On 12/21/2021 5:27 AM, smitra wrote:
On 20-12-2021 23:15, Brent Meeker wrote:
On 12/20/2021 1:03 AM, smitra wrote:
On 20-12-2021 03:05, Bruce Kellett wrote:
On Mon, Dec 20, 2021 at 12:23 PM John Clark <[email protected]>
wrote:
On Sun, Dec 19, 2021 at 7:59 PM Brent Meeker <[email protected]>
wrote:
On 12/19/2021 5:25 AM, John Clark wrote:
By contrast the Many Worlds Theory only makes one assumption,
Schrodinger's Equation means what it says. So Many Worlds wins.
_> It also makes the assumption that the eigenvalues of a
measurement are realized probabilistically._
What is the eigenvalue of a temperature of 72°F? It doesn't have one.
A measurement doesn't have an eigenvalue but a matrix does, such as
the one that describes the Schrodinger Wave. And no quantum
interpretation needs to assume there is a relationship between the
square of the absolute value of that wave and probability because it
is observed to be true.
The Born Rule cannot be derived from the Schrodinger equation; it has
to be added as a further independent assumption. So it is not true
that Many Worlds makes only one assumption. It requires just as many
assumptions as collapse theories.
Bruce
Yes, but with those assumptions it yields an unambiguous framework
for a fundamental theory. In case of collapse theories, you're stuck
with a phenomenological theory that cannot be improved, because you
are not allowed to describe observers and observations within the
collapse frameworks. It's a bit like the difference between
statistical mechanics and thermodynamics, if in the latter case
textbooks were to insist that you are only allowed to consider
certain types of heat engines that operate in the quasistatic limit.
Yes, but it is decoherence theory that extends the theory of
measurement beyond just phenomenological projectors. And it doesn't
reach to explaining the probabilistic nature of QM. ISTM that the
steps in Everett's account of measurement where instrument variables
become correlated with quantum system variables and cross terms form
superpositions are set to zero are almost has "hand wavy" as the CI
projection operators. They seem to be just motivated by "This must
be the way the Schroedinger equation works for macroscopic instruments
in order that we get the same answer as the CI projector after we
assume Born's rule."
Brent
I agree that this is a problem. But as as I explained just now to
Jesse Mazer, one should be able to make progress by including an
observer defined as an algorithm. This should amount to the same thing
as is done by Everett, but it's then motivated by the actual physics.
That would be better than just hand waving. But can a macroscopic
observer really be approximated by a simple algorithm? One of the
things that makes an "observer" is that it interacts with an environment
and has an effectively infinite degrees of freedom.
Brent
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