On Monday, March 17, 2025 at 9:45:50 PM UTC-6 Brent Meeker wrote:
On 3/16/2025 1:51 PM, Alan Grayson wrote: 1) What necessitates the use of complex numbers (whereas in GR only real numbers are used)? QM exhibits interference so it must have wave-like phases that can add and subtract. It predicts probabilities which must be positive numbers. So one way to do this mathematically is to have probability *amplitudes*, Psi, that are the "square root" of probabilities, Psi*Psi (where * denotes the Hermitian conjugate), that have phases so they can interfere. Then the dynamics are linear in the Psi. 2) What necessitates the postulates that some, but presumably not all operators are non commuting? 3) With respect to 2), why is the non commuting difference i*h (or i*hbar)? It is conjugate pairs that fail to commute. See attached. Brent That's the definition of conjugate pairs, that they don't commute. I notice that E and t are also considered conjugate pairs, but since t is a parameter in QM and not an operator, how can that be intelligible? AG -- 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/14f9ce66-10af-4272-8574-a8b5a8799414n%40googlegroups.com.
