On 27-04-2022 04:01, Bruce Kellett wrote:
On Wed, Apr 27, 2022 at 11:35 AM smitra <smi...@zonnet.nl> wrote:
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
It would seem that you are claiming that QM without collapse is not
based on Everett's ideas. If you claim that such a theory exists and
is consistent, then you really should present that theory, and point
out that it has nothing to do with Everett, or with obtaining every
outcome of a trial on different branches.
QM without collapse is just that: QM without collapse, nothing more,
nothing less. Everett worked out this idea added the concept of branches
and developed an effective theory and also attempted to derive the Born
rule. But that latter attempt is now recognized to not work and other
physicists have later used similar and also other approaches to get to a
derivation of the Born rule. But so far no one has succeeded.
My impression is that you do not have any worked-out theory -- you
just throw arbitrary objections to my working through the consequences
of Everett's approach to quantum mechanics. I have shown that many
problems exist with Everettian QM.
There only exists a problem with getting to the Born rule, not with QM
without collapse.
If you agree, and are prepared,
with me, to throw out Everett, then we agree, and there is nothing
more to be argued about (at least, until you present some different
complete theory).
I'm open to the idea that QM itself may only be an approximation to a
more fundamental theory. The arguments in favor of no collapse are
strong arguments but you then do get this issue with probability that
you have discussed here. The disagreement with you about this is that I
don't see it as a fatal inconsistency that would prove the MWI to be
wrong. Probabilities for the different branches do not have to be equal.
But that doesn't mean that this looks to be a rather unnatural feature
of the theory. This suggests that a more fundamental theory exists from
which one could derive quantum mechanics with its formalism involving
amplitudes and the Born rule as an approximation.
Saibal
Bruce
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