The Equivalence Principal in four *spatial* dimensions.

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This article is a collaboration between Benny Creemers, a proponent of Super Relativity and Jeff.  Please visit his web site to gain a different perspective on this subject and Mark Fiorentino site for a discussion of the principals of Super Relativity.)

We have shown throughout this blog there would be many advantages to defining our universe in term of four *spatial* dimensions instead of four-dimensional space-time.

One of them is that it would allow one to derive Einstein’s principal of Equivalence, gravity and electromagnetism from perspective of four *spatial* dimensions as well as four dimensional space time thereby giving a better understanding of the mechanisms responsible for their interactions.

 

For example as was shown in the article “Unification of Gravity and Electromagnetism” May 15, 2008 one can define a common casually for them by deriving gravity in terms displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension while defining the electromagnetic properties of radiation in terms of a displacement caused by a matter wave moving on that “surface”.

The unification is achieved in terms of the common displacement which defines them.

However if one defines gravity in terms of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension one should be able derive the Equivalence principal in those same terms.

In the physics the equivalence principle refers to several related concepts dealing with the equivalence of gravitational and inertial mass, and that the gravitational “force” as experienced locally while standing on a massive body (such as the Earth) is actually the same as the force experienced by an observer in a non-inertial (accelerated) frame of reference.

In the article “Defining energy” Nov. 26, 2007 it was shown all forms of energy including inertia and momentum can be derived in terms of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension which is identical to the one the article Unification of Gravity and Electromagnetism showed is responsible for gravity and electromagnetism. 

However the article “Why Space-time?” Sept. 27, 2007 showed that one can also derive the energy associated with the rest mass of an object or particle in terms of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  Additionally it was shown one can derive the causality of all accelerations including gravitational in terms of an interaction of mass with the slope of a curvature in a “surface” of a three-dimensional space caused by that displacement.

(This curvature is analogous to a curvature in a four-dimensional space-time manifold Einstein theorized was the causality of gravitational accelerations.)

Therefore, according to the theoretical concepts presented in those articles the magnitude of inertia or momentum would be defined by the sum of two components.

The first would be the displacement in a “surface” of a three-dimensional space associated with the rest mass of an object, whose magnitude as the article “Why Space-time?” showed is defined by the magnitude of that mass.  While second would be the momentum or the magnitude of a displacement that “surface” that the article “Defining energy” showed was the casualty of the energy or momentum of its relative motion.  (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.)

Therefore to define the total energy of an object or particle one would have to add the displacements in a “surface” of a three-dimensional space manifold associated with the energy of its rest mass to that associated with its relative motion.  

However, as mentioned earlier the article “Why Space-time?” showed that gravitational accelerations are caused by an object or particle interacting with a curved “surface” of a three-dimensional space manifold caused by it interacting with another surface which was at a different “level” respect to a fourth *spatial* dimension.

Additionally as that article also showed the rest mass of an object would directly proportional to the magnitude of its displacement a “surface” of three-dimensional space with respect to a fourth spatial dimension.

Therefore the curvature in space cause by the interaction of a mass with another object would be directly proportional to magnitude of the displacement created by them with respect to adjacent volumes of space.

This means as was shown in the article “Defining energy” there will be a 1 to 1 correspondence between a mass and the curvature in space associated with the energy required to make a unit change in its displacement with respect to a fourth *spatial* dimension.  Therefore, the inertia of an object would be directly related to its mass.  Additionally it showed that the energy associated with its velocity is also directly proportional to that displacement.  This defines the reason why the momentum of an object is also directly proportional to its velocity.

In other words the causality of the equivalence between inertial and gravitational mass in terms of a spatial interaction or displacement between a “surfaces” of a three-dimensional space manifold and a fourth *spatial* dimension because it derives one in terms of the other.

However it also defines the reason the force experienced locally while standing on a massive body (such as the Earth) is Equivalent to the force experienced by an observer in a non-inertial (accelerated) frame of reference.

As mentioned earlier the article Why Space-time?” showed all forces including gravitational are the result of a curvature in a “surface” of a three-dimensional space manifold.  Therefore the reason an observer standing on a massive body experiences the same force as one in accelerated reference frames is because they are both caused by a common curvature in a “surface” of three-dimensional space.

This identifies an alternative explanation for Einstein’s Principal of Equivalence in terms of four *spatial* dimensions.

This demonstrates one of the advantages of using both Einstein space time concepts and their equivalent in four spatial dimensions is that it allows one to derive a common causality for Einstein’s principal of Equivalence, gravity and electromagnetism.

Later Jeff

Copyright 2008 Jeffrey O’Callaghan

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