On Friday, June 8, 2018 at 12:55:13 PM UTC, Bruce wrote:
>
> From: *Bruno Marchal* <[email protected] <javascript:>>
>
> On 8 Jun 2018, at 02:32, Bruce Kellett < <javascript:>
> [email protected] <javascript:>> 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.
*If we measure E, aren't we defacto measuring p, since the two observables
are related by a simple mathematical expression? Yet you assert they
represent different worlds. Is this because the measuring apparatus differs
if the observable are different? AG *
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.
*You seem to be regressing, or shall we say relapsing into the fallacy.
ISTM you have previously acknowledged that we don't see superpositions of
live and dead cats because of the fallacy of including macro entities in a
superposition -- which is what Edwin was trying to warn us against. Nothing
to do about robustness against environmental decoherence, which assumes an
actual superposition exists for some short duration. CMIIAW. AG *
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
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