On Sun, Mar 8, 2020 at 5:32 PM Russell Standish <[email protected]>
wrote:
> On Fri, Mar 06, 2020 at 10:44:37AM +1100, Bruce Kellett wrote:
>
> > That is, in fact, false. It does not generate the same strings as
> flipping a
> > coin in single world. Sure, each of the strings in Everett could have
> been
> > obtained from coin flips -- but then the probability of a sequence of
> 10,000
> > heads is very low, whereas in many-worlds you are guaranteed that one
> observer
> > will obtain this sequence. There is a profound difference between the two
> > cases.
>
> You have made this statement multiple times, and it appears to be at
> the heart of our disagreement. I don't see what the profound
> difference is.
>
> If I select a subset from the set of all strings of length N, for example
> all strings with exactly N/3 1s, then I get a quite specific value for the
> proportion of the whole that match it:
>
> / N \
> | | 2^{-N} = p.
> \N/3/
>
> Now this number p will also equal the probability of seeing exactly
> N/3 coins land head up when N coins are tossed.
>
> What is the profound difference?
>
Take a more extreme case. The probability of getting 1000 heads on 1000
coin tosses is 1/2^1000.
If you measure the spin components of an ensemble of identical spin-half
particles, there will certainly be one observer who sees 1000 spin-up
results. That is the difference -- the difference between probability of
1/2^1000 and a probability of one.
In fact in a recent podcast by Sean Carroll (that has been discussed on the
list previously), he makes the statement that this rare event (with
probability p = 1/2^1000) certainly occurs. In other words, he is claiming
that the probability is both 1/2^1000 and one. That this is a flat
contradiction appears to escape him. The difference in probabilities
between coin tosses and Everettian measurements couldn't be more stark.
Bruce
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