On 1/1/2021 5:26 AM, John Clark wrote:
On Thu, Dec 31, 2020 at 7:58 PM Bruce Kellett <[email protected]
<mailto:[email protected]>> wrote:
>///her starting assumption is that one wants probabilities from
the theory,/
That's not an assumption that's a goal, from experimentation we know
what the correct probability is, if a theory doesn't end up with that
probability then that theory is wrong.
/> it does not stem from any firmer basis than a desire to get the
known right answer/
Yes, but what's wrong with that? All theoreticians try to develop
theories that conform with the right answer, aka experimental results.
That's the entire point of science.
>///so she assumes a uniform probability distribution over her
original Hilbert space./
All theories have assumptions but you should always make the simplest
assumptions, and since nobody has found a reason to think otherwise a
uniform probability distributionis the simplest.
> /The trick, of course, is to justify the assumption of a
probability distribution in the first place. One can appeal to
experiment, and claim that the fact that it works is justification
enough. But that fails to satisfy one's reductionist principles,/
Ultimately one's reductionist desires will always be frustrated. A new
strange physical phenomenon is discovered, let's call it "A".
Eventually somebody develops a brilliant new theory that says B causes
A, but that leads to the question what causes B? Eventually somebody
develops a brilliant new theory that says C causes B, but that leads
to the question what causes C? There are only two possibilities,
either this chain of questions goes on forever or it doesn't and it
ends in a brute fact that has no cause, a hardcore reductionist would
be unhappy with either outcome so I fear a hard-core reductionist is
destined to be unhappy.
> /is equivalent to assuming Born's rule as an independent axiom,
not in need of further justification. If one's claim, as made by
MWI enthusiasts, is that the Schrodinger equation is all that one
needs, taking the Born rule as an independent axiom does not work,
and one needs to derive probabilities from the underlying
deterministic theory./
Assuming that Many Worlds is true and the multiverse is completely
determined by Schrodinger's equation and there are therefore an
astronomically large number (perhaps an infinite number) of Bruce
Kelletts with microscopic or submicroscopic differences between them,
and those Bruce Kelletts were observing a stream of photons polarized
at angle X hit a polarizing filter set to angle X+Y; would any one of
those Bruce Kelletts be able to predict with certainty that Bruce
Kellett would or would not observe the photon pass through that
filter? No. Would Bruce Kellett have to resort to probability? Yes.
How would Bruce Kellett calculate the probability? If Bruce Kellett
wanted to avoid logical self contradictions there is only one method
Bruce Kellett could use, the Born Rule.
I don't think that's quite true. Suppose for example BK decided to
predict that the polarization with the highest value of |psi|^2 is the
one that would pass thru. He wouldn't run into any logical
contradiction because he's not interpreting it as probability, and so
the fact that it doesn't provide a measure satisfying Kolomogorov's
axioms is irrelevant. And he wouldn't run into an empirical
contradiction unless he assumed the actual process was producing a
probability distribution and so he needed to predict a distribution and
not just a value. But then that's the point, one has to add that
interpretive step to Schroedinger's equation. Once you know that you
need a probability distribution from the wave function...then Born's
rule is the only choice. But it's the step from the wave-function and
"everything happens" to a probability distribution where MWI leaves a gap.
Brent
John K Clark See my new list at Extropolis
<https://groups.google.com/g/extropolis>
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