On 11/18/2019 1:23 PM, Philip Thrift wrote:
On Monday, November 18, 2019 at 12:08:39 PM UTC-6, Brent wrote:
On 11/17/2019 11:39 PM, Philip Thrift wrote:
Stochastic modeling has nothing (in general) to do with Bayesian
modeling. (Though the latter of course can be considered a
special case of the former.) And quantum mechanics works fine as
a stochastic model without ever introducing Bayesian probability
densities.
You avoided the point that when you get a measurement result to
you change something. You denied it was knowledge. So what is it?
Brent
*There is no measurement.*
How then does the path-integral [theory of quantal histories, without
ever needing to call on state-vectors, *measurement*s, or external
agents as fundamental notions] offer an alternative to the textbook
formalism of state-vectors, Hamiltonians, and external observers? A
first answer is that from the path integral one can derive a
functional μ_quantum -- the quantal measure -- which directly
furnishes the probability of any desired "instrument-event" E. (This
measure is closely related to the so called decoherence functional.)
In saying this, I am presupposing that the Born rule (or rule of
thumb!) is correct, and then just taking note of the fact that the
Bornian probabilities for any specified set of "pointer readings" are
furnished directly by μ_quantum, without any appeal to Schroedinger
evolution of the wave-function or its "collapse" during the
measurement. In this way μ_quantum is analogous to the classical
measure μ_classical that furnishes the probability of a set of
histories -- an "event" -- in the case of a purely classical
stochastic process like diffusion or Brownian motion. If one construes
the path-integral in this way, namely as a generalized measure on a
space of "histories", then one sees not only how quantal processes
differ from classical stochastic processes, but also how closely the
two resemble each other, the primary difference being simply that
μ_classical and μ_quantum satisfy different sum-rules.
https://www.perimeterinstitute.ca/people/rafael-sorkin
In using path integrals you arrive a probabilities for various possible
outcomes. But that's not the end of the science. You also
observe/measure/experience some particular outcome. And then you
compute future path integrals starting from the observed state...using
the observed state implies you went from a state of uncertainty
expressed by probabilities to a state of certainty regarding the new
state....aka using knowledge.
Brent
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