Is quantum indeterminacy a result of experiment design?

Oh, and my guess is that if I ever went back to doing the mathematics of quantum mechanics, it would be much simpler to put determinism in a small folder in the loft labelled "Beautiful ideas" and only bring it down once a year with the Christmas tree and fairy lights

reilly
RandallB said:
So just to be clear on what you mean by saying “QM and QFT are local” does not mean local in a classical sense i.e. with a dependent background. But local against a structure of reality built on a independent background as Lee Smolin describes both GR and QM have.
Thus there is no true tracking of “local” positions between separated points. Just the relative interrelation of interactions, each acting as a kind of independent local system.
Is that how some "theoretical reasons" can get “local” onto QM.

I haven't a clue about what you are saying. Perhaps it's my lack of knowledge about Dr. Smolin's ideas. Maybe you could provide a brief explanation of independent vs. dependent reality, or of the structure of reality, whatever that is, or "relative interrelation of interactions, whatever that is. Beats me.

And, by the way, how can a position be anything but local? I'd be very intrigued to know what a nonlocal position is.

Locality, as I've known it while doing physics is a rather simple concept -- to paraphrase a TV commercial, What happens here, is here, and is always face-to-face. And, with the restrictions imposed by relativity, something there can influence something here only by transmission of some "signal", at or less than the speed of light. So, "local" gives the following picture of electric and magnetic forces -- charge particle A emits a photon, which is absorbed by B, and vica versa. This goes on all the time, and the emission and absorbtion of photons is the specific mechanism behind the electromagnetic forces -- as is shown in numerous QED text books. All these words describe a very concise mathematical formulation, based on a field theory of local, that is point, interactions.

Regards,
Reilly Atkinson

vanesch
Staff Emeritus
Gold Member
Coucou ! Here I am again with my pet interpretation of QM, which is of course, MWI :uhh:

The way MWI sees QM is related to the issues here, because it combines both the locality and apparent non-local effects of QM, and the relationship between determinism and the essential randomness (of which the HUP is of course a cornerstone).

In MWI, the wavefunction of the universe is evolving *deterministically* and *via local dynamics*, always. The only dynamical law of the wavefunction is the Schroedinger equation, resulting in a unitary evolution operator ; moreover, this unitary evolution operator is such, that it only evolves subsystems in local contact. It is not the structure of quantum theory per se that requires this, but one can impose it, and in fact all postulated interactions (from which this unitary operator is build up) are local point interactions.

The Schroedinger equation being a first-order partial differential equation (over Hilbert space), this evolution is as deterministic as the flow in classical phase space: if we know the state exactly at one spacelike slice, we know it everywhere. As such, the dynamics of quantum theory (in this viewpoint: the Schroedinger equation is ALWAYS valid) is totally deterministic.

Where does the randomness come from then ? In the standard von Neumann view, it comes from the collapse, when a "measurement" (non-physical interaction) is performed. An explicitly stochastic prescription for the change of the state is given. But in MWI, there is no collapse. Nevertheless, there is something equivalent of course, namely the RANDOMNESS IN THE ASSOCIATION OF THE STATE AND THE SUBJECTIVE EXPERIENCE. You have to pick ONE observer state to be aware of, and the randomness is entirely related to that choice. This can sound like a trick: instead of saying that *nature* is random, you say that your *perception of nature* is random. What's the difference ? The difference is that you can save locality. Indeed, the explicit non-locality in the projection postulate (after all, you project the entire state at the moment of your (local) measurement, while that state describes subsystems all over the place, and hence your local, non-physical measurement changes the physical state of all subsystems of the universe) is only AN APPARENT EFFECT, DUE TO YOUR - ERRONEOUS - EXTRAPOLATION BACK IN TIME OF THE DEFINITENESS OF A REMOTE MEASUREMENT RESULT. It is this error (Alice - when learning about Bob's result - extrapolating back in time that Bob had a definite result - while in fact he was in a superposition) which is entirely responsible for the riddle of the violation of the Bell relationships, while retaining the respect of signal locality.

As such, when we stick to strictly unitary physical dynamics, we gain back determinism and locality. The randomness is only due to *our window on the state of nature* and the non-locality due to our erroneous extrapolation that observed results existed back in time.
It is this, together with the fact that I do not have to assume a non-physical measurement process, which makes me favor the MWI view.

Now, I place my usual caveat: MWI is of course just ONE view upon QM - one needs not to adhere to it. But I think it is interesting to know that there IS a view on QM which avoids the problems which are discussed here (while of course introducing another one: the total weirdness of the concept!).

reilly said:
I haven't a clue about what you are saying. Perhaps it's my lack of knowledge about Dr. Smolin's ideas.
Likely so, google scholar will get you to Smolin articles on backgound(s)
And, by the way, how can a position be anything but local? I'd be very intrigued to know what a nonlocal position is.
Positions not position
If QM were "local" it would have a classical direct solution to entanglement - it does not, it has non-local superposition where two things remain connected, via some non-local means, while in two space like seperated positionS.
QED of photon A to B does no better at resolving entanglement "localy" does it?

RB

vanesch said:
Coucou ! Here I am again with my pet interpretation of QM, which is of course, MWI :uhh:
In your opinion, does MWI offer any explanation for why we observe peculiarities/features on a large scale? An example of what I mean is that there are 9 planets in our solar system, but this can clearly not be derived from maths or laws alone without observation. Can we say it is just a feature of our universe?

Last edited:
vanesch
Staff Emeritus
Gold Member
jackle said:
In your opinion, does MWI offer any explanation for why we observe peculiarities/features on a large scale? An example of what I mean is that there are 9 planets in our solar system, but this can clearly not be derived from maths or laws alone without observation. Can we say it is just a feature of our universe?
Well, two caveats of course. I'm only offering MWI as an interpretation for unitary QM (where I think it is vastly superior to unitary QM + projection a la Copenhagen). All cosmological stuff is going to involve gravity and as is known, unitary QM has some serious difficulties with gravity. It has LESS difficulties with it than any projection postulate (which is in violent disagreement even with SR), but nevertheless. So I don't know if it is meaningful to discuss seriously a view on unitary QM of phenomena where gravity plays a role ; after all, this may alter entirely the structure of QM, and might do away with unitarity all together (though most people seem to stick to unitarity even in this case, but with not much success).
Of course MWI drops dead when strict unitarity is gone.
The second caveat is that MWI has no more predictive power than standard QM ; in fact it IS standard QM !

But the question you ask can be answered almost in the same way as in classical physics: we see 9 planets because the initial conditions were such that 9 planets were going to arise. Of course, with a slight change: we now probably have an initial condition (a quantum state) where a term with 9 planets could arrise, but also other terms. Nevertheless, the 9 planets must have had a relatively high hilbert norm over the others, so that when we were to "pick our state", we picked this one, with 9 planets. It must not be the highest hilbert norm of course, just not a totally ridiculously small one (or we are just "lucky"...).
Because of decoherence, this relatively high hilbert norm is more or less conserved, and a more or less "classical" evolution happened in this term. No significant mixing occured with other terms. So this behaved very very much in the same way as if we had a classical evolution from a classical statistical distribution, once the most important quantum effects that could have effected the formation of the number of planets, decohered. That's also why the history of our solar system "makes sense" when analysed from a classical perspective.

But maybe, loosely speaking, there's a copy of you, posting on a copy of PF, in another term, and wondering if it can be answered why there are 15 planets and 2 suns, right now ! Because of decoherence, however, you'll never hear of him :-)

JesseM
RandallB said:
If QM were "local" it would have a classical direct solution to entanglement - it does not, it has non-local superposition where two things remain connected, via some non-local means, while in two space like seperated positionS.
But if you use some type of many-worlds approach, QM can be local in principle. If Alice and Bob make a measurement on a pair of entangled particles at different locations, then you can imagine Alice splitting into multiple copies when she makes her measurement, and Bob splitting into multiple copies when he makes his, with the universe not having to decide which copy of Alice is mapped to which copy of Bob until there has been time for a signal moving at the speed of light to cross between them.

For example, suppose Alice and Bob each measure the spin of our particle on one of three separate axes, a, b, or c, and Bell's inequality predicts that when they pick different axes, they must get opposite spins at least 1/3 of the time (see my first post on this thread for the logic behind this prediction), but QM predicts they'll get opposite spins only 1/4 of the time. To make things easier, assume they are both using some deterministic pseudorandom process to decide which axis to measure on each trial, so on one particular trial, all the copies of Bob will measure axis b and all the copies of Alice will measure axis a. Then when Bob makes his measurement, say he splits into multiple copies, 1/2 of which measure spin up (b+) and 1/2 of which measure spin down (b-):

Bob 1: b+
Bob 2: b+
Bob 3: b+
Bob 4: b+
Bob 5: b-
Bob 6: b-
Bob 7: b-
Bob 8: b-

And the same thing happens to Alice:

Alice 1: a+
Alice 2: a+
Alice 3: a+
Alice 4: a+
Alice 5: a-
Alice 6: a-
Alice 7: a-
Alice 8: a-

Notice that each split in the same way, just based on the local probabilities of measuring spin-up vs. spin-down. The spooky correlations of entanglement only appear when you decide which copy of Bob is mapped to which copy of Alice, and it's easy to do this mapping in a way that ensures that there's only a 1/4 chance they will get opposite spins:

Bob 1 <-> Alice 1 (same)
Bob 2 <-> Alice 2 (same)
Bob 3 <-> Alice 3 (same)
Bob 4 <-> Alice 5 (opposite)
Bob 5 <-> Alice 4 (opposite)
Bob 6 <-> Alice 6 (same)
Bob 7 <-> Alice 7 (same)
Bob 8 <-> Alice 8 (same)

On the other hand, suppose they had both measured axis a, so QM predicts there's a 100% chance they'll get opposite spins. Again, you can assume each initially splits based purely on local probabilities:

Bob 1: a+
Bob 2: a+
Bob 3: a+
Bob 4: a+
Bob 5: a-
Bob 6: a-
Bob 7: a-
Bob 8: a-

and

Alice 1: a+
Alice 2: a+
Alice 3: a+
Alice 4: a+
Alice 5: a-
Alice 6: a-
Alice 7: a-
Alice 8: a-

Only this time, once a signal has had time to cross between them, the mapping would work differently:

Bob 1 <-> Alice 5 (opposite)
Bob 2 <-> Alice 6 (opposite)
Bob 3 <-> Alice 7 (opposite)
Bob 4 <-> Alice 8 (opposite)
Bob 5 <-> Alice 1 (opposite)
Bob 6 <-> Alice 2 (opposite)
Bob 7 <-> Alice 3 (opposite)
Bob 8 <-> Alice 4 (opposite)

So, this is basically how many-worlds could explain the results of the EPR experiment in a purely local way. You could simulate this on two ordinary classical computers, one simulating the location of Bob and the other simulating the location of Alice, with the computers not allowed to communicate until after each one's measurement had been made--by programming in the right mapping rule, you could insure that a randomly-selected Alice copy will see the same probabilities that "her Bob" (the one she's mapped to) gets a given result as are precicted by quantum mechanics, even though the computers are totally classical ones.

Here are some papers arguing that the many-worlds interpretation is local in basically the same way, although I don't have the expertise to judge if their arguments are convincing (there has always been a problem explaining how to get any notion of probabilities from the universal wavefunction postulated by the MWI):

http://www.arxiv.org/abs/quant-ph/0003146
http://www.arxiv.org/abs/quant-ph/0103079
http://www.arxiv.org/abs/quant-ph/0204024

reilly
RandallB said:
Likely so, google scholar will get you to Smolin articles on backgound(s) (Thanks)
Positions not position RA So?

If QM were "local" it would have a classical direct solution to entanglement - it does not, it has non-local superposition where two things remain connected, via some non-local means, while in two space like seperated positionS.

RA Why ? What is the non-local means? What is a classical direct solution?

Entanglement is just another way of talking about conditional probability. There's plenty of entanglement in classical physics, due to conservation laws, but, of course, the probability rules for classical and quantum physics are a bit different. (Control engineering deals with such issues, classical state vectors and all,among others.)

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>.

QED of photon A to B does no better at resolving entanglement "localy" does it?
RB
RA
Who's talking resolving? I've provided you with a standard formal definition of locality in QED. What's the problem?

Regards,
Reilly Atkinson

vanesch
Staff Emeritus
Gold Member
JesseM said:
But if you use some type of many-worlds approach, QM can be local in principle. If Alice and Bob make a measurement on a pair of entangled particles at different locations, then you can imagine Alice splitting into multiple copies when she makes her measurement, and Bob splitting into multiple copies when he makes his, with the universe not having to decide which copy of Alice is mapped to which copy of Bob until there has been time for a signal moving at the speed of light to cross between them.

Right on !

reilly said:
RA
Who's talking resolving? I've provided you with a standard formal definition of locality in QED. What's the problem?
No you didn’t – you said
By the way, there are sound theoretical reasons why QM and QFT are local—
To people that were looking and causality and QM non-locality. Effectively telling them they wrong to think that way. And they are not, a non-local QM an appropriate way for them to look at QM.
I was just looking for you to clarify whatever you saying and put it proper context.
The problem is, instead of addressing their issues; you were just promoting your opinions. At least you could say you or some think, QM can be local in principle, because - - -whatever --.

And just for the record IMO (in my opinion) MWI is one of the more ridiculous ideals getting ink to come out of QM.

vanesch
Staff Emeritus
Gold Member
RandallB said:
And just for the record IMO (in my opinion) MWI is one of the more ridiculous ideals getting ink to come out of QM.
The usual, well-argumented rebuttal against MWI

vanesch said:
The usual, well-argumented rebuttal against MWI
As compared to the agreements & proofs provided in favor of it your correct.

vanesch
Staff Emeritus
Gold Member
RandallB said:
As compared to the agreements & proofs provided in favor of it your correct.
It is hard to find out if you are ironic, but here are the main arguments in favor of MWI (as an interpretation of QM):

1) respect of unitarity (as postulated in QM) and possibility to represent the state of the universe as a ray in Hilbertspace (as postulated in QM)

2) no non-physical (because non-unitary) phenomenon in the measurement apparatus

3) the theory DOES describe a reality (although it is different from the one we perceive directly) - so no positivism which denies reality all together

4) we can save locality (any collapse is non-local) so that we can keep SR

The downside is that we have to postulate a non-trivial relationship between reality and subjective experience, but if this is done, no contradiction is derived between the postulated subjective experience and actually perceived subjective experience as we know it.

I consider the above as a rather solid ARGUMENTATION when compared to:
"one of the more ridiculous ideas"
or:
"a meaningless string of words"
or:
"naah, can't be true".

Mind you, I'm not claiming that MWI is necessarily true. I'm claiming that, when you consider the many formal advantages of this viewpoint (see argument above) that other viewpoints (as long as they don't touch upon the formalism of QM; in other words, as long as they are an INTERPRETATION of QM, and not simply a different theory) pale against it: The Copenhagen view is inconsistent with the basic axioms of QM (as Schoedinger found out rather early with his cat) and non-local, and the probabilistic view (although I can have some sympathy for it) denies any link with reality.

I note that the only "arguments" against the viewpoint are simply emotional statements and do not include a solid reasoning.

So the only way I can consider a non-MWI viewpoint, is by presenting another theory, with a clearer interpretation, which will explain all the QM successes.
There are two "candidates": local realist theories starting from classically relativistic field theories (we already KNOW that they will not be equivalent to QM thanks to Bell) and Bohmian mechanics. Bohmian mechanics is not compatible in its workings with the principle of relativity (it is non-local) and has also some of its own interpretational problems.

reilly
vanesch --

A knowledge based QM interp, as with any probabilistic theory, necessarily obeys unitarity. Further, with QM so interpreted, than all, repeat, all theories involving probability are resting on the same basis -- there's always a probability (wave)(function) collapse, by necessity in fact, and it occurs in people's brains -- that's quite close to certainty,in fact I'm fairly certain that brain scans can actually show such a collapse.

QM describes at least the reality of the experimentalist, and, when, the fabric of experimental results is woven, it, metaphorically, looks strangely like normal reality -- the reality of common experience.

As usually formuted, QM is local, point interactions and all that.

I've always thought of MWI as odd. Seems to me that it's just another attempt to subvert probability. If it is such a great idea, why has it not been in place since at least Fermat's notions about games of chance? Why is this ideas absent from virtually all books on probability and statistis? (I would say all, but there are such books that i've never read.)Why not a universe in which I broke the Bank at Monte Carlo, when I found and extra million in my bank acount, why not a universe in which the Boston Red Sox won 25 World Series in a row? What good does such speculation bring?

The kindest thing I can say about MWI is that it is rather peculiar.

The knowledge approach works, and, I have yet to hear of any practical arguments against it.

I will admit that the stupendous ego of David Deutsch, which permeates his book, The Fabric of Realty, turned me away, in part, from MWI. It's one of these books that says,"Trust me, I'm right." He's a great spinner, probably could do well as a political consultant, with such catchy ideas as shadow photons. Small wonder that his views remain relatively unknown.

With all due respect, I have yet to see anything about MWI that solves any problem of QM other than with fanciful suppositions of universes we can never know. Deus ex Machina

Regards,
Reilly Atkinson

gstafleu said:
In case of the cat the design incorporates a known indeterminate element: the decay of an atom. We do not have a model that will predict the exact time when a given atom will decay, but we do have a statistical model, and that model is incorporated into the cat experiment. That model predicts that, if we open the box at t=Lambda, we have a 50% chance of a dead cat. Before we open the box we of course don't know the state of the cat, but that is what was designed into the experiment. How does this show any indeterminacy beyond that which was designed into the experiment?
The issue here is that an observer inside the box has a very clear knowledge about the state of the cat, but an observer outside of the box, has just an information about the state of the cat with 50% uncertainty.

This means that the same physical system (the box with the cat) provides to the inside observer scientific information which comes from constant observation that is not available to the outside observer. This difference in status produce the dramatic difference between the uncertainty of the information about the status of the system for each observer.

If you put the solar system in a box, and you have an internal observer constantly observing the planets and an external observer having a snapshot observation, they share the same certainty regarding the information about the status of the solar system in the box. The internal observer can observe constantly the orbits of the planets and he can guide a space vehicle from earth to another planet based on his scientific information gathered by the continues observations, with the same certainty with which the external observer can guide another space vehicle from earth to another planet based on the scientific information gathered from the system, in a snapshot. Both observers having informations from the system, the one from real time observations from inside and the other from a snapshot observation before being locked outside from the system, they share the same certainty about the status of the system during the passage of time.

In the solar system in a box example, the position of the observer is irrelevant from the degree of certainty of the scientific information for the status of the system.

gstafleu said:
With the double slit experiment we seem to have a similar situation. The indeterminacy designed into the experiment is that we don't know exactly which slit a given electron will go through. But we do know that 50% of the electrons will go through one, 50% through the other slit. The actual probability distribution turns out to be a wave function, which is perhaps a bit unusual, but no more than that. As a result the distribution of electrons on the detector screen displays an interference pattern. So far I fail to see any indeterminacy beyond what was designed into the experiment.

We can then change the experiment by removing the indeterminacy: we add some sort of apparatus that tells us through which slit each electron passed. This apparently changes the probability distribution from a wave to a classic particle yes-or-no distribution. OK, so that is maybe strange, but I still see no indeterminacy here.
This is a similar situation, like the cat in the box situation, where the information known to the observer affected the certainty about the information of the status of the cat.

The information that the observer has in hand affect the distribution of electrons on the screen.

The status of each observer, regarding the "position" of observation, affects the certainty of the information that the system is providing about the system's status.

(edit) In an analogy, the opposite thing happens in the observation of the solar system. The certainty of the scientific information about the status of the solar system is the same in both cases: when the observer makes observations from outside using information from starting and end points from the movements of the planet, or when the observer makes observations by using position traps gathering information from positions in between the starting and end points from the movements of planets. Both observers share the same certainty of the information of the status of the solar system. In the experiment with the electrons the certainty of the information of the status of the system is different for each observer, when the one knows the in between positions of the electrons and the other one does not.

In both experiments, the indeterminacy is about the diferrent degrees of certainty of the information of the system which depends on the "position" of the observer. You come to the right conclusion, that all local observers share the same uncertainty, and that all non-local observers share the same uncertainty. There is no indeterminacy, for the same class of observers. The indeterminacy is about having two classes of observers, the local and the non-local. Within each class the certainty of the scientific information of the status of the system is consistent. But the experiment is inconsistent when we compare the certainty of the scientific information of the status of the system between the two classes of observers.

This incosistency, between classes of observers, is NOT happening in systems of classic physics (like the solar system). This is not a measurement problem. It is an intrinsic paradox. The same system, in quantum physics, provides different degrees of certainty of scientific informations to the observer, depending on the "position" of the observer.

So, I think that the answer to your question "Is quantum indeterminacy a result of experiment design?" is NO. The indeterminacy is an intrinsic behaviour of the systems of quantum physics.

Leandros

Last edited:
leandros_p said:
The issue here is that an observer inside the box has a very clear knowledge about the state of the cat, but an observer outside of the box, has just an information about the state of the cat with 50% uncertainty.
Isn't that equally the case if we replace the cat+atom with a coin flipping machine? The observer inside the box knows exactly which side came up, the one outside lives in uncertainty. Until the two communicate, that is, or the outsider looks in, at which point both will agree. Which is the same situation as with the cat+atom.

Now for you solar system example, doesn't the same apply? Assuming the outside observer (1) cannot peek and (2) does not have pre-knowledge of the solar system (he just zapped over from a galaxy far far away and has never seen the solar system before), then the insider knows and the outsider doesn't.

The solar system example has the drawback that we have a pretty good deterministic model of the planetary positions, while we do not have such a model of atom decay. As a result, if both observers know the initial state, and then close the box at time T, they can then both come up with, agreeing, descriptions of the state at T+t. You cannot do that with the cat+atom (catom?), but that is because we don't have a deterministic catom model, which we knew when we started.

In other words, if you design an experiment such that all its components have well established deterministic models, then observers both inside and outside any surrounding boxes will have the same knowledge of the system's status. If you throw in a component for which you "only" have a stochastic model, well, then those on the inside will know more.

gstafleu said:
Isn't that equally the case if we replace the cat+atom with a coin flipping machine? ...Which is the same situation as with the cat+atom.

...You cannot do that with the cat+atom (catom?), but that is because we don't have a deterministic catom model, which we knew when we started.

If you understand that the the cat+atom model is a non-deterministic model by itself, then the experiment is not "producing" the result. It just provides non-deterministic information to the observer.

The "quantum inteterminacy" is not a product from the desigh of the experiment.

The "quantum inteterminacy" is made known, as a scientific information, by the design of the experiment. Each experiment is designed in order to aquire information. This expreriment provides the "information" of "inteterminacy", but it does not produce this "information".

Leandros

vanesch
Staff Emeritus
Gold Member
reilly said:
vanesch --
A knowledge based QM interp, as with any probabilistic theory, necessarily obeys unitarity.
I don't understand what this could mean.

As usually formuted, QM is local, point interactions and all that.
The *unitary* part of QM is local, yes.

I wonder what it could possibly mean for something to interact "locally" if it is just a knowledge description. What does it mean that my "knowledge of electron A" interacts locally with "my knowledge of proton B" ?
Assuming that this is not the objective state of the electron A or the proton B, I don't see what can be "local" to it, and why my 'knowledge of electron A' cannot have any interaction with my knowledge of muon C, which is - or rather, I know that it is - 7 lightyears from here.
So how do you implement something like lorentz invariance for knowledge ?

I've always thought of MWI as odd. Seems to me that it's just another attempt to subvert probability. If it is such a great idea, why has it not been in place since at least Fermat's notions about games of chance?
The reason for MWI is of course NOT to circumvert probability or something. In fact (although many MWI proponents trick themselves IMO into the belief that they can do without it - I'm convinced that they are wrong, and that probabilistic concepts are needed also there) the only reason for MWI is to be able to take the wavefunction as an objective description of reality. You run into a lot of problems and paradoxes if you take the wavefunction as describing objective reality while accepting the probabilistic projection, but the problem is not the probabilistic aspect of it ; the problem is twofold:
1) the fact that all elementary interactions between quantum systems are described as strictly unitary operations on the quantum state (its derivative being a Hermitean operator which we call the Hamiltonian) - so there is no known mechanism to implement a non-unitary evolution, which is a projection
2) the fact that this projection cannot be formulated in a Lorentz invariant way

The problem is NOT, the probabilistic aspect.

There is a difference between the relationship between classical physics and probability, and between the quantum state and probability, and that's the following. When we use probability in classical physics, the probability distribution itself plays no physical role.
When a classical system evolves from A to A', and from B to B', then, if we assign probability p1 to A and p2 to B, we'll have an outcome B with probability p1 and an outcome B' with probability p2. If we learn that the system was finally in B', then we can "update backward" our probabilities, say that the system, after all, was in state B, and that A was just part of our ignorance. As you state, there's no reason to introduce a "parallel world" in which A was there, after all, but we happen to be in a universe where B happened.
The reason why this is superfluous is that the numbers p1 and p2 never enter into any physical consideration. They are just carried along, with the classical physics, WITHOUT INFLUENCING THE DYNAMICS.

But in quantum theory, this is not true. If the state is a |u> + b |v> , and if we now evolve this into the state a |u'> + b |v'> and we work now in the basis |x> = |u'> + |v'> and |y> = |u'> - |v'>, and measure x/y, then the probability of having x or y will depend on the numbers a and b. It is not that the coefficients a and b are somehow, a measure of our lack of knowledge, which get updated after the measurement. Because if this were true, there would be no difference between a STATISTICAL MIXTURE of states |u> and |v> and the state a|u> + b|v>
To illustrate that this is not the case, consider a = b. A statistical mixture of 50% |u> and 50% |v> will yield in an outcome which gives us 50% |x> and 50% |y>. Nevertheless, the state |u> + |v> (which has identical statistical value, right) will result in 100% state |x> and 0% state |y>.
So the values of a and b CANNOT be interpreted as describing our lack of knowledge which gets updated during the measurement. It would be hard to imagine that NOT KNOWING something (having non-zero values for a and b) would make it impossible to obtain the outcome |y>, while KNOWING something (like knowing that a = 1 and b = 0) would suddenly make the states |x> and |y> appear 50% each.
So those numbers a and b HAVE PHYSICAL MEANING. They influence what will happen later, and this cannot be seen in a purely "I didn't know, and now I learned" fashion, as probability CAN be seen in a classical context. It is the phenomenon of quantum interference which makes the "knowledge" view of the wavefunction, IMO, untenable.
The state |u> + |v> has simply DIFFERENT PHYSICAL CONSEQUENCES than the state |u>. One cannot say that |u> + |v> expresses our lack of knowledge about whether it is |u> or |v>, while the state |u> expresses our certainty of having the system in state u for sure, because if that were so, then it is strange that a lack of knowledge leads to more certainty (namely, that we will NOT have the result y) than when we know more.

Why is this ideas absent from virtually all books on probability and statistis? (I would say all, but there are such books that i've never read.)Why not a universe in which I broke the Bank at Monte Carlo, when I found and extra million in my bank acount, why not a universe in which the Boston Red Sox won 25 World Series in a row? What good does such speculation bring?
It doesn't bring any good in a classical setting, because of the fact that this "parallel possibility" has no influence what so ever on the physical dynamics. You can say, in this context, that the "parallel universe" where the initial conditions where such that the Boston Red Sox will win 25 World series in a row, has, FROM THE BEGINNING, never been there, and that we just entertained its possibility because we didn't knew all the details. When we did find out that this didn't happen, we could simply scrap this parallel universe from our list with no harm, BECAUSE IT HAS NEVER BEEN PART OF THE ONTOLOGICAL STATE OF THE UNIVERSE in the first place (only, we didn't know).

But when we know that the state is |u>, and we find |x>, we cannot go back 'scrap' somehow a state from our list. We cannot say that it actually meant that the state was actually |u> + |v>, back then. Because we MEASURED u back then, and we found u, and not v. So it is not "an imaginary parallel universe which turned out not to be the right one".

The knowledge approach works, and, I have yet to hear of any practical arguments against it.
The most important argument against it IMO, is that there is no description of reality in this view. It is hard to work with things of which you have constantly to remind yourself that "it isn't really there", and nevertheless devellop a physical intuition for.

I will admit that the stupendous ego of David Deutsch, which permeates his book, The Fabric of Realty, turned me away, in part, from MWI. It's one of these books that says,"Trust me, I'm right." He's a great spinner, probably could do well as a political consultant, with such catchy ideas as shadow photons. Small wonder that his views remain relatively unknown.
Didn't read it. My only attempt was to write a paper showing that his proof was flawed, but (as has been discussed here), it was not accepted.

With all due respect, I have yet to see anything about MWI that solves any problem of QM other than with fanciful suppositions of universes we can never know. Deus ex Machina
You are probably right that it doesn't have much practical implications. In my opinion, the most important function of MWI is to rehabilitate QM as a description of reality, and to be able to put all this positivist considerations aside. As such, it removes all ambiguity about WHEN one should apply the projection postulate, and removes the need of the distinction between a physical interaction and a non-physical measurement. In most situations, this distinction is so clear, that it doesn't need any specific treatment, but in situations such as delayed choice quantum erasers or EPR setups, one can wonder about when one should apply the projection postulate. Well, MWI solves that situation unambiguously.

I would also like to point out that "the universes we can never know" are NOT introduced or postulated. They are simply not ELIMINATED by a projection postulate.