We have shown throughout the Imagineer’s Chronicles and its companion book "The Reality of the Fourth *Spatial* Dimension" there would many theoretical advantages to defining the universe in terms of four *spatial* dimensions instead of four dimensional space-time.
One of them is that it would give explanation of why time is dilated in bodies that are in relative motion or a gravitational field that is more consistent with its observed properties than is provided by the space-time concepts of Albert Einstein’s Special and General Theories of Relativity.
For example observations made by both physicists and non physicists alike suggests that time is only a non-physical measure of when in relation to other events a physical, chemical, and biological change take place similar to how a unit of length is a non-physical measure of the where in relation to other objects one is located in a three dimensional environment. This is because similar to time, length is not perceived as having the physical properties of matter or space but only as measurement of where one object is located relative to another.
In other words observations regarding time suggest that it only has the non-physical properties associated with a measurement and not the physical properties of Einstein’s time or space-time dimension.
Additionally our perception of irreversibly of time or that it always moves in one direction, forward also appears to contradict the concept that it has physical properties because it is possible to reverse the position of an object in a spatial dimension whereas one cannot in a time or space-time dimensions. For example, one can move an object to a different position with respect to where it was and then reverse the process and move it back to its original position three-dimensional space whereas one cannot in a move an object forward in a space-time dimension time and then move it back to its original position with respect to time. Therefore observations suggest that a time or a space-time dimension does not share the physical properties associated with the spatial dimensions.
Therefore, defining a space-time dimension in terms of its physical properties as Einstein did does not appear to be consistent with the observation that time is irreversible.
However, this same observation, as was shown in the earlier article "Defining time" Sept 20, 2007 suggest that time may only be a non-physical a measure of the sequential ordering of the casualty of events because one cannot reverse the causality of an event without creating a new event thereby making it consistent with the perception of its irreversibility.
That article also showed why assuming time only has the non-physical properties of a measurement would provide an unambiguous definition of it that is more consistent with both physical and mathematical observations of time than defining it in terms of the physical properties of a dimension as Einstein had done.
It also points out one of the most obvious observational flaws with Einstein’s assumption of the physicality of time or a space-time dimension is that no one has ever observed any of its physical properties and therefore it is difficult to explain or understand how it can interact with the physicality of three-dimensional space to cause gravity.
Yet Einstein gave us a way of translating the non observable physical properties of time to the physically observable properties of a spatial dimension when he defined its geometry in terms of the constancy of the velocity of light.
Einstein defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2. However when he used the constant velocity of light in the equation E=mc^2 to define that balance he provided a method of converting a unit of space he associated with mass to a unit of space-time he associated with energy. Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.
In other words by defining the geometric properties of a space-time universe in terms of energy/mass and the constant velocity of light he provided a quantitative means of redefining his space-time universe in terms of geometry of four *spatial* dimensions.
Observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence defined by Einstein’s one must assume that energy also must have spatial properties.
As mentioned earlier Einstein equation E=mc^2 tell us there is a dynamic relationship between the geometric properties of our universe and mass/energy in that when one coverts mass to energy in a closed three-dimensional *spatial* environment, the space it is made up of expands while if one coverts energy to mass that environment contracts. Yet it is difficult to understand how three-dimensional space can both expand and contract in a space-time universe because our experiences tell with time tells us that it only moves in one direction forward. However it is easy to understand how it could in one consisting of four *spatial* dimension because our experiences it tell us that we can move in two direction in a spatial environment up down forwards of backwards.
The fact that one can use the equation E=mc^2 to qualitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions is one the bases of assuming as was done in the article “Defining potential and kinetic energy?” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. In other words one can use Einstein’s equations to quantitatively and conceptually define energy in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimensions.
However, as was shown in the article “Gravity in four spatial dimensions” Dec. 01, 2007 one can use the same technique to derive a one to one qualitative and quantitative correspondence between the space-time curvature Einstein postulated was responsible for gravity and the curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension that article postulated was responsible for it. Additionally because they are both based on constancy of the velocity of light the relative magnitude of the "curvature" caused by given quantity of energy/mass in a space-time universe and one consisting of fourth *spatial* dimensions will be identical. In other word the magnitude of a gravitational field in both a space-time environment and one of four *spatial* dimensions would be dependent on the quantity of energy/mass that environment contained.
However as was mentioned earlier a worldview based on the existence of four *spatial* dimension instead of four dimensional space-time has an advantage in that it also allows one to explain time dilation and predict relativistic properties of space, time, mass, and energy in terms of the observable spatial properties of a three-dimensional environment instead of as Einstein did of using the unobservable ones of a time or a space-time dimension.
For example we observe that the kinetic energy associated with a satellite opposes the gravitational energy of the object it is orbiting.
It is difficult to understand why in terms of four dimensional space-time because as mentioned earlier all forms of energy in a space-time environment are defined in terms of a curvature in its geometry. However because time is observed to only move in one direction this curvature for both kinetic and gravitational energy must always be in the same direction thereby making it difficult to explain why they oppose each other.
However this is not a problem if one defines energy as was done in the article "Defining potential and kinetic energy?" in terms of the geometry of four *spatial* dimensions because we observe that we can move in two direction upwards and downwards or backwards and forwards in a *spatial* dimension.
Therefore one can explain and understand why kinetic and gravitational energy oppose each other by deriving them in terms of oppositely directed curvatures in "surface’ of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
However this means according the concepts outlined above the total energy/mass of an object would be equal to the sum of the absolute value of the displacements in a "surface" of a three-dimensional space manifold caused by the rest mass of an object and that caused by its relative velocities. This is because the total curvature associated the kinetic and gravitational energy in a given volume of space would be equal to sum of the difference between their magnitudes and because there are opposite or negatively directed with respect to the each other one would have to add their absolute magnitudes to get the total energy/mass in a given volume space.
Therefore, the total 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 oppositely directed curvatures in four *spatial* dimensions not only defines the reason for the mass increases associated with relative velocities that is more consistent with observations but it also provides an more consistent 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, according to that definition time will become dilated in reference frames that are in relative 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 "Defining potential and kinetic energy?" showed 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 also define the foreshortening of the length of an object in a gravitational field in terms of the cord to the arc similar to how it was earlier derive in terms of the curvature caused by the kinetic energy of an object. 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 why time dilated with gravitational field 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 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 qualitative and quantitative predictions of relativity by assuming space is composed of four *spatial* dimensions.
However as was mentioned earlier a worldview based on the existence of four *spatial* dimension instead of four dimensional space-time has an advantage in that it also allows one to derive them by extrapolating the observable spatial properties of a three-dimensional environment to a fourth *spatial* dimension instead of as Einstein did by extrapolating the unobservable property of time to a space-time dimension.
Copyright 2012 Jeffrey O’Callaghan
Vol. 3 — 2012