STR with "Snow Globe Theory"
UFO (U) flies past me (B) at high speed v. At the same moment, I send a beam of light in the direction of flight.
Since the UFO is moving close to the speed of light c, I find it with sensors not far behind the light front (N).
Unfortunately, I can't see this despite the dusty cloud, because light takes a certain amount of time.
The light could just as easily have been emitted by the UFO, with the same light front; otherwise,
there would be superluminal speed. The short distance N-U makes it seem as if light were moving more slowly in system U.*
However, with the "snow globe theory" and Theorem S3, the speed of light there is the same as everywhere else in the world.
After time t, the distance N-U is measured as (c-v)·t.
Can I use this to determine the factor of scale changes (F)?
This distance from U to N has a length c·t' in system U, where t' is time there.
The inverse of the observed length contraction and thus the time dilation is:
The time t' in system U corresponds to the time it takes for light to travel from U to N. For me (B), however, t is the time it takes for light to travel from B to N, my time from the beginning. The corresponding path in U is v·t'+c·t'. Velocity is length divided by time, so time is length divided by velocity. The time tU from B to N for light is t'·(v+c)/c . The factor for proper time (1/F) is calculated as t'·(v/c+1)/t. Solving for t:
Substituting this into the above equation and using the binomial formula, this gives F²=1/(1-v²/c²). Thus:
The factor of scale changes or time dilation is therefore the famous Lorentz factor.
Length shortening in STR
This is a fallacy. The UFO could just as easily fly in the other direction.
In that case, the speed would be negative, and the same formulas would apply.
t easily explains the Minkowski cone. The light fronts to the right and left of the UFO appear to be at different distances. Local, relative to a center line, they are the same distance away.
Ludwig Resch