On Tuesday, November 5, 2024 at 12:27:55 AM UTC-7 Russell Standish wrote:
On Mon, Nov 04, 2024 at 10:12:39PM -0800, Brent Meeker wrote: > > > > On 11/4/2024 9:47 PM, Alan Grayson wrote: > > > On an unrelated issue, I recall your mention that wrt the S. Cat thought > experiment, there is no > operator which has Alive and Dead as eigenvalues. IMO, this implies that > the S. Cat thought > experiment just doesn't fit into any quantum thought experiment. I then > realized that the P > operator for momentum must have a real value for its eigenvalues since it's > Hermitian, BUT > how can a real value represent momentum, which is a vector? TY, AG > > The eigenvector would be momentum. > Sorry Brent - the measured momentum values are still eigenvalues. Pick 3 orthogonal directions to measure the momentum, say x, y and z. Then the momentum operators are -iℏ∂/∂x, -iℏ∂/∂y and -iℏ∂/∂z, and the 3 eigenvalues are the 3 components of momentum. One could also write it in vector form iℏ∇, in which case the operator has a vector-valued eigenvalue. I don't think this is correct. Quantum operators are chosen to be Hermitian, that is, self-adjoint IIRC, so that their eigenvalues will be real. This is something that can be proven. So the question remains; how can a real eigenvalue be a measured momentum, which is a vector? AG ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders [email protected] http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- 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/bda8d28c-74ff-4c44-aaa6-311d30f7f640n%40googlegroups.com.
