From: scerir (scerir@libero.it)
Date: Thu Dec 05 2002 - 15:02:28 MST
[B. de Witt]
> > > "The universe is constantly splitting into a stupendous
> > > number of branches, all resulting from the measurement
> > > like interactions between its myriads of components.
> > > Moreover, every quantum transition taking place on
> > > every galaxy, in every remote corner of the universe
> > > is splitting our local world into myriads of copies
> > > of itself"
[me]
> > So: just measurements (irreversible) or also quantum
> > interactions (not irreversible) can cause the splitting
> > of the worlds? [Imo quantum interaction could also cause
> > a sort of de-splitting, or fusion of worlds, because of the
> > unavoidable interference].
[Rafal]
> This is interesting. Did he mean an instantaneous splitting,
> or something moving with a finite speed?
So: when precisely does the branching happens?
QM does not determine the time at which the (supposed!)
branching happens. But the question above has a 'quantic'
nature. Hence we can expect its answer (if any) must be
probabilistic.
I would reject an answer like 'the branching happens
instantaneously' because this would mean that QM
can give a 'sharp' answer to the branching timing.
And also because the mathematical 'exact' description
of those splitted 'relatives states' (in the configuration
space) is not 'precisely' attained (in realistic, physical
cases). (This one is a big problem, because
the MWI was invented not as an interpretation but as
a metatheorem: 'the mathematical formalism of QM yields
its own interpretation'. But very soon Everett and de Witt
attached physical corollaries to that 'mathematical
formalism'....).
But in a very speculative way we can define a projection
operator "SPLIT" with the (eigen)value = 1 meaning "the
branching has happened", and the (eigen)value = 0 meaning
"the branching has not happened".
If Psi(t) is the state of (two) coupled quantum systems,
evolving fron t=t1 to t=t2, we can write
P(t) = <Psi(t)|SPLIT|Psi(t)>
where P(t) is the probability that the branching happened.
And we can also write
p(t) = <Psi(t)|[SPLIT,H]|Psi(t)>
where p(t) is the probability density that a branching
occurred between t and t+dt, and H is the Hamiltonian
of the coupled systems.
I can imagine that P(t) grows monotonically from zero
to one, while p(t) should be a 'bell' curve defining
the time at which the branching happens.
Sometimes de Witt, according to his postulate of complexity,
decomposes the world into systems and apparata. In this case
the branching takes places at a measurement. And we can
use the (SPLIT) model above, thus (perhaps) avoiding the
so called von Neumann 'cut' ('How does one define a
measurement? Where does a measurement take place?')
and the so called Heisenberg 'prohibition' ('We must
abstain from asking "in between" questions').
Sometimes de Witt presents the alternative possibility
that the branching takes place at any interaction. In this
case we can ask: how strong must be this interaction before
the branching actually occurs and the interference vanishes?
John Bell writes:" Thus the structure of the wave function
is not fundamentally tree-like. It does not associate a
particular branch at the present time with any particular branch
in the past any more than with any particular branch in the future.
Moreover, it even seems reasonable to regard the coalescence
of previously different branches, and the resulting
interference phenomena, as *the* characteristic feature of
quantum mechanics. In this respect an accurate picture, which
does not have any tree-like character, is the sum over all possible
paths' of Feynman".
.... at uncertain times and places, it is thus indeterminate
and unpredictable, an aspect of random dispersion ...
Illud in his quoque te rebus cognoscere avemus
Corpora cum deorsum rectum per inane feruntur
Ponderibus propriis, incerto tempore ferme
Incertisque locis spatio depellere paulum,
Tantum quod momen mutatum dicere possis.
- Titus Lucretius Carus, De Rerum Natura,
II, 216-224
Or, in other terms: "[The following words] have no place
in a formulation with any pretension to physical precision:
system, apparatus, environment, microscopic, macroscopic,
reversible, irreversible, observable, information, measurement ..."
- John Bell, "Against Measurement", Physics World, August 1990
Illud in his quoque te rebus cognoscere avemusCorpora cumdeorsum rectum per
inane ferunturPonderibus propriis, incerto tempore ferme Incertisque locis
spatio depellere paulum,Illud in his quoque te rebus cognoscere
avemusCorpora cumdeorsum rectum per inane ferunturPonderibus propriis,
incerto tempore ferme Incertisque locis spatio depellere paulum,
Illud in his quoque te rebus cognoscere avemusCorpora cumdeorsum rectum per
inane ferunturPonderibus propriis, incerto tempore ferme Incertisque locis
spatio depellere paulum,
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