On Mon, Jul 28, 2025 at 1:11 AM Alan Grayson <[email protected]> wrote:
*> Really?* *Yes really, except when complex numbers are required. * *> **a quantum state is a linear sum of the possible states of a > system after measurement. Do you disagree with this definition? * *I don't disagree with your definition but we know from experiment that quantum objects behave differently than classical objects, therefore they MUST be treated differently mathematically. A** spinning electron is in a linear sum of complex quantum states in abstract 2D Hilbert space, BUT a spinning basketball is in a sum of real directions and magnitudes in real 3-D space. Your problem is not in the manipulation of mathematical symbols, your problem is knowing what mathematical device should be associated with what physical trait. To summarize: * *Quantum amplitudes are complex; classical vector components are real.* *Electron spin lives in abstract 2D Hilbert space; classical angular momentum lives in real 3D physical space.* *Quantum states are abstract mathematical objects; classical vectors represent measurable physical quantities in space.* *And although it has some analogist behaviors, an electron isn't really "spinning" at all, it's a completely different beast. * John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis> akk -- 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/CAJPayv2SXcxLoHpnp1ELtFCiVs9H0Rj6Xjve-wbzbhO5C2B61A%40mail.gmail.com.
