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 @philipthrift -- 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/9dfa4136-b5ac-4ff1-adae-2953f541ec81%40googlegroups.com.
