On Thu, Mar 5, 2020 at 10:39 AM Russell Standish <li...@hpcoders.com.au>
wrote:
> On Thu, Mar 05, 2020 at 09:46:34AM +1100, Bruce Kellett wrote:
>
> > The greater problem is that any idea of probability founders when all
> outcomes
> > occur for any measurement. Or have you not followed the arguments I have
> been
> > making that shows this to be the case?
> >
>
> I must admit I haven't followed the arguments either - admittedly, I
> haven't read your cited material.
>
> ISTM - probability is all about what an observer observes. Since the
> observer cannot see all outcomes, an objection based on all outcomes
> occurring seems moot to me.
>
The fact that the observer cannot see all outcomes is actually central to
the argument. If, in the person-duplication scenario, the participant
naively assumes a probability p = 0.5 for each outcome, such an intuition
can only be tested by repeating the duplication a number of times and
inferring a probability value from the observed outcomes. Since each
observer can see only the outcomes along his or her particular branch (and,
ipso facto, is unaware of the outcomes on other branches), as the number of
trials N becomes very large, only a vanishingly small proportion of
observers will confirm their 50/50 prediction . This is a trivial
calculation involving only the binomial coefficient -- Brent and I
discussed this a while ago, and Brent could not fault the maths.
The crux of the matter is that all branches are equivalent when both
outcomes occur on every trial, so all observers will infer that their
observed relative frequencies reflect the actual probabilities. Since there
are observers for all possibilities for p in the range [0,1], and not all
can be correct, no sensible probability value can be assigned to such
duplication experiments.
The problem is even worse in quantum mechanics, where you measure a state
such as
|psi> = a|0> + b|1>.
When both outcomes occur on every trial, the result of a sequence of N
trials is all possible binary strings of length N, (all 2^N of them). You
then notice that this set of all possible strings is obtained whatever
non-zero values of a and b you assume. The assignment of some propbability
relation to the coefficients is thus seen to be meaningless -- all
probabilities occur equal for any non-zero choices of a and b.
> You may counter that the assumption that an observer cannot see all
> outcomes is an extra thing "put in by hand", and you would be right,
> of course. It is not part of the Schroedinger equation. But I would
> strongly suspect that this assumption will be a natural outcome of a
> proper theory of consciousness, if/when we have one. Indeed, I
> highlight it in my book with the name "PROJECTION postulate".
>
> This is, of course, at the heart of the 1p/3p distinction - and of
> course the classic taunts and misunderstandings between BM and JC
> (1p-3p confusion).
>
I know that it is a factor of the 1p/3p distinction. My complaint has
frequently been that advocates of the "p = 0.5 is obvious" school are often
guilty of this confusion.
Incidently, I've started reading Colin Hales's "Revolution of
> Scientific Structure", a fellow Melburnian and member of this
> list. The interesting proposition about this is Colin is proposing
> we're on the verge of a Kuhnian paradigm shift in relation to the role
> of the observer in science, and the that this sort of misunderstanding
> is a classic symptom of such a shift.
>
Elimination of the observer from physics was one of the prime motivations
for Everett's 'relative state' idea. Given that 'measurement' and 'the
observer' play central roles in variants of the 'Copenhagen' interpretation.
Bruce
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