On 27-04-2022 03:11, Bruce Kellett wrote:
On Wed, Apr 27, 2022 at 10:32 AM smitra <smi...@zonnet.nl> wrote:
On 27-04-2022 01:37, Bruce Kellett wrote:
I think you
should pay more attention to the mathematics of the binomial
distribution. Let me explain it once more: If every outcome is
realized on every trial of a binary process, then after the first
trial, we have a branch with result 0 and a branch with result 1.
After two trials we have four branches, with results 00, 01,
10,and
11; after 3 trials, we have branches registering 000, 001, 011,
010,
100, 101, 110, and 111. Notice that these branches represent all
possible binary strings of length 3.
After N trials, there are 2^N distinct branches, representing all
possible binary sequences of length N. (This is just like Pascal's
triangle) As N becomes very large, we can approximate the binomial
distribution with the normal distribution, with mean 0.5 and
standard
deviation that decreases as 1/sqrt(N). In other words, the
majority of
trials will have equal, or approximately equal, numbers of 0s and
1s.
Observers in these branches will naturally take the probability to
be
approximated by the relative frequencies of 0s and 1s. In other
words,
they will take the probability of each outcome to be 0.5.
The problem with this is that you just assume that all branches are
equally probable. You don't make that explicit, it's implicitly
assumed,
but it's just an assumption. You are simply doing branch counting.
The distinctive feature of Everettian Many worlds theory is that every
possible outcome is realized on every trial. I don't think that you
have absorbed the full significance of this revolutionary idea. There
is no classical analogue of this behaviour, which is why your lottery
example is irrelevant. I spelled out the sequences that Everett
implies in my earlier response. These clearly must have equal
probability -- that is what the theory requires.
QM without collapse does not require equal probabilities. Branches are
not a fundamental concept of the theory. You just put this in by hand.
It is not an
assumption on my part -- it is a consequence of Everett's basic idea.
Everett's (or for that matter any other person's) ideas cannot be the
basis for doing physics in a rigorous way. Your argument is not based on
QM without collapse, you are making ad hoc assumptions about branching
when branching isn't a fundamental process in QM.
So there is no branch counting involved. That is just another red
herring that you have thrown up to distract yourself from the cold
hard logic of the situation.
You just presented an elaborate presentation involving N branching steps
and counted all 2^N branches as equal. That's branch counting and it's
known to not be compatible with QM. The MWI can be taken to be QM
without collapse and this is known to be a consistent theory. So, if you
arrive at a contradiction, you are making assumptions that are not
implied by the theory.
Saibal
Bruce
The important point to notice is that this result of all possible
binary sequences for N trials is independent of the coefficients
in
the binary expansion of the state:
|psi> = a|0> + b|1>.
Changing the weights of the components in the superposition does
not
change the conclusion of most observers that the actual
probabilities
are 0.5 for each result. This is simple mathematics, and I am
amazed
that even after all these years, and all the times I have spelled
this
out, you still seek to deny the obvious result. Your logical and
mathematical skill are on a par with those of John Clark.
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