On 3/19/2025 4:32 AM, Alan Grayson wrote:
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.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. BrentWhat above waves in spacetime? What's waving, and do they interfere with each other? AG
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