Why MWI cannot explain the Born rule

[yossell]

Those options are not the ones that are competing here. The assumption that QM doesn't tell us what actually happens is the "ensemble interpretation". That's an anti-realist interpretation. This is not a debate about realism vs. anti-realism. We're just trying to determine if the MWI is the minimal realist interpretation or not.

If by 'actually happens' you mean 'uniquely predicts a single outcome' then (a) it's pretty standard to say that QM doesn't predict a unique standard outcome; forget any funny business with cats half dead and alive - just is just what happens in the laws are probabilistic and, again, it's pretty standard to say that QM is indeterministic. This is not anti-realism. That the laws are irreducibly chancy has nothing to do with anti-realism. (b) There's a natural - and as far as I can tell - entirely standard way of understanding $\rho\rightarrow \sum_i P_i\rho P_i$: it's a description of how the probabiilties will actually evolve in certain conditions. One can be an objectivist about probabilities and think that there are objective facts about probability - so it's entirely neutral on the anti-realism debate.

Everything hinges on how you physically interpret these mathematical states, how you interpret probabilities, how you interpret the terms that will necessarily appear in probabilistic theories. There mere appearance of these terms in the mathematical description of the evolution of the probabilities doesn't get you anything about other the physical reality of worlds corresponding to these terms.

Actually - I'm still not sure I know which axioms you have in mind when you say Dirac-von Neumann. I tried to follow a previous link, but my Dutch is...ahh... a little rusty. Plus the pages didn't show. Do you have a link where the axioms are given explicitly - sorry if you already provided it somewhere.

 

[Dmitry67]

When you define probability in statistical mechanics you pretty much start from the same symmetry/unitarity assumptions. You have some symmetric system and you postulate that due to the symmetry probabilities to find the system in the symmetric states must be equal. You also postulate that the sum of probabilities must be equal to one.

After that you have the notion of probability. And you can apply the probability theory to find which states of the system are going to be probable or improbable.

Now in MWI we assume unitarity (sum of probabilities is 1). And again we can start with some symmetric system. The only troubling part is the observer. I think that the key here is the BPP (boundary of a boundary is zero) postulate - the identity - because the observer is calculating the probability to find himself in some state.

1 statistical mechanics describe single-history, in MWI we have multiple histories.

2 I don't see any problems with "the observer is calculating the probability to find himself in some state."

Please explain. I have random generator with 2 outcomes: Frequent (probability 99.9999%) and Rare (0.0001%). After a trial I have 2 branches: F and R (with the different 'measure of existence').

The question is, why I almost always end in F branch? That claim is naive from the MWI point of view. But denying it is denying any predictive power of QM.

MWI predicts 2 branches after the decoherence: F and R with surprised R-observer. Why, why F branch is 'more important'?

 

[pellman]

Demystifier, is the argument about the Born rule similar to what I am saying here https://www.physicsforums.com/showthread.php?t=230032&highlight=many+worlds ?

 

[Fredrik]

If by 'actually happens' you mean 'uniquely predicts a single outcome'

I mean that what the theory says is happening is actually happening. There's no way to define that concept in other terms.

The fact that you're talking about "outcomes" suggests that you're too focused on the results of experiments, or more generally, on the final state after an interaction. A description of "what actually happens" must also tell us how the state changes during any kind of interaction, including measurements. If it doesn't, it's not a realistic model, it's just a theory.

(I can't believe I just used the phrase "just a theory" ).

then (a) it's pretty standard to say that QM doesn't predict a unique standard outcome;

The standard is to talk about the results of experiments and not about the time evolution during a measurement, because all that's required by a theory is that it's able to make accurate predictions about probabilities of possible results.

forget any funny business with cats half dead and alive - just is just what happens in the laws are probabilistic and, again, it's pretty standard to say that QM is indeterministic. This is not anti-realism.

No, but it isn't realism either. A realistic model tells us what happens during a measurement as well as the final state after the measurement.

(b) There's a natural - and as far as I can tell - entirely standard way of understanding $\rho\rightarrow \sum_i P_i\rho P_i$: it's a description of how the probabiilties will actually evolve in certain conditions.

A realistic model tells us how the system evolves, not just how the probabilities of final results evolves.

Everything hinges on how you physically interpret these mathematical states, how you interpret probabilities, how you interpret the terms that will necessarily appear in probabilistic theories.

I don't think "interpretation of probability" is an idea that even makes sense, as I explained in the other thread. The interpretation of state operators are fixed by the requirement of realism: A state operator is a mathematical representation of the system.

There mere appearance of these terms in the mathematical description of the evolution of the probabilities doesn't get you anything about other the physical reality of worlds corresponding to these terms.

No, but the appearence of those terms in the evolution of the system does.

Actually - I'm still not sure I know which axioms you have in mind when you say Dirac-von Neumann. I tried to follow a previous link, but my Dutch is...ahh... a little rusty. Plus the pages didn't show. Do you have a link where the axioms are given explicitly - sorry if you already provided it somewhere.

That's weird. I did a Google search for "dirac-von neumann axioms" (without the quotes) and clicked the first link in the search results. It took me directly to the right page in the book. Then I copied and pasted the URL that appeared in the address field of the browser. I got a third URL for the page by using the "link" link in the upper right corner, and it worked, but only a couple of times. By the time I had included it here and previewed, it had stopped working. So I suggest you do the Google search yourself, and don't expect the link you find to work more than 2-3 times.

These axioms are the ones that appear in just about any book on QM, but sometimes in a slightly diffferent form. I don't know if many books call them "Dirac-von Neumann axioms" though.

 

[Fredrik]

MWI predicts 2 branches after the decoherence: F and R with surprised R-observer. Why, why F branch is 'more important'?

The MWI doesn't answer that. It just says that it is, by including the Born rule in its definition.

 

[Dmitry67]

Fredrik, I believe we are mixing 2 different things:

1. "Reptrospective" probability (frequentist view) - when I remember the history or look at the log of the experiment with many tries, I see frequent events more often.

2. "Predictive" probability (Bayesian view) - when I am observing Uranium atom, I would be quite surprised if it decays. For some reason "my consicusness" almost always end at one of the probable branches. If definitely ends at ALL branches, but it is stupid to deny that... hm... it does nto affect my life.

So both approaches can be applied to MWI. Discussing Born rule, what exactly are we discussing?

P.S. I always have an impressing that many people are somehow applying the frequentist approach to #2: like, if my consciousness jumps into random branch, it more probably ends at more probable one?

 

[Fredrik]

The definition of science (at least the definition I'm using) requires that we test theories by comparing the probabilities (numbers between 0 and 1) that a theory associates with possible results of experiments, to the relative frequencies of actual results in a large but finite number of actual experiments. This doesn't really have anything to do with interpretations of probability, which I consider meaningless nonsense, but it has a lot to do with the definition of science.

The Born rule assigns numbers between 0 and 1 to results that an observer can experience that he has obtained. It's necessary to say it this way, because in the MWI, an observer who hasn't performed the experiment yet will get all the results, and they will be correlated with different states of "his" memory. Because of that last thing, it's conventional to describe these memory states as properties of different observers.

 

[Dmitry67]

The Born rule assigns numbers between 0 and 1 to results that an observer can experience that he has obtained. It's necessary to say it this way, because in the MWI, an observer who hasn't performed the experiment yet will get all the results

The statement above is a denial of any predictive power of QM. Why are we trying to make devices more robust? Now matter how poor they are constructed, there are always branches where they will work!

We use Born rule for the past and for the future

 

[Fredrik]

Huh? This rule is what turns QM into an actual theory. Without it, it would be a model with nothing that connects it to results of experiments. This rule doesn't remove the predictive power of QM. It is the predictive power of QM.

 

[Dmitry67]

Huh? This rule is what turns QM into an actual theory. Without it, it would be a model with nothing that connects it to results of experiments. This rule doesn't remove the predictive power of QM. It is the predictive power of QM.

Ok, but is it a part of a PHYSICAL theory?

Imagine that our universe in virtual (purely mathematical). We emulate it on super powerful computer. I enter initial conditions, and I get the Universe wavefunction for any given moment. So I get Omnium(t).

Obviously, I don't need Born rule to solve the TOE equations and to calculate Omnium(t). Now, as for me this Universe is virtual I look at it from Gods/Birds view. I say: "ok, it is solved, next one please"

Frog: wait, wait, but what's about the probability?
Bird: what probability?
Frog: what observers see and what that mostly anticipate in the future
Bird: there is no future. These is a static solution. Let me take a project to some basis... yes, in that Universe frogs are talking about some "born rule"
Frog: But are they prepare to the most "probable" events, not to the almost impossible ones?
Bird: Yes, this is because of the natural selection. This is the correlation of their history and their consciousness. It is an illusion of their consciousness, like "flat space", "time flow", "past you can't change and fuzzy future". So it is purely psycological thing. Not physical.

 

[Fredrik]

Ok, but is it a part of a PHYSICAL theory?

I assume that what you mean by "physical theory" is what I've been calling a "realistic model". QM without the Born rule can be interpreted as a realistic model of the universe/omnium, but I'm reluctant to call this an interpretation of QM, because QM without the Born rule isn't QM. It isn't even a theory. It also doesn't tell us which things in the model that we should think of as "worlds" or "experiences".

 

[Dmitry67]

Why? What is wrong with a solution of Omnium(t)?

But I agree, there is some kind of anti-realism, you can not say "what had actually happened" until you specify the basis (decomposition into systems)

 

[Muppetmaster]

I really don't see where the parsimony of Occam's razor comes in here, that's a philosophical axiom at best, certainly it is a generalised trend rule not a rule of science?

Perhaps I'm missing something.

Plus Copenhagen Interpretation (CI) or MWI are indistinguishable from each other except one is deterministic the other probabilistic. So that basically means that MWI loses out as it has nothing to distinguish it from CI?

 

[Fredrik]

Why? What is wrong with a solution of Omnium(t)?

I didn't say that there's something wrong with it. It might very well be the correct objective description of what actually happens, but it still doesn't qualify as a theory if it doesn't tell us how to interpret the mathematics as predictions about the results of experiments. If it isn't a theory, then its description of what actually happens can't be considered an interpretation of a theory.

A different but still important concern is that "QM minus the Born rule" also doesn't tell us how to identify something in the mathematical model (the Hilbert space of the omnium) that we can think of as "worlds" or "experiences".

 

[Dmitry67]

So, what you are saying is "Mathematics is not enough. There must be also a way to translate Birds view into Frogs view". Is this correct?

 

[Fredrik]

Yes. Without that, we have a model that might possibly be correct, but doesn't qualify as a theory and shouldn't be called "many-worlds interpretation" since it doesn't tell us what the worlds are.

 

[Dmitry67]

Ok.
There is only one Bird, but infinitely many Frogs.
So it is required to translate Bird->Frog, then what is a choice of a Frog (preferred basis)?
What kind of basis should be used? All possible? Some subset? Based on what criteria?

 

[dmtr]

Please explain. I have random generator with 2 outcomes: Frequent (probability 99.9999%) and Rare (0.0001%). After a trial I have 2 branches: F and R (with the different 'measure of existence').

The question is, why I almost always end in F branch? That claim is naive from the MWI point of view. But denying it is denying any predictive power of QM.

Because of the symmetry and unitarity. Because of the claim that if the outcomes are symmetric there is an equal probability to see each outcome. And the claim that the sum of probabilities should add to 1.

 

[Dmitry67]

Because of the symmetry and unitarity. Because of the claim that if the outcomes are symmetric there is an equal probability to see each outcome. And the claim that the sum of probabilities should add to 1.

I don't follow your logic.

Or probably you don't realize that the verb "to see" needs additional clarification in the muti-history theory where basic can be define anyway you want.

F and R are symmetric from the 'number of observers', but not symmetric from 'measure of existence' approach.

 

[Fredrik]

Ok.
There is only one Bird, but infinitely many Frogs.
So it is required to translate Bird->Frog, then what is a choice of a Frog (preferred basis)?
What kind of basis should be used? All possible? Some subset? Based on what criteria?

It's not sufficient to just pick a basis. The first thing we need to do is to decompose the omnium/universe into subsystems. Mathematically this corresponds to expressing the Hilbert space as a tensor product of two (or more) Hilbert spaces: $\matcal H=\mathcal H_1\otimes\mathcal H_2$. Then we can consider bases for those two spaces. Let's say that $\{|\psi_\mu\rangle\}$ is a basis for $\mathcal H_1$ and that $\{|\phi_\alpha\rangle\}$ is a basis for $\mathcal H_2$. Then we can define $|\psi_\mu,\phi_\alpha\rangle=|\psi_\mu\rangle\otimes|\phi_\alpha\rangle$. This definition ensures that $\{|\psi_\mu,\phi_\alpha\rangle\}$ is a basis for $\mathcal H$.

The question is now, which bases for $\mathcal H_1$ and $\mathcal H_2$ should we be using? We can use any pair of bases, but the ones that are of particular interest are the ones that are such that stable records of the system's state (e.g. the memory of having measured spin "up" in a physicist's brain) will exist for some time in the system's environment. I think that decoherence theory singles out a unique pair of bases (or perhaps a class of pairs of bases) that have that property.

The state operator (=density matrix) is almost diagonal in such a basis for $\mathcal H$. We interpret the terms of the state operator expressed in such a basis as representing "worlds". We can interpret the terms of the state operator expressed in some other basis as worlds too, but we prefer not to call them that, because they don't describe the environment as containing a stable record of the system's state, which means that they can't describe conscious observers with well-defined memory states.

It's possible that I'm way off about something here, because I don't know decoherence very well. Chances are pretty good that if you ask me something about the details of what decoherence theory says, I won't be able to answer.

 

[dmtr]

Or probably you don't realize that the verb "to see" needs additional clarification in the muti-history theory where basic can be define anyway you want.

I do realize that. It is likely that you'll need an additional postulate. Boundary of a boundary principle.

F and R are symmetric from the 'number of observers', but not symmetric from 'measure of existence' approach.

The relevant symmetry is the symmetry of a physical system (like a 50/50 beam splitter), not some imaginary symmetry of some not very well defined quantities.

 

[Count Iblis]

Muppetmaster:

Plus Copenhagen Interpretation (CI) or MWI are indistinguishable from each other except one is deterministic the other probabilistic. So that basically means that MWI loses out as it has nothing to distinguish it from CI?

That's only true in practice, not in principle. And we all know that thought experiments that you can only perform in principle have been very important in theoretical physics.

According to the MWI, it is possible to measure a system (which would irreversibly collapse the wavefunction in the CI), keep a record of the fact that the system has been measured but then erase the result of the measurement by applying the inverse of the unitary transform that describes the measurement process. This will then undo the collapse of the wavefunction. The observer does have the memory of having measured the system, but his memory of the measurement result has been erased. That information has been dumped back on the system itself, allowing the original state of the system to be restored.

The CI also makes a definite prediction for this thought experiment: After the exeriment the system, which was initially in a pure state, will be found in a mixed state. The attempt to restore the original state will fail because only one branch of the wavefunction after measurement really exists. So, the unitary transform describing the "inverse" measurement process only acts on one branch, not on all the branches.

 

[RUTA]

I do realize that. It is likely that you'll need an additional postulate. Boundary of a boundary principle.

Why BBP?

 

[dmtr]

Why BBP?

It's a guess, based on the criteria that the postulate should:
* have something to do with mathematical identity;
* be 'fundamental enough'.

Also BBP is a very safe guess. :)

 

[RUTA]

It's a guess, based on the criteria that the postulate should:
* have something to do with mathematical identity;
* be 'fundamental enough'.

Also BBP is a very safe guess. :)

Are you working on anything relating quantum and BBP? Do you have any papers on this topic? Read 0908.4348 to see why I ask.

 

[Muppetmaster]

So, what you are saying is "Mathematics is not enough. There must be also a way to translate Birds view into Frogs view". Is this correct?

Yes String Theory is philosophy and barely even a hypothesis let alone a theory. MWI is the latest in a long line of totally unprovable fairy tales.

Maths is just a model. Shut up and calculate.

 

[dmtr]

Are you working on anything relating quantum and BBP? Do you have any papers on this topic? Read 0908.4348 to see why I ask.

Sorry. I'm not a physicist. I've studied the 'basic modern minimum' - CM, SR/CFT, SM, GR, QM, but that's pretty much it. This QFT interpretation paper is interesting, but it is also a way over my head.

Still, I really like the idea of how they interpret the "probability amplitudes" as "symmetry amplitudes". It's just change of wording, but it makes a lot of sense. I couldn't get if they use the MWI approach (many subjective histories) or some kind of superdeterminism (one history). And how they use BBP I couldn't understand at all.

 

[Muppetmaster]

Sorry. I'm not a physicist. I've studied the 'basic modern minimum' - CM, SR/CFT, SM, GR, QM, but that's pretty much it. This QFT interpretation paper is interesting, but it is also a way over my head.

Still, I really like the idea of how they interpret the "probability amplitudes" as "symmetry amplitudes". It's just change of wording, but it makes a lot of sense. I couldn't get if they use the MWI approach (many subjective histories) or some kind of superdeterminism (one history). And how they use BBP I couldn't understand at all.

The equations for both would be identical if you think about it, the only difference being one is imaginary and one is real, if you see what I mean.

The usual Dirac equation would create 2 versions: Dirac=MWI+CI

ie.

$\left(\beta mc^2 + \sum_{k = 1}^3 \alpha_k p_k \, c\right) \psi (\mathbf{x},t) = i \hbar \frac{\partial\psi(\mathbf{x},t) }{\partial t}$

1 version would be all possible words ie $MW_{wave}$=all real states in different dimensions/realities ie $\int_a^{b} x_p=\infty$ the other would be superposition $CI_{wave}^{i}$=imaginary solutions of the wave function and one possible "real" state probabilistically.

$x_p=$probability of x where x = variable of wave function.

 

[Dmitry67]

I think the additional assumption is:

"We are on the NORMAL branch"

Otherwise Born rule can not be proven even experimentally. No matter what results you get one must deny them saying "we are just on one of the unprobable branches"

 

[RUTA]

Still, I really like the idea of how they interpret the "probability amplitudes" as "symmetry amplitudes". It's just change of wording, but it makes a lot of sense.

The different wording is to emphasize the fact that the amplitude Z is independent of the field Q, so the fundamental mathematical objects being "evaluated" by the path integral are the discrete differential operator K and source J. That is, K and J are the mathematical objects describing the experimental arrangement and Q is merely an integration variable or "tool" to analyze K and J.

I couldn't get if they use the MWI approach (many subjective histories) or some kind of superdeterminism (one history). And how they use BBP I couldn't understand at all.

There is only one configuration being analyzed, that described by K and J. No Many Worlds. So, the question is, What constrains K and J in Z? The answer is BBP, which gives Kx = J where x is the vector of plaquettes, links or nodes, depending on whether you're doing tensor, vector or scalar field theory, respectively. So, you start off with Kx = J at the graphical level and compute Z for the graph. But, what good is that? You need to recover classical field theory (CFT) at some point which all about Q and your mathematical object Z is totally void of Q. Answer: You know Z is a partition function in this case (Kx = J gives a Euclidean action), so you use Z to compute the probability of measuring some particular value of Q at a particular graphical location, e.g., the k^th node, i.e., the probability that Q_k=Q_o. That's easy enough to compute since Z is a partition function we know that the probability simply equals Z(Q_k=Q_o)/Z. When you're finding such probabilities you're doing QFT (actually, a discrete counterpart). You recover the discrete counterpart to CFT when you attempt to find the most probable value of Q_o at Q_k. You obtain KQ_o = J, which you recognize as CFT and which you know conforms to BBP. So, you assume BBP at the fundamental graphical level and find that it leads to both CFT in accord with BBP (as required), as well as a new interpretation of QFT that resolves all its foundational issues (as explained in the paper).

Anyway, that's why I was wondering how you used BBP to explain quantum physics. I wanted to compare your method with that of this paper.

 

[Demystifier]

Demystifier, is the argument about the Born rule similar to what I am saying here https://www.physicsforums.com/showthread.php?t=230032&highlight=many+worlds ?

Yes it is.

 

[dmtr]

Interesting paper on the subject: http://www.ensmp.fr/aflb/AFLB-333/aflb333m533.pdf

RUTA: I'll try to understand/answer the "K and J constrains/BBP" part and if I like it or not, but that will need time.

 

[pellman]

Yes it is.

Very cool.

Isn't the failure of the MWI to predict the statistics a rather glaring problem? I would think some MWI proponent has covered this. Surely we're not covering new ground here?

 

[Demystifier]

Isn't the failure of the MWI to predict the statistics a rather glaring problem? I would think some MWI proponent has covered this. Surely we're not covering new ground here?

You are right. However, most literature on that issue is not very easy to read. My intention is to present and discuss this issue in a simpler way, so that all physicists can easily understand it.

 

[hamster143]

Very cool.

Isn't the failure of the MWI to predict the statistics a rather glaring problem? I would think some MWI proponent has covered this. Surely we're not covering new ground here?

See my comments earlier in the thread, I believe I've addressed that specific issue.

If you repeat an experiment that branches the wavefunction as

$$|\psi\rangle = \sqrt{\frac{1}{1000}}|A\rangle + \sqrt{\frac{999}{1000}}|B\rangle$$And you throw in some decoherence and an outcome counter, after 1000 runs you'll have 2^1000 branches of the whole universe, but only 1001 branches of the counter, all with varying amplitudes. And the branch of the counter with the largest amplitude will be the one that counted 1 outcome A and 999 outcomes B.

Your approach seems to be a straw man argument. Sure, if you take MWI and add an axiom that all observers are equally likely in any branching, you can arrive at all sorts of contradictions (including the most obvious one - you can't have 2^1000 equally likely histories and 1001 equally likely counter outcomes at the same time). If you allow that every branch has an amplitude and the "likelihood" is in some way monotonically related to the absolute value of the amplitude, you can naturally deduce that the relationship has to take form of the Born rule, $P_i = |c_i|^2 / \sum_k |c_k|^2$.