From: "mcintosh@servidor.unam.mx" <mcintosh@servidor.unam.mx> To: math-fun <math-fun@mailman.xmission.com> Cc: mcintosh@servidor.unam.mx Sent: Mon, December 28, 2009 3:53:34 PM Subject: Re: [math-fun] discrete version of exp(d/dz) Quoting Eugene Salamin <gene_salamin@yahoo.com>:
Can you explain the "strike at the roots of quantum mechanics"?
As Dirac noted, that commutation relation distinguished classical hamiltonian mechanics from the new quantum mechanics; he saw it as the harbinger of a whole new kind of science (oops! Ive quoted the wrong authority), with q-numbers and c-numbers. That was his reaction to Heisenberg's preprint (or rather, galley proofs). -hvm ________________________________ To quote you more fully: "Wintner's paper, as I recall, used the trace argument and the ladder operators had infinite traces, so there was a convergenceanomaly; in 1950 this did seem to strike at the roots of quantum mechanics." But what was the "strike at the roots of quantum mechanics" in 1950? By that date, quantum mechanics was generally well accepted. And what were the trace arguments that led to this strike? That the Heisenberg algebra has no finite dimensional representation should have no bearing on everyday quantum theory, though it perhaps excludes a [q,p]= i hbar type mechanics over finite spaces. -- Gene