or why do objects in a state of uniform motion tend to remain in that state of motion unless an external force is applied to it.

(This article is a collaboration between Israel Sadovnik and Jeff.) 

We have shown throughout "The Imagineer’s Chronicles" many aspects of our environment suggest space is composed of four *spatial* dimensions instead of four-dimensional space-time. 

Newton’s First Law The Law of Inertia

The property of inertia is one of them.

Newton, in his laws of motion defined how the inertia of an object interacts with its environment and the effects gravity has 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, one can define a casual relationship between inertia, mass and forces if one defines them in terms of four *spatial* dimensions instead of four-dimensional space-time. 

In the article "Defining energy" Nov. 26, 2007 it was shown potential energy can be derived in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  While the article "Why Space-time?" Sept 27, 2007 showed one could derive magnitude of a force in terms of the slop of a curvature in that surface.

(This curvature is analogous to a curvature in a four-dimensional space-time manifold Einstein theorized was responsible for gravity.)

This means the rest mass or potential energy of an object would be derivable in terms of the magnitude of a displacement caused by a curvature in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Isaac Newton defined inertial as being responsible for why an object at rest will remain at rest, and an object in motion will remain in motion in a straight line at a constant speed, and if a repulsive force acts between two bodies of the same mass, they will acquire equal velocities in equal amounts of time.

However, as mentioned earlier the article "Defining energy" derived potential energy in terms of displacement with respect to a fourth "spatial" dimension of a volume of three-dimensional space.

Therefore, one could define the energy associated with inertia or momentum in terms of a constant or non-curved displacement in a "surface" of a three dimensional space manifold with respect to a fourth spatial dimension.

This means that an object at rest will remain at rest, and an object in motion will remain in motion in a straight line at a constant speed unless the magnitude of that displacement associated with it moment is changed.

As mentioned earlier the article "Defining energy" showed forces are the result of with a curvature in a "surface" of a three-dimensional space manifold.  Therefore, object at rest will remain at rest, and an object in motion will remain in motion in a straight line at a constant speed, unless the displacement of a "surface" of three-dimension space associated with it interacts with the a curvature in that “surface” associated with a force.

The reason a force that acts between two bodies of the with same masses causes them to acquire equal velocities in equal times is because, as was shown in article the "Defining energy" force is the result of a movement of a displacement in three-dimensional space manifold with respect to a fourth *spatial* dimension.  Therefore, if an equal force were applied to two masses in the three-dimension space the displacements associated with those masses would move with equal magnitudes and in opposite directions with respect to a common point in four-dimensional space.

As mentioned earlier article "Defining energy" showed that one can define the magnitude of energy in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, according to the concepts presented here the inertia or momentum of an object would be defined by the sum of two components.  The first would be magnitude of the displacement in a "surface" of a three-dimensional space caused by the curvature associated with the rest mass of an object. The second would be the magnitude of displacement of that surface with respect to a fourth *spatial* dimension caused by the energy of the relative motion of an object.  (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.)

This defines a causal link between the inertia and mass in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Einstein could define the casualty of gravity but not inertia in terms of a four-dimensional space-time manifold because the "surface" of three-dimensional space cannot be displaced with respect to time or a time dimension.

Later Jeff

The "Shadows" of four spatial dimensions

Copyright 2009 Jeffrey O’Callaghan

(In a PDF format)

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