or why do objects in a state of uniform motion tend to remain in that state unless an external force is applied to it.
(This article is a collaboration between Israel Sadovnik and Jeff.)Â
We have shown throughout Our blog “The Road to Unification†many aspects of our environment suggest it is composed of four *spatial* dimensions instead of four-dimensional space-time.Â
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.Â
However, one can define a causal link between inertia, mass and gravity if one defines the universe in terms four *spatial* dimensions.
Einstein gave us the ability to do this when he used the constant velocity of light and the equation E=mc^2 to define the dynamic balance between mass, energy, space and time because that provided a method of converting the time displacement he associated with energy in a space-time universe to one to a spatial one in a universe consisting of only four *spatial* dimensions. Additionally because the velocity of light is constant he also allows us to defined a one to one quantitative and qualitative correspondence between his space-time universe and one made up of only four *spatial* dimensions.
In other words by defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of only four *spatial* dimensions.
This fact is the bases for assuming as was done in the article “Defining energy” Nov. 26, 2007 that all forms of energy can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension including as was shown in the article “Why Space-time?” Sept. 27, 2007 showed that associated with rest mass.
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 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 its mass. While second would be the magnitude of the displacement in that “surface” 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 be zero.)
Therefore to define the inertia or 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. Â
However, as mentioned earlier the article “Why Space-time?“ showed that accelerations are caused by an object or particle interacting with a curved “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
Therefore, as mentioned earlier if the momentum of an object is caused by a displacement of a “surface” of a three-dimension space manifold it would tent to stay rest or ones in uniform motion would tend to stay in inform motion unless it interacted with a “surface” that was curved with respect to a fourth *spatial* dimension.
As mentioned earlier, the rest mass of an object is directly proportional to a displacement a “surface” of three-dimensional space. Therefore, as was shown in the article “Defining energy” there will be a 1 to 1 correspondence between it 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 is 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 proportional to its velocity.
This defines a causal link between the inertia, mass and gravity in terms of an interaction or displacement between a “surfaces” of a three-dimensional space manifold and a fourth *spatial* dimension.
Additionally it means the casualty of Newton’s first law motion that “An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force” can be understood in terms of in terms of an interaction between a third and fourth *spatial* dimensions.
Later Jeff
Copyright Jeffrey O’Callaghan 2009