|
|
|
|
|
|
|
Chapter one hypothesized a volume of space is composed of four *spatial* dimensions instead of four-dimensional space-time and defined some theoretical advantage to doing so. One of these is that it allows one, as was shown in Chapter sixteen to derive a common mechanism for gravity and the quantum properties of mass and energy.
However, it also allows one to define a mechanism responsible for "The Principal of Equivalence" or the fact that the laws of physics are the same in a gravitational or accelerated reference frame in terms of the classical laws of physics.
Chapter twelve derived gravitational accelerations in terms of a "slope" caused by a "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
(This "depression" in a "surface" of the three-dimensional space manifold with respect to a fourth *spatial* dimension is analogous to a depression or curvature in a space-time manifold the General Theory of Relativity is postulates is responsible for gravitational accelerations.)
Chapter seventeen derived causality of non-gravitational accelerations in terms of the "slope" caused by an "elevation" a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
The laws of physics are the same in a gravitational field as in an accelerated reference frame because, as was shown in Chapters twelve and seventeen the forces responsible for those laws are generated by the absolute value of a "slope" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Since the absolute magnitude of a "negative slope" generated by a "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would be indistinguishable from the absolute magnitude of a "positive slope" generated by an "elevation" in the "surface" of a three-dimensional space manifold the laws of physics will be the same in a gravitational field and as in an accelerated reference frame.
This means that one can apply the classical laws of Euclidian geometry of four spatial dimensions to derive the Principal of Equivalence instead of have to rely on the non-classical concept of Relativity.
Another aspect of "The Principal of Equivalence" is that all mass free falls with the same acceleration in a gravitational field.
The mechanism responsible for this can be understood by examining how a particle defined in Chapter two interacts with four *spatial* dimensions.
Chapter two derived a particle in terms of resonant "systems" formed in space by oscillations in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
The reason all masses free fall with the same acceleration in a gravitational field can be understood by comparing the forces generated by a gravitational field to the forces in an accelerated reference frame such as that generated by a rockets exhaust on a box of marbles.
The box will represent a mass and the marbles in the box will represent the individual particles in that mass.
If a constant force, such as that produced from rocket's exhaust were applied to a box containing marbles it would move with a constant acceleration. However, the rate of acceleration of the box would be inversely proportional to the number of marbles in the box because the mass of the box is directly proportional to it.
Another way of describing this would be to attach a string to each marble and apply a force individually to each string.
If the total force applied to all of the strings were kept constant, the rate of acceleration of the box of marbles would be inversely proportional to the number of marbles in the box.
However, if a constant uniform force was applied individually to each string the total force on the box will vary in direct proportion to the number of marbles in the box and the rate of acceleration of the box will remain unchanged no matter how many marbles it contained.
Attaching a string to each marble in a box and applying constant uniform force individually to each string illustrates why all masses "freefall" with the same acceleration in a uniform gravitational field.
The string will represent the "attachment" or interaction each individual particle in an object has with a "surface" of three-dimensional space manifold with respect to a fourth *spatial* dimension.
The conclusion that particles interact with the "surface of a three dimensional space manifold is consistent, as mentioned earlier with fact they are made up of resonant "systems" on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
As mentioned earlier Chapter twelve derived the magnitude of gravitational force to be directly related to the magnitude of the "slope" caused by a "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Additionally, it was shown the mass of an object was directly related to the number of particles it contained.
Because each individual particle in an object would be "attached" to a "surface" of a three-dimension space manifold associated with a gravitational field the total force experienced by an object in gravitational field will be a directly proportional to the number of particles is contains.
This is analogous to why the total force experienced by the box of marbles with the strings attached in the earlier example varied in direct proportion the number of marbles contained in the box.
Therefore the reason all masses free fall with the same acceleration in a gravitational field is because the mass of an object would be directly proportional to the number of particles it contains, the total gravitational force on an object will be directly proportional to is mass. Therefore, all masses will freefall in a gravitational field with the same acceleration.
This explains another aspect of "The Principal of Equivalence", that an observer inside a laboratory could not determine if he or she was in a gravitational field or was in constant accelerated motion. This is because each particle that makes up a laboratory in a gravitational field or an accelerated reference frame will be interacting "freely" with the curvature in space associated with that form of acceleration.
This means an observer inside a laboratory could not determine if his or her laboratory was in uniform accelerated motion or a gravitational field because as mentioned earlier the absolute value of the "slope" in a "surface" of a three-dimensional space manifold with respect to fourth *spatial* dimension caused by a gravitational or non-gravitational acceleration is indistinguishable.
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
