Question about something in the Elegant Universe book I am reading...(KelseyMH?)

Ok, here it goes:   In the description concerning general relativity, the following scenario is depicted:  Jim and Slim are riding a "Tornado" ride (goes by different names, but essentially is a centrifuge that pins you against the outer wall and then drops the floor out from under you. Sometimes calle d PUKE machine).
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?  :-)

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rimar20005 years ago
Just in case, when driving do not go near the speed of light.
Goodhart (author)  rimar20005 years ago
whether slow of fast, the effects are still there, just a LOT harder to measure at slower speeds :-D
Yesterday afternoon, a woman who had using cellphone while driving hit my rear bumper, after a ten meters braking. Fortunately neither my wife nor me nor the woman had hurt, but the rear of my car YES. Now I have two new tasks: 1) get the compensation from her insurance company, and 2) make repair the rear of the car, including trunk. Light's speed is not practical fron driving!.
Goodhart (author)  rimar20005 years ago
No, and too bad the other driver's forward motion was not "shortened" by linear compression enough to avoid the accident :-) I am glad all are well however.
Kiteman5 years ago
Mergh!

I think you're right - if they are measuring the circumference with a ruler on the circumference, then they would both be subject to the same effects.

Maybe they are comparing the circumference to an external, stationary scale? Kind of like a circular ruler, just outside the spinning area?
Goodhart (author)  Kiteman5 years ago
He claims he is using he same "ruler" to measure each time. It really bothered me to see what appears to be a rather poor analogy being used by Brian Greene. :-( But since the movement is not linear, maybe he is speaking of the warping of space (as on a sphere)?
kelseymh5 years ago
Hi, Goodhart. The description of the experiment you've written is certainly wrong.

For a "stationary" observer far from the rotating ring, we would measure the circumference = pi * diameter.

For an observer co-rotating with the ring, who measured the circumference by walking around it, they would also get pi*diameter. That's because (as Kiteman and you noted) that observer is at rest in the frame of the rotating ring.

The complex relativistic effects kick in if, for example, the folks on the ring were actually spinning around past a nice marked ruler on the ground below the ring. In that case, if they tried to measure the marked ruler as it spun "backwards" past them, then they would indeed observe a shorter length. Hence, they would infer that the circumference of that painted ruler was < pi*diameter.
Goodhart (author)  kelseymh5 years ago
It just struck me while I was reading that he possibly meant something other than what was written. His explanation later on states that the spinning "ride" is in warped or curved space, and so the circumference becomes < the stationary point of view. But this only leaves more questions in my brain about why the stationary person, viewing warped space would not see the same measurements as the one insid the ride. But then, maybe his analolgy was not meant to cover all of this, just the motion of the person?
Ah, I see your point.

There are differences between rotational motion and linear motion in general relativity. In particular, uniform rotation has an accelative component, which we know (from GR) is equivalent to a (kind of weird :-) gravitational field.

That means the rotating ride in flat spacetime can be described equivalently as being at rest in a special curved spacetime (please don't ask be to write down the solution!). Therefore, it is plausible that observers on the ring itself might well measure a non-Euclidean circumference, but I don't know how to derive the result quantitatively.
Goodhart (author)  kelseymh5 years ago
Ok, I wouldn't "get" the math anyways. That part wasn't explained well, he just kind of said it happened, and didn't mention (outright) that the rotational motion were different. So, I can't "find fault" in what he said, just in how he explained it then :-) Thank you for your help in working through this one !