On Sat, Feb 22, 2020 at 12:43 PM 'Brent Meeker' via Everything List < [email protected]> wrote:
> On 2/21/2020 4:57 PM, Bruce Kellett wrote: > > On Sat, Feb 22, 2020 at 11:35 AM 'Brent Meeker' via Everything List < > [email protected]> wrote: > >> On 2/21/2020 4:19 PM, Bruce Kellett wrote: >> >> On Sat, Feb 22, 2020 at 11:11 AM smitra <[email protected]> wrote: >> >>> On 16-02-2020 06:34, Bruce Kellett wrote: >>> > >>> > The probabilistic interpretation of QM arose in a single-world, >>> > collapse, model. Attempting to graft probability on to many-worlds is >>> > a failure, as my arguments against Everett show. If the data for any >>> > sequence of trials are independent of the amplitudes, then some ad hoc >>> > probability interpretation of the amplitudes is not going to affect >>> > the data. But the data is what we use to infer that Born rule >>> > probabilities are what we observe. This is a single-world result. >>> > >>> > Bruce >>> >>> It's only a failure when attempting to describe the state in the >>> multiverse in that particular way where you can argue that the >>> amplitudes don't matter. It's not an argument against the multiverse >>> idea, as whether or not you have a large number of copies should not >>> affect the statistical outcome observed in any experiment. >>> >> >> No. And it has not been suggested that it will. But that is just to take >> a single-world approach: statistics work fine in each branch of the >> multiverse (each world), but the concepts of probability and the Born rule >> break down when every result is obtained in experiments because the data >> obtained in each world are independent of the amplitudes of the original >> state. >> >> >> This objection seems to rest on the idea that the set of sequences >> (across all the worlds) cannot be regarded as an ensemble from which one is >> picked by self-location. >> > > I am not sure what this means. The set of all sequences (all branches or > worlds) is just the set of all 2^N possible binary strings, so any set of > results that an individual might obtain is a selection from this set. If > you want to regard this as self-location, then fine, but I don't know what > that gains you. > > > If you regard his self-location as equi-probable over the ensemble then > his expectation values and other statistics are the same as for a N-string > in one world. > That is not the case since the empirical probabilities are different in different branches. An expectation value over branches will not be the same as one branch statistics. But then, there is no way in which you can observe an expectation value over branches -- they are distinct worlds, after all. > Otherwise applying probability theory to the ensemble recovers the >> one-world statistics. Right? >> > > In the two-outcome case, any branch of the ensemble is just a one-world > set of Bernoulli trials, so the statistics of that branch correspond to the > binomial distribution with a probability characteristic of the branch. > Different branches will, in general, correspond to different p-values. The > argument against Everett is that this set of binary strings is independent > of the amplitudes of the initial quantum state so there is no room for the > Born rule. > > > Yes, that's true. But all the advocates of MWI I know of assume that > there is some kind of weighting that follows from the state preparation, so > that if you are measuring a state with is in a superposition a|up>+b|dwn> > in the instrument up/dwn basis, then the branches are in proportion to a > and b, rather than just one each. I don't know whether you can justify > this by a detailed interaction term in the Hamiltonian, but it is commonly > assumed as "that's the way it must be". > I know that they argue in this way. But that is just say "It must be this way or else my theory fails." My argument against this is quite secure. Linear evolution via the SWE and Everett means that there is only one "relative state" or branch for each term in the original superposition. There is no room for a "weight" in such linear evolution. Looking at repeated trials simply highlights this fact -- the sequence of bit strings is necessarily independent of the original amplitudes -- there are no "weights", and MWI advocates are simply fooling themselves. Bruce -- 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/CAFxXSLRtyQgqthq_WnQ79drxO3tP1UHOS%2BoMAKXGWiR3zMwLPA%40mail.gmail.com.
