Spacetime

 

It’s About Time

It's about time,
It's about space,
About strange people in the strangest place.
It's about time,
It's about flight,
Travelin' faster than the speed of light.

It's about Minkowski spacetime!

Minkowski space combines inertial space and time manifolds (x,y) with a non-inertial reference frame of space and time (x',t') into a four-dimensional model relating a position (inertial frame of reference) to the field (physics). A four-vector (x,y,z,t) consisting of coordinate axes such as a Euclidean space plus time may be used with the non-inertial frame to illustrate specifics of motion, but should not be confused with the spacetime model generally.          

 https://en.wikipedia.org/wiki/Minkowski_space

What this says!!!!  I may not understand this, but Einstein apparently did!

If space time is hyperbolic and not Euclidean how does this change things?

Minkowski space is used to describe the light cone , e.g. world lines of light, moving through space.

This cone looks very much like a one-sheet hyperboloid narrowed to a point at the origin, which is identical to a two-sheet hyperboloid where the separation between the two sheets is zero.

I have previously suggested that the shape of the universe is hyperbolic. (IMHO it appears locally Euclidean but is universally hyperbolic, much like geometry on the surface of the earth appears locally Euclidean but, over very large distances comparable to the radius of the Earth, is non-Euclidean and spherical.  I know that am not the originator of that hypothesis.  https://dbeagan.blogspot.com/2022/07/forever.html

If the shape of the universe is hyperbolic, then mathematics should seek non-Euclidean solutions. This has an implication on the speed-volume curve used in my field of traffic engineering, but also seems to have a bearing on:

·        physics, the Lorentz transform might be γ=1+ln(cosh(v/c)±sinh(v/c)), gravity might be only an apparent force and not one of the three intrinsic forces;

·        statistics, the only valid normal distribution might be the logistics distribution with s=0.5;

·        sociology and political science, tolerance, a SD of 0.6413, may be an intrinsic part of group dynamics, and

·        many other disciplines ( e. g. I suspect that my speed-volume curve findings will have an implication on Fluid Dynamics.)