On 28-04-2022 07:23, Brent Meeker wrote:
On 4/27/2022 10:38 AM, smitra wrote:
On 27-04-2022 04:08, Brent Meeker wrote:
On 4/26/2022 5:32 PM, smitra wrote:
On 27-04-2022 01:37, Bruce Kellett wrote:
On Tue, Apr 26, 2022 at 10:03 AM smitra <smi...@zonnet.nl> wrote:
On 24-04-2022 03:16, Bruce Kellett wrote:
A moment's thought should make it clear to you that this is not
possible. If both possibilities are realized, it cannot be the
case
that one has twice the probability of the other. In the long run,
if
both are realized they have equal probabilities of 1/2.
The probabilities do not have to be 1/2. Suppose one million people
participate in a lottery such that there will be exactly one winner.
The
probability that one given person will win, is then one in a
million.
Suppose now that we create one million people using a machine and
then
organize such a lottery. The probability that one given newly
created
person will win is then also one in a million. The machine can be
adjusted to create any set of persons we like, it can create one
million
identical persons, or almost identical persons, or totally different
persons. If we then create one million almost identical persons, the
probability is still one one in a million. This means that the limit
of
identical persons, the probability will be one in a million.
Why would the probability suddenly become 1/2 if the machine is set
to
create exactly identical persons while the probability would be one
in a
million if we create persons that are almost, but not quite
identical?
Your lottery example is completely beside the point.
It provides for an example of a case where your logic does not apply.
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.
But it shows why you can't use branch counting. There's no physical
mechanism for translating the _a_ and _b_ of _|psi> = a|0> + b|1>_
into numbers of branches. To implement that you have put it in "by
hand" that the branches have weights or numerousity of _a _and _b_.
This is possible, but it gives the lie to the MWI mantra of "It's
just
the Schroedinger equation."
The problem is with giving a physical interpretation to the
mathematics here. If we take MWI to be QM without collapse, then we
have not specified anything about branches yet. Different MWI
advocates have published different ideas about this, and they can't
all be right. But at heart MWI is just QM without collapse. To proceed
in a rigorous way, one has to start with what counts as a branch. It
seems to me that this has to involve the definition of an observer,
and that requires a theory about what observation is. I.m.o, this has
to be done by defining an observer as an algorithm, but many people
think that you need to invoke environmental decoherence. People like
e.g. Zurek using the latter definition have attempted to derive the
Born rule based on that idea.
I.m.o., one has to start working out a theory based on rigorous
definitions and then see where that leads to, instead of arguing based
on vague, ill defined notions.
"Observer as an algorithm" seems pretty ill defined to me. Which
algorithm? applied to what input? How does the algorithm, a Platonic
construct, interface with the physical universe? Decoherence seems
much better defined. And so does QBism.
Any human observer is arguably implemented by an algorithm run by a
brain. So, for any given observer at some time, there exists a precisely
defined algorithm that defines that observer. In practice we cannot
provide for any such definition, but from the point of view of the
theory, it's important to takr into account the way an observer should
be rigorously defined.
Decoherence should be irrelevant to this issue. It's a process that
happens at the macroscopic scale that is associate with observation. But
ultimately observation is just the entanglement of the state of the
observer with the measured system, it doesn't matter of that information
also leaks out to an astronomically large number of other degrees of
freedom.
Saibal
Brent
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