I am still confused. I thought velocity in the Time Region was a second power expression of velocity in the Time Space Region.
Yes, Larson is confusing. His lack of diagrams make it very difficult to understand a lot of the concepts.
In the time region, motion is in time, only. Space is fixed at a unity. Speed is s/t. But you cannot have "s" in the time region, so he substitutes 1/t for s in the speed equation, resulting in s/t = (1/t)/t = 1/t
2, the time region speed--as measured inside the time region. We cannot observe or measure time directly, only spatial relationships, so we only see that 2nd-power temporal relation indirectly in atomic properties and behavior.
But you are saying equivalent space is a second power version of space "projected from the time region". How can both these statements be true?
Larson is not very clear on equivalent space. Nehru does a much better job in his papers, particularly the one on sunspots where he uses equivalent space to explain a new form of magnetism--thermal motion (a speed) in the 2nd-power equivalent space becomes a magnetic motion.
Essentially, equivalent space is the observable and measureable effect that motion in time has upon spatial relationships. All of the force field effects, like electric charge, magnetism and gravity, are in equivalent space because they are an effect of motion in time, the "shadow on the wall" of Plato's cave. We cannot see the actual, temporal motions involved.
Just as when entering the time region, you had to replace s with 1/t to get 1/t
2, coming back out you have to do the same thing, and replace t with 1/s, so you get 1/(1/s)
2 = s
2-- the 2nd power relation of equivalent space.
I apologize for my ignorance and i appreciate your time to correct my thinking.
Not a problem... I remember the difficulties when I started learning the RS!