- #1
etotheipi
Hey, sorry if this is a dumb question but I wondered if someone could clarify. If you have two Cartesian coordinate systems ##\mathcal{F}## and ##\mathcal{F}'## whose origins coincide except their ##x## axes point in opposite directions (i.e. ##\hat{x} = -\hat{x}'##), then the spin operators along their respective positive ##x## directions would seem to be related via. ##\hat{S}_x = - \hat{S}_{x'}##. AFAIK they're compatible because ##[\hat{S}_x, \hat{S}_{x'}] = 0##.
Does that mean that if you measure the observable corresponding to ##\hat{S}_x## to be a definite ##S_x##, then this automatically fixes ##S_{x'} = -S_x##? That's to say, does a single measurement cut it, or do you still need to actually measure the spin in each coordinate system individually?
Sorry if this doesn't make sense
Does that mean that if you measure the observable corresponding to ##\hat{S}_x## to be a definite ##S_x##, then this automatically fixes ##S_{x'} = -S_x##? That's to say, does a single measurement cut it, or do you still need to actually measure the spin in each coordinate system individually?
Sorry if this doesn't make sense