The Born Equivocation

I think the difference is that the MWI claims to be more economical by disposing with the difference between unitary evolution and collapse, and (relatedly) between the classical-quantum divide. Everything is quantum and evolves according to some universal Schrodinger equation.

This is very appealing until you start asking very obvious questions, like the one about reproducing the Born rule. Without deriving that using only unitary evolution you are left with having to add that rule as an extra ingredient, in which case the difference from the Copenhagen interpretation become purely semantic (just imagine that other options "keep on existing" after the collapse). This is why deriving the Born rule is more important for MWI than for other interpretations.

The problem with the science fiction that comes out about many worlds is that it does assume each outcome is equally probable, and really, no matter what that is not possible. If you have a superposition of two states, those two states are possible. You do not somehow magically get to have any number of states just by waving your wand and saying "many worlds".

One problem is that naive counting of branches/worlds does not give the Born probabilities. This raises the question what the Born probabilities are actually about in the m.w.i.
The papers of Adrian Kent are an obvious reference to this kind of criticism but I assume you are familiar with them already.

wolfgang, "naive counting of branches" doesn't even make any sense. The wavefunction just evolves continuously, it's not as if there are discrete branchings which you can "count" in a naive way.

An awful lot of the structure of quantum mechanics seems to involve having a Hilbert space, and a Hilbert space comes equipped with an inner product, and all the Born rule says is that the right measure is the one that comes from this inner product. Honestly, I don't see why we should expect anything more minimal, or find this answer very unsatisfying.

onymous: That smells a little circular to me. The Born rule is what it is because of the structure of the Hilbert space, but the Hilbert space's structure is chosen in anticipation of the Born rule.

Chad,
The argument is about why we should use the usual methods of statistics in a many-worlds scenario, e.g. counting relative frequencies to estimate what probabilities we should assign in the future. It is not simply about whether we can find a mathematical formula that obeys the axioms of probability, which we can clearly do just by postulating the Born rule, but rather it is about why observers in the multiverse should have any reason to care about it. Isn't it obvious that this isn't obvious?
N.B. I don't think the (worthy) objections are based on implicitly assigning equal weight to each possible outcome, but rather they are based on the idea that observers don't have any legitimate reason to assign any weight whatsoever, equal or not.

Chad, the problem is that the Born rule is logically inconsistent with the number of "branches" in MWI. We can't just say, "apply the ____ rule" to whatever in a given interpretation without asking how compatible it is there. I agree that it is not that the whole idea of probability would be meaningless in MWI -instead, MWI per se would get the wrong answer. And it is easier to make the Born rule work logically (even if we still don't understand it) in other ways of looking at things as I will explain.

First, imagine standing QM concept of the collapse. Suppose for example I have an asymmetric beamsplitter, such that amplitude 0.6 goes through and 0.8 is reflected. That is equivalent to intensity allocations of 36% and 64%. Well of course, that is in effect the BR but let's look at the case of a single photon. The photon wave function is split into those amplitudes, and both continue to exist as they move towards detectors. The "stronger" WF has a greater chance of making a detector ping. Whenever a detector pings, the other "branch" of the WF just isn't around anymore, because the energy just isn't available (or whatever, we really *do not* understand what goes on and there's no point in pretending anyone does. Can't we just live with that?) Well then, the chance is 36% at Ch. A and 64% at Ch. B. (Note, no need to use interference to prove a point since the *model* of a WF is already established. REM also that we can recombine them later instead, so doesn't the WF have to start out this way in any case?)

Now, try to imagine what happens in MWI. (No interference, so add that into things if you want but I say it's a red herring for continued significance, once it's been used to show what WFs are like earlier.) Somehow there ends up being both outcomes, ping in DA and in DB also. Well let's be charitable and forget about how the total energy can be multiplied etc. If "you" the observer can be entangled with either the DA outcome or the DB outcome, then "you" in effect have a 50/50 chance of ending up seeing DA click or DB click. There is no reasonable way to *get* the 36:64 split, because *there really isn't a chance of one happening instead of the other.* With any real unfair coin etc, of course you can but not when both outcomes really do exist. (And please folks, don't imagine that there's a different chance of "you" entering one branch or the other, there is not supposed to be a unique or favored "you" that enters or not. The whole point is to say "both" exist. If so, then there's no frequentist distribution to make for a different probability distribution than 50/50. I've heard stuff about "thickness" of branches but it sounds like mumbo-jumbo.

(Chad, it's OK to reply to this, it's been long enough. I mean, this is a relevant point.)

(Shorter point re the branches: you can't "assign" probability weights to the branches, because they all simply do exist. They aren't really chances! There isn't some other extra chance about them, what in the world would it be and how would that work? Nor can you have 36 of one and 64 of the other, why the arbitrary total - and infinite sets can't be properly compared.)

The argument is about why we should use the usual methods of statistics in a many-worlds scenario, e.g. counting relative frequencies to estimate what probabilities we should assign in the future. It is not simply about whether we can find a mathematical formula that obeys the axioms of probability, which we can clearly do just by postulating the Born rule, but rather it is about why observers in the multiverse should have any reason to care about it. Isn't it obvious that this isn't obvious?

In a word, no.
I guess I'm just a committed empiricist, but given that my experience of the world involves seeing a series of measurements with well-defined outcomes whose probabilities measured over many repeated experiments give values that match the Born rule, then I think I have ample reason to care about the Born rule.

I realize that, in some other branch of the wavefunction there is some other version of "me" who saw different outcomes to specific measurements. And even a version of "me" who lives in some "Rosenkrantz and Guildenstern Are Dead" branch of the wavefunction in which the repeated sequence of measurements give results that don't match the Born rule, or make any sense at all. What's not obvious to me is why I should care about what they see. Given that they're in other branches of the wavefunction that are inaccessible to me, the fact that they see something bizarre does nothing to reduce the utility of the Born rule in my little corner of the wavefunction.

As for why the Born rule should be true: I see justification made in terms of analogy to field energy being proportional to field amplitude. So, with lots of photons entering the asymmetric BS, the ratio of classical field intensity at Ch. A to intensity at Ch. B is 36:64. Presumably that is equivalent to adding up many WF amplitudes (simplest anyway, why not and why anything else?) If each photon has a given unit of energy, then for consistency the cumulative ratio of photon hits must be 36:64 also, which then is the chance of a given hit in a given instance.

Sorry, careless: I meant field energy is proportional to the square of field amplitude. The classical field intensity ratio is 6:8 and the energy and corresponding ratio of photon hits is 36:64.

Chad: I think Matt and yourself are saying the same thing. If you allow me to paraphrase - the Born rule (with frequency based probabilities) is in practice the basis for any empirical test of QM, if the MWI does not reproduce this part of QM then it is simply incorrect. The burden of proof, once you allow things like the "Rosenkrantz and Guildenstern Are Dead" branch of the wavefunction, is to explain why the world around us looks nothing like that. In other words, why committed empiricists are almost always right in making deductions based on making repeated observations and looking at the probabilities of possible outcomes.

Given that the ability to use such deduction is not part of the basic rules of the game in the MWI, it has to come from somewhere, and it is far from obvious (to me) where it could possibly come from. To reiterate my point, if the only way to achieve that is by including this rule as a separate postulate, much of the rationale for the MWI (presumably as a more economical framework) is gone.

Moshe, the ability to use "probability" could in principle be a part of MWI even though all outcomes occur - the problem is, it doesn't work in the right way. For example, take my ABS example again. Imagine it done 100 times, and each time there's a branching in the sense that both outcomes do exist each time (or else, what is the point of denying the collapse idea?) Well then after that there are 2^100 "worlds" containing all the final possible permutations of hits, true? And so there is indeed a frequentist issue of how many of one outcome or outcome category versus another.

It's just not the usual sense of, doing something so many times in sequence and comparing that. So MWI-ld enthusiasts could say, "the 'chance' is like how many of the outcomes exist, rather than the conventional chance they will happen. You are 'more likely' to be in a numerous type of outcome" etc.

But again, that doesn't work because the number of branches with various outcomes reflects a spurious 50/50 probability outcome. Again, we can't intelligibly just "assign" extra chance or reallocate chance (chanciness?) to branches, since they just "are" and all exist. Some people try, but as I said it sounds like psychobabble. How about just quit trying to impose intuitive demands like "economical" on our universe?

(BTW, I figured out why I kept flubbing about derivation of BR. It's from use of ambiguous term "intensity", which can mean either amplitude (magnitude) of a field vector like volts of E, or it can mean energy "intensity" as of illumination etc. Well, the latter is the square of the former, that's the logical basis of the consistency of BR in a normal "one outcome per experiment" universe.)

Oops, clicking on one of your links I now realize we've been that particular rabbit hole before (another evidence for the cyclic theory of the blogosphere). Sorry for not realizing this before.

This sort of discussion bothers me because I see two different things being discussed. One is an INTERPRETATION of standard classical non-relativistic quantum mechanics, while the other seems to be an alternative version of quantum mechanics. It makes no sense at all to me to talk about deriving something within an interpretation as if the interpretation was an actual theory.

CCPhysicist, that sounds helpful - could you elaborate? BTW check out my FQXi article, it's a proposed test of the decoherence interpretation.

But what benefits does MWI offer? It doesn't solve or clarify anything, it just masks problems with ill-defined concepts.

Say we have a photon and it went to detector A and not B, so there had to be a collapse. MWI tries to get around this by saying that no, no, both outcomes happened. But this is BS, its an empirical fact that the photon went to detector A. To pretend that "both outcomes happened" MWI adherents have to redefine what it actually means that something "happened," so we arrive at imaginary parallel branches which "exist" but are unobservable. But if they are unobservable then they are completely irrelevant, science deals with empirical facts and the facts are simple - there was some sort of collapse as the photon arrived at detector A, not both of them.

Another example - get a bit of radioactive material, a detector, and time the interval between first two recorded decays - you get a number, again this is an empirical measurement, whether there are unobservable branches, ghosts or gods is completely irrelevant here, we get an empirical fact and it needs an explanation - where did it came from? How do you get it from an unitary evolution of wavefunction representing the system? There has to be a collapse of some sort, there is simply no way around it.

One can invoke decoherence but then there is no reason to put up with all the ill-defined MWI nonsense at all. Decoherence is still a form of collapse induced by environment, and if we say that it was decoherence which picked one particular observed outcome then it is no longer true that "both/all" outcomes "happen," so MWI offers no benefit.

Even in many worlds, only what is possible can happen. For example, there's no universe in which we're ruled by intelligent alligators. A given moment has a finite number of outcomes, so there are a finite number of branches on the tree. And reality doesn't just branch willy-nilly, it branches when we force it to. The less one pays attention, the fewer branches on the tree of one's life. But if every awareness lingers to the farthest tips of probability, many of us will die of old age, remembering those who passed before their time.

I think MWI really is more parsimonious than the Copenhagen Interpretation. In Copenhagen, quantum mechanics is described by unitary evolution together with "measurements" which cause non-unitary events of wavefunction collapse. MWI, as I understand it, asserts that "measurement" does not need to be added as a separate aspect of the theory. In MWI "measurement" is what happens when an observer (as a large system of particles described within a wavefunction) becomes entangled with a quantum event. Really MWI encompasses everything the Copenhagen interpretation does, including Born rule probabilities for experimental outcomes. And it makes a falsifiable prediction on top of this, that there is no new physics to be found separating "observers" and "measurements" from the kinds of systems already described by QM.

I think the confusion about MWI probabilities is just a misunderstanding of what the physics actually covers. When you ask the question, "what is the probability that in some of the many worlds I will be alive?", you are asking a question that the physics of MWI doesn't answer. The physics only asserts probabilities for observable events. You can use the Born rule to calculate the probability the world will observe me to be alive in 1000 years. That is an observable event, with a tiny but nonzero probability. But the event that some branch of the many worlds will observe me to be alive in 1000 years is not an observable event. There is no way to construct an experiment to light up a light bulb depending on whether I am alive in one of the other inaccessible branches of the many worlds. So the physics doesn't assign a probability to that event -- it's non-measurable.

Helpful? If you think you can test an interpretation in the sense of showing it is somehow superior to the theory itself, I haven't helped you at all.

The prediction comes from the theory. If what you have is actually an INTERPRETATION of that theory, it must produce "predictions" that agree, in all respects, with those of the theory -- and thus with those of any other valid interpretation of that same theory. If it doesn't, all you have proved is that it is not an interpretation of that theory or the interpretation is too vague to be used quantitatively.

Ccphysicist: I think that it is a misnomer to say that Multiple Worlds "Interpretation" and Copenhagen "Interpretation" are merely interprerations of the same theory. Really MWI offers a more complete theory than CI. CI (in my understanding) doesn't specify precisely what sorts of observer can collapse a wavefunction in what sorts of measurement scenario. It just says, if you have an observer (whatever that is) who performs a measurement (whatever that is) the wavefunction collapses. (I'm on purpose ignoring the religious fools who would say that only a human -- endowed as we are with souls -- can act as an observer.). MWI extends the theory to say that QM predictions apply at arbitrarily large scales, including the observer inside the system. This makes clear predictions in thought experiments where (say) you put one observer inside an information-tight box and have another observer outside performing measurements on them. CI with its notion of collapse of the wavefunction doesn't really properly cover such experiments.

Hello dzdt, CCP et al: Per dzdt "Really MWI encompasses everything the Copenhagen interpretation does, including Born rule probabilities for experimental outcomes." I just told you why that is not true, and you didn't even study that or respond. (Think "branchings" versus "squared probabilities.") The conceptual basis for MWI is flawed anyway, considering that a WF is supposed to be a single particle etc. distributed and not in any intelligible sense a way to imagine the discordant jamming together of multiplicity of location AND localization - as well recognized by earlier, more cognizant founders of QM. CI doesn't make sense? The universe just doesn't, who are we to say it should ... In any case, no distaste for a given problem justifies flaws in the alleged cure.

I always had the impression that QM invoked many worlds, but in the past, not the future. Don't you have to sum over all of the possible pasts to understand where any measurement came from? I can't see why this process doesn't work for the future as well.

On the other hand, I find many worlds uncomfortable, because it suggests that there is actually a universe in which all the air in every room moves from one side of the room to the other every five minutes, all the time. I suppose our universe with its relatively evenly distributed air would sound equally peculiar to the inhabitants of that universe, though much more likely. I can only imagine what explanations their scientists would offer for the extreme improbability of their existence. Would they be creationists, or would they measure the probabilities differently so that we would be the unlikely universe?

Neil B: It's not literally branching, in the sense that a singular point history splits at some time t into two. A wave is a continuous phenomena. The wave spreads out in space, interacting with itself/other waves to form superpositions. If you look at some region of the wave it'll be at a different amplitude than another region. Because it's continuous you can speak of area (or whatever higher dimensional extension is appropriate): In 33% of this wave photon A interacted with photon detector B. I as an observer have no a priori knowledge of where exactly on the wave I exist. Arguments about "branch thickness" or any other geometric reasoning for probability aren't hand-wavings, they're valid arguments based on waves having a geometry, not merely a point existence.

Regarding concerns about the degenerate branches where we all transform suddenly into pizzas, I personally suspect MWI implies a "Planck's probability", if not for a single quantum event then at least for a series of them. Just like the wavelike nature of reality blurs out the infinitesimally small and the infinitesimally brief, I suspect the infinitesimally unlikely are also destroyed by a fundamental limit to what's represented in the universe.

If you like MWI, you're left with the question of "how can we theorize about universes you can't see?". If you like CI, you're left with the question of "how can we theorize about a collapse we have no observation of and no basis for in normal wave mathematics." Bell's theorem insists we're in a nonlocal universe or one that doesn't meaningfully exist when we aren't looking. Pick your poison, but quantum mechanics is too non-intuitive to insist that of course it's unlike reality as we know it in way X, not way Y.

ADP, for now: sorry Paul, but just talking about "percents of the wave" make no sense about *actual probability of outcomes* unless you mean either:
1. That is the actual chance of the event happening, one way or the other. Like tossing dice, etc. That means, we have something giving the chance of whatever *particular* exclusive outcome.
XOR
2. In some sense, both outcomes occur. You can hand-wave all you want, but if you say "both" results happen in each trial, and we only see one, then the alternative is "another world" whatever you call it. And if so, then you have to have instances to build up a frequentist concept.

Sorry, what you are trying to accomplish is indeed hand-waving. And CI and MWI are not equivalently problematical. CI is just enigmatic, it doesn't "make sense" but is not literally contradictory - we can't imagine how the WF turns into a specific result, but the chance of what happens at least doesn't contradict other claims. But in MWI, the number of outcomes - nothing else makes sense - does not add up properly to unequal percentages. REM that in MWI each experiment is literally the same outcome of all routes. Percents of a wave is just how much amplitude is there, so either you really mean chances of happening after all, or you mean "both all the time" which is the wrong answer. You're just indulging in careless metaphors and characterizations.

I am so saddened by how many people have fallen for sloppy, fallacious attempts to rationalize these faulty concepts. Fortunately there is an experiment we could do to test some of what's related to MWI, see my FQXi link. That's better than endless metaphysical bickering. I think you'd also like the thought-experiment I linked to in the first "Hippies" post here.

Neil, I'll try to respond, but I don't follow everything you've said. In the parts I do follow I think there are some problems.

The 64% / 36% beamsplitter experiment is an easy case. Your claim of 50/50 subjective probabilities for an observer to see the outcomes misses the point of Chad's original post completely. MWI will predict the same observables as any QM will for this experiment: 64% you see DA and 36% you see DB.

The interpretation is that post-experiment the multi-world wavefunction has you (as 10^30 some particles) entangled with the photon that passed through the splitter. There is 0.8 ampitude for the version of you entangled with DA. To that version of you, the experience is that the photon wavefunction collapsed to state A. It is rather irrelevant to that version of you that there is another less-likely version of yourself still represented in the multi-world wavefunction, because you are too big and too entangled with the rest of the environment to ever interfere with that other version of yourself. For all practical purposes you can just as well assume Copenhagen-style that they don't exist.

The point of the original post is that in MWI you still use Born rule to assign probabilities. How do you know that is what MWI predicts? Because (also per the original post) you include Born rule as a foundational assumption of the theory.

The main point I've tried to add to the original post is sort of a converse. The OP said you can calculate probability by Born rule in MWI. My converse is that the ONLY valid way to calculate probability in MWI is by Born rule. If you ask "what is the probability of ______ in MWI", where _______ is anything besides an observable you can use Born rule on, you've asked a question that is outside the scope of the theory. For instance, "what is the probability that, across the many worlds, some version of myself will observe DA?" We're tempted to say P=1 ("everything possible happens in some branch"), but I would hesitate even to go that far. The event described is not actually observable, so it is really outside the scope of the theory.

Dzdt, the trouble with saying the Born rule will work in MWI is that you have to show that the consequence of the theory is consistent with the BR. You can't specify a description, and then say "because (also per the original post) you include Born rule as a foundational assumption of the theory." Sorry, that is not how logic works. If you assume "A", that has consequences. You can't just assume A and then add whatever B you want. It's like saying "I say it's a quadratic equation, but I need five solutions so that's what there are." No, if you can find five solutions it means you were wrong to assume it was a quadratic equation in the first place.

First you come up with a theory. Then you ask what it predicts as a logical consequence, you don't just get to make up a description and then demand that will produce whatever you want. Then you ask if that's what really happens. MWI does not give the right answer on the face of it. (Maybe with much fiddling that ruins the supposed simplicity, but not as is.) Once you make the claim of what you start with, consequences *follow* - they aren't a matter of choice. Same with other theories.

I already explained in reply to ADP that if both outcomes really exist in each instance, then frequentist proportions give 50/50 chances. That's what is "produced" by the assumptions, you can't make up the consequences you like to make an otherwise bad theory seem good. Note that even if we consider the "portion" of the wave in each output as amplitude, the probability is supposed to be the squared modulus of amplitude, not amplitude. In order for MWI to predict 38:64 ratio of outcomes, there has to *be* that proportion of outcomes (or else it is gibberish.) You can't get that from comparing the number of different outcomes in MWI because each experiment produces both results. In effect, the differential "strength" of the two waves goes to waste, since each is simply an existential entity and not the occasion for genuine statistics. There is no meaning for "less likely version" unless there are a bunch of them and the ratios are correct.

Finally, funny that you should bring up observability as a complaint at the end, since the other outcome in any single instance is not observable either. Isn't that supposed to be a big deal in science? Thanks in any case to you and ADP for taking the time to directly address my concerns.

Orzel, I have sent you a ton of info showing why MWI doesn't work, check your inbox.

I'm sorry, but what is the need for an interpretation as it just settles for the born rule?
I am not a phycisist, but it seems to me that interpretation's are only there to make it deterministic, or just settle that it isn't deterministic, the dumb thing of mwi, is it says look it's deterministic, because 60 percent happens here, or something, and 40 percent happens where we don't see it, or something, that doesn't really make any logic sense at all? because why? there still has to be some device that makes it happen here, or there, in that percent. It cannot be derived from all those universes. So it doesn't add any new insights, just new no meaningless universes, I may be wrong, but for me it is evident from the poll I did, that close to no physicist believes in the mwi, and the vast majority rejects it. that should be enough, in fact no noble laureate subscribes to it. It is also quite remarkable that everyone promoting mwi (the literal version) is lying (tegmark: bullshit polls that should have no place in any scientific article, david raub: clearly false poll currently unfindable and so at odds with my poll an logic it's insane, Michio Kaku says qm has proven free will (!!!) but says mwi could be true and has the ethical consequence it doesn't matter what you do it happens anyway somewhere else. Deutsch that said to me he believed in a complex niche provided by mystics, and students to shut the professors up. Yet al the quantum mystics seem to like everett interpretation, and most of the proponents are very young. To which Tegmark replies they are openminded, and older people also dislike homosexuality. It's al so bizarre, but so persistent, that it seems to me to be religion whiteout the redeeming factors (trying to give hope). It's just a bunch of nonsense in my eyes, and the vast majority of theoretical physicists, and astrophysicists (the ones where it should be popular anyway.) It's also a dangerous theory, cause schizophrenic people are very likely to buy in to these bullshit. So it should flatter you, if you just came to the conclusion.
It's nonsense, and dangerous nonsense, to make it worse.

I'm sorry, but what is the need for an interpretation as it just settles for the born rule?
I am not a phycisist, but it seems to me that interpretations are only there to make it deterministic, or just settle that it isn't deterministic, the dumb thing of mwi, is it says look it's deterministic, because 60 percent happens here, or something, and 40 percent happens where we don't see it, or something, that doesn't really make any logic sense at all? because why? there still has to be some device that makes it happen here, or there, in that percent. It cannot be derived from all those universes. So it doesn't add any new insights, just new meaningless universes, I may be wrong, when I give this explanation. But I think it it is evident from the poll I did (you can search it on my name), that close to no physicist believes in the mwi, and the vast majority rejects it. that should be enough, in fact no noble laureate subscribes to it. It is also quite remarkable that everyone promoting mwi (the literal version) is lying (tegmark: bullshit polls that should have no place in any scientific article, david raub: clearly false poll currently unfindable and so at odds with my poll an logic itself it's insane, Michio Kaku says qm has proven free will (!!!) but says mwi could be true and has the ethical consequence it doesn't matter what you do it happens anyway somewhere else. Deutsch that said to me he believed in a complex niche provided by mystics, and students to shut the professors up. Yet al the quantum mystics seem to like everett interpretation, and most of the proponents are very young. To which Tegmark replies they are openminded, and older people also dislike homosexuality. It's al so bizarre, but so persistent, that it seems to me to be religion whit out the redeeming factors (trying to give hope). It's just a bunch of nonsense in my eyes, and the eyes of the vast majority of theoretical physicists, and astrophysicists (the ones where it should be popular anyway) don't believe it. It's also a dangerous theory, cause schizophrenic people are very likely to buy in to these bullshit. So it should flatter you, if you just came to the conclusion.
It's nonsense, and dangerous nonsense, to make it worse.

to be very short, for any layman this should be enough to sleep tight if they kept awake about this:
1 the prominent people who promote mwi are crazy or lying, (as I showed above)
2 the people who believe it are in the vast minority, also in the sensical non-religious world

and then my point of view, which is layman itself (so not really relevant perhaps):
the mwi is an interpretation that tries to solve randomness by saying it is random in an infinite amount of universes.