Inertial geometry What is it?

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We have shown throughout this blog and its companion book “The Reality of the Fourth *Spatial* Dimension” that there are many advantages to redefining Einstein space-time universe in terms of four *spatial* dimensions.

One is that it could allow for the development of a theoretical link between gravity, mass and inertia in terms of interactions between a third and fourth *spatial* dimension.

Newton, in his laws of motion defined how the inertia of an object interacts with its environment and the effect forces have on them.  However, he was unable to define the causality of gravity or inertia.

Einstein was able to define the causality of gravity and the relativistic properties of motion in terms of a four-dimensional space-time manifold but he was unable to define the causality of inertia. 

However, as mentioned earlier one can derive the causality of both if one redefines Einstein’s space-time universe in terms of four *spatial* dimension.

Einstein gave us the ability to do this when he use the equation E=mc^2 and the constant velocity of light to define the geometric properties of space-time because that provided a method of converting a unit of space-time associated with energy to unit of space associated with position.  Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

This was the basis for, as was done in the article  “Defining energy” Nov. 26, 2007 for defining all forms of energy including inertia or momentum in terms of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

While the article “The “Relativity” of four spatial dimensions” Dec. 01, 2007 showed that one can derive the causality of all forces or accelerations including gravitational in terms of an interaction of a mass with the slope of a curvature in a “surface” of a three-dimensional space.  Additionally it was shown the magnitude of gravitational mass was directly proportional to the magnitude of the displacement caused by that curvature.

(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 the momentum of an object 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 “The “Relativity” of four spatial dimensions” Dec. 01, 2007 showed is defined by the magnitude of that mass.  While second would be the magnitude of a displacement in that “surface” that the article “Defining energy” Nov. 26, 2007 associated with ita 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.)

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

However the article “Defining energy” Nov. 26, 2007 also derives the causality of inertia in terms of the constant geometric displacement of a “surface” of a three dimensional space manifold with respect to four *spatial* dimension associated while showing why there will be a 1 to 1 correspondence between it and the curvature in space required to make a unit change in its displacement with respect to a fourth *spatial* dimension.

In other words it derives the causality of Newton’s law of inertia or the fact that “Every body remains in a state of rest or constant velocity unless acted upon by an external unbalanced force” in terms of a linear displacement in a “surface” of a three dimension space manifold with respect to fourth *spatial* dimension because that displacement would remain unchanged unless in interacted the curvature associated with an accelerative force defined in the “The “Relativity” of four spatial dimensions” Dec. 01, 2007

Additionally because as that article showed there is a one to one correspondence between the rest mass or inertia of an object and the magnitude of the curvature in a “surface” of a three-dimensional space associated with its gravitational component the relative accelerations of all objects will be the same in all gravitational fields.

This defines a causal link between the inertia, mass and gravity in terms of a geometric interaction between the third and a fourth *spatial* dimension.

Later Jeff

Copyright Jeffrey O’Callaghan 2010

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