From: *Lawrence Crowell* <[email protected]
<mailto:[email protected]>>
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
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