We have and will shown in "The Imagineer’s Chronicles" the existence of four *spatial* dimensions gives a more consistent explanation of the relativistic properties of space, time gravity and its equivalence to accelerated reference frames than is provided by the "Theory of Relativity".

In the article "Defining energy" Nov. 26, 2007 it was showed deriving the properties of relative motion, gravity and  accelerated reference frames in terms of a curvature or displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension was more consistent than defining them in terms of a space-time manifold.

However, it is also possible to define a mechanism that can explain and predict the relativistic time dilation and length foreshortening associated with gravity and relative velocities in terms of a curvature in a "surface" of a three-dimensional space manifold.

As mentioned earlier, the article Defining energy showed one can derive the properties of gravity in terms of a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial*dimension.

However, this also defines the reason why the length of objects would be foreshortened, due to gravitational effects when viewed by three-dimensional beings because as was shown in that article all forms of energy create a curvature in a "surface" of a three-dimensional space manifold.  Therefore, they could only view the cord of the arc generated by a curvature in a "surface" of a three-dimensional space created by a gravitational field.  But because the cord of an arc is shorter than the arc itself they will view the distance between events to be shorter than would be if they were not sounded by a gravitational field.

The same would be true for objects in relative motion because, as was shown in that same article the kinetic energy of relative motion also generates a curvature in a "surface" of a three-dimension space manifold with respect to a fourth *spatial* dimension.  Therefore, each observer would view the length of an object in relative motion as being shorter because they will view the cord of the arc generated by a curvature in that "surface" caused by the relative motion of the objects.

But this curvature will also affect time because, as mentioned earlier three-dimensional beings can only view the cord of the arc in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by gravity motion.

Therefore, time would be dilated with respect to an external reference frame that was in motion or in a gravitational field because of the foreshortening of length, the measurement of the distance between events would be greater for an observer in that reference frame than for one who is outside of it.  Therefore, measurement of time between two events would be longer in a moving reference frame or in a gravitational field with respect to an observer who is outside of it because it will take longer for events to “travel” the greater distance between them.

This indicates one can explain and predict the relativistic properties of space and time in terms of the existence of four *spatial* dimension just as logically consistently as can be done in terms of four-dimensional space-time.

When you combine these observations regarding time dilation, gravity and momentum with the others presented in "The Imagineer’s Chronicles" it becomes difficult to dispute that fact the universe is composed of four *spatial* dimensions instead of four dimensional space-time.

Later Jeff

The "Shadows" of four spatial dimensions

Copyright 2010 Jeffrey O’Callaghan

(In a PDF format)

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