On 01-07-2021 02:04, Bruce Kellett wrote:
On Thu, Jul 1, 2021 at 2:29 AM smitra <smi...@zonnet.nl> wrote:
On 29-06-2021 01:46, Bruce Kellett wrote:
I think John's trouble here is that he still adheres to David
Deutsch's concept of worlds. Deutch talks as though every
component of
a superposition is a separate world. This leaves Deutsch no
language
to talk about decohered worlds, pointer states, and all the other
usual apparatus of quantum interpretations. The trouble with
taking
every component of a superposition as a separate world is that in
Hilbert space (as in any vector space) you can define an infinite
number of different sets of basis vectors, so any vector in the
space
is represented by an infinity of different worlds, and there is no
way
to distinguish between these.
I think Bruno has flirted with this idea as well. Deutsch, through
his
popular writings, has done an immense amount of harm to the cause
of
quantum interpretations.
Bruce
There ids a large body of rigorous work in this field, it's not that
you
have just a handful of advocates who are defending the MWI based on
dodgy nonrigorous arguments. Of course, you can't just take nay
component of a superposition as a separate world.
But that is precisely what people like John, Deutsch, and Bruno do.
But given that Worlds
do exist
A world exists. That is all that we can be sure of.
and given that time evolution is given as a linear operator, it
follows that if QM is a fundamental theory that also describes
observers, that you inevitably end up with superpositions of entire
Worlds.
Worlds have to be carefully defined. According to decoherence theory
(which is also a consequence of the linearity of the Schrodinger
equation), decohered worlds are truly separate and do not recombine.
Non-decohered elements of a superposition do not constitute separate
worlds.
This definition only works when you replace the real physical world by
an approximation obtained by taking an appropriate infinite scaling
limit that allows decoherence to involve an infinite number of degrees
of freedom. You can do this by e.g. letting hbar tend to zero. While we
as macroscopic observers are in some sense close to this limit, the
world we actually live in only has a finite number of physical degrees
of freedom in a finite volume. And locality implies that in a finite
time after some experiment, only a finite volume can be physically
affected by the experiments, therefore the decoherence is in reality
nothing more than an entanglement with a finite number of environmental
degrees of freedom.
The exact physical state of the system plus environment therefore does
not become a mixed state. The fact that one cannot demonstrate that the
state after measuring a superposition is still a superposition using an
interference experiment does not mean that it isn't a superposition. The
observer itself has become entangled with the measured system, which is
the real reason why the observer cannot even in principle detect the
superposition. The practical obstacle that the massive entanglement
involves an astronomically large number of degrees of freedom is of
course also true, but this cannot be physically relevant.
So, if you measure the z-component of a spin polarized in the
x-direction and I'm not aware of the measurement result, then my mind
will not have been entangled with the measurement result (you can also
put me outside your light cone for argument's sake). The spin entangled
with you and a large but finite number of degrees of freedom will
therefore be in a superposition. The fact that hidden variables don't
exist means that it cannot be the case that you have made a definite
observation that I'm unaware of. But obviously if I ask what you've
measured I'll always get an answer that I can verify to be correct. So,
the only way out of this problem is to assume that these suppositions
after measurements exist as different worlds where different
experimental outcomes have been found.
This conclusion does not depend on any assumptions of how observers
should be defined rigorously, how experiments and ultimately
observations arise out of the physics. These issues that are not yet
100% solved, are totally irrelevant provided QM is indeed a
fundamental
theory.
It's not any different from someone claiming that conservation of
momentum may not be true. How do we convince this person that it is
true? We can appeal to fundamental laws of physics and argue on the
basis of symmetries, Noether's theorem and then say that this
rigorously
establishes conservation of momentum. But the skeptic can then take
issue with the assumption about the validity of the fundamental
laws,
he will insist that it's still possible for momentum to get lost. If
he
does an experiment involving many particles, then he'll say that
unless
you measure the momentum of each particle to infinite accuracy, you
can't really tell that momentum is conserved. He'll then turn the
logic
about the fundamental laws upside down by arguing that because you
can't
really be sure about momentum conservation, you can't therefore say
that
the fundamental laws have been all that well established.
Of course, there is then a lot to argue about this reasoning
suggesting
that there is room for momentum nonconservation. But the arguments
against MWI (regardless of whether or not you need to add Born's
rule as
a postulate and if so, regardless about any discussions about this
then
invalidating the original goals of some MWI advocates), are of the
same
nature.
Not really. You can accept the Schrodinger equation as fundamental
without agreeing to MWI. The fact that you can't derive the Born rule
from the Schrodinger equation in a non-circular fashion is quite
telling. It means that the Schrodinger equation is more naturally seen
as a way of calculating the time evolution of probabilities. QM is a
probabilistic theory, so its fundamental laws give probabilities. And
probabilities are not worlds.
Bruce
Probabilities only become rigorously defined after an infinite number of
measurements and cannot therefore be invoked to define real physical
quantities. The Born rule can at best only be an effective physical
quantity, like e.g. thermodynamic quantities like temperature and
entropy. They can only be rigorously defined for idealized systems where
strictly speaking unphysical mathematical limits must be taken.
Saibal
Here you have a supposedly fundamental theory, QM and it implies
in a rather straightforward way the existence of parallel Worlds,
and
because people don't like that conclusion, you have arguments
against it
that can only work if QM is not true as a fundamental theory. The
problem with those arguments is then that it's invoked as a
standalone
argument against the MWI. If these arguments were well motivated on
their own merits, then they would form the basis of a lot of physics
research in many different fields ranging from condensed matter,
particle physics etc. But that's not the case.
Saibal
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