On Saturday, July 26, 2025 at 1:05:27 PM UTC-6 John Clark wrote:
On Sat, Jul 26, 2025 at 1:17 PM Alan Grayson <agrays...@gmail.com> wrote: *>> If you make a measurement with a Stern–Gerlach magnet and determine that an electron is spin up, that is equivalent to saying the electron is in a superposition of spin left PLUS spin right along the orthogonal axis. And it would be the same for spin down except that then, instead of being a superposition of spin left PLUS spin right, it would be a superposition of spin left MINUS spin right.* *> What orientation of the axes are you using to get that result? Please be explicit. AG * *I'm not sure what you mean by that. Place a point at the center of a Stern–Gerlach magnet and place another point randomly at any point on the outside circumference, draw a line between those two points in extended in both directions to infinity, that is one axis, arbitrarily call one direction along that axis "up" and the other direction "down". Now draw another line 90° from the first one, that is your other axis, pick one direction along that axis at random and call it "left", and the other direction "right" * *> I don't follow. Isn't UP / DN along the path taken by the electrons when they exit the apparatus?* *The direction you want to call UP/DN is entirely up to you, but whatever axis you pick if an unmeasured electron enters a Stern–Gerlach magnet** that is oriented along that axis then there's a 50% chance it will go up and a 50% chance it will go down.* *Suppose I choose UP/DN axis along the path the electron moves when exiting the apparatus, and RT/LT perpendicular to that axis. In this case, you cannot write UP or DN as a linear combination of RT/LT. It's like the situation I previously cited in the plane using the orthogonal unit vectors as basis vectors. AG * *And if you now rotate the magnet by 90° and call one end of that new axis left and the other end right and an unmeasured electron enters the magnet then there's a 50% chance it will go left and a 50% chance it will go right, and you'd get exactly the same result if the electron had not been unmeasured but instead had been measured to be spin up. * *> How is RT / LT defined? AG * *Spin left is defined as the superposition of spin up PLUS spin down. Spin right is the superposition of spin up MINUS spin down.* *You might object that the minus sign makes no observable difference because the probability is the square of the absolute value of the quantum wave function and a minus times a minus is a plus; and that's true in some circumstances but not in others. If X interacts with Y and then I measure the outcome it makes no difference, BUT if X interacts with Y and then I do NOT measure the result, but whatever the result is if I let it interact with Z and then measure it, then it does make a difference. That's why engineers who make quantum computers have to make sure that there's no way intermediate results of the machine can be determined, because if there is it would destroy the superposition and the computation. * John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis> otm -- 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 everything-list+unsubscr...@googlegroups.com. To view this discussion visit https://groups.google.com/d/msgid/everything-list/677d7646-5c22-4227-801e-5c848140f4d6n%40googlegroups.com.
