Carleas wrote:James S Saint wrote:So??
So the distance traveled by a point on the edge of the spinner is the arc length. Since the arc length differs for the two observers, but the speed is the same (it's c for both observers), the time it takes the point to travel that distance differs for the two observers.
Still, what's the point? Are you saying that the train will see its light spinner turning slower because it is moving?
Carleas wrote:James S Saint wrote:the two line count will be steadily twice the one line count
While I agree with PhysBang that these infinities aren't countable,
Whole number lines ARE "countable".
Carleas wrote:There's an isomorphism that maps each entity in a single number line onto each entity in two number lines, so the two infinite sets contain the same number of entities.
The counts do not converge. They stay exactly different by a factor of 2 from zero up to infinity. What rationale do you have for proposing that magically at infinity they suddenly become the same?
I wasn't "arguing" using the point. I mentioned that such was how I knew.Carleas wrote:James S Saint wrote:I am not going to go through that on this thread.
That's fine, it's a complex issue. But if you don't go through it, you can't use it as an assumption in the argument that "distance doesn't dilate because what causes distance is the number of points between one affect and another." I dispute that distance dilation requires that there be a different number of points between two events in different frames, and I will not accept it as a premise in an argument.