What is inertia

or why do objects at rest tend to stay at rest and ones in motion tend to stay in motion.  

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

We have shown through out this blog observations of our environment suggest space may be composed of four *spatial* dimensions instead of four-dimensional space-time.

The inertial property of objects is one of those observations.

Newton, in his laws of motion defined how the inertia of an object interacted 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 gravitational accelerations on objects and the relative properties of their movements in terms of a curvature in a four-dimensional space-time manifold but he was unable to define the causality of inertia.

However, one can define a casual relationship between the inertial properties of objects and gravity 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 all forms of energy including the inertia or momentum of an object 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 gravitational accelerations in terms of a curvature in a four-dimensional space metric as well as one in four-dimensional space-time.

However, defining them in terms of four *spatial* dimensions gives one the ability to define the causality of both gravity and inertia in terms of a displacement in a "surface" of three-dimensional space.

As was shown in article "Defining energy" a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is the causality of the gravitational accelerations.  While a gravitational potential was derived in terms of a displacement in the "surface" of that manifold 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.)

However, according to the concepts presented in that article the causality of inertia, momentum or "potential energy" of an object due to its motion would be defined by a displacement in the entire "surface" of a three-dimensional manifold.  Therefore, the displacement associated with its inertia would be the sum of two components.  The first would be caused by the gravitational curvature associated with the mass of the object and second would be a displacement of the "surface" of the three-dimensional space manifold with respect to a fourth *spatial* dimension where that curvature is located.  (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.)

That article showed forces or the ability to change the momentum of an object is caused by it interacting with a curved "surface" of a three-dimensional space manifold.  However, if, as mentioned earlier the momentum of objects is caused by a constant or flat displacement of a "surface" of a three-dimension space manifold they would tent to stay rest or ones in motion would tend to stay in motion is because they are occupying a "surface" of a three-dimensional plane that is not curved with respect to a fourth *spatial* dimension and therefore would not experience any forces.

This defines a causal link between the inertial properties of objects and gravity 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 its "surface" can be curved but cannot be displaced as is possible for a three-dimensional manifold contained in four-dimensional space.