[extropy-chat] Is Many Worlds testable?
scerir
scerir at libero.it
Tue Jan 2 20:43:54 UTC 2007
>> It seems difficult to believe that MWI has nothing
>> to do with measurements.
John writes:
> It may be hard to believe but it's every bit
> as consistent as Copenhagen. In Copenhagen before
> a measurement is made the cat is both alive and dead;
> in Many Worlds the cat is either alive or dead.
> True, we will need a measurement to find out
> which state the cat is in, but our observation
> will not effect the cat. [...]
This is correct.
But I would say that in Copenhagen a quantum state
is more 'available information' (hence the collapse)
than physical entity. On the contrary, in MWI it is
a physical entity. Of course, there are 'nuances'
both in the Copenhagen and in the MWI.
>From the 'Everett faq' I get (if I understand
what I read) that measurement causes
the 'split' [1].
More carefully Bryce deWitt, in his last paper,
writes (following Everett and Wheeler) that
the total state vector |Psi> takes the form
|Psi> = Sum_s c_s |s> |Phi(s)>
which means that, relative to each system state
|s>, the apparatus state, represented by the
vector |Phi>, as a result of a _coupling_
between the state and the apparatus, goes into
the corresponding state |Phi(s)>. All the possible
outcomes of the measurement are contained
in the superposition above, weighted by
coefficients c_s determined by the system state
vector.
So, according to deWitt, it is more a
_coupling_ than a measurement.
Having in mind the infamous example we can write
|Psi> = c_1 |p. hits scintill.1 at t1>|flash at t1>
c_2 |p. hits scintill.2 at t2>|flash at t2>.
I have no problem with that. But if in MWI
"the mathematical formalism of quantum mechanics
is sufficient as it stands. No metaphysics needs
to be added to it." (deWitt) and "the mathematical
formalism of the quantum theory is capable of
yielding its own interpretation." (deWitt) it seems
to me that MWI (not to mention Copenhagen!) does not
tell us what happens between times t1 and t2 (in the
usual laboratory frame, but we can choose a different
reference frame) of the example above.
This is not the only problem I have with the MWI.
Another problem I have is the one-slit diffraction
(different from the two-slit interference)
since the 'splitting' must have a rather complex dynamics.
Another problem is with the diffraction in time
(one-slit moving very fast, up and down, so that
we get interference on the screen because we cannot
know if the photon entered the slit when it was up
or when it was down).
Regards,
s.
[1]
"The wavefunction obeys the empirically derived standard
linear deterministic wave equations at all times.
The observer plays no special role in the theory and,
consequently, there is no collapse of the wavefunction.
For non-relativistic systems the Schrodinger wave equation
is a good approximation to reality.
The rest of the theory is just working out consequences
of the above assumptions. Measurements and observations
by a subject on an object are modelled by applying
the wave equation to the joint subject-object system.
Some consequences are:
1) That each measurement causes a decomposition or
decoherence of the universal wavefunction into
non-interacting and mostly non-interfering branches,
histories or worlds. The histories form a branching
tree which encompasses all the possible outcomes
of each interaction. Every historical what-if
compatible with the initial conditions and physical
law is realised.
2) That the conventional statistical Born interpretation
of the amplitudes in quantum theory is derived
from within the theory rather than having to be
assumed as an additional axiom."
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