Re: Relativity

["Paul Camp" <pjcamp@coastal.edu>]

>   Hi,
>
> 	Concerning the relatisticly rotating and translating wheel:
> Two comments:
>
> 	1.  To the observer translating relative to the
> wheel, each part of the wheel is in a different reference frame.
>
> 	2.   Special relativity does not really apply to a 
> any part of the rim of a rotating wheel because each piece is
> accelerating, and NOT an inertial frame.
I had thought about this too (I'm still thinking about David's 
most recent comments). While it is not true that special relativity 
can only be applied to non-accelerated frames (the explanation of 
Thomas Precession is a good example of this), it is not clear to me 
that this case is similar to those, at least for anything resembling 
a real object. As I commented back at the beginning of this thread, 
there is a reason why you seldom see consideration of extended 
objects in relativity -- most of the simplifying assumptions that 
make the corresponding Newtonian problems tractable turn out to be 
invalid.

> 	But it is an interesting problem.  On first thought, 
> the path to the solution would seem to be to consider a non- rotating
> wheel next to the rotating one ( or a non-rotating groove containing the 
> rotating ring with a very small clearance).  Thus it would seem
> that the shapes of the rotating and non-rotating wheels must vary in the 
> same way.  BUT there is the problem of simultaneity,  like the problem of
> something longer than the barn in one frame being momentarily enclosed by
> the barn in another frame.
>
>
> Thanks
> roger haar U of AZ

That is a very interesting comment and is essentially what Terrell 
and other were on about many years ago. The appearance of a rapidly 
moving extended object should, it seems to me, depend not only on the 
relative speed but also on where you stand to observe it. If it flies 
directly at your eyeballs, light from the left and right hand sides 
take the same amount of time to reach you. If you stand off to one 
side, light from the near side gets there first. If the object is 
moving fast enough for Lorentz effects to be important, it is moving 
fast enough for this effect to be important too. (This is basically 
similar to the superluminal illusion in some quasar jets.) Oh dear, I 
think I'll stop there right now since this thread is in danger of 
leaking into the movie camera thread. 8-)

Paul J. Camp                   "The Beauty of the Universe
Assistant Professor of Physics  consists not only of unity
Coastal Carolina University     in variety but also of 
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pjcamp@coastal.edu                    --Umberto Eco
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