On Sunday, July 27, 2025 at 5:45:27 AM UTC-6 John Clark wrote:
On Sat, Jul 26, 2025 at 6:34 PM Alan Grayson <[email protected]> wrote: > *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.* [...] *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. * *Your reasoning would be perfectly correct if we were dealing with classical vectors where the components of directional vectors are real numbers in 3D space and orthogonal components are 100% independent. But quantum spin states are not like that, they're vectors in 2-dimensional Hilbert space and, unlike the sort of vectors that classical physics usually uses, they absolutely require imaginary numbers. And even though the experiment is being performed in 3-D space the electron only has two independent bases states not three. Regardless of if you choose to measure up-down or right-left you're working in the same 2D Hilbert space where any state expressible in one basis can be written in the other.* *Vector spaces have associated fields such as complex numbers, and I never heard that Von Neumann changed the rules of vectors spaces when he applied them to QM. Can you cite such a change? It's so radical that it must be clearly documented. AG* *I know that everything I said in the above sounds very weird verging on the ridiculous, however the truth of it has been experimentally confirmed! If you prepare electrons in the up state and then measure them along the right left orthogonal axis you always get a 50-50 probability. That would be impossible with classical vectors made of independent components, but not if the vectors are composed of quantum states. And it's important to remember that although we use the words up, down, right and left they should be thought of as quantum states NOT directions. Your intuition is fine in classical physics but nobody's intuition is of much use in Quantum Mechanics. * John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis> tig -- 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/09cf11ba-f4b9-4497-a73f-978942d1f2adn%40googlegroups.com.
