I recently wrote about spatial rest and time here. This post is about the opposite: immediate motion, arriving at a destination instantly.
Immediate motion means an infinite speed. An infinite speed results in an immediate change of place: something moves from one location to another in an instant. It’s here and there at the same time. The departure and arrival are simultaneous.
A body at infinite speed is at two places at the same time, but a speed ratio has a finite time interval. If it’s the same time, how can there be a finite time interval?
For speed the time interval is fixed as the length changes. If the speed approaches infinity, then the travel length in the numerator approaches infinity, so the time interval in the denominator becomes a smaller and smaller proportion and the ratio approaches infinity. The body is at two places sinultaneously.
Immediate motion also means a zero pace. A zero pace results in an immediate change of time: something moves from one time to another in an instant. It’s now and then at the same location. The departure time and arrival time are at the same location. I’m calling this simulocus.
But wait, two times at the same location seems like no motion at all. What gives?
For pace the length interval is fixed as the time changes. If the pace approaches zero, then the travel time in the numerator approaches zero, so the length interval in the denominator becomes a larger and larger proportion and the ratio approaches zero. The body is at two times simulocusly.
Does immediate motion exist? Not under the Lorentz transformation, in which there is a finite maximum speed. But the Galilean transformation implicitly uses an infinite speed of light. And the dual Galilean transformation implicitly uses a zero pace of light.