On Wednesday, March 19, 2025 at 3:23:16 PM UTC-6 Brent Meeker wrote:
On 3/19/2025 4:32 AM, Alan Grayson wrote: 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 What above waves in spacetime? What's waving, and do they interfere with each other? AG That would be gravitational waves and what's waving is the gravitational potential, i.e. local curvature of the metric. And yes they interfere, although I can't think of any direct measurement of that. Brent As I recall, the gravitational potential is the negative derivative of the gravitational force, but if there's no force in GR, how is that measured? 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 everything-list+unsubscr...@googlegroups.com. To view this discussion visit https://groups.google.com/d/msgid/everything-list/84a3ce75-63b9-41d8-8372-57103d6ca0ccn%40googlegroups.com.
