The Born rule, understood as probabilities are predicted by state vector
amplitudes squared, is not a problem. Gleason's theorem shows that this
is the only mathematically consistent probability measure on a Hilbert
space. The other part of the Born rule, that QM results/are
probabilistic and depend only on the state vector/, does /not/ follow
from Schroedinger's equation, although they are natural and well tested
hypotheses.
Where I have doubts about Everett and many-worlds is (1) the many-worlds
are NOT observable and have no empirical content and (2) the
diagonalization of the density matrix seems to beg the question of how
the Schroedinger equation defines a measurement just as much as the
projection postulate. Nobody writes down the Hamiltonian of the
instrument and the interaction explicitly and applies the Schroedinger
equation; they just assume the Hamiltonian of the instrument and the
interaction are such as to act like a projection operator. Dieter Zeh
has suggested that there is a kind quantum Darwinism that produces this
result, but I've not seen an explicit calculation showing it.
Brent
On 12/20/2021 3:54 AM, John Clark wrote:
On Sun, Dec 19, 2021 at 10:04 PM Bruce Kellett <[email protected]>
wrote:
/>>> 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./
>> No quantum interpretation needs to derive the Schrodinger
Equation nor does it need to be assumedbecause it can be
experimentally verified to be true. And no quantum
interpretationis inconsistent with observation, at least not
so far.
/> Why do we need any theory at all then? We just have to observe
the experimental results and they are true. Perhaps science is
about understanding the experimental results, not just accepting
them as the truth./
Some productive scientists are satisfied with the Shut Up And
Calculate quantum "interpretation" and that's fine, there is no
disputing matters of taste, but some who don't dislike philosophy
would like a bit more. The point I was trying to make was that nobody
"assumes" the Born Rule anymore than somebody assumes that a body at
rest or moving at a constant speed in a straight line will remain at
rest or keep moving in a straight line at constant speed unless it is
acted upon by a force. Neither the Born Rule or Newton's first law of
motion were "assumed" to be true, they were OBSERVED to be true , and
in science observation always outranks theory. If a theory concludes
that a certain observation can't occur but it is observed to occur
then the theory is wrong. A theory needs to be confirmed by
observation, but an observation doesn't need to be confirmed by a theory.
Unfortunately none of the quantum interpretations conflicts with
observation so to decide on a favorite one should pick the one that
makes the fewest assumptions (*NOT* the one that produces the simplest
outcome). And that's why I like Many Worlds, it only makes one
assumption. And that's why I think superdeterminism is the very worst
quantum interpretation possible, it needs, quite literally, an
infinite number of assumptions to work. If that was the best anybody
could come up with I'd stick with Shut Up And Calculate, but
fortunately we can do better.
Of courseI can't denyit would be great if a quantum
interpretationcould lead us straight to the Born Rule. It may be
premature to claim victory but I think Many Worlds has made much more
progress towards accomplishing that goal than any other:
Many Worlds, the Born Rule, and Self-Locating Uncertainty
<https://arxiv.org/pdf/1405.7907.pdf>
John K Clark See what's on my new list at Extropolis
<https://groups.google.com/g/extropolis>
mwc
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send
an email to [email protected].
To view this discussion on the web visit
https://groups.google.com/d/msgid/everything-list/CAJPayv3w0msj6mPxTBwCUr9mwV40AjAVwwHyrHvzOy9eHuNbNw%40mail.gmail.com
<https://groups.google.com/d/msgid/everything-list/CAJPayv3w0msj6mPxTBwCUr9mwV40AjAVwwHyrHvzOy9eHuNbNw%40mail.gmail.com?utm_medium=email&utm_source=footer>.
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To view this discussion on the web visit
https://groups.google.com/d/msgid/everything-list/2fa30790-a1ca-0089-be73-78dbf03d1a76%40gmail.com.
