From: *Bruno Marchal* <[email protected] <mailto:[email protected]>>
On 8 Jun 2018, at 02:32, Bruce Kellett <[email protected]
<mailto:[email protected]>> wrote:
The SWE does not give a preferred basis. Basing MWI on the
Schrödinger equation runs into the basis problem. Few MWI advocates
actually take this seriously. And they should.
The relative proportion of histories do not depend on the choice of
the base, so the base we use are chosen endemically, like the present
moment for example, in the whole of physics. Obviously, we needs brain
to assess our results and communicating, and some works, like sure and
others, justify the indexical importance of the position base, with
respect to the branch where intelligence can develop.
What on earth are you talking about? The position basis is not
well-defined either. The Hilbert space corresponding to the position
operator X has an infinite number of possible bases -- just like any
other Hilbert space. Any linear vector space has an infinite number of
possible bases. How do you choose which one you are going to use?
Talking about the relative proportion of histories sounds just like the
long-since refuted branch counting approach to probabilities. And the
probabilities for various outcomes most certainly depend on the chosen
base, as do the outcomes themselves.
*In this situation, what is the role of the SWE since the wf is
usually asserted without any reference to it? Now consider a general
case where the wf for a system is determined using the SWE. Since
the solution can be expanded using difference bases, say E or p,
does each possible expansion, each implying a different possible set
of measurements, imply a different set of worlds using the SWE? TIA, AG*
The Schrödinger equation merely gives the time evolution of the
system. To define the problem you have to specify a wave function. It
is in the expansion of this wave function in terms of a set of
possible eigenvalues that the preferred basis problem arises. So it
is not really down to the SE itself, it is a matter for the wave
function. Each expansion basis defines a set of worlds, and all bases
give different worlds.
That is correct, but the choice of the basis don’t change the relative
“proportion of histories”.
The choice of basis makes all the difference in the world. Now that we
understand decoherence, the only bases that are useful are those that
are robust against environmental decoherence. That is why we don't see
superpositions of live and dead cats -- that superposition base is not
robust.
It threats only the naïve conception of “worlds”, which has led to the
works of Griffith and Omnes (and Gel Mann & Hartle). That works
remains still a bit naïve with respect of the type of histories we can
encounter in arithmetic.
The consistent histories approach is just another way of considering
many worlds. The histories are no more unique than are the worlds.
Bruce
--
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 [email protected].
To post to this group, send email to [email protected].
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
