On Monday, October 14, 2019 at 6:52:24 PM UTC-5, Lawrence Crowell wrote: > > On Monday, October 14, 2019 at 4:44:42 PM UTC-5, Bruce wrote: >> >> On Tue, Oct 15, 2019 at 5:38 AM Philip Thrift <[email protected]> wrote: >> >>> On Monday, October 14, 2019 at 1:20:39 PM UTC-5, Brent wrote: >>>> >>>> Part of the dislike of the MWI is that its proponents assume a purity >>>> that is not an evident virtue of the intepretation. For example, >>>> interpreting the squared amplitudes as probabilities seems to be assumed, >>>> along with the existence of the preferred basis in which the amplitudes >>>> are >>>> defined. Together these are almost the same as CI. If you ask >>>> "probabilities of what?" in MWI the answer can't be probability of >>>> existing >>>> because MWI has committed to all solutions, however improbable, existing. >>>> So it becomes probability of finding yourself in a particular >>>> world...which >>>> depends on a theory of consciousness and seems to regress to von Neumann >>>> and Wigner. >>>> >>>> Zurek's envariance attempts to answer these questions and provide a >>>> justification for preferred bases and what probability refers to. But >>>> notice that to the extent he succeeds he is justifying taking a simple >>>> probabilistic view and saying one of those preferred states happens and >>>> the >>>> others don't. >>>> >>>> Brent >>>> >>>> >>>> >>> In the single-particle double-slit experiment*, an observer could see a >>> dot appear anywhere on a screen where path interference does not reduce the >>> probability to zero. So with the literal many-world-branching theory, how >>> many different worlds are produced, each on with its own observer seeing a >>> dot on the screen? >>> >> >> According to MWI, an infinite number. Each world will have the dot at a >> different place on the screen. >> >> Bruce >> > > What you say may open up a bit of a hole or snag in MWI. This is something > I have been pondering some since Carroll's popularization. If MWI > fundamentally preserves unitarity by splitting off worlds then localization > of a measurement is an illusion.Consider a particle measured somewhere on a > path from x and x'. The path integral and the nonlocality of paths is a > sum over all possible measurements in all space containing x and x', then > there must be a continuum of possible worlds splitting off. If the operator > has a continuum of eigenvalues *x*|x> = x|x> there must then be a > continuum of possible worlds if there is indeed no fundamental localization > with a measurement. This is not just infinite, but uncountably infinite. > > This is different from how decoherence maintains unitarity and conserves > qubits. There a local interaction occurs that induces quantum phase to > enter into a set of ancillary states or reservoir of states. Then we can > consider quantum states as finite, but unbounded from above, so that local > observations and measurements are possible. > > This does seem to run into some oddities that either need to be worked out > or that might indicate some gap in MWI. The persistence of nonlocality in > MWI is interesting for possible quantum gravitation work. In that case I > can think of maybe a way around this, where this uncountably infinite set > of g_{ij} configurations, or Ψ[g_{ij}], can be identified with "exotic" > manifolds that are removed. It is less clear how this can happen with > ordinary quantum fields that have local realizations. > > LC >
To mix an analysis (or a theory) of the path integral with an analysis (or a theory) of MWI is mixing two fundamentally contradictory frameworks that only leads to confusion. @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/c95c6678-aa57-4efd-aeb0-f7b133d8ef31%40googlegroups.com.
