On Tuesday, June 12, 2018 at 9:16:31 PM UTC-5, Bruce wrote: > > From: Lawrence Crowell <goldenfield...@gmail.com <javascript:>> > > > On Tuesday, June 12, 2018 at 7:05:34 PM UTC-5, Bruce wrote: >> >> >> >> No problem for QM -- one does it all the time. It might not be the most >> useful basis, but that doesn't mean it isn't possible. In general, however, >> one has a 'preferred basis'; a basis which is stable against environmental >> decoherence -- the one corresponding to what one actually sees in the >> laboratory. >> >> Bruce >> > > The basis that is stable against environmental quantum noise has energy > eigenvalues. > > > There may be an energy basis that is stable against environmental > decoherence, but that is not the only one. There is also a position basis, > a momentum basis, and so on. > > Energy is tied to entropy and information. Bases such as for angle (Stern > Gerlach measurements etc) or angular momentum without breaking the SO(3) > symmetry so Bessel functions --> Legendre functions and L_z defines energy > have no such einselection property. > > > What are you talking about? > > The many bases for the rotations of a spin half particle are all stable > against decoherence, unless one introduces magnetic fields into the > interaction with the environment. In other words, orienting one's SG magnet > at some angle produces a stable eigenstate. But one actually requires a > position measurement to determine which state this is. Energy does not come > into the picture. > > Bruce >
This is an ill-formed idea I will admit. The thought is that something such as the spin basis is selected by the orientation of an apparatus or magnetic field imposed on the system. The energy basis seems a bit different in that for energy of atomic spectra this is einselected more by the system measured. I can choose the basis for spin as anything with 4π steradians, but have less freedom with respect to energy.eigenvalues. Momentum and position are proper conjugate variables, but there is no such thing as a time operator. A quantum time operator would imply time is a generator of energy and this can be continuous and unbounded below. That is trouble. Of course there are AdS and Taub-NUT spacetimes where this might happen, but ... for later. Energy is a bit odd in both relativity and quantum mechanics. I maintain it is the basis which has some natural einselection process when the number of Planck units S = Nħ is large. I seems possible the other quantum observables are only stabilized as a classical outcome when there is some outside action by a classical-like system or one with a large number of states or S = Nħ is large. LC -- 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 post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
