Sunday, January 22, 2012

A Simpler Spacetime Distance

RANT 23: In Rant 21 it all started out OK but got bogged down in some tedious math. It has occurred to me that there's a much straighter road to the result that is really more dramatic. The axes in Rant 21 of Imag vs Real vs Time really harken back to a similar set of axes in Rant 6 where I tried to show that the Argand axes of Re and Im can be expanded into perpendicular planes. If now we apply the cross (vector)product to Re X Im we still get the third perpendiculcar axis BUT it will still lie in the Im plane. IF that axis is in fact TIME then it must be multiplied by i, the square root of -1. Now when we consider the Pythygorian theorem in "spacetime" to obtain what is called the "proper distance" (D) which includes the time axis as well as the space axis, we would write D^2 = R^2 + (iT)^2 = R^2 - T^2. We know that R^2 = X^2 + Y^2 + Z^2 so D = Square Root of (X^2+Y^2+Z^2-T^2). This is precisely the formula used by Einstein that showed that time is not disconnected from space and that SPACETIME is a integrated concept.