Energy minus momentum has a constant value (which we call rest mass).
Reviewing *EQ9 with c = 1 and hence
Omitting reference to v for simplicity
Note that the motion in general has x, y and z components, so x2 can be replaced by
in *EQ18 and *EQ19.
These equations have an intriguing interpretation. Recall that on a number plane the square of the distance between two points is:
In three dimensions the square of the distance is:
where x, y, z denote the differences between the co-ordinates of the points. In Newtonian physics the value of d is the same no matter what the velocity of the source.
The theory of relativity, which apparently better reflects reality, predicts that such measures are not invariant but that the following is:
This formula is expressed using four parameters or dimensions, the three Newtonian ones (x, y, z), called the spatial dimensions, plus time. Note that the time dimension has a special place in the equation and cannot be interchanged (like x, y and z can) without effecting r. The four dimensional universe described by the four parameters is therefore called Space-time.
where k is some constant, is also independent of changes due to velocity in the same way as Px + Py + Pz for conservation of momentum in Newtonian Physics.
Note that these constants can be either positive or negative, unlike the Newtonian measure which is always positive.
If then the measure is said to be time like, and r is a real number, otherwise, the measure is space like and r is an imaginary number. All events which can effect an object at a particular time have a space like measure relative to the object at that time.
Hence *EQ17 is the law of conservative of momentum, improved to meet the theoretical and experimental results. The implication is that Energy is a special kind of momentum in the time or fourth dimension. As an object increases in velocity its space and time characteristics blend together as seen by a stationary observer.
Throughout this essay assumptions have been made, where others might just as well have been. The justification for the accuracy of a theory does not lie in the elegance of the mathematics, but in confirmation by experiment. So far relativity has proved a better approximation to reality than any other theory. If a start is made with the concepts of conservation of momentum, mass and energy and distance in four dimensions, the variations in time, distance in three dimensions and mass are direct consequences.
This document was created on 23 August 1995
last modified on 23 August 1995
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