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The Imagineer's Chronicles:
A theoretical blog
Chapter Fifteen
Einstein’s "Theory of Relativity" has been one of the most successful theories in the history of modern science.
It has had remarkable success in explaining and predicting the causality of gravitational forces and the experimentally observed time dilation and mass increase associated with velocities based primarily on the consistency of the velocity of light.
However, it has also had some remarkable failures in that it has been unable to define a mechanism that can simultaneously explain or predict both the quantum properties of mass and the relativistic properties of space and time.
This paper has and will shown that it is possible to explain and predict both the relativistic properties of space, time and the quantum properties of mass and energy in terms of a common mechanism with respect to the geometry of four *spatial* dimensions.
Chapter one postulated that space was composed of four *spatial* dimensions.
Chapter two showed how and why the quantum characteristics of mass could be explained and predicted terms of a resonant "structure" formed by a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension.
This chapter will shown how and why the relativistic properties of space, time, and mass can be explained and predicted in terms of four *spatial* dimensions.
Time is defined only as being a measure of the sequential ordering of the causality of an event and will be linked to each coordinate plane of four-dimensional space by the mathematical and experimentally observed sequential ordering of events that occur in each coordinate plane. It will be shown the geometric properties of four *spatial* dimensions is responsible for time dilation.
Chapter twelve defined gravitational energy and mass in terms of a curvature or displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. The magnitude of the "rest" mass of an object was derived in terms of the magnitude of a curvature or displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
(The curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension this paper postulates is responsible for gravitation force would be analogous to the space-time curvature the "General Theory of Relativity" postulates is responsible for gravitational forces.)
Chapter ten showed a "displacement" in a "surface" of a three-dimensional space manifold with respect to a fourth "spatial" dimension is responsible for all forces and that the magnitude of a displacement in a "surface" of a three-dimensional space manifold determines the magnitude of the force of a system.
Therefore, if the rest mass object is related to a "displacement" in a "surface of a three-dimensional space manifold one should be able define the mass associated with kinetic energy of velocity in terms of a oppositely directed displacement with respect to a fourth *spatial* dimension in that surface.
There is observation evidence to support this conclusion. For example, the kinetic energy of the mass of an orbiting satellite opposes the gravitational energy of the mass it is orbiting.
However, this means that the total displacement of a "surface" of a three-dimensional space manifold caused by mass of a object relative to another object would be the sum of the absolute value of the displacements, with respect to a fourth *spatial* dimension associated with their rest mass and relative velocities.
Therefore, the mass of objects in relative motion increase because one must add the mass associated with the kinetic energy of that motion to its rest mass.
This defines the mechanism responsible for why the mass of an object increases when viewed by an observer who is in relative motion to it in terms of four spatial dimensions..
The following analogy can be used to understand and define the relativistic properties length and time
Assume that two "2 dimensional creatures” are living on the surface of two pieces of paper resting on a desktop.
Also, assume the two creatures can view the surfaces of the other piece of paper, which are separated a pencil.
If the diameter of the pencil is increased, the curvature between the surfaces of the two pieces of paper will increase.
Each of these creatures, when viewing the other piece of paper will only perceive the two-dimensional translation of the three-dimensional curvature generated by the pencil.
Therefore, each will view the distance between two points on the surface of the other as shorter since they will view that distance as a two-dimensional translation of a three-dimensional curvature in the surface of the paper.
Similarly, because three-dimensional beings can only view a three-dimensional translation of a "curvature" or displacement in four *spatial* dimension caused by the motion of an object the distance it moves will be longer with respect to a similar object that is not in motion.
The "movement" of “time” on both surfaces will also be affected.
Each two dimensional creature will view the others “time” as moving slower because the three-dimensional curvature in the paper makes the distance longer than its two dimensional translation. Therefore, it will take longer for events "move" through a curvature in three-dimensional space relative to the time it would take for them to occur if there were no curvature.
As mentioned earlier, time will be defined as only being a measure of the sequential ordering of the causality of an event.
Therefore time will become dilated in reference frames that are in motion because three-dimensional beings can only view a three-dimensional translation of a "curvature" in four *spatial* dimension caused by that motion. This means they will view the distance traveled to be longer than it would be relative to non-curved space. Therefore, time is dilated because it takes longer for events to "move" through curvature in four *spatial* dimensions that it would if there were no curvature.
However, as was mentioned earlier the magnitude of the displacement or the "curvature" an object generates in a fourth *spatial* dimension is dependent on its velocity Therefore the magnitude of the time dilation and the foreshortening of length will be related to its relative velocity of an object.
The velocity of light is constant despite the relative motion of an observer because the foreshortening of the length or distance the light travels is proportional to the motion of the observer. Therefore, the velocity of light will be constant in all reference frames despite the relative velocities of the observers to those reference frames.
It should be remember this scenario applies to all forms of energy including gravitational because, as Chapter ten showed, three-dimensional beings perceive energy in terms of the magnitude of a "curvature" in "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
The Lorentz transformations derived from this theoretical model will take on the same form as the Lorentz transformations derived from Relativity.
This is because this theoretical model postulates that a displacement or curvature in "surface" of a three-dimensional space manifold, with respect to a fourth *spatial* dimension caused by the gravitational or kinetic energy of an object is proportional to the velocity of light.
Therefore, because both Relativity and the above mechanism predict a physical shortening of length and a slowing of time are the result of a "curvature" or displacement in space related velocity of light, the form of the Lorentz transformations associated with the foreshortening of an object and slowing of time will be identical for both of these models.
However, this theoretical model defines the magnitude of a foreshortening of length and a slowing or dilation of time in terms of a "curvature" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of curvature in four dimensional space-time manifold as Einstein did.
As mentioned earlier Gravitational energy also causes time to slow and length to decrease for the same reason a relative velocity causes time to slow and length to decrease.
Chapter twelve derived the mechanism responsible for gravitational energy in terms of a "curvature" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
Earlier the mechanism responsible for kinetic energy or velocity was derived in terms of a oppositely directed “curvature” in a "surface" of a three-dimensional space manifold.
Therefore, because both gravitational and kinetic energies are derived from a common "curvature" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension they will have a similar effect on physical properties of length and time.
This means both Relativity and this paper predict an observer in a gravitational field will measure the length of an object to be shorter and passage of time to be slower with respect to an observer who is located outside of a gravitational field.
However, as mentioned earlier this paper defines this shortening of length and slowing of time in a gravitational field in terms of four *spatial* dimension instead of four-dimensional space-time manifold.
The "relative" characteristics of a "curvature" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension associated with kinetic and gravitational energy would also make it impossible for an observer to determine if an acceleration is caused by a gravitational field or kinetic energy such as that from an exhaust of a rockets engine.
This is because the mechanism defined above indicates the magnitude of a force associated with both gravitational and kinetic energy is related to the absolute magnitude of a "curvature" a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
Therefore, because a three-dimension observer can only observe the three-dimensional effects of a curvature in four spatial dimensions he or she could not determine whether an he or she is in a gravitational field or an accelerated reference frame.
Therefore, both this paper and Relativity make identical predictions with respect to the relativistic properties of space and time and the inability to determine what is causing acceleration.
However, as mentioned earlier the model presented in the Shadows paper is a broader based because it has and will define a common mechanism responsible for both the relativistic properties of space and time and the quantum properties of mass and energy in terms four spatial dimensions.
The universe's
most powerful enabling tool is not
knowledge or understanding but
imagination
because it extends the reality of
one's environment.""
Copyright 1995 Jeffrey O'Callaghan