On Thu, May 5, 2022 at 5:27 AM smitra <smi...@zonnet.nl> wrote:
> On 04-05-2022 01:49, Bruce Kellett wrote:
> >
> > I have not introduced any concept of probability. The 2^N branches
> > that are constructed when both outcomes are realized on each of N
> > Bernoulli trials are all on the same basis.
>
> If you ignore the amplitudes in the states, and that means modifying QM
> into something else.
>
QM does not assume that all branches exist equally. In Everett you have
already modified QM into something else.
The Schrodinger equation is insensitive to the amplitudes. You get the same
set of 2^N branches from the Schrodinger equation, whatever amplitudes you
have. The weights of these branches certainly depend on the amplitudes: if
there are n zeros in the set of N trials, there are N-n ones. The weight of
the corresponding binary string is a^n b^(N-n), but without further
assumption, this plays no role in the future development of the state or in
the interpretation of the binary string. If you interpret it as the
probability of the string, you again have a conflict, since all binary
strings are constructed on an equal basis, the natural probability for each
is 2^{-N}. Because of these obvious problems, most writers on MWI interpret
the coefficients as weights, and are careful to avoid calling the
amplitudes probabilities. The Born rule is taken to sit alongside the
theory, but it is not part of the theory because there are no probabilities
in the Schrodinger equation itself.
Bruce
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