On Fri, Jul 25, 2025 at 10:56 AM Alan Grayson <[email protected]> wrote:
> *>>>>If we're working with spin-1/2 particles like an electron then the UP > and DOWN states form one complete basis, while LEFT and RIGHT states form > another complete basis. Since both are bases for the same two-dimensional > Hilbert space, any state in one basis can be expressed as a linear > combination of states in the other basis. But if you've not actually made a > UP vs Down measurement then the particle is still in a superposition of UP > and DOWN, and if you then make a measurement of Left vs Right then there's > no way to ever know if the particle was ever originally UP or DOWN. That is > very weird but that's the way nature behaves. * > > > *>>> My problem is I can't imagine the geometry. AG* > > > *>> Think of up-down as being the x-axis and right-left being the > orthogonal Y-axis. An unmeasured electron is in a superposition, not > necessarily 50-50, of up-down and left-right. If you knew exactly where > that unmeasured electron should be on those two axes then you would know > it's exact position and momentum, but that is impossible because if you > measure the exact up-down then you have no idea of the left-right, and if > you measure the left-right exactly then you have no idea of the up-down, > although you can make approximate measurements of both. * > > > *> But before the measurement in the SG experiment, the electron is > entirely in the Y-axis?* > *Before the experiment the right-left orientation was unknown and so was its position on the Y-axis, and the same thing could be said about up-down and the X-axis. * > *> What's the logic for inferring a superposition in this situation? AG * > *If you randomly rotate a Stern–Gerlach magnet and arbitrarily give that direction the name "the up-down axis" then if you measure a number of previously unmeasured electrons with that device you will always find that it will detect 50% of them as being spin up and 50% as spin down. So before it was measured physicists say the electron was in a superposition of spin-up and spin-down. * *After that measurement we now know that every electron is definitely spin-up or spin-down, but the electrons are still in a superposition of spin-right and spin-left. We could rotate the SG magnet 90° and measure the electrons again and if we did we would definitely know that every electron was either spin right or spin left, but if we did that we would no longer know anything about spin-up or spin-down.* John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis> dsu -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/CAJPayv24cdrOt4Dcn3a3JJntf20wo853_LZv8VQt2-3cuTzS%3Dw%40mail.gmail.com.
