Why MWI cannot explain the Born rule

[Demystifier]

It will not necessarily satisfy i) in the limit, i.e. you can find an A for which P(A) -> p, p>0, while P'(A) -> 0.

It must be due to the fact that i) insists on L2-norm, and not on some other norm such as L4. But then the natural questions is: Why one should insist on L2-norm and not some other norm? Isn't the requirement of L2-norm rather than some other norm actually a hidden ASSUMPTION of the Born rule? If so, can such a "derivation" of the Born rule really be considered an explanation of the Born rule?

 

[toho]

It must be due to the fact that i) insists on L2-norm, and not on some other norm such as L4. But then the natural questions is: Why one should insist on L2-norm and not some other norm? Isn't the requirement of L2-norm rather than some other norm actually a hidden ASSUMPTION of the Born rule? If so, can such a "derivation" of the Born rule really be considered an explanation of the Born rule?

Well, the fact that P and P' have measure 0 for different sets (i.e. they are not what I believe is called equivalent) is not a consequence of the choice of L2-norm. However, the fact that P is preferrable over P' obviously is.

But, the L2-norm is natural as it is defined by the inner product, and we do have an inner product space.

 

[Demystifier]

But, the L2-norm is natural as it is defined by the inner product, and we do have an inner product space.

OK, but why this natural norm should have anything to do with probability? For example, the linear wave equation describing water waves also shares the same mathematical structure, including the inner product of solutions, yet this inner product of water wave solutions has nothing to do with probability.

 

[toho]

OK, but why this natural norm should have anything to do with probability? For example, the linear wave equation describing water waves also shares the same mathematical structure, including the inner product of solutions, yet this inner product of water wave solutions has nothing to do with probability.

The water wave is deterministic to an outside observer of the wave, just as the wave function of MWI would be deterministic to an outside observer. However, to an observer inside a universe according to MWI the future (as well as the past, btw) is indeed unpredictable. This is (as I understand MWI) because of entanglement of the brain of the observer with the state of the universe.

Now, the choice to use probability is indeed a choice (in my opinion), but if you do choose to use probability, I argue that there is only one probability measure that works. Why then would you expect or want the probability to be zero when the norm of the wave function is zero? Well, when the norm of the wave function is zero the wave function contains no information, i.e. it can't possibly describe the universe in those branches, or for those events (or rather, for projections of the wave function down to those sub-spaces). On the other hand, if the norm is not zero, (the projection of) the wave function will influence the future of the universe, so you don't want the probability to be zero.

(Just a further point with regards to the water wave analogy. Imagine that you are not an outside observer of the wave, but a perfect sine wave propagating in an idealised euclidean sea. Your perception of the sea is determined by your interaction with the rest of the waves in the sea. But since you are orthogonal to most of them you will not perceive much of the other waves. Despite the fact that you as a sine wave "are everywhere", you will not have information to predict the sea.)

 

[Demystifier]

It will not necessarily satisfy i) in the limit, i.e. you can find an A for which P(A) -> p, p>0, while P'(A) -> 0.

My intuition tells me that examples supporting this claim have a rather pathological form and do not correspond to cases of physical interest in practice. If I am right, then the axiom i) makes sense only if it is a fundamental axiom, not only a rule relevant in practical applications. But then MWI is FUNDAMENTALLY a probabilistic theory.

 

[toho]

My intuition tells me that examples supporting this claim have a rather pathological form and do not correspond to cases of physical interest in practice. If I am right, then the axiom i) makes sense only if it is a fundamental axiom, not only a rule relevant in practical applications. But then MWI is FUNDAMENTALLY a probabilistic theory.

I beg to differ. Let me give you an example:
Let the universe at any time have N+1 branches, where N is an unbounded, increasing function of time. Let one branch, called A, have a P-probability of 0.5. Furthermore, let each of the remaining branches (the union of which we call B) each have a P-probability of 0.5/N. Then P(B) = 0.5. Let's calculate:
P'(A) = 0.25/(0.25 + N*0.25/N^2) = N/(N+1)
P'(B) = 1/(N+1)
Thus, P'(B) quickly -> 0 with time. In general, the rate of branching will determine probability under P'.

 

[Demystifier]

I beg to differ. Let me give you an example:
Let the universe at any time have N+1 branches, where N is an unbounded, increasing function of time. Let one branch, called A, have a P-probability of 0.5. Furthermore, let each of the remaining branches (the union of which we call B) each have a P-probability of 0.5/N. Then P(B) = 0.5. Let's calculate:
P'(A) = 0.25/(0.25 + N*0.25/N^2) = N/(N+1)
P'(B) = 1/(N+1)
Thus, P'(B) quickly -> 0 with time. In general, the rate of branching will determine probability under P'.

I see. Now I see why axiom i) is formulated by referring to the limit t->inf. But what if I don't consider the limit t->inf? For example, if I only want to know what is the probability NOW, why is it relevant how the system will evolve LATER?

 

[Demystifier]

Secondly, it is really not enough to assign a probability to each branch. We have to assign a probability to each testable outcome at each point in time. This makes a difference, at least if we have a finite number of branches.

I'm afraid I don't understand it. In my understanding of practical utility of quantum mechanics, each branch at a given time corresponds to one and only one possible measurement outcome at this time. Therefore, at each time it is enough to assign a probability to each branch at that time. How do you comment on this?

 

[toho]

I see. Now I see why axiom i) is formulated by referring to the limit t->inf. But what if I don't consider the limit t->inf? For example, if I only want to know what is the probability NOW, why is it relevant how the system will evolve LATER?

That's a good point. I want a theory to make sense not just now, but for any future time. One way to assure this is to include the infinity limit as well.

I am not sure that the limit t->inf is strictly necessary, though. As long as the Hilbert space is infinitely-dimensional, you can in principle construct infinite countable sequences by splitting up sub-spaces into ever smaller sub-spaces, and computing probabilities for projections onto such sub-spaces. Then you could construct a similar argument with regard to a non-Born probability measure without any reference to the t->inf limit (I think).

 

[Demystifier]

That's a good point. I want a theory to make sense not just now, but for any future time. One way to assure this is to include the infinity limit as well.

I would accept that argument if probability were a fundamental part of the theory. But if probability is EMERGENT (as MWI usually claims), then it is emergent at the time I am doing the experiment. In this case the probabilistic interpretation is not a part of the fundamental self-consistent theory, but is a rule of thumb applicable at the time the experiment is done.

 

[toho]

I'm afraid I don't understand it. In my understanding of practical utility of quantum mechanics, each branch at a given time corresponds to one and only one possible measurement outcome at this time. Therefore, at each time it is enough to assign a probability to each branch at that time. How do you comment on this?

Yes, I guess that is true with regard to the practical utility of QM (but depending on what you mean by "to each branch at that time"). At each point in time you would have to assign a probability to each branch in the future of that time. That may be enough for practical purposes (but don't ask me to prove it - what if an action I take depends on a calculated probability of an event that will never occur due to the fact that I calculated its probability), as it would provide a probability for each potential event that will happen in some branch of the Universe, rather than one for each event that could happen.

 

[Demystifier]

I am not sure that the limit t->inf is strictly necessary, though. As long as the Hilbert space is infinitely-dimensional, you can in principle construct infinite countable sequences by splitting up sub-spaces into ever smaller sub-spaces, and computing probabilities for projections onto such sub-spaces. Then you could construct a similar argument with regard to a non-Born probability measure without any reference to the t->inf limit (I think).

But if there is only a finite number of branches at some initial time, then typical realistic evolution makes only a finite number of branches at any finite later time. (For example, the beam splitter or the Stern-Gerlach apparatus evolves one initial branch into two new branches.) Do you agree?

 

[toho]

I would accept that argument if probability were a fundamental part of the theory. But if probability is EMERGENT (as MWI usually claims), then it is emergent at the time I am doing the experiment. In this case the probabilistic interpretation is not a part of the fundamental self-consistent theory, but is a rule of thumb applicable at the time the experiment is done.

Well, don't blame me what other MWI-proponents claim

I believe that using probability in MWI is a choice, just as it is a choice to use probability when gambling. It isn't possible to prove in some fundamental sense that 1:1 is fair odds in a coin flipping game. You have to accept that probability is somehow applicable to a deterministic game (albeit with initial conditions unknown).

But just to take the gambling analogy a bit further - assume two people, let's call them D and T, play a betting game on the outcome of quantum events in a world according to MWI (without the Born postulate). D provides whatever odds he thinks is fair and T is allowed to decide which side to take. If D does not provide odds according to the Born rule, and T bets according to the Born rule, then in the limit as the number of rounds -> infinity, T will be rich if the norm of the wave function is non-zero and D will be poor unless the norm of the wave function is zero.

 

[toho]

But if there is only a finite number of branches at some initial time, then typical realistic evolution makes only a finite number of branches at any finite later time. (For example, the beam splitter or the Stern-Gerlach apparatus evolves one initial branch into two new branches.) Do you agree?

I see no reason to believe that there is only a finite number of branches. For instance, the time of decay of an atom has a continuous value, and each decay time corresponds to one branch, if measured.

 

[Demystifier]

I see no reason to believe that there is only a finite number of branches. For instance, the time of decay of an atom has a continuous value, and each decay time corresponds to one branch, if measured.

I disagree. If you measure time, then you measure it with finite resolution and you don't wait for an infinite time to see the decay. Thus, the set of all possible measurement outcomes is finite.

 

[Demystifier]

But just to take the gambling analogy a bit further - assume two people, let's call them D and T, play a betting game on the outcome of quantum events in a world according to MWI (without the Born postulate). D provides whatever odds he thinks is fair and T is allowed to decide which side to take. If D does not provide odds according to the Born rule, and T bets according to the Born rule, then in the limit as the number of rounds -> infinity, T will be rich if the norm of the wave function is non-zero and D will be poor unless the norm of the wave function is zero.

That's true. But the question is: Can MWI EXPLAIN why it is true?

 

[toho]

I disagree. If you measure time, then you measure it with finite resolution and you don't wait for an infinite time to see the decay. Thus, the set of all possible measurement outcomes is finite.

That is an assumption that you are not free to make. If you measure something with a digital instrument, it is true, but not if you use an analog instrument, or if you register events with the brain.

In general, the wave function varies smoothly, and it lives in an infinite-dimensional space. You cannot just assume that it can be represented in a finite-dimensional space (which effectively is what you are doing).

If we move a few steps beyond the Schrödinger equation and early QM, I believe there are measurable quantities in field theory that are limit values of infinitely many interactions, and then your argument breaks down anyway (although I might very well be wrong with regards to field theory).

 

[Demystifier]

In general, the wave function varies smoothly ...

That's true, but my point is that the set of BRANCHES (induced by decoherence) is discrete. And it is this set of branches that defines the set of possible measurement outcomes. And it is this set of decoherence-induced branches that makes MWI meaningful (at least to me) in the first place. Without these branches induced by decoherence, I would not even waste my time to think or read about details of the MWI program.

 

[toho]

That's true, but my point is that the set of BRANCHES (induced by decoherence) is discrete. And it is this set of branches that defines the set of possible measurement outcomes. And it is this set of decoherence-induced branches that makes MWI meaningful (at least to me) in the first place. Without these branches induced by decoherence, I would not even waste my time to think or read about details of the MWI program.

I understand, but your argument (that I can't remove the t->inf limit in the conjecture by dividing up the Hilbert space of the wave function into a countable sequence of sub-spaces) depends on a finite number of branches AND that the evolution of the universe can be described in terms of (the probability of) those branches. Both of those can't be true (or you have revolutionized QM ) because you need an infinite-dimensional Hilbert space to describe any interesting QM universe.

Now, I don't agree with your conjecture that there is only a finite number of branches (not without more of a proof anyway), but the notion of branches is somewhat fuzzy, and there may well be some version of MWI where it is true. However, for the discussion about the uniqueness of the probability measure I can't see how it matters.

EDIT: Thinking about it a little bit more, it seems reasonable that the number of decoherence-induced branches may indeed be finite. But that does not further your argument against the removal of the t->inf limit, because the decoherence-induced branches do not determine the future of the universe exactly (they only do so with high probability).

 

[Demystifier]

Now, I don't agree with your conjecture that there is only a finite number of branches (not without more of a proof anyway), but the notion of branches is somewhat fuzzy, and there may well be some version of MWI where it is true.

I agree that it is fuzzy, but that's the only version of MWI I'm interested about. Other versions do not make much sense to me.

 

[Demystifier]

EDIT: Thinking about it a little bit more, it seems reasonable that the number of decoherence-induced branches may indeed be finite. But that does not further your argument against the removal of the t->inf limit, because the decoherence-induced branches do not determine the future of the universe exactly (they only do so with high probability).

Let me remind you that I find the t->inf limit irrelevant because emerging probabilities emerge "now", not in the far future.

 

[Dmitry67]

I agree that it is fuzzy, but that's the only version of MWI I'm interested about. Other versions do not make much sense to me.

... while I am still thinking about the idea with he proof...

What "other versions"?
What flavors of MWI do you know?

 

[toho]

That's true. But the question is: Can MWI EXPLAIN why it is true?

Yes, it does. I believe that I have done so, in the sense that it can be proven to be true (again, provided my conjecture or something similar holds).

I get the feeling that what you really are after is a some kind of explanation of the nature of uncertainty. I cannot provide that. What I can do is try to explain how I see uncertainty and probability, but that is just my mental picture of it. You will have to acquire your own mental picture somehow (and I am sure that you do have one).

Most physicists (me included) are brainwashed from an early stage in their careers to believe that there is some kind of "true" randomness in quantum mechanics that is different from all other randomness. This belief is not something that can be tested or proven (not even with Bell). It is just something a generation of physicists have been told to believe. In cryptography there is even a market for devices measuring quantum noise to produce "true" random numbers, used where security demands are extra high. (I think that is a terrible idea btw - such devices are much, much more likely to malfunction and give biased random numbers than conventional "pseudo" random number generators, thus compromising the security of the crypto). I don't believe in different kinds of uncertainty. All uncertainty obeys the same laws of probability.

Probability theory is the study of uncertainty. Any type of uncertainty, regardless of why there is uncertainty, can be studied with probability theory. Probability theory is based on a few simple axioms, and it allows you to compute the limit behavior of a system, e.g. for number of trials -> infinity. That all it does, and that is all than can be hoped for (unless the probability of something is unity, and then there really isn't uncertainty anymore). The axioms of probability theory includes the notion of a probability measure. Any limit behavior that you derive from probability theory is highly dependent on this probability measure. In general there are more than one probability measure to choose from. If that is the case, probability theory will not give you a unique result. If, however, the probability measure can be fixed somehow (by using statistics of a representative sample, symmetry arguments or - best of all - by proving that there can only be one unique measure) then probability theory will provide a unique answer to the question of what you will get in the limit. It can, however, not tell you what result you will get over the next N trials.

Anyone is free to question the utility of probability theory on the grounds that what happens in the limit is really not applicable to them in the case of just N trials. Anyone is also free to find their own explanations as to why things play out as they do over a limited number of trials (it was fate, an act of God, it was the initial conditions, there is hidden information that I can't access...). Indeed, anyone is free to develop their own probability theory with different axioms and different results, on the grounds that it will only matter in the limit anyway.

Now, why does an inhabitant in a world according to MWI experience uncertainty when the equations of the universe are deterministic? It isn't really because of uncertain initial conditions (Although, initial conditions are really only known from the perspective of an outside observer. Each branch of the universe will have a branched history as well. The histories of all branches will sum to the true history of the universe.) Instead it is because the state of the brain is entangled with the state of the rest of the universe (whether by decoherence or not). Because of that, any memory of the past that is stored in the brain in one branch of the Universe can at any point in time only include events that took place in the history of that branch. Thus, any state of a brain in a given branch will perceive to have experienced uncertainty. Consequently, any brain is uncertain of what it will perceive to have experienced next. That is where the uncertainty comes in - not about what will in fact happen, but about what events that in the future will be perceived to have happened.

 

[Demystifier]

What "other versions"?
What flavors of MWI do you know?

Well, MWI was invented before the phenomenon of decoherence has been understood.

 

[Demystifier]

You will have to acquire your own mental picture somehow (and I am sure that you do have one).

I believe I have explained my mental picture in post #71 of this thread:
https://www.physicsforums.com/showpost.php?p=2500938&postcount=71

 

[toho]

Let me remind you that I find the t->inf limit irrelevant because emerging probabilities emerge "now", not in the far future.

But the notion of probability only has meaning as a limit behavior - that is true in any application of probability theory, not just QM. Saying that a probability emerges now does not make any sense, if you don't somehow consider the limit behavior of infinitely many trials.

Anyway, we were discussing if the t->inf limit could be removed from the conjecture. Mathematically, are there other probability measures that are equivalent (have probability 0 for the same events) to the Born rule probability measure for any finite time period? Your argument that it can't be removed does not hold, as far as I can tell (that does not prove that it can be removed, of course).

 

[toho]

I believe I have explained my mental picture in post #71 of this thread:
https://www.physicsforums.com/showpost.php?p=2500938&postcount=71

In the house analogy the probability measure is not unique. I think that was your point also. I argue that in MWI it is.

Btw, I hope you didn't take my "nature of uncertainty" post as an insult - it surely wasn't meant that way. I like this discussion as it is intellectually challenging, and I find your comments quite insightful, even though I do think that you are wrong (wrt can the Born rule be derived). My somewhat metaphysical ramblings about the nature of uncertainty was just meant to provide a context to the rest of my messages.

 

[Dmitry67]

Well, MWI was invented before the phenomenon of decoherence has been understood.

Ah, old naive MWI "when measurement occurs, all the universe splits"? :)
But do you know... I don;t think Everett was so naive... Even he was not aware about the decoherence, he was suspecting something, right?

 

[Demystifier]

Ah, old naive MWI "when measurement occurs, all the universe splits"? :)
But do you know... I don;t think Everett was so naive... Even he was not aware about the decoherence, he was suspecting something, right?

I agree with all the statements above.

 

[Demystifier]

In the house analogy the probability measure is not unique. I think that was your point also.

Yes, it was the first of two points. The second point had something to do with adding additional variables, but that's another story ...

I argue that in MWI it is.

In your view, what is the crucial difference between MWI and the house analogy?

Btw, I hope you didn't take my "nature of uncertainty" post as an insult - it surely wasn't meant that way. I like this discussion as it is intellectually challenging, and I find your comments quite insightful, even though I do think that you are wrong (wrt can the Born rule be derived).

I didn't take any of your posts as an insult and I find your comments insightful too, even though I am not yet completely satisfied with them.

 

[Demystifier]

But the notion of probability only has meaning as a limit behavior - that is true in any application of probability theory, not just QM. Saying that a probability emerges now does not make any sense, if you don't somehow consider the limit behavior of infinitely many trials.

Are you a mathematician?
I mean, your comment above may be correct from the point of view of rigorous mathematical theory of probability, but it is certainly wrong from the practical physical point of view. In practice, the Born rule is tested experimentally by doing statistics on a large but finite ensemble of measurement outcomes. What I want to understand as a physicist, is why the Born rule describes well (not perfect, of course) a large but finite ensemble of measurement outcomes. So far, I don't see how to apply your arguments on finite ensembles.

Or to quote Einstein:
"As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality."

 

[toho]

Are you a mathematician? I mean, your comment above may be correct from the point of view of rigorous mathematical theory of probability, but it is certainly wrong from the practical physical point of view. In practice, the Born rule is tested experimentally by doing statistics on a large but finite ensemble of measurement outcomes.

No, I am a physicist. Same school as Tegmark actually. Like so many other physicists I work with financial modelling. That is probably why I have strong opinions about uncertainty and the nature of probabilities. I am exposed to a lot of uncertainty in a very fundamental sense every day. I don't think I am wrong, and my view really does not have much to do with rigour in mathematics - it is something that has grown over the years, starting from a very similar position to yours. It isn't limited to uncertainty in QM either. It is just a fact of life, as I see it.

With regards to physics, If you derive the Born rule from statistical inference, then sure, the fact that you can only do a finite number of experiments is important and that limits your knowledge. But if you derive the Born rule by means of mathematical deduction from first principles, then I don't see how you can argue that the conclusions are not valid just because in real life you can only do a limited number of experiments. You could argue against general relativity the same way - there is an unlimited number of non-linear equations that could explain any finite set of observations, and general relativity is just a very complex theory that may be correct from the point of view of rigorous mathematics, but so what?

What I want to understand as a physicist, is why the Born rule describes well (not perfect, of course) a large but finite ensemble of measurement outcomes.

That is because you get something close to the limit behavior with very high probability if you do a large number of independent trials. That is a trivial fact. (I know that is not what you are meaning to ask, but I seem to have trouble to understand what you are really after.)

So far, I don't see how to apply your arguments on finite ensembles.

I don't apply them to finite ensembles. (I am not the one who keep bringing finite ensembles up.)

The only way to limit ourselves to finite ensembles is to view physics in MWI as superdeterministic with a finite number of branches. Then we could arbitrarily assign probabilities to each branching event and have a theory that would describe everything (although not a very pretty theory).

As soon as we want to have a realistic theory that could describe all experiments that could conceivably be performed, then we need an infinite set of events that we have to assign probabilities to. Furthermore, in QM there is no set of (disjoint) atomic events that we can combine to produce any possible measurement (whether in an inifinitesimal sense or not). This gives constraints on how to construct a probability measure.

Essentially, a probability measure in the MWI would be a function that takes a state and a projection as arguments and produces a probability. That function has to work for any state and any orthonormal basis of Hilbert space (this makes your P' measure ill-defined.). It must sum to unity for any state when you sum over all the basis vectors. If you make a basis transformation it must still sum to unity. In order for it to be compatible with QM it would also have to generate a 0 probability if and only if the Born probability is 0. (Furthermore, in MWI it must conserve probability for branches, whatever a branch is.)

You argue that there can only be a finite number of trials in any realistic experiment, therefore we don't have to worry about limit behavior. But the sequence of experiments (where only the cumulative average result is recorded) is a Cauchy sequence and Hilbert space is complete, so the limit is a state in Hilbert space too. Therefore, any probability measure that is a universal law of physics must be applicable to the limit as well as to any finite ensemble of experiments (yes, I know this isn't rigorous).

I just want to make one more point. Once we have the wave equation and initial state in MWI, any externally imposed postulates of probability make no difference whatsoever to how the universe actually evolves. The inhabitants in a universe according to MWI are blissfully ignorant of any probability postulates an outside observer might make, and any probability postulates do not influence their actual experiences or perceptions of uncertainty in the slightest. The Born rule postulate in CI has meaning only because of wave function collapse. If MWI is a correct decription of the universe, the Born rule must follow from the wave function. In a correct axiomatic system for MWI, any Born rule postulate must be redundant. Consequently a proof that the Born rule can not be derived from the wave function should be fatal to MWI.


But to summarise, my argument essentially goes as follows:

1. In MWI, the future of the universe is exactly determined by the wave equation.

2. From the point of view of an observer with memory in a universe according to MWI, there is uncertainty about how any future version of the observer will remember its past and perceive its present.

3. Uncertainty can be described by the axioms of probability theory (this is a leap of faith).

4. There is a unique probability measure that is compatible with the wave function. (At least one such compatible probability measure exists - the Born rule. It is possible that you might have to make additional assumptions in order to rule all other probability measures out, but in my mind at least, it is clear that you can derive the Born rule from a small set of axioms, whatever those axioms may be. As Dmtry67 pointed out, there are a number of theorems that actually prove you can derive the Born rule from first principles, and at least some of those theorems seem to be very similar to my conjecture.)

I am actually not clear about which one of these points it is we are debating, or if there is something else that I am missing.

 

[Dmitry67]

I wish I had more time... Very busy at work, so I am not fully convinced - need time to walk and to think. But if it is true then Max Trgmork (you mentioned him) is right, because Born rule is the last non-mathematical axiom in MWI

 

[Demystifier]

The only way to limit ourselves to finite ensembles is to view physics in MWI as superdeterministic with a finite number of branches. Then we could arbitrarily assign probabilities to each branching event and have a theory that would describe everything ...

Good point!
I indeed view MWI as superdeterministic with a finite number of branches.
And we agree that with such a view, MWI cannot explain the Born rule. Good!

 

[Dmitry67]

Finite number of branches in finite volume? or in infinite universe?

 

[toho]

Good point!
I indeed view MWI as superdeterministic with a finite number of branches.
And we agree that with such a view, MWI cannot explain the Born rule. Good!

You misunderstand me. The way out would be to postulate a theory with an enourmous number of free parameters, curve fit to produce observed phenomena. I don't think your view of the MWI is such.

 

[Demystifier]

Finite number of branches in finite volume? or in infinite universe?

In finite volume, of course.

 

[Dmitry67]

Finite Systems in QM can be in finite number of states (in a single branch)
How the branching ratio can be infinite?

 

[toho]

But to summarise, my argument essentially goes as follows:

1. In MWI, the future of the universe is exactly determined by the wave equation.

2. From the point of view of an observer with memory in a universe according to MWI, there is uncertainty about how any future version of the observer will remember its past and perceive its present.

3. Uncertainty can be described by the axioms of probability theory (this is a leap of faith).

4. There is a unique probability measure that is compatible with the wave function.

Looking around a little, I see that 4 follows directly from http://www.iumj.indiana.edu/IUMJ/FULLTEXT/1957/6/56050" without any additional assumptions (and without any t-inf limit assumptions). Since 1 and 2 follow directly from MWI, i guess that leaves 3 open to debate...

 

[qsa]

What I want to understand as a physicist, is why the Born rule describes well (not perfect, of course) a large but finite ensemble of measurement outcomes. So far, I don't see how to apply your arguments on finite ensembles.

In my model (http://www.qsa.netne.net) the Born rule is automatic and it is the starting concept. I throw two random numbers, one denotes position and the other a length of a piece of line. I get a particle in a box, the position probabilities are (2/L)(sin x)^2 the lengths when added at each point and plotted you get the energy(when averaged) and its shape is very close to sin x for the particle width . But the lines can go to the end of the universe(creating Gravity), I believe the Diracs Large Number law is very clearly implied by this model. The model is comprehensive with interactions included.

I do strongly blieve in Tegmarks other multiuniverses levels. So in regard to borns rule, it seems to be just a fact of the micro world just like it was originally thought, that is why so far I give the Everret interpretation some slim chance (maybe something will come up after theory is more developed).

 

[rodolfoalvare]

I think what I call "Statistical Quantum Continuum Universe interpretation" SQCUI is more in accordance with what we see.
I wrote it in form of a letter to explain the interpretation to a friend.
I will appreciate any comments. If you are interested the 2 first letters are posted in: https://www.physicsforums.com/showthread.php?p=3299340

LETTER #2 Thursday, May 12, 2011
Statistical Quantum Continuum Universe (SQCUI)

Hi Anahi in this letter I will try to explain a little about my Interpretation, of quantum reality.
WHO WE ARE? WHAT WE ARE? WHERE ARE WE?...
Ever since we are little kids, we are broad up to believe that the Universe surrounds us, which is to say that we are immerse into the reality that we perceive.
One of the reasons that the concept of this Statistical Quantum Continuum Universe is so difficult to grasp is because of the misconceptions that this perceived reality give us.
To commence to explain this new approach to see the world in which we live on, we must define a few ideas that even though are common sense, they are the basis of who we are.
Every living organism of certain complexity, has two parts that are common to them; Some way of connecting to the environment (sensors); and some center were this data is use for the benefit of the organism (intelligence) This definition is very broad and you could argue that at certain levels of organization this characteristics bluer out (like in plants and bacteria).
If we think of ourselves is becomes pretty obvious that our connection to the Universe are our senses, (close your eyes, cover your ears and you’ll begin to realize that). Every single thing that you know of, it has arrived to your brain through one of these senses (there is other information that was hardwire to your brain genetically, but we will cover that latter), your brain takes this information, and makes sense (little by little) of your surroundings, in essence sees the Universe that surrounds you.
A cockroach will have the same parts (sensors and intelligence), but is very clear to us that if we see one on the floor next to us, their interpretation of the universe that surrounds it, (molecular markers, vibrations in the ground, pressure waves, etc.) will be very different than ours.
We tend to think that our interpretation of the universe if the correct one (the complete), and the cockroach is limited to their senses and intelligence. But we have to realize that our interpretation is limited by our senses (we cannot see at infrared wavelengths, etc.) and very probably by our intelligence.
Now with this bit of information let’s step back to what we know about Quantum Physics, and let’s see if we can make a little more sense of what we see around us.
Remember the tree in the forest, quantum physics says that the tree does not exist until you see it fallen or standing. In reality it says that the tree exists in the Multiverse (a fancy name for a Universe we don’t see but that it has all the possibilities in it, of all possible Universes) in a superposition of states (standing/fallen being only two of them), but when we get to the forest you only collapse one of them.
Well, to make sense of this “mambo Jambo” we will have to agree in a couple of things:

1. If what we see is one of the possible outcomes of the Multiverse (I like to call this the statistical Universe, the term Multiverse was used by Everett’s and could be misleading in my interpretation), then we are inside this “Multiverse” (Statistical Universe).

2. What we interpret as our reality is only a “slice” of this Multiverse.

3. If we take a very simplistic 2 dimensional plane to model this multiverse, imagine hills and valleys representing the statistical possibilities of an event, and “our reality” as a line that goes on one direction and angles to pass from one possibility or another, the likelihood of an event depending on the fiber of the Multiverse on this region (the laws of physics us we know them), that is to say the possibilities of an event are intrinsic to the laws of physics on this region of the multiverse (the local fiber of the Universe).

4. Our “linea de vivencia” (need a term in English) is really the collapse of the reality that we see, the “thickness” of this line is a representation of how intelligent we are (that is how much can we connect with the Statistical Quantum Continuum Universe).

Up to now you must think that this is like “you say Potato and I say Potairo” but when you start to analyze the Universe under this new interpretation, our whole conception of what this is (the Universe) changes.
Imagine for a moment that the universe is the way I listed above then:

• you are the center of the Universe you are collapsing (interpreting). Even though I see the same Universe, you are seen, is only because we are in the same statistical region of the multiverse, and we have basically the same sensors and intelligence.
• Like we mention before you have to be a superposition of Anahis, because at any given time any of you follows different statistical paths, If the structure of any Anahis in that statistical region ceases to be, (that Anahi dies) the ones that continue interpreting the universe are the only ones left, that is to say YOU WILL NEVER SEE YOUSELF DEAD! (Boggles the mind!, unfortunately this may became like a Quantum religion…)

Note: I know that this sound like total none sense but is absolutely in accordance with the physics that we see, ask any Quantum Physicist.

• Because the Universe we collapse depends of our intelligence and our sensors (or transducers for our sensors, that is to say, a thermal imaging camera permits us to see the infrared radiation translated to our eyes, therefore collapsing that reality).
This is why, when during and experiment we use a detector of spin for example to measure that characteristic of an electron, the electron in our reality (Universe) does NOT exist in any other characteristic but the Spin (in the statistical Universe that electron exists in every possible characteristic there is).
I think this interpretation successfully explains this estrange behavior that we see in quantum mechanics, that has not been satisfactory explained before.

Well Anahi I hope my explanation was good enough to transmit the message, I stop now so that I don’t give you a headache (I know I’m getting one).
In the letter that follow I will explain in detail the four point listed above, also why there is not Grandfather paradox traveling back in time (you never do), if you think you live forever when does it end? If we somehow we get better with time (the only way not to die) then entropy reverses from Chaos to Order? (Nooouu!), if not; how is it possible?
Well baby thank you for been such a patient friend, and I hope I’m a much better Physicist than writer.
Sweet dreams!