We have show there are many observations suggesting the universe may be composed of four *spatial* dimensions instead of four-dimensional space-time.

The observation that the energy contained in systems is related to distance not time is one of them.

For example, the momentum of a moving object is dependent on its velocity and the potential energy per unit volume of water in a dam is related to the distance separating the surface of the water from the bottom of the dam.

However, the energy in all system appears to be independent of time because the energy of the water in a dam and the velocity or distance an object travels per unit of time remains constant no matter how much time has passed unless it is acted upon by some outside force.

Granted the power an energy source can generate is determined by the rate or time required for the dissipation its energy however, the total quantity of energy in a closed system is never observed to be effected by the passage of time.

This suggests that potential energy is related to a spatial not a time property of space.

In the earlier article "Embedded dimensions" Oct. 26 2006 it was shown why it is possible to define potential energy, including that contained in mass in terms of a spatial displacement or curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

This displacement is analogous to the space-time displacement Einstein used to define the potential energy of mass in terms the equation E=mc^2. 

However, it is more consistent with the observation mentioned earlier that potential energy appears to be related to a spatial not a time property of a dimension.

Another observation that supports the assumption the universe is made up of four *spatial* dimensions is that it gives a more consistent explanation for the observed asymmetry between gravitational and kinetic forces than is provided by the space-time concepts of relativity.

Observations of our environment show that it is possible to move in only one direction in time but two in space.  For example, we observe that it is possible to move up or down, backwards or forwards in space but only forward in time.   We also observe the momentum and kinetic energy of an orbiting satellite opposes or is oppositely directed with respect to the gravitational field associated with the mass it is orbiting.

If, as was done in the article “Embedded Dimensions” one defines gravitational energy in terms of a spatial "depression" in a "surface" of a three-dimension space manifold with respect to a fourth *spatial* dimension then the asymmetry between the momentum could be explained in terms of a oppositely directed "elevation" in a "surface" of three-dimensions space with respect to a fourth "spatial" dimension.

However, this explanation is more consistent with the observations, mentioned earlier in that the momentum of a system appears to be dependent on a spatial not a time property of space.

This indicates that the observations regarding potential energy of mass can be more consistently explained in terms of the existence of four *spatial* dimensions than four dimensional space time.

Later Jeff

The "Shadows" of four spatial dimensions

Copyright 2007 Jeffrey O’Callaghan

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