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 energy 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 and the existence of a continuous non-quantized form of mass and energy.

Chapter one postulated that space was composed of four *spatial* dimensions and a continuous non-quantized form of mass and energy.

Chapter two showed how and why the quantum characteristics of mass could be explained and predicted terms of a resonant "structure" formed in a continuous non-quantized form of mass and energy.

This chapter will shown how and why the relativistic properties of space, time, mass and energy can be explained and predicted in terms of four *spatial* dimensions and the existence of a continuous non-quantized form of mass.

The "dimension" of time will be defined as only being a measure of the sequential ordering of the causality of an event and is 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.

(The justification for defining a time only in terms of a measure of the sequential ordering of the causality of an event is because there are no mathematical or experimental observations that contradict this definition.)

Chapter twelve defined the gravitational force in terms of a curvature or "depression" 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 a quantity of a continuous non-quantized form of mass "contained" in a displacement or “depression” a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by that curvature.

(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.)

However, Chapter ten showed a "displacement" between two "surfaces" of a three-dimensional space manifold with respect to a fourth "spatial" dimension is the casualty of all forms of energy and that the magnitude of a displacement in a "surface" of a three-dimensional space manifold determines the magnitude of the energy of a system.

Therefore, if all energy is related to a displacement in a "surface of a three-dimensional space manifold one can define the kinetic energy of a velocity in terms of a "elevation" in a "surface" of a three-dimensional space manifold.

This is because Observations show that it is possible to move in only one direction in time but two in space.  For example, it is possible to move up or down, backwards or forwards in space but only move forward in time.

However, kinetic and gravitational energy posses a similar type of symmetry in that the kinetic energy of a mass opposes or is oppositely directed from the gravitational energy of a mass.  For example, the kinetic energy of the mass of an orbiting satellite opposes the gravitation energy of the mass it is orbiting. 

Therefore, if the mechanism responsible for gravitational energy is definable in terms of a "depression" in a "surface" of a three-dimensional space manifold, kinetic energy would be definable in terms of a symmetrically opposite "elevation" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  This is possible because observations of spatial dimensions tell us the surface of a spatial dimension can move in two directions, "up" and become "elevated" or "down" and become depressed.

This means that the total mass of an object in motion would sum of two components.

The first will be the rest mass of the object defined in Chapter twelve or the quantity of a continuous non-quantized form of mass "contained" displacement associated with the "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension responsible for a gravitational field.

The second will be the quantity of a continuous non-quantized form of mass "contained" in the displacement    between the different "surfaces" of a three-dimensional space manifold caused by the kinetic energy of the relative velocity of the objects.

Therefore, the mass of an object viewed by an observer who is in motion relative to that object will be greater that the rest mass of that object and the difference will be dependent on the kinetic energy or velocity of the object.

This defines the mechanism responsible for why the mass of an object is increase when viewed by an observer who is in relative motion to that mass.

The following analogy can be used to understand and define the relationship between time, length, and velocities.

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.

The "movement" of “time” on both surfaces will also be affected.

Each will view the others “time” as moving slower because they will view a two-dimensional translation of its "movement" through a curvature in three-dimensional space.

Similarly, because three-dimensional beings can only view a three-dimensional translation of a "curvature" or displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the motion of an object they will view the length of an object to be shorter with respect to a similar object that is not in motion.

This is analogous to why the length of a line would appear shorter to the two-dimensional "creature" viewing the surface of the paper that was separated by the pencil.

Time will also appear to "move" slower or become dilated for objects that are motion because three-dimensional beings can only view a three-dimensional translation of a "curvature" or displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the motion of an object they will view the passage of time on that object to be slower that it would be if the object were not moving.

This is analogous to why the passage of time would appear slower to the two-dimensional "creature" viewing the surface of the paper that was separated by the pencil.

Therefore, because the magnitude of the displacement or the "curvature" an object generates in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is dependent on its velocity 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 same 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 because, as Chapter ten showed, three-dimensional beings perceive energy in terms of the magnitude of a relative "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 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.

Gravitational energy will also cause 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" caused by a "depression” 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 “curvature” caused by an “displacement” in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

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, this paper defines this shortening of length and slowing of time in a gravitational field  in terms of a three-dimensional space manifold with respect to a fourth *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 between two points in space.

Therefore, an observer could only "view" the absolute magnitude of a "curvature"  in a three-dimensional space manifold with respect to a fourth *spatial* dimension associated with an acceleration he or she was experiencing and therefore he or she would have no way to determine if it was caused by 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, the model presented here 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 and a continuous non-quantized mass and energy component of space.

“The universe's most powerful enabling tool is
not knowledge or understanding
but imagination"
Jeffrey O'Callaghan

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