Einstein in four *spatial* dimension

Why many physicists chose to define the universe in terms of the physical properties of a time or space-time dimension instead of four *spatial* dimensions is puzzling because, as was shown in the earlier article "Defining time" Sept 20, 2007 there is no observational evidence supporting it having physical properties. 

Gravity and space-time

But even more damaging is that assuming it is composed of four *spatial* dimensions instead of four-dimensional space-time, would allow physicists more logical and consistent explanation based on physical observations or our environment for time dilation, length foreshortening, the mass increases associated with relative velocities, gravitational and kinetic energy than can be provided by space-time concepts of the Special and General Theories of Relativity.

Einstein himself defined a universe composed of four *spatial* dimension and one of four-dimensional space-time when he mathematically defined its geometric properties in terms of the constant velocity of light.  This is because it allows one to redefine a unit of time he associated with energy in his space-time universe to unit of space in a one consisting of only four *spatial* dimensions. 

However as was mentioned earlier viewing the universe in terms of four *spatial* dimensions instead of four-dimensional space-time, would allow one to define the mechanism responsible for time dilation, length foreshortening, the mass increases associated with relative velocities, and gravity based on the physical observations instead of the abstract mathematical properties of the Special and General Theories of Relativity.

One of the advantages of deriving all forms of energy in terms of their spatial instead of their time or space time properties is that it allows one to form a physical image of the opposing nature of kinetic and gravitational forces in terms of our observable properties of our environment

For example we observe that the kinetic energy associated a satellite opposes the gravitational energy of the object it is orbiting.

However because of observations of our three-dimensional environment tell us one can move in two directions upward or downwards in a *spatial* dimension one can form a clearer image of opposing properties of these forces by defining gravity in terms of a "downward directed" displacement in a surface of a three-dimensional space manifold with respect to a fourth spatial dimension while define kinetic energy in terms of oppositely or upward directed or up displacement in that surface.  Granted the one can do the same using the properties of a space-time dimension however it is much more difficult to understand the opposing nature of these force because we only observe time to move in one direction forward.

This is the observational basis for defining, as was done in the article "Defining potential and kinetic energy?" gravitational and kinetic energy in terms of oppositely directed movements or displacements in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

In other words if one defined the energy/mass in a volume associated with mass in terms of downward directed displacement in a "surface" of a three-dimensional space manifold with respect to a four *spatial* dimension one would define the energy associated with its relative motion in terms of an oppositely or upward displacement in that "surface".

This would allow one to form a physical image of the relative mass increase due to relative velocities based on observation of our three-dimensional world because according to the concepts contained in that article the total energy/mass of an object would be equal to the sum of the displacements of a "surface" of a three-dimensional space manifold caused by its rest mass and that caused by their relative velocities.

However defining space in terms of four spatial dimension not only provides observational basis for causality of the gravity and kinetic energy but it also provides an explanation for the casualty of time dilation and the length foreshortening in gravitational environments and moving reference frames based on physical observations made in a three-dimensional environment.

The following analogy can be used to understand and define the relativistic properties length and time based on observations made in a three-dimensional environment.

Assume that two "2 dimensional creatures” are living on the surface of two pieces of paper resting on a desktop.

Also, assume the two creatures can view the surfaces of the other piece of paper, which are separated a pencil.

If the diameter of the pencil is increased, the curvature between the surfaces of the two pieces of paper will increase.

Each of these creatures, when viewing the other piece of paper will only perceive the two-dimensional translation of the three-dimensional curvature generated by the pencil.

Therefore, each will view the distance between two points on the surface of the other as shorter since they will view that distance as a two-dimensional translation of a three-dimensional curvature in the surface of the paper.  Therefore each will measure the distance between them on their piece of paper as being longer as the diameter of the pencil increases then they would if they viewed it on the other piece.

Similarly, because three-dimensional beings could only "view" a three-dimensional translation of a "curvature" or displacement in four *spatial* dimension caused by the relative motion of a reference frame they will measure distance or length in them as being longer than they would be if viewed as an observer who is in relative motion to it.

This is the mechanism responsible for the relativistic properties of length in terms of the geometry of four *spatial* dimensions.

The two-dimensional creatures in the earlier example will also notice that time is effected by a curvature in the surface of their paper.

Each of them will view the others “time” as moving slower because the three-dimensional curvature in the paper makes the distance between events longer than the two dimensional translation of that curvature. Therefore, it will take longer for events "move" through a curvature in three-dimensional space on the surface of the others piece of paper relative to the time it would take for it to move thought the two-dimensional translation of that curvature.

Earlier it was mentioned that time can be defined as only being the measure or the "distance between" the sequential ordering of the causality of an event.

Therefore time would be dilated with respect to a reference frame that is external to a gravitational field or was in motion because as mentioned earlier the length of the arc generated in three-dimensional space by a gravitational field or the kinetic energy of relative motion to be longer than the cord of that arc.  Therefore, the distance between events would be greater for an observer in those reference frames than for one who is outside of it.  However, this means an observer outside of those reference frames would measure the time between those events as being dilated with respect to an observer who is inside because the time required for objects to move between events in that reference frame will be longer.

As mentioned earlier article both “Gravity” and kinetic energy can be define in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension as well as one in a space-time manifold.

However, this means that one can define the foreshortening of the length of an object in relative motion or in a gravitational field in terms of the cord to the arc generated by that curvature.  This is because the cord of an arc created by that displacement is always shorter than the arc itself and since three-dimensional beings can only observe the three-dimensional cord of an arc in four-dimensional space they would view the length of the objects to be shorter when viewed in relative motion or in a gravitational field.

However it would also provide a mechanism for the time dilatational associated with gravity and motion that is consistent with our observations of three-dimensional space.

This shows one the benefits of viewing Einstein relativistic theories in terms of four *spatial* dimension is that it allows one to form a more logical and consistent explanation based on physical observations or our environment for time dilation, length foreshortening, the mass increases associated with relative velocities, gravitational and kinetic energy than can be provided by the space-time concepts of the Special and General Theories of Relativity.

As was shown earlier Einstein’s mathematics allows us to choose to define our universe in terms of either a space-time environment or one consisting of only four *spatial* dimension when he defined its geometry in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories thereby giving us a new perspective on its relativistic properties.

Later Jeff

Copyright 2007 Jeffrey O’Callaghan

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