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

One is that it would allow for the integration of the quantum and wave properties of matter and energy in terms of the classical laws of three-dimensional space.

In 1924 Louis de Broglie was the first to theorize that all particles are, in part composed of a transverse wave.  In his paper, “Theory of the double solution“ he attempted to define a causal interpretation of their wave properties in the classical terms of space and time.  He later abandoned it in the face of the almost universal adherence of physicists to the theories presented by Born, Bohr, and Heisenberg regarding the uncertainties and probabilistic interpretation of quantum particles.

One of the difficulties he may have faced in this endeavor is that he assume along with most other scientists of his day the universe was composed of four-dimensional space-time.

This presented a problem because observations of a space-time environment indicate that a time dimension can only move in one direction, forward.  Therefore, it could not support bidirectional movement required for the propagation of a transverse wave. 

However, if he had assumed, as we have done in The Imagineer’s Chronicles the universe was composed of four *spatial* dimensions he may have been able to define the transverse wave properties of particles in terms of sinusoidal oscillations or displacements in a "surface" of three-dimensional space with respect to a fourth *spatial* dimension.

Classical mechanics tells us transverse oscillations in a surface of water will form resonant systems or structures that when view from distance would appear to be made up of discrete units of water with finite boundaries.

Summarily, if the microscopic transverse waves theorized by de Broglie were a result of oscillations in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension he have been able to, as was shown in the article "Why is mass and energy quantized?" Oct. 4, 2007 define their particle properties by extrapolating the laws of classical resonance in three-dimensional space to a fourth *spatial* dimension.

He then could have defined a causal interpretation of the Quantum Mechanical equation for a particles energy; E=hv (where "h" is Planck’s constant "v" is a particles frequency and "E" is the magnitude or its energy)

Classical mechanics tells us that the energy of a resonant system is quantized in terms of multiples of the harmonics of the fundamental frequency of its environment. 

Therefore, he could have interpreted the equation E=hv as defining the quantization of a particle’s energy in terms of a resonant system with a fundamental harmonic "h" of an environment consisting of four *spatial* dimensions..

However, this would have also allowed him to define a casual mechanism responsible for Planck’s constant, the uncertainty principal and the probability functions of Quantum Mechanics by extrapolating the three-dimensional laws of classical resonance to four *spatial* dimensions.

As mentioned earlier, a classical interpretation of Planck’s constant would be that it defines magnitude of the incremental energy deference between harmonics of a resonant frequency of four *spatial* dimensions.

This means there would be an inherent uncertainty in one’s ability to define the exact position or momentum of a particle because it would be distributed over the finite volume associated with the wavelength of its resonant frequency.  Therefore, one could only define its specific position or momentum in terms of an uncertainty related to where relative to its wavelength an observation is made.

The reason why quantum mechanics must rely on probably functions to define particle interaction is because they are composed of waves that do not have a ridged structure.  Therefore, because their wave components vary with time one can only define their interactions in terms of a probably function related to how their time varying wave components would interact.

This shows that one can explain and predict all of the quantum mechanical properties of particle if one assumes they are made up of transverse waves in the classical terms of the geometry of four *spatial* dimensions.

However, as mentioned earlier this cannot be done if one assumes space it made up of four-dimensional space-time because its geometry cannot support the transverse wave properties Louis de Broglie associated with particles.

Later Jeff

The "Shadows" of four *spatial* dimensions

Copyright 2009 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)

Articles posted  2009 in 2008, and 2007

The purpose this blog is to show it is more consistent with observations to define the universe in terms of the existence of four *spatial* dimensions than four-dimensional space-time.

Your comments will be appreciated.

Thank you

Jeff

Articles posted  2009 in 2008, and 2007

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)