Dimensions

 

The Twilight Zone

You are about to enter another dimension.
A dimension not only of sight and sound, but of mind.
A journey into a wondrous land of imagination.
Next stop, the Twilight Zone!

A dimension of the imagination?

Herman Minkowski realized that the special theory of relativity, introduced by his former student Albert Einstein,  could best be understood in a four-dimensional space, which has come to be known as "Minkowski spacetime", in which time and space are not separated, but combined in a four-dimensional space–time. Then special relativity can be effectively represented using an invariant constant which is equal to  x²+y²+z²-c²t^{2 .} or (x²+y²+z²)-c²t². Pythagoras’s Theorem is only the special case when eccentricity is equal to one and is only true for a flat surface. In case anyone needs a hint,
x²-y²= 1 is the formula for a hyperbola. Only if time OR space is equal to zero should this be solved using Pythagoras’s Theorem. Unfortunately, the Lorentz Transform solved it using Pythagoras’s Theorem.

Graphically, Minkowski space typically has been presented as a two dimensional graph where the three spatial dimensions: x, y and z; were combined into one dimension of space versus another dimension of time. But because the invariant constant involves squares, this should really be not solved for a flat, Euclidean, surface. It should be solved for a hyperbolic surface, and a third dimension should be added which is indeed one of imagination, based on the imaginary number, √-1. This cone of events should be plotted with dimensions of space, time, AND imagination. Hyperbolic functions of space and time only repeat in imaginary planes and would be a single function on a hyperbolic surface. E.g. Cosh(x) has a period of 2πi which repeats only in the imaginary plane. These other planes of the imagination can  be thought of as the multiverse, which is distinguished from the “real” plane on which we live. Using the three dimensions,  the event space would be two cones which intersect at the origin, the Big Bang, which is the opposite of Twilight Zone, where all imaginations are zero.