On 02-07-2021 03:50, Bruce Kellett wrote:
On Fri, Jul 2, 2021 at 4:02 AM smitra <smi...@zonnet.nl> wrote:
On 01-07-2021 02:04, Bruce Kellett wrote:
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.
This is not true. You can have decoherence with the involvement of
only a very small number of environmental degrees of freedom. The
buckyball experiments show precisely this -- it only takes the escape
of one or two IR photons of an appropriate wavelength to cause
complete decoherence and the destruction of interference.
You are then considering the reduced density matrix by tracing out some
of the degrees of freedom, in this case the IR photons. That's an ad-hoc
way of defining the reduced system, not much better than interpreting
part of a superposition as a world.
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 important point to notice is that decoherence always involves the
escape of IR photons at the speed of light. These are never
recoverable, so the laws of physics ensure that the decoherence is, in
general, irreversible. You have to take extreme care in very
controlled settings to have things reversible. And if they are
reversible, there can be no permanent environmental record of the
result of the experiment, so one could reasonably say that no
measurement has been made.
It's implausible that escaping IR photons should be relevant for the
question of what an observer is, what observations are etc. How can it
matter whether or not very far away all IR photons are captured and
billions of years later the entire original state is restored?
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.
No. The real reason is that decoherence, and the recording of a
result, is irreversible.
These things are not irreversible in principle, only FAPP. Decoherence
only involves a finite number of degrees of freedom and can therefore be
simulated by a large quantum computer. Observers implemented virtually
in a quantum computer can perform measurements, the system will
decohere, but the entire setup can then be such that the original state
gets restored. How can it matter for the measurements that much later
the original state gets restored?
And in case of our real universe, how can it be relevant that time
evolution is really irreversible? What if the universe is closed and
will end up evolving back in time according to exact time reversal
invariance in 10^40 years. How can that be relevant for measuring a
spin here and now?
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.
Of course the irreversibility, even without involving a large number
of degrees of freedom, is physically relevant. Whereas, the presumed
persistence of the superposition in the mythical "universal wave
function" is, indeed, physically irrelevant.
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).
That does not always work -- consider entanglement and Bell pairs.
Locality is not always true.
Locality in the sense needed here is always valid, it's not violated in
Bell-type experiments. In those experiments you have to create an
entangled pair using local interactions and then bring those some
distant away from each other. But then then what is demonstrated in such
experiments is that local hidden variables don't exist in general. So,
we can then make use of the fact that when you measure the spin, the
result is actually not determined if I'm not aware of what you found,
which implies the existence of multiple worlds.
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.
Of course that can be the case. It is the formation of a permanent
record in the environment that is relevant to the existence of the
measurement, whether you are aware of the result or not. You can be
entangled with the spin-up state without being aware of it.
The permanent record will then also be in a superposition (involving all
the degrees of freedom, including escaping IR photons). Part of my body
can be entangled with that superposition, but the relevant brain parts
that implements my mind will not be entangled If it were entangled then
that would imply that at least in principle, I could know the
measurement result, because the information about it it would be present
in my brain.
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.
That conclusion does not follow.
It follows from the assumption that QM is a fundamental theory, so we
then don't invoke effective macroscopic physics that is only true FAPP,
like escaping IR photons.
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.
I do not accept the frequentist definition of probability as the limit
of an infinite number of trials. If probability is a primitive (as in
the propensity interpretation), then frequencies can be used to
estimate probabilities, but they do not serve to define them. The
frequentist notion of probability is so problematic that it is not
really accepted by anyone any more.
Bruce
Yes, Bayesian interpretation makes more sense, but i.m.o. one should
then reinterpret the probability in terms of information. So, when we
perform a measurement we gain information depending on the measurement
outcome. The lower the probability of an outcome, the more information
is gained after measuring that outcome. Unitary time evolution plus Born
rule is then a principle of conservation of information.
Saibal
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
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