Goldstein pg 151 says "it is clear that an inversion of a right-handed system into a left-handed one cannot be accomplished by any rigid change in the coordinate axis..." I am trying to understand what he means by a rigid change... is he saying that an inversion is a discontinuous jump that is impossible for an object to achieve? why can't it?
I can see clearly that the inversion (improper rotation) will be associated with a sort of jump(discontinuity) upon the mirror reflection... but I'm a little confused on the definition of a "rigid change". maybe the problem isn't the discontinuity of a mirror reflection but has to do with the change of handedness upon reflection??
goldstein also writes: " An inversion never corresponds to a physical displacement of a rigid body."
i'm a little confused as to what is the problem with inverting the z-axis??? how does that change the physics?
also, please do not talk about the quantum tunnelling aspect, I am having a problem understanding this classically and I don't want to get into all that ...
( let's say you take the vector r = (1,0,1) in a right handed cartesian coordinate system, then you rotate it 180 degrees you get the vector r' = (-1,0,1) in the new coordinate system, now if you "invert" the z-axis what is the problem with that in terms of "rigid change". why is that not a rigid change????)
as a further note in the example I am working with I think it's important to keep the transformations passive ( rotate the coordinate system 180 degrees counterclockwise and then do the inversion).