On 5/9/2013 11:28 AM, Jason Resch wrote:
On Thu, May 9, 2013 at 1:11 PM, meekerdb <[email protected]
<mailto:[email protected]>> wrote:
On 5/9/2013 10:02 AM, Jason Resch wrote:
Von Neumann thought the extra baggage was required to make the model match
our
observations, but Everett later showed that step was unnecessary. The
model (free
of additional baggage) predicts the same observations as the model with it.
He showed that IF the wave function separates into orthogonal components (an
irreversible process) then FPI explains the observations. But the model
says it
never does that; it only approximates that, in certain bases.
Could you explain this? I don't understand in what sense the Schrodinger equation can
only approximate itself?
If you include the observer and the system observed then when the observer interacts with
system in superposition the observers state becomes a superposition in the same basis.
The cross-terms in the superposition are not zero. They can be shown to become
approximately zero if you include interaction with an environment that has a large number
of degrees of freedom and you trace over the environment variables. But that last step
isn't part of the Schrodinger equation, it's a separate assumption comparable to
Boltzmann's assumption of molecular chaos.
Decoherence theory tries to fill in the process by which this occurs give
a
statistical mechanics type account of irreversibility.
It gives an account of the appearance of an "irreversible wave-function collapse"
without their having to be one. It is derived entirely from the theory of QM and is not
an extra postulate.
It depends on the choice of basis. In general there's other some basis in which state is
pure. Decoherence says the density of the subsystem is approximately diagonal in a
particular basis. This involves assumptions about the environment and is not part of the
wave function.
But you could also take the epistemological interpretation of Peres and
Fuchs
instead of inventing other worlds just to save the determinism of an
equation.
The other worlds are a required element of the theory, unless you deny the reality of
superposition. I think Everett's thought experiment explains the situation the best:
Imagine a box with an observe in it who will be measuring the state of a particle and
writing the result in a notebook. This box is entirely sealed off from the external
world such that the internal result of the experiment remains in a superposition until
it is opened. Now a second, external observer models the entire evolution of this box
over time, including before and after the observer inside measures the state of the
particle and records the result in a notebook. He determines the superposition of all
the possible handwritings of all the possible results in the notebook. Is the internal
observer not conscious in each of the various superpositions resulting from the measurement?
Depends on what you mean by THE internal observer. There is a superposition of states
that represents the external observers theory of the internal observer.
Epistemological interpretations seem to deny there is any fundamental reality at all,
aside from what we can see and learn, which to me seems like a dead end in the search
for truth.
Shifting the truth off to undetectable realms doesn't help much.
I like MWI and Bruno's FPI idea, but without some testable prediction (not
retrodiction) I don't find them compelling.
Why do you find compelling about the idea that all other superpositions (except for one)
vanish?
It comports with experiment. What do you find compelling about the idea that the unity of
your consciousness is an illusion.
Brent
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