On 10/8/2019 2:59 PM, Philip Thrift wrote:
On Tuesday, October 8, 2019 at 2:40:33 PM UTC-5, Brent wrote:
That MWI entails other, unobservable "worlds" is neither a bug or
a feature, it's just one answer to the measurement problem. If
you have a better answer, feel free to state it.
Brent
MWI, according to Sabine Hossenfelder, is not an answer - in the final
analysis - to the measurement problem
http://backreaction.blogspot.com/2019/09/the-trouble-with-many-worlds.html
The many world interpretation, now, supposedly does away with the
problem of the quantum measurement and it does this by just saying
there isn’t such a thing as wavefunction collapse. Instead, many
worlds people say, every time you make a measurement, the universe
splits into several parallel worlds, one for each possible measurement
outcome. This universe splitting is also sometimes called branching.
Some people have a problem with the branching because it’s not clear
just exactly when or where it should take place, but I do not think
this is a serious problem, it’s just a matter of definition. No, the
real problem is that after throwing out the measurement postulate, the
many worlds interpretation needs another assumption, that brings the
measurement problem back.
The reason is this. In the many worlds interpretation, if you set up a
detector for a measurement, then the detector will also split into
several universes. Therefore, if you just ask “what will the detector
measure”, then the answer is “The detector will measure anything
that’s possible with probability 1.”
This, of course, is not what we observe. We observe only one
measurement outcome.
The implication is that the above two sentences are contrasting. But
nobody asks "what will the detector measure". The question asked by the
experimenter is "which measurement outcome will the detector detect",
which is perfectly consistent with "we observe only one measurement outcome"
The many worlds people explain this as follows. Of course you are not
supposed to calculate the probability for each branch of the detector.
Because when we say detector, we don’t mean all detector branches
together. You should only evaluate the probability relative to the
detector in one specific branch at a time.
I can't even parse that. You are supposed to calculate the probability
of each possible measurement outcome and those characterize the branch.
It is NOT calculating "each branch of the detector" unless you are
defining those "branches" by what the measurement outcome is.
That sounds reasonable. Indeed, it is reasonable. It is just as
reasonable as the measurement postulate. In fact, it is logically
entirely equivalent to the measurement postulate.
It's not clear here what "logically" equivalent means. It is
instrumentally equivalent...which is why it's an interpretation and not
a different theory (as GRW is). It's different from the measurement
postulate in that the measurement postulate says the wave function
instantaneously changes to match the observed measured value. MWI says
those other measured values obtain in other orthogonal subspaces of the
Hilbert space and you are only observing one. Those are not "logically"
the same.
The measurement postulate says: Update probability at measurement to
100%. The detector definition in many worlds says: The “Detector” is
by definition only the thing in one branch.
What does "only the thing in one branch mean". In MWI there are
projections of the detector in subspaces which differ only by the value
detected.
Now evaluate probabilities relative to this, which gives you 100% in
each branch. Same thing.
And because it’s the same thing you already know that you cannot
derive this detector definition from the Schrödinger equation.
?? You can't derive the definition of any physical object from the
Schroedinger equation. You put in the Hamiltonian of the object and
whatever it interacts with and the initial ray in Hilbert space and the
Schroedinger equation tells you how it evolves
It’s not possible. What the many worlds people are now trying instead
is to derive this postulate from rational choice theory. But of course
that brings back in macroscopic terms, like actors who make decisions
and so on. In other words, this reference to knowledge is equally in
conflict with reductionism as is the Copenhagen interpretation.
I agree with that point. But once you suppose a probabilistic
interpretation of the Hilbert space, then Gleason's theorem implies the
Born rule. That still leaves a small gap in saying why it has
probabilistic interpretation at all. Whether "self-locating
uncertainty" is an adequate answer seems to me to require more analysis
of human thought; although showing the brain is a quasi-classical
information processor goes a long way.
Brent
*And that’s why the many worlds interpretation does not solve the
measurement problem* and therefore it is equally troubled as all other
interpretations of quantum mechanics. What’s the trouble with the
other interpretations? We will talk about this some other time. So
stay tuned.
@philipthrift
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