From: *Bruno Marchal* <[email protected] <mailto:[email protected]>
On 8 Jun 2018, at 14:55, Bruce Kellett <[email protected]> wrote:
From: *Bruno Marchal* <[email protected] <mailto:[email protected]>>
On 8 Jun 2018, at 02:32, Bruce Kellett <[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.
Measure is quite different from counting.
And the probabilities for various outcomes most certainly depend on
the chosen base, as do the outcomes themselves.
Well, we can use what we call in French “le peigne de Dirac”. To make
that precise Laurent Schwartz has invented the theory of distribution.
I simplify things here. Consider that space has been quantised, like
in Loop-Gravity or something. Here, you do a 1004 fallacy, with
respect to the goal (helping Grayson to have an idea of what is
QM-without-collapse).
?
*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.
Everett prove the contrary, and he convinced me when I read it. I
found “his proof” used in many books on quantum computing, although
with different motivation. Thee result of an experiment, obviously
depend of what you measure, but when you embed the observer in the
wave, you get that what they find is independent of the choice of the
base used to describe the “observer” and the “observed”. If not, the
MW would already be refuted.
In that case, MW is refuted. Clearly, what the observer finds is
dependent on the basis in which he is described. Or else experiments
would not have definite results when described in the laboratory from
the 1p perspective. Even if you take the 'bird' view of the whole
multiverse -- which is, I agree, independent of the basis in which it is
described -- the view of any observer embedded in the multiverse is
totally basis-dependent. That is, after all, what we mean by 'worlds' --
the view from within, or the 1p view. But that view depends on how you
describe it: the way in which you partition the multiverse itself. Only
certain very special bases are robust against environmental decoherence
-- how else do you resolve the Schrödinger cat issue?
Bruce
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