Question about something in the Elegant Universe book I am reading...(KelseyMH?)
Anyways, looking at the ride from a bird's eye view, one measures the circumference and the radius and we find that the ratio is two times PI or about 6.28.
Now that is from OUR perspective, but from Slim's and Jim's measuring the circumference (so says the book) will give a different answer since they are traveling at high speed (assuming the speed is fast enough to invoke the Lorentz contraction). Thus, he says in the book that his measurement will come up short and therefore not be the same ratio noted. I don't doubt this, but I have a problem with not taking into account the lengthing of the circumference because of IT'S motion forward.
Am I missing something? Why wouldn't the same effect be proportional to the lengthening of the ruler used to measure the circumference, seeing they are traveling at the same speed?
Am I taking his example TOO FAR (in other words, he is assuming the ride is there but not physical)? Maybe I over analyze? :-)