Relativity Paradox: Resolving Hand-Waving Questions

[Reshma]

Suppose two observers are in relative motion each carrying a meter stick in a position parallel to the relative motion. Each observer on measurement finds the other's stick shorter than his.
On a lighter note; isn't this situation similar to a situation in which "A" waves his hand to "B", in the rear of a moving vechicle driving away from "B". "A" says "B" gets smaller and "B" says "A" gets smaller?

However, by the Lorentz transformation equations, the length of a body transverse to relative motion is measured the same by all inertial observers. So how is the above apparent paradox resolved?

 

[Jimmy Snyder]

Suppose two observers are in relative motion each carrying a meter stick in a position parallel to the relative motion. Each observer on measurement finds the other's stick shorter than his.
On a lighter note; isn't this situation similar to a situation in which "A" waves his hand to "B", in the rear of a moving vechicle driving away from "B". "A" says "B" gets smaller and "B" says "A" gets smaller?

The issue is not what you would see, but rather what you would measure. While it is true that we see objects getting smaller as they recede, it is not true that they are changing size. If we measure a thing as 1 meter when it is close and seems large, we will still measure it to be 1 meter when it is far and seems small.

 

[kleinwolf]

I would say the apparent paradox could be resolved by a third observer : moving away from A makes A smaller but B bigger. However, taking two "similar bodies" A and B, C will measure the same sizes in A and arriving in B... However let's take 2 synchonized clocks by a signal sender in the center of mass of them. Then a moving observer would synchronize when passing in A and arriving in B he will notice his clock is not showing the same as B..(? at least I suppose)...

 

[JesseM]

jimmysnyder already gave the answer to this problem, the lorentz contraction formula does not apply to what observers see using light-signals, it applies to the coordinates they assign events in their own reference frame. See jtbell's comment on this thread on the difference between "seeing" and "observing" in relativity.