Science Forums 2

[Jeffocal]

Originally Posted by modest

This is fine. Relativity describes 3 curved dimensions. If you want to say that they curve into a 4th dimension that is somehow hidden to us then that's not an unusual thing to think. It would be called extrinsic curvature. But, you still need time as a dimension—a curved dimension. It is the curvature of time that results in the gravity we feel here on earth. It is (as far as I know) an indispensable part of general relativity.

~modest

Would it still be necessary to define time as a dimensions if one defined it only in terms of a measure of the sequential ordering of the casualty of events and then defined the relativistic curvature Einstein associated with its dimensional properties in terms of a curvature in four *spatial* dimensions as we have tried to do in the following article.

BTW you can find a complete listing of 58 different subjects we have discussed to point at Articles posted after 01-09 | The Imagineer's Chronicles

Thanks
Jeff

The Relativity of four *spatial* dimensions

We have shown in this blog that there is more observational evidence supporting the existence of four *spatial* dimensions than four-dimensional space-time.

One of these observations is the relativistic properties of space and time.

The article "Defining energy" Nov. 26, 2007 showed one could define a mechanism responsible for gravitational and kinetic energy that is more consistent with observations in terms of a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension than one in four-dimensional space-time manifold.

However, this also gives one the ability to define a mechanism responsible relativistic length foreshortening associated with a gravitational field and velocities in terms of a curvature in a "surface" of a three-dimensional space manifold.

This is because, as was shown in the article "Embedded Dimensions" Oct. 22, 2007 three-dimensional beings would only able to observe the cord of the arc generated by a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, the length of objects will appear foreshortened when viewed from a gravitational field because the cord of the arc generated by a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension by a gravitational field will be shorter than the arc itself.

The same would be true for objects in relative motion because as was shown in the article "What is energy" Nov. 26, 2007 the kinetic energy of their motion is a result of an "oppositely directed" 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 the "surface" of a three-dimensional space manifold caused by the relative motion of the objects.

However, the fact that 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 kinetic or gravitational energy will also affect the movement of time in all reference frames.

In the article "Defining time?" Sept 20, 2007 it was shown defining it only in terms of a measure of the sequential ordering of the causality of an event would provide an unambiguous definition of time that is consistent with both the physical and mathematical observations of time.

If this is a valid definition, 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, time in a gravitatonal or moving reference frame would dilate or move slower with respect to one outside of it because the ordering of the causality of those events in those reference frames would take longer to complete than they would with respect to an external observer becuase they are seperated by a greater distance.

This indicates one can explain and predict the relativistic properties of gravity, space and time in terms of a curvature in a "surface" of a three-dimensional space manifold as logically consistently as can be done in terms of a curvature in four-dimensional space-time manifold.

When you combine these observations regarding time dilation, gravitational and kinetic energy with the others presented in this blog it becomes extremely difficult for anyone to dispute that fact the universe is composed of four *spatial* dimensions instead of four dimensional space-time.

Later Jeff

Copyright 2007 Jeffrey O'Callaghan