On 4/26/2022 7:01 PM, 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.
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. 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 think Everett's idea was just to get rid of wave-function collapse and
instead assert that the apparently incompatible results of an experiment
were just different entanglements of one's brain/instrument with
different superposed components of the state of the system measured.
This is all consistent with the Copenhagen interpretation, except in CI
all but one of the orthogonal components is discarded. Decoherence has
cast some light on why the components quickly become orthogonal and why
they become orthogonal only in certain bases.
Brent
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