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Why Space-time?

Why many physicists chose to define the universe in terms of the physical properties of a time or space-time dimension 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.  However, there is considerable observation evidence, as that article showed that defining it only in terms of a measure of the sequential ordering of the causality of an event would provide an unambiguous definition that is more consistent with both physical and mathematical observations of a three-dimensional environment than defining it in terms of its physical properties.

Gravity and space-time

But even more damaging to that assumption is that assuming the universe is composed of four *spatial* dimensions instead of four-dimensional space-time, would give physicists a broader more logical and consistent explanation for time dilation, length foreshortening, the mass increases associated with relative velocities, gravitational and kinetic energy based on observations made in a three-dimensional environment than can be provided by both the Special and General theories of relativity.

The General Theory of Relativity postulates gravity is the result of a curvature in four-dimensional space-time manifold even though no one has ever physically observed a time or a space-time dimension.

However, as will be shown in the article “Gravity in four spatial dimensions” Dec. 01, 2007 one can define it by extrapolating the observable properties of a three-dimensional environment to derive why a curvature in "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension will make predictions identical to those of General Relativity regarding the properties of a gravitational field.  Additionally it showed the magnitude of mass and energy in a given volume is directly related to the magnitude of the displacement in the "surface" of the three dimensional space manifold caused by that curvature.

However as will be shown it has the additional advantage in that it also allows one to explain and predict relativistic properties of space, time, mass, and energy in terms of the observable properties of a three-dimensional environment instead of as Einstein did of using the unobservable one of a time or a space-time dimension.

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

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

As mentioned earlier this has the advantage over the space-time concepts of relativity in that observations of our three-dimensional environment tell us one can move in two directions upward or downwards in a *spatial* dimension.  This gives physicals an observation basis for assuming that a three-dimensional volume can move in two directions with respect to a fourth *spatial* dimension.  However, no has ever observed how time or a space-time dimension can move with respect to three-dimensional space because no one has ever observed a time or space time dimension.

Therefore, if one defined the energy/mass in a volume associated with gravitational field 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 a oppositely or upward displacement in that "surface".

This means according 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 the rest mass of an object and that caused by their relative velocities.

Therefore, the energy/mass of an object would be dependent on its relative motion because one must add the energy/mass associated with its motion to its rest energy/mass.

However defining the gravity and kinetic energy in terms of curvature in four *spatial* dimensions can not only define the reason for the mass increases associated with relative velocities but it also provides an explanation for the casualty of time dilation and the length foreshortening observed in gravitational 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 only being the measure or the "distance between" the sequential ordering of the causality of an event.

Therefore, time will become dilated in reference frames that are in motion because the curvature generated in three-dimensional space by its motion will cause three-dimensional beings in that reference frame to view the distance between events to be longer in than it would be for an observer who is outside of it.  Therefore, they will view time in a reference frame that is in motion relative to them as moving slower than if they were in that reference frame.

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

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.

This shows one can theoretically define a mechanism responsible for both the time dilation and foreshortening of the length associated with objects in relative motion or in a gravitational field based on physical observations of a three-dimensional environment that is fully consistent with the predictions of relativity by assuming space is composed of four *spatial* dimensions.  Whereas one cannot in a time or a space-time dimension because as mentioned earlier they do not have any observables physical properties.

However there are many more advantages as will be shown in future articles of "

The Imagineer’s Chronicles" to defining the universe in terms of four *spatial* dimensions instead of four-dimensional space-time including deriving a common mechanism responsible for both wave and the quantum or particle properties energy/mass and linking them to the relativistic properties of the universe.

So please remember to revisit us to learn more about why a universe made up of only four *spatial* dimensions is more logical and consistent with observations that one made up of four-dimensional space-time.

Later Jeff

Copyright 2007 Jeffrey O’Callaghan

   

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Why Space-time?

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