Oh you brought that up too soon in the thread. I would run across the one bright guy so soon. You have a good point (I think) that if a spinning ring dilates to an observer, it will appear to have a shorter circumference. I will have to calculate to see if it matches the track properly. I am just trying to come up with situations to bring out an error that I know is there already due to other issues. Perhaps this is insufficient.
Lorentz assumes the distance to dilate and then adjusts everything to match it. That forms a “consistent system of logic” that can possibly be perfect as long as it doesn’t ever violate anything else (no other assumption will be free in that nothing is independent of anything else, but you can use a single one as a base). I’ll have to give this some more thought. Thank you.
They each choose time and distance to measure velocity. If either chooses a different ratio between those, they WILL measure a different velocity. There is nothing magical about that. The track is seen as shorter by special relativity (distance). It seems far more magical to me to assume that they see the same track as a different length.
Lorentz assumes distance dilation
Saint assumes velocity dilation
The only question is which of those cannot fit the rest of reality without making even more non-intuitive assumptions, if either.
Think of it like this:
On the roof of the train, there is a sodium light bulb. There is an equivalent bulb hanging over the tracks at the station. Also on the train is an observer with a spectroscope, and there is a second observer with an equivalent spectroscope at the station. As the train approaches the station, the observation of the light from the train’s bulb by the observer at the platform will show that the spectral lines of the sodium bulb have been blue-shifted, proportionally to the velocity of the train. The observer on the train will see an exactly equal blue-shifting of the light from the bulb at the station. This is obvious, and easily experimentally tested. There’s no need to measure lengths to calculate relative velocity; one can do it purely using this method. This avoids any question of whether the observer on the train can measure a different velocity because of the length or time dilation issues - it’s impossible. Plain and simple.
Such shifting is an issue of time and distance. The distance between the wave peaks determines the spectrum as time passes (frequency). The source of the light is proposed to be causing a faster cycle time due to its motion toward the station. But it also assumes the consistency of the speed of light travel to the observer (each peak). One assumption offsets the other. So even seeing the effect you mention, doesn’t resolve which of 2 possible variables is “right”.
Special relativity says the speed of light IS consistent (not merely observed to be).
Saint says the speed of light is not consistent, but will merely be observed to be.
It is an issue of two wrongs may not make a right, but lefts will. The question is who is really making the 3 lefts?
It is similar to Galileo and the Church concerning the Helical universe.