Joined: June 2006
|Yes. Messiah actually is proving <x^2><p^2> >= (.5h/2Pi)^2, but says that the results are analogous if one replaces x by x - <x>. He also says that the same reasoning applies to three spatial dimensions, but why do something three times when once will suffice? And once again, even if I screwed up, the choice of constant in the original differential equation is arbitrary. |
The choice of constant is simply to keep the vector in Hilbert space and serve as an accurate statistical tool for quantum mechanics. That is precisely the ratio for the deBroiglie, Heisenberg, and Schroedinger equations; nothing mysterious, just a statistical consequence. As for this:
|The "twist" is the node in the figure eight; this represents the boundary between information and physical space.|
You need to define what "information" and what "physical space" are. Is "information" U "physical space" = Hilbert Space? Is "information" c= "physical space"/Hilbert space? What are the properties of "information"/"physical space"? Does "information" represent square-integrable wave functions? How do "information" elements describe a quantum system? I understand this is a pathetic level of detail, but quantum mechanics as used in any discipline requires at a basic level of this kind of formalism.