On 2/9/2021 7:55 PM, Alan Grayson wrote:
Hilbert space is a kind of vector space. Vectors can always be
expressed in terms of different basis vectors.
*I've refreshed my understanding of Hilbert spaces. So, if you really
believe your second sentence above, doesn't it make the idea many
worlds, whose existence depends on the selection of basis, ambiguous
(to say the least)? AG *
Many worlds does not depend on an arbitrary selection of basis by us.
It depends on there being some basis selected by nature as the one
stable against environmental variations, "pointer basis". Presumably
this is selected by the dynamics of the Schroedinger equation although
that hasn't been worked out. So "selected" means two different things
in those cases.
Bent
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