’s wave function or equation.  However, according to the Copenhagen‎ interpretation it only defines the probability of particle being there.  Therefore, it assumes it only comes into existence after one observes it.

The reason is before it is observed it existed only as a wave function with an extended spatial environment.  Therefore, it did not have the properties of a particle.  However, after one observes it a particle appears in a compact region space while the wave function that was in that region collapses or disappears.  Therefore, quantum mechanics assumes that the act of observing a wave function is the causality of a particles existence.

However, one can define a perfectly logical reason why the act of observing the wave function results in its collapse and the formation of particle by extrapolating the laws Newtonian mechanics to four *spatial* dimensions.

The earlier article "Why is mass and energy quantized?" Oct. 4, 2007 showed that one can derive the existence of a particle in terms of a classically resonating system or "structure" formed by matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension.  Additionally it was showed all energy exists in resonant systems and therefore must be quantized. 

This would solve the Enigma as to what is waving in the wave function by defining the medium supporting it in terms of space itself.  This is because, as was shown in that article the vibrations of three-dimensional space with respect to a fourth *spatial* dimension is responsible for the both wave and resonant structure that defines a particle’s energy and wave function.

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 wave function at points corresponding to them 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?" a particle is defined by the energy of its resonant structure.  Therefore, when one looks at a particular spot within the confines of a wave function one would either find a particle or nothing at all because the volumes between its peaks and troughs would not contain enough energy to allow its resonant structure to be redirect towards an observer. 

This is analogous to how the potential 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. 

Additionally, the fact that a particle is made up of the energy of its wave function means they both cannot exist at the same time.  Therefore, if one chooses to observe it as a particle such as an electron one would not be able to observe its wave properties because the energy associated with it would be redirected towards the observer from a specific point in space.  However if one chooses to observe its wave properties, such as the diffuse orbit of an electron around a nucleus one could not observe it as a particle because its energy is contained in the diffuse environment of the electrons orbit.

This means contrary to the Copenhagen‎ interoperation the act of observing a wave function does not create a particle but only transforms or redirects its energy from a specific point within the extended spatial environment associated its wave function. 

In other words, when we observe a wave function, we are not causing its collapse while creating a particle but only redirecting its wave energy from a compact source within the confines of that wave function.  The reason it appears as a particle is that its energy is observed to be originating from a specific point within the confines of the wave function that is observed.

This is analogous to how one can change the form of water from a solid to a liquid or vice versa by either cooling or heating it.  However, the act of cooling or heating water does not create anything that was not there before it just changes the form of the water from a liquid to a solid.

This also explains why, in classical terms a particle appears to be simultaneously in many places at one time within the confines of its wave function because it shows its position relative to that volume would be dependent on where one observed its wave function.  In other words, a wave function contains only one not multiple copies of a particle whose position within the wave function is defined by where one chooses to observe it. 

It also defines the randomness of quantum mechanics in classical terms because it shows the probability of finding a particle in a specific point in space would depend on where in the time varying environment of a wave function an observer made contact with it.  Since an observer is unable to view a wave function before his or her instruments interacted with it he or she could only determine the probably of where a particle will appear in its extended spatial environment.

Additionally, it defines a classical reason why consciousness appears to play a role in the outcome of an observation.  If one chooses to view an electron orbiting an atom from afar, so to speak he or she would only "see" the interference pattern generated by wave function.  However, if one chose to measure where it was he or she only would “see” it as a compact or point source called a particle centered within the volume defined by the peaks and troughs of its wave function.

Finally, it defines why how we chose to observe a quantum system effects what we observe.  For example, if chose to look at a specific region of space occupied by a wave function we will not be able to see the interference that it causes because, as mentioned earlier the act of observing it causes its energy to be redirected to a particle format.  Therefore, we will only be able to observe quantum or particle properties associated with its energy.  However, if we chose not to look in a specific region of space and just observe the wave function we will always observe the interference associated with its wave properties.

This shows that one can derive a classical common sense explanation of the wave particle duality of existence if one assumes, as we have done in the article "Why is mass and energy quantized?" that the quantum mechanical properties of nature are the caused by 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.   Additionally, it completes the theoretical structure of quantum mechanics by providing an answer to the quantum enigma of why the conscience actions or awareness of an observer appear to affect physically reality as is demanded by the Copenhagen interpretation.

Later Jeff

The Shadows of four spatial dimensions

Copyright Jeffrey O’Callaghan 2010

(In a PDF format)

In physics and cosmology, the anthropic principle is a way of understanding why the observations of our physical universe must be compatible with the life.  Many feel it is the only way to explain the observations that the laws of nature and its fundamental physical constants remarkably take on values that are consistent with conditions for existence of life, as we know it.  It states that this apparent coincidence is actually a necessity because living observers would not be able to exist, and hence, observe the universe, were these laws and constants not constituted in this way. 

However, there may be another reason why they take on these values.

We have shown throughout The Imagineer’s Chronicles that all forms of mass and energy including life are related to the existence of four *spatial* dimensions instead of four dimensional space-time

For example, in the article "Why Space-time?" Sept 27, 2007 we conceptually derived the laws governing the relativistic properties of motion, space, time, gravity and its equivalence to acceleration in terms of a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

While the articles "The geometry of quarks" Mar. 1, 2009 and "Why is mass and energy quantized?" Oct. 4, 2007 showed the laws governing the properties of particle are also related to the existence of four *spatial* dimensions.

However, this provides a testable mechanism for defining the why the fundamental physical constants of nature support life based on the existence of only four *spatial* dimensions.  It is testable because we have assumed that each of the four *spatial* dimensions have unvarying identical properties.  Therefore, there can only be one solution using these ideas, which must define what we observer the universe to be.

However there are multiple solutions regard the physical constants of the universe if one assumes the universe is composed of four-dimensional space-time because the integration of space and time defined by Einstein do not allow for defining an invariant relationship between them.

For example, the two-dimensional "surface" of a balloon stretches and curves uniformly as it moves in three-dimensional space.  Similarly the "surface" of three dimensional space would curve and stretch uniformly as it moves in fourth *spatial* dimensions

As was shown in the article “Why Space-time?“ the movement of a "surface" of a three-dimensional space manifold though a fourth *spatial* dimension would define the physical constants associated with gravitational and accelerated reference frames.  This is analogous how the movement of a balloons surface through three-dimensional space defines its physical constants.

In the article “The geometry of quarks” it was shown the fundamental constants associated with the 2/3 fractional charge of the Up, Charm and Top is related to the energy directed along a "surface" of a displaced three-dimensional space manifold with respect to a four *spatial* dimension while those of the -1/3 charge of The Down, Strange and Bottom is associated with the energy that is directed perpendicular to that "surface".  Therefore, because quarks are the fundamental components of particles one should be able, using those concepts to derive the fundamental constants governing particle formation and why they interact with an environment of four *spatial* dimensions to generated life as we know it.

In other words it may not be a coincidence that the laws of nature are such that they support life it may be the fact that the existence four-dimensional space will only support the laws of nature that allow life to form in it.

However, this would mean science would not have to rely on the Anthropic principle to understand why the fundamental physical constants our universe are such that they support life because it may be an inevitable outcome of the existence of only four *spatial* dimensions.

Later Jeff

The "Shadows" of four spatial dimensions

Copyright Jeffrey O’Callaghan 2010

(In a PDF format)

We have shown throughout The Imagineer’s Chronicles there would be many theoretical advantages to defining the universe in terms of four *spatial* dimensions instead of four-dimensional space-time.

One of them is it would allow for a common theoretical explanation of gravity and how space is expanding.

In 1915, Albert Einstein wrote the General Theory of Relativity, which defined how gravity works.  He showed that gravity could be explained in terms of a curvature in a "surface" of a four-dimensional space-time manifold. 

However, when he applied his theory to the whole universe, he found that it predicted space should not be stable.

Later, in 1929 Edwin Hubble determined the redshifts of a number of distant galaxies and their relative distances and found it increased as a linear function of their distance.  The only explanation for this observation is that the universe was expanding.

These observations made by Hubble confirmed Einstein theoretical predictions that his four-dimensional space-time geometry was unstable and that it was expanding.  However, neither he nor Einstein could define how or in what direction this expansion was occurring.

This is because Hubble’s observation showed three-dimensional space was not expanding through a time dimension but in a spatial one.  Therefore, one must add dimensions to Einstein’s gravitational theory to explain how three-dimensional space can be undergoing a uniform spatial expansion.

However, if one could, as done in the article "Defining gravity" Dec 15, 2007 define it and the relativistic properties of motion, as was done in the article "The relativity of four *spatial* dimensions" Dec. 01, 2007 in terms of a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of one in a four-dimensional space time manifold one could replace the time dimension with a spatial one.

But if true one should also be able to explain how and why the expansion of the universe is so uniform in terms of four *spatial* dimensions. 

As was shown in the article “Embedded Dimensions" Oct. 24, 2007 each axis of three-dimensional space is scalar invariant with respect to a fourth *spatial* dimension.  Therefore, the movement of any point in three-dimensional space with respect to a fourth *spatial* dimension would result in the expansion of three-dimensional space around that point. 

One way of understanding how this would be to compare it to the expansion of a balloon’s surface. 

As a balloon is inflated, the length and width of its surface expands around a point on it.  However, the magnitude of this expansion is not defined by its movement through three-dimensional space but by the bending or curvature caused by its movement in it.  This is illustrated by the fact that the surface of a balloon only stretches when its curvature is increased by inflation and not when one moves it in its entirety to a different point in space.

This shows that the expansion of each axis of the surface of a balloon is scalar invariant with respect to its movement in a third dimension.

A similar effect would occur if three-dimensional space were scalar invariant with respect to a fourth *spatial* dimension.  Its movement "outward" with respect to a fourth *spatial* dimension would result in a uniform stretching of the three-dimension around a point in three-dimensional space.

Therefore, one could understand how space is expanding and eliminate the problem of having to explain why, as mentioned earlier it is so uniform if one assumes three-dimensional space is expanding towards a fourth *spatial* dimension and that it’s individual axes are scalar invariant with respect to it.

However, this also provides a theoretical connection gravity and the observed properties of an expanding universe because it defines both in terms of a common mechanism related to the existence of a fourth *spatial* dimension.  This is  because if three-dimensional space is scalar invariant with respect to a four *spatial* dimension, the movement of a point in three-dimensional space "inward" with respect to it would result in its "contracting" spherical along all three-dimensional axis.  This contraction would result in a force being directed towards its center, which can be shown, as was done in the article “Gravity in terms of four *spatial* dimensions” Jun 01, 2009 to be responsible for gravity.

This cannot be done as mentioned earlier if one assumes as Einstein did that gravity is caused by a curvature in a space-time manifold because one cannot define the spatial expansion of the universe in terms of only three spatial and one time dimension.

Later Jeff

The *Shadows* of four spatial dimensions

Copyright 2010 Jeffrey O’Callaghan

(In a PDF format)

We have shown throughout "The Imagineer’s Chronicles" there are many theoretical advantages to defining the universe in terms of four *spatial* dimensions instead of four-dimensional space-time.

Understanding the origins of the force called of Dark Energy is one of them.

On May 30, 2009, "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."

It also mentioned some researchers suggest Dark Energy is caused by a uniform sea of quantum zero-point energy.  However the problem with this proposal is the zero-point energy density would have to be precisely tuned to a value that is an unbelievable factor of 10¹²⁰ below the theoretical prediction and as of yet no one has been able give a reason why that is consistent with theory.

While others have suggested that it would possible to modify Einstein General Theory of Relativity to incorporate, Dark energy, or a cosmological constant into its theoretical structure.

However, Einstein, because of his preconceived feeling that the universe was static has already tried to integrate a mechanism into it to counter the destabilizing forces of gravity.  He realized a static universe is not sustainable in General Relativity because if the universe were static at one instance in time, then gravity, due to its attractive properties would cause it to collapse.  Therefore, he added a term to it that would counteract it. 

This term, which effectively gives the vacuum a repelling force similar to that of dark energy, came to be called a cosmological constant.

However, he could not develop a theoretical argument to justify incorporating it.  Therefore, to satisfy his preconception that the universe was static he simply added it in an "adhoc" manner.

But if its author could not modify the General Theory of Relativity to incorporate an accelerative force into its theoretical structure it would seem highly unlikely that anyone else would be able to, as was suggested in the "physicsworld.com" article.

However, it may be possible to understand the origins of Dark Energy and theoretically integrate it with gravity if one defines their casualty in terms of the existence of four *spatial* dimensions instead of four dimensional space-time.

We have shown throughout "The Imagineer’s Chronicles" that it is possible to theoretically define a universe in terms of four *spatial* dimensions in such a manner that makes predictions identical to those of Einstein’s theories.  However, unlike his theories it would allow for the seamless integration of the properties of dark energy into its theoretical structure.

Observations of Dark Energy indicate it opposes gravity and that it is causing a *spatial* not a time component of the universe to expand.

The article “Defining energy" Nov. 26, 2007 showed one could theoretically derive all forms of energy including gravitational in terms of a curvature or deformation in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

(This curvature is analogous to a curvature in a four dimensional space-time manifold Einstein predicted was responsible for gravity.)

However, 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.  Since this expansion would be in addition to the expansion associated with the Big Bang, it would be perceived as an acceleration.

Additionally the article ”Defining energy" 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 with respect to a fourth *spatial* dimension.  Therefore, as the universe cools the magnitude that curvature would decrease and cause three-dimensional space where that cooling took place to expand for the same reason as a conversion of mass to energy does.  This expansion would be perceived as an acceleration because it would be viewed in addition to the linear expansion associated with the big bang.

This demonstrates 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 rather than basing it on expectations as Einstein had to.

The reason Einstein could not integrate it into his theories was that time or a space-time dimension does not have spatial properties required to support the spatial expansion associated with Dark Energy.

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

One can also use a theoretical model based on the existence of four *spatial* dimensions to understand why the rate of acceleration appears to be increasing and predicts there should be a crossover 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 its mass density decreases, therefore the accelerative properties associated with mass being converted to energy would be larger in proportion to the decelerative gravitational forces. 

This shown that one can seamlessly integrate the observed properties of Dark Energy into a relativistic theory based on the existence of four *spatial* dimensions and why one cannot based four-dimensional space-time.

Later Jeff

The "Shadows" of four spatial dimensions

Copyright Jeffrey O’Callaghan 2009

(In a PDF format)

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)

to completely define the reality of our universe?

Einstein was able to define the relativistic properties of motion and the equivalence of gravitational and accelerated reference frames in terms of the geometry of space-time.  However, as Lee Smolin mentions in Chapter Three (page 49) of his book "The Trouble with Physics" he was unable to physically connect them to electromagnetic energy. 

Einstein himself acknowledges this when he said, "I have often tortured my mind in order to bridge the gap between gravitation and electromagnetism.”

One of the reasons may be because electromagnetism is observed to have the bi-directional spatial properties of a transverse wave while Einstein defines gravity in terms of a time component of a space-time dimension.  However, time is observed to move only in one direction forward therefore it is difficult to explain the bi-directional spatial properties of the transverse wave associated with electromagnetism in terms of space-time geometry.

But as Lee Smolin also mentions (page 39) Gunnar Nordstrom discovered electromagnetism "pops out" of Einstein’s theory if one increases the dimensions of space by one.  In other words, just by adding an extra dimension of space you get a unification of gravity with electromagnetism that was consistent with Einstein’s Special Theory of Relativity."

However, Einstein’s theories predicted that light would be bent by gravity while Nordstrom’s did not. 

In 1919, Arthur Eddinngton observed that light was bent by gravity thereby verifying that Einstein’s theory was more consistent with observations and that gravity was not the result of an extra dimension as Nordstrom had postulated.

Since then there have been many attempts to unite gravity with electromagnetism simply by adding dimensions to Einstein’s space-time manifold.

The most promising of these is called string theory, which attempts to define all of the observed properties of our universe in terms of as many as ten dimensions.

However, as is pointed out on page 51 of "The Trouble with Physics" all attempts at unifying physics through extra dimensions suffer from the same problem.  There are a few solutions that lead to the world we observe but there are many which do not.  One has to set the initial conditions, which are found by observing our world to determine which solutions define what we observe.  The use of the circular methodology means its validity is not based on its theoretical structure but on its flexibility.

But it may be possible to develop a theoretical connection between electromagnetism, gravity and its equivalence to accelerated reference frames if instead of adding a spatial dimension as Nordstrom did to Einstein’s space-time we replace its time component with a spatial one. 

In the article "The "relativity" of four spatial dimensions" Dec 2007 it was shown one can derive a mechanism responsible for the relativistic properties of motion, space, and time in terms of the existence of four *spatial* dimensions in a manner that makes predictions identical to those of Einstein’s Special Theory of Relativity.

While the articles “Defining gravity“ Dec. 15, 2007 "The Equivalence Principal: an alternative" July 15 2008 showed the observed properties of gravity and its equivalence to an accelerated reference frame can be derived in terms of a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension, again in a manner that makes predictions identical to those made in the General Theory of Relativity

Additionally the article "The Photon: a matter wave?" Oct. 1 2007 showed one could derive the wave and quantum mechanical properties of electromagnetism in terms of resonant system or structure formed in space by oscillations or spatial displacements in a "surface" of a three-dimensional space manifold with respect to fourth *spatial* dimension.

This means that one could explain the bi-directional spatial properties of a transverse electromagnetic wave in terms of a spatial displacement in a three dimensional space manifold with respect to a fourth *spatial* dimension caused by the peaks and valleys of a matter wave on its "surface".

However, as mentioned earlier gravity can also be defined in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This suggests that assuming the universe is composed of four *spatial* dimensions instead of four dimensional space-time may allow one to theoretically "bridge the gap between gravitation and electromagnetism".  This is because one can define a common casualty for them in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial*( dimension.

Additionally, if one can derive the quantum mechanical properties of electromagnetism as was done in the article "The Photon: a matter wave?" in terms of a matter wave moving on a "surface" of three-dimensional space manifold with respect to a fourth *spatial* dimension and gravity in terms of a curvature in a "surface" of that manifold it would be bent by the same degree as is predicted by Einstein’s theories.

This means one may not have to increase number of spatial dimensions "in order to bridge the gap between gravity and electromagnetism" as Nordstrom did because, as we have shown in "The Imagineer’s Chronicles" it is possible define a theory that makes predictions identical to those of Einstein’s and define a bridge between gravity and electromagnetism not by adding a dimension but by replacing his time dimension with a spatial one.

Therefore, the answer to the question as to "How many dimensions do we need to completely define the reality of our universe?" may be four.

Later Jeff

The "Shadows" of four spatial dimensions

Copyright Jeffrey O’Callaghan 2009

(In a PDF format)

We have shown throughout “The Imagineer’s Chronicles” there are many theoretical advantages to defining the universe in terms of four *spatial* dimensions instead of four-dimensional space-time.

One is that it allows for defining a common mechanism responsible for 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.

But since its discovery, no one has been able to define a mechanism that can account for its existence in terms of four-dimensional space-time.

However, one can if one assumes the universe is composed of four *spatial* dimension.

In the article “Defining energy” Nov. 26, 2007 it was shown it is possible to derive all forces including gravitational in terms of a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimensions in a manner that makes predictions identical to those made by Einstein theories.

(This curvature is analogous to the curvature in a space-time manifold Einstein theorized was responsible for gravity.)

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

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 or converting mass to energy as is does in the nuclear reaction is stars 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 expansion that occurs in addition to any resulting from the expansive energy associated with the Big Bang therefore it will be viewed as acceleration.

This means that one can explain the causality of forces Dark energy and gravity in terms of a common mechanism related to the geometry 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. 

This is because the relative "concentration" of the forces associated with dark energy and gravity would be defined by the equation E=mc^2" because as mentioned earlier a theory based on four *spatial* dimension makes predictions identical to those made by Einstein theories.  Therefore, because, as that equation shows the expansive effects it has on space are considerably less "concentrated" by factor of c^2 than the contractive forces associated with it would be extremely difficult to observe it between gravitationally bound objects.

However, the expansive forces caused by the conversion of mass to energy in gravitational bound objects would be distributed throughout the entire universe causing its overall acceleration.

This shows that one advantages to defining the universe in terms of the geometry four *spatial* dimensions instead of four dimension space-time is that it would 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

(In a PDF format)

or why do objects in a state of uniform motion tend to remain in that state of motion unless an external force is applied to it.

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

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

Newton’s First Law The Law of Inertia

The property of inertia is one of them.

Newton, in his laws of motion defined how the inertia of an object interacts 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 gravity and the relativistic properties of motion in terms of a four-dimensional space-time manifold but he was unable to define the causality of inertia. 

However, one can define a casual relationship between inertia, mass and forces 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 potential energy 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 magnitude of a force in terms of the slop of a curvature in that surface.

(This curvature is analogous to a curvature in a four-dimensional space-time manifold Einstein theorized was responsible for gravity.)

This means the rest mass or potential energy of an object would be derivable in terms of the magnitude of a displacement caused by a curvature in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Isaac Newton defined inertial as being responsible for why an object at rest will remain at rest, and an object in motion will remain in motion in a straight line at a constant speed, and if a repulsive force acts between two bodies of the same mass, they will acquire equal velocities in equal amounts of time.

However, as mentioned earlier the article "Defining energy" derived potential energy in terms of displacement with respect to a fourth "spatial" dimension of a volume of three-dimensional space.

Therefore, one could define the energy associated with inertia or momentum in terms of a constant or non-curved displacement in a "surface" of a three dimensional space manifold with respect to a fourth spatial dimension.

This means that an object at rest will remain at rest, and an object in motion will remain in motion in a straight line at a constant speed unless the magnitude of that displacement associated with it moment is changed.

As mentioned earlier the article "Defining energy" showed forces are the result of with a curvature in a "surface" of a three-dimensional space manifold.  Therefore, object at rest will remain at rest, and an object in motion will remain in motion in a straight line at a constant speed, unless the displacement of a "surface" of three-dimension space associated with it interacts with the a curvature in that “surface” associated with a force.

The reason a force that acts between two bodies of the with same masses causes them to acquire equal velocities in equal times is because, as was shown in article the "Defining energy" force is the result of a movement of a displacement in three-dimensional space manifold with respect to a fourth *spatial* dimension.  Therefore, if an equal force were applied to two masses in the three-dimension space the displacements associated with those masses would move with equal magnitudes and in opposite directions with respect to a common point in four-dimensional space.

As mentioned earlier article "Defining energy" showed that one can define the magnitude of energy in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, according to the concepts presented here the inertia or momentum of an object would be defined by the sum of two components.  The first would be magnitude of the displacement in a "surface" of a three-dimensional space caused by the curvature associated with the rest mass of an object. The second would be the magnitude of displacement of that surface with respect to a fourth *spatial* dimension caused by the energy of the relative motion of an object.  (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.)

This defines a causal link between the inertia and mass 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 the "surface" of three-dimensional space cannot be displaced with respect to time or a time dimension.

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)