Many Worlds Interpretation: Does Quantum Mechanics Work This Way?

[pellman]

Suppose there is a quantum observable that can take two values, A or B. If a state is prepared that it is a superposition of the states A and B, then if I make an observation, according to many worlds interpretation, there will then be a superposition of two me's, one that observed A and one that observed B.

But suppose the state prepared is

|\psi\rangle = \sqrt{\frac{1}{3}}|A\rangle + \sqrt{\frac{2}{3}}|B\rangle

If I perform the experiment 1000 times, then there will be a superposition of 2^1000 me's, one for each possible set of results of the observations. But this can't be right. In such a case a typical "me" in the ensemble will have observed approximately 50% A's and 50% Bs. But the answer should be 1/3 and 2/3.

The only way for the statistical nature of quantum mechanics to be due to such an all-possible-outcomes-happen picture is for the result of one an observation of the state above to result in 1 me that observed A and 2 me's that observed B. Then everything counts up correctly.

Do I understand this right? So if we have instead

|\psi\rangle = \sqrt{\frac{79}{162}}|A\rangle + \sqrt{\frac{83}{162}}|B\rangle

an experiment results in 79 me's that get A and 83's me that get B?

If this is really the many-worlds answer to the statistical aspect of observations, then it is even kookier than I thought.

 

[Hurkyl]

Each "you" has a different amplitude associated to it. And if you compute the transition 'probabilities' from
<br /> | \text{You haven&#039;t counted yet} \rangle \otimes | \psi \rangle^{\otimes 1000}<br />
to
<br /> | \text{You have counted yet n Bs} \rangle \otimes | \psi \rangle^{\otimes 1000}<br />

you will find they are distributed according to the binomial distribution for 1000 trials with probability of success 2/3.

 

[Crazy Tosser]

I never knew you could mix amplitudes of two different quantum states D=

 

[pellman]

Each "you" has a different amplitude associated to it. And if you compute the transition 'probabilities':

I don't know what this means.

The point to many-worlds--I thought--was to do away with the collapse of the wavefunction. Each potential outcome actually happens.

In the usual intepretation, only one outcome happens, with a probability that is proportional to the amplitude's modulus squared.

If each outcome actually happens, in what way is an amplitude "associated" with it.

If every time we make one measurment, there is only one me in the resulting superposition that observes an A and one me that observes a B, the resulting distribution is necessarily symmetric with respect to As and Bs. After 1000 tries there will be one me that got all As, one me that got all Bs, 1000 me's that got 999 As + one B, 1000 me's that got 999 Bs + one A, etc.

 

[Hurkyl]

The point to many-worlds--I thought--was to do away with the collapse of the wavefunction.

The central tenet of MWI is that unitary evolution (e.g. evolution according to Schrödinger's equation) proceeds without exception.

If we scale back to performing one experiment with a 'counting' device, then that means the state

| \text{unmeasured} \rangle \otimes | \psi \rangle

evolves into

\sqrt{ \frac{1}{3} } |\text{measured 0}, 0\rangle + \sqrt{ \frac{2}{3} } |\text{measured 1}, 1\rangle

and through thermodynamic interactions with the environment, it will further decohere into the mixed state

Proportion 1/3 of |measured 0, 0> and proportion 2/3 of |measured 1, 1>.

If we focus just on the measuring device, it is in the mixed state

Proportion 1/3 of |measured 0> and proportion 2/3 of |measured 1>.


Because the components of the mixed state cannot interact (except possibly through an extremely unusual interaction with the environment), it is not unreasonable to describe the state as if it has separated into two different 'worlds', one where the device measured 0, and the other where the device measured 1, and each 'world' does have a real number coefficient between 0 and 1 attached to it. (And the coefficients will add up to 1)

 

[pellman]

Sure. The wave function never collapses and the amplitudes persist. So what then do the amplitudes have to do with the statistics?

Let's take another example.

|\psi\rangle = \sqrt{\frac{1}{1000}}|A\rangle + \sqrt{\frac{999}{1000}}|B\rangle

After two measurements, the state of the measuring device (which ultimately includes me) is

\frac{1}{1000}|A,A\rangle + \frac{\sqrt{999}}{1000}}|A,B\rangle + \frac{\sqrt{999}}{1000}}|B,A\rangle + \frac{999}{1000}|B,B\rangle

Right? But what is the statistical significance of these amplitudes? The amplitude of 2 Bs is much larger than 2 As but there is still only one me that got two As and one that got two Bs. In what sense is 2 Bs likelier than two As?

 

[Ken G]

The central tenet of MWI is that unitary evolution (e.g. evolution according to Schrödinger's equation) proceeds without exception.

Yes, you are describing the situation correctly, and interestingly you thereby show the flaw in MWI thinking.

If we scale back to performing one experiment with a 'counting' device, then that means the state

| \text{unmeasured} \rangle \otimes | \psi \rangle

evolves into

\sqrt{ \frac{1}{3} } |\text{measured 0}, 0\rangle + \sqrt{ \frac{2}{3} } |\text{measured 1}, 1\rangle

and through thermodynamic interactions with the environment, it will further decohere into the mixed state

Proportion 1/3 of |measured 0, 0> and proportion 2/3 of |measured 1, 1>.

There's the flaw right there, in bold. Let's call your above stages an initial state, a first step, and a final step. How is the first step separable from the final one, so you can plunk a "further" in there? The whole way that the "measured associations" you cite in the first step are achieved is via the decoherence, that's exactly what the measuring apparatus does, so that's what a measurement is. Since the MWI approach has to break that single happening into two separate happenings, the first being unitary and the second breaking the unitariness (but only after the MWI step has already appeared, that's the point of it), it shows quite clearly that the MWI step is a fiction. In other words, your analysis is identically the same if you simply omit that first step. So why include it?

 

[Ken G]

But what is the statistical significance of these amplitudes? The amplitude of 2 Bs is much larger than 2 As but there is still only one me that got two As and one that got two Bs. In what sense is 2 Bs likelier than two As?

That's another flaw in MWI thinking. Hurkyl is certainly right that even though there is one "me" that got two As and one "me" that got two B's, the latter "me" is far more likely to be actualized in the final decohering step. So what this means is that "counting the me's" doesn't tell you anything at all, what matters is their amplitudes. But again, I point out that there is actually no "amplitude stage" anyone could point to or isolate in any way, the decoherence is already there, so the mixed state is already achieved-- the superposition stage is a fiction. So that's the other reason there's no point in "counting the me's". It's like, if I enter an olympic track meet, it makes no difference at all how many other racers are competing, one or a hundred. I have no chance of winning, either way.

 

[Hurkyl]

But what is the statistical significance of these amplitudes?

There is the obvious significance that the amplitudes will decohere into a probability distribution on the possible outcomes (assuming you've written the state relative to the correct basis). But as to what the "meaning" of that probability?

(aside: it might be useful to ponder the "meaning" of statistics as applied to pre-quantum physics, or to anything else related to 'reality'. One of the things I find aesthetically pleasing about QM is that some of the probabilities actually correspond to something)

One thing you can check is that these probability distributions are, if you assume a mild continuity argument, consistent with the frequentist interpretation of probabilities. Consider a device that makes the following measurement:

Output |0> if the proportion of B's is outside the range [1/3 - e, 1/3 + e]
Output |1> if the proportion of B's is in the range [1/3 - e, 1/3 + e]

For any positve e, in the limit of the number of trials approaching +infinity, the state under consideration device converges to the pure state |1>.

 

[Hurkyl]

How is the first step separable from the final one, so you can plunk a "further" in there?

For pedagogical reasons, it seems clearer to describe a measurement that proceeded in two phases. And such a procedure is certainly applicable to certain situations -- e.g. a half-silvered mirror splitting a photon is an example of a 'coherent measurement', which we are demonstratably capable of erasing before it decoheres.

the latter "me" is far more likely to be actualized in the final decohering step.

I'm not exactly sure what that means -- if we ignore the information that escapes into the environment, decoherence collapses the state into a mixture of all possible outcomes, with coefficient equal to what we usually call the probability of that outcome.

 

[Ken G]

For pedagogical reasons, it seemed clearer to describe a measurement that proceeded in two phases.

And there's nothing wrong with MWI as mere pedagogy-- but that's not how it's argued.

And such a procedure is certainly applicable to certain situations -- e.g. a half-silvered mirror splitting a photon is an example of a 'coherent measurement', which we are demonstratably capable of erasing before it decoheres.

No, the fact that you can "quantum erase" the connection proves that there is no such state as |mirror sends 1, 1> unless you decohere it. You may as well claim there is a state in a two-slit experiment |slit sends photon left, left> and |slit sends photon right, right> without decohering those results. Can you cite any difference at all between that fictional state and just |left> and |right>?

I'm not exactly sure what that means -- if we ignore the information that escapes into the environemnt, decoherence collapses the state into a mixture of all possible outcomes, with coefficient equal to what we usually call the probability of that outcome. I'm not sure what that has to do with "actualizing" anything.

The scientific method involves things that are actualized, because the actualizing is how we do the tests that define science. Can you cite any counterexamples to support your idea that science can be done on mixed states without actualizing them?

 

[Hurkyl]

And there's nothing wrong with MWI as mere pedagogy-- but that's not how it's argued.

Who said it was?

No, the fact that you can "quantum erase" the connection proves that there is no such state

Let's consider the very simplest 'coherent measurement': a CNOT gate, with one input initialized to |0>. Actually, let's not -- I believe the original poster's intent was to actually learn what MWI says, so derailing it into a debate about the "correct" metaphysics would not be appropriate here. A new thread on the topic would be fine though. (And if you do start one, and use the word 'actualize' in it, you really ought to try and give it some sort of definition)

 

[Ken G]

Who said it was?

Here's from Wiki: (http://mail.google.com/mail/#inbox/11969e65e7cad267)
" Many-worlds denies the objective reality of wavefunction collapse."

Here's from the Stanford Encyclopedia of Philosophy (http://plato.stanford.edu/entries/qm-manyworlds/):
"The Many-Worlds Interpretation (MWI) is an approach to quantum mechanics according to which, in addition to the world we are aware of directly, there are many other similar worlds which exist in parallel at the same space and time. "

Or there's this poll result from ( ):
""Political scientist" L David Raub reports a poll of 72 of the "leading cosmologists and other quantum field theorists" about the "Many-Worlds Interpretation" and gives the following response breakdown [T].

1) "Yes, I think MWI is true" 58%
2) "No, I don't accept MWI" 18%
3) "Maybe it's true but I'm not yet convinced" 13%
4) "I have no opinion one way or the other" 11%"

and that article goes on to describe a key assumption of the MWI:"The metaphysical assumption: That the wavefunction does not merely encode all the information about an object, but has an observer-independent objective existence and actually is the object. For a non-relativistic N-particle system the wavefunction is a complex-valued field in a 3-N dimensional space."

Those are just the first three Google hits. Need I go on? Note that none of those statements describe a pedagogy (which is a way to teach something, essentially a conceptual mnemonic). They are all quite clearly statements of a world view, and whenever I discuss MWI with anyone, it is usually quite clear that they also take it in that light. The Wiki hit says it "denies" things, which pedagogies do not do, they are expressed entirely constructively. The second hit uses the ontological word "exists", and being a philosophy text, it would know the difference between that and a pedagogy. The third hit goes so far as to cite "objective existence", this despite the well-known fact that it cannot be objectively demonstrated (which is why Everett originally termed it a meta-theory, a far more appropriate term than either "interpretation" or "pedagogy").

A new thread on the topic would be fine though. (And if you do start one, and use the word 'actualize' in it, you really ought to try and give it some sort of definition)

Agreed. But the OPer might also be interested in whether the MWI is a theory, a metatheory, or a pedagogy. And since you mention it, the word "actualize" is trivial to define in a scientific context. This would work fine: a mixed state is "actualized" into an "outcome" whenever the results of an experiment are tabulated. Indeed, every scientific experiment ever done invoked the concept of actualization, there can be no more obvious condemnation of the MWI approach than that it seems to engender the idea that "actualization", which has always been a crucial step in science, is somehow a less central concept in science than "unitarity", which is a mathematical model.

 

[Hurkyl]

You misunderstood -- when I said "who said it was", I was (rhetorically) asking who said that MWI was a mere pedagogy. Recall that when I invoked the term, I was justifying my choice of example to present.

Agreed. But the OPer might also be interested in whether the MWI is a theory, a metatheory, or a pedagogy.

The MWI is, as its very name suggests, is primarily an interpretation -- a (metaphysical) mapping from the fundamental notions of the mathematical theory of quantum mechanics to "reality".

Also MWI has apparently spawned a new round of philosophical discussion on the notion of nondeterminism -- and I have seen this discussion also called labelled as MWI, but I don't know if that is by scientists who use MWI, or by people eager to find reasons to dismiss MWI unfairly.

And since you mention it, the word "actualize" is trivial to define in a scientific context. This would work fine: a mixed state is "actualized" into an "outcome" whenever the results of an experiment are tabulated.

If this is an accurate definition, then according to MWI, each possible outcome is 'actualized' in one or more components of the decohered state.

there can be no more obvious condemnation of the MWI approach than that it seems to engender the idea that "actualization", which has always been a crucial step in science, is somehow a less central concept in science than "unitarity", which is a mathematical model.

The only thing MWI endangers in this respect is our confidence that we can make meaningful assertions about things that are unobservable. The most commen alternative is to assert that some unobservable facet of reality does not exist... and the price for making that assertion is that you have to assume that quantum mechanics works only when we're not looking.

 

[Ken G]

If this is an accurate definition, then according to MWI, each possible outcome is 'actualized' in one or more components of the decohered state.

Certainly, that is just what the MWI would say, but it must still confront the clear fact that each scientist, doing science, experiences only one set of actualizations. That is my point, MWI does not represent a scientist doing science. As such, it cannot be claimed to arise from science-- it arises from philosophy. It arises from building an exoskeleton around science, mimicking the skeleton we observe when we interact with our classical instruments, but that cannot be tested by science, for purposes of sheer "mental aggrandizement". I would say that description applies equally well to all other efforts at external and untestable scaffold-building, including religion. But that's the stuff of another thread.

The only thing MWI endangers in this respect is our confidence that we can make meaningful assertions about things that are unobservable.

How does MWI endanger that, it seems to me it is an effort to do gain precisely that confidence. To me, what MWI endangers is the idea that meaningful assertions come from what is observable, i.e., that scientific enlightenment stems from doing science as it has defined itself ever since it started actually doing something other than creating self-styled authorities on all things metaphysical.

The most commen alternative is to assert that some unobservable facet of reality does not exist... and the price for making that assertion is that you have to assume that quantum mechanics works only when we're not looking.

No, you only have to define quantum mechanics in a way that is restricted to something that is demonstrable using the scientific method.

 

[pellman]

I'm not getting it, guys. But thanks for trying. - Todd

 

[Hurkyl]

Certainly, that is just what the MWI would say, but it must still confront the clear fact that each scientist, doing science, experiences only one set of actualizations. That is my point, MWI does not represent a scientist doing science. As such, it cannot be claimed to arise from science-- it arises from philosophy.
...
but that cannot be tested by science, for purposes of sheer "mental aggrandizement".

Until you provide an actual experiment where your assertions and the predictions of MWI differ, perform it, and observe the results disagree with MWI, you are a verbose hypocrit.


Note that for the most obvious ways of empirically counting 'actualizations', MWI predicts that any experiment will certainly result in the answer 1. (e.g. repeatedly ask an honest scientist what answer he observed for a particular experiment)

 

[Ken G]

I'm not getting it, guys.

OK, then getting back to the OP, the MWI is exactly the same as looking at a superposition state from the outside. So saying that we have "many worlds" when the scientist is part of the system is exactly that same as saying a photon in a double slit experiment is part of "many worlds" which we are observing from the outside. So you can reform your OP in exactly those terms-- set up an experiment where the photon has a 1/root(3) amplitude of going through one slit, and a root(2/3) amplitude of going through the other slit. Now "count the photon possibilities"-- you still have two "photon-worlds", one that is more likely than the other. So there's no inconsistencies there-- and there's also no need to think in terms of these separate "photon worlds". It's an empty model, the amplitudes are all you need, and all you use to check the predictions.

 

[Ken G]

Until you provide an actual experiment where your assertions and the predictions of MWI differ, perform it, and observe the results disagree with MWI, you are a verbose hypocrit.

At no time did I claim the flaw of MWI is that it is contradicted by science, my claim is that it is simply not science. Is the existence of a supreme being contradicted by science? Would I also be a "verbose hypocrite" to claim that belief in a supreme being is not science, unless I had an experiment that proved it? That is precisely your logic here.

 

[Hurkyl]

At no time did I claim the flaw of MWI is that it is contradicted by science, my claim is that it is simply not science.

However,
(1) you make assertions about the untestable
(2) you criticize the consideration of untestable things
thus satisfying the connotative and denotative meanings of the word "hypocrit".


Incidentally, science is a subfield of philosophy, so you have no grounds for criticizing anything on the basis of it being philosophy. And besides, the metaphysical assignment of the notions in a mathematical theory with facets of reality is an integral part of science.

 

[Ken G]

However,
(1) you make assertions about the untestable

Quite true, I asserted it was untestable. That is all. You see that as hypocritical in some way?

(2) you criticize the consideration of untestable things

No, I don't. That would mean criticizing religion, art, philosophy. Instead, what I criticized was calling it science. If I was not clear on that before, let me be so now.

Incidentally, science is a subfield of philosophy, so you have no grounds for criticizing anything on the basis of it being philosophy.

Just look up the definition of the scientific method. Wiki does a fine job. You will find a complete stress on demonstrability and objective reproducibility of all facets of what is being claimed to be true. My argument requires nothing else-- this is the whole point, in the "old days" people thought ideas could be scientific just because they sounded really good to philosophers and deep thinkers. Then Galileo put them all on their keesters. What goes around, comes around.

And besides, the metaphysical assignment of the notions in a mathematical theory with facets of reality is an integral part of science.

The issue is whether or not untestable mathematical models can be counted as authoritative in science entirely based on how they make us feel to believe them. I have argued that is not enough to be science, and again I cite the scientific method as defined in any of a number of good sources.

 

[Hurkyl]

My argument requires nothing else--

Please demonstrate, and indicate how to objectively reproduce, an experiment that disagrees with the predictions of MWI, and thus supporting your argument that it is flawed.

Please demonstrate, and indicate how to objectively reproduce, an experiment that is inconsistent with the hypothesis that a scientist is in a mixed state of experiencing different 'actualizations', and thus supporting your argument that there is only one actualization.

The issue is whether or not untestable mathematical models can be counted as authoritative in science entirely based on how they make us feel to believe them.

No, that is not the issue. (AFAIK) The main observations leading to the MW interpretation are:

(1) We have empirical evidence supporting the unitary evolution dynamics of QM
(2) We do not have empirical evidence supporting the notion that unitary evolution is broken in favor of wavefunction collapse

The line of reasoning is that we should adopt the interpretation that most closely matches both the mathematical theory and the empirical data -- i.e. an interpretation where wavefunctions evolve unitarily and do not collapse.

Furthermore, MWI is a conservative interpretation -- it posits nothing beyond the unitary time evolution of QM, and is thus interprable within any other interpretation of QM.



And, incidentally, you can go minimalist in other directions too -- e.g. since many different wavefunctions can be empirically indistinguishable, you can view them as simply being different descriptions of the same state of the universe. (Compare to representing space-time via coordinate charts)



Incidentally, I earlier missed a comment that you made:

Since the MWI approach has to break that single happening into two separate happenings, the first being unitary and the second breaking the unitariness (but only after the MWI step has already appeared, that's the point of it), it shows quite clearly that the MWI step is a fiction.

The second step doesn't break unitariness; decoherence (of the relative state of a system interacting thermodynamically with the environment) is the predicted result of unitary evolution of the universe.

 

[Ken G]

Please demonstrate, and indicate how to objectively reproduce, an experiment that disagrees with the predictions of MWI, and thus supporting your argument that it is flawed.

I have already stated, quite clearly, that the "flaw" in MWI is not that it disagrees with experiment, it is that it does not show up in any experiment. In that sense, as science, it suffers from the same flaw as religion. As religion, it's fine, indeed it is religion that doesn't contradict science, so it's a popular choice among scientists. If you don't think scientists use it in ways quite similar to religions, look up Max Tegmark's "quantum suicide thought experiment".

Please demonstrate, and indicate how to objectively reproduce, an experiment that is inconsistent with the hypothesis that a scientist is in a mixed state of experiencing different 'actualizations', and thus supporting your argument that there is only one actualization.

That's easy-- just do science. You won't be in a mixed state, although if you pretend you are in one, you will certainly be in a mixed-up state. You cannot prove that things are as you measure and perceive them-- but you can never prove science anyway, all you can do is demonstrate it. Now, how will you demonstrate being in a mixed state? All you can do is imagine it, exactly like an article of faith.

No, that is not the issue. (AFAIK) The main observations leading to the MW interpretation are:

(1) We have empirical evidence supporting the unitary evolution dynamics of QM
(2) We do not have empirical evidence supporting the notion that unitary evolution is broken in favor of wavefunction collapse

I agree this is the crux, and where the MWI position falls apart:

(1) is correct only within the framework of the scientific method, i.e., the only unitary evolution dynamics we have ever witnessed has simply made contact between two classical measurements. The first "prepares" the system, and the second "collapses" it. What is unitary only applies to what lies in between, that is all that has ever been shown to be true. The remaining unitariness is make believe, an alluring fiction that loses contact with science. Indeed, why do we always focus on the "collapse" at the end, and give a free pass to the "initial preparation"? How are "initial conditions" unitary? Experiments either start from non-unitary mixed states, or approximate a system as a pure state by docohering (nonunitarily) the true history of that system. So yes, we note that the central stage is unitary, while the system is evolving as a closed system, but we only know this when it is sandwiched between these two open parts, and we have no idea what happens to systems not so sandwiched, because the sandwiching is science. Thus I say "the projection of reality onto science gives the Copenhagen interpretation".

(2) is false, we have perfect understanding of wavefunction collapse within the postulates of quantum mechanics, you merely have to recognize that all measurements involve open systems. The quantum postulates only say that closed systems evolve unitarily when sandwiched between classical decoherences, is that not true? The reason measured systems are open is that we do not include the necessary information to close them. We can say "the experimenter is part of the system", but that means the experimenter's entire life is, and everything that influenced it, i.e., the entire history of the universe. There is thus only one closed system, the "universal wave function", and that is the only one that needs to evolve unitarily. Obviously no science has ever demonstrated that it does, because science requires objectivity, and objectivity requires getting outside the universe. Correct? That is what objectivity means. That's why MWI is not science, it violates the most basic assumption of objectivity.

The line of reasoning is that we should adopt the interpretation that most closely matches both the mathematical theory and the empirical data -- i.e. an interpretation where wavefunctions evolve unitarily and do not collapse.

Correction, wavefunctions of closed systems evolve unitarily. Those of open systems collapse, you understand that, that's what decoherence is all about. There is no mystery at all as to the source of collapse, the only issue is whether we are limited by the requirements of objectivity to treat systems we observe as open (by that observation), or whether we can imagine that we too are part of the system, but as I said, that sacrifices both objectivity and the core values of science. By science, we are not qualified to make observations of systems that we are part of, because that would be a definitively subjective interaction, not an objective one. This is the blind hole in MWI.

And what benefit do we achieve by dropping the most basic scientific value of objectivity? Any increase in predictive power? None, all we get is a quasi-religious world view we cannot even test. No, the CI had it right-- separate the experimenter from the experiment, find a working definition of objectivity, open the system we are doing science on (both when we prepare it and when we measure it), and recognize that wave functions of open systems collapse when interacting with classical measuring devices. What's the big deal, I'm mystified.

Furthermore, MWI is a conservative interpretation -- it posits nothing beyond the unitary time evolution of QM, and is thus interprable within any other interpretation of QM.

No, it posits a universal wave function that includes the person conceptualizing said wave function. That's its ascientific element, and it's not even internally consistent. How does a mind conceptualize a wave function that includes that mind?

And, incidentally, you can go minimalist in other directions too -- e.g. since many different wavefunctions can be empirically indistinguishable, you can view them as simply being different descriptions of the same state of the universe. (Compare to representing space-time via coordinate charts)

I am all for equating all physical representations that spawn the same testable outcomes. Physics is not the pictures we use to imagine how physics ticks, we know well that we have great freedom in forming those pictures. It is when we take those nonunique pictures too seriously that we lose touch with what we are really doing.

The second step doesn't break unitariness; decoherence (of the relative state of a system interacting thermodynamically with the environment) is the predicted result of unitary evolution of the universe.

It does break the unitariness on the open substate being experimented on. That is all we actually measure and experience, the substate that is "actualized", yes. You can always imagine the existence of other subspaces that are not in evidence in the experiment, and that's just what MWI does, in order to artificially reconstitute the unitariness.

Don't you see what that means? It means we place a desire to force the evolution to be unitary above our desire to actually treat a scientific outcome as a scientific outcome! Since when does science take such an active role in its own discoveries? We're supposed to step back and take what we observe at face value, that's the breakthrough of science. The forcing here is being done just to give ourselves a nice warm fuzzy feeling about the unitarity of the universe. I know plenty of people who find simpler ways to get that feeling, knowing no physics at all. The only thing that distinguishes that from the MWI path of achieving the same thing is that the latter does not contradict science, so let's call it what it is-- not a science, but a philosophy that is consistent with science.

 

[peter0302]

Ken G is right. Even though I believe in MWI, it's not science until we find a way to prove it or disprove it. The fact that we cannot disprove it makes it, by definition, not science. For example, scientists state that intelligent design is not science because it cannot be tested using the methods of science. Same goes for MWI.

And Hurkyl, if you're going to call people names like hypocrite, you probably should spell them correctly.

 

[Ken G]

Yes, I want to stress I don't think there's anything wrong with believing that MWI is true in some deep metaphysical sense, and I also think it's a perfectly scientific attitude to choose a MWI picture as a kind of conceptual mnemonic to help one set up the equations of science. Those are both subjective personal choices, more power to ya. The problem is mistaking either of those for a scientific conclusion, which, to distinguish science from other human pursuits, must be based in demonstrability (by which I mean you can actually show the many worlds unfolding) and objectivity (by which I mean your conclusions survive the separation of the observer from what is being observed, precisely what MWI does not do).

 

[Hurkyl]

Ken G is right. Even though I believe in MWI, it's not science until we find a way to prove it or disprove it.

Correction -- it's not an empirical fact until we find a way to prove or disprove it. Theory-making is part of what makes it science. Without the theory-making, you're doing nothing more than collecting a bunch of anecdotal tales.

And, for the record, the testability of any hypothesis requires an ontology -- you can't test a hypothesis unless you have some means of connecting the hypothesis with the results of your experiment.

And Hurkyl, if you're going to call people names like hypocrite, you probably should spell them correctly.

That's a red herring: I should always spell correctly. (except when the situation calls for intentional misspelling) And "hypocrite" isn't name-calling: it's an evaluation of his argument. Specifically, my evaluation that Ken G simultaneously makes a lot of metaphysical assertions while dismissing other metaphysical arguments on the grounds that they are merely metaphysics. (And, to me, it looks like he thinks his metaphysical assertions are scientific fact. I suppose if that's true, he isn't being intentionally hypocritical)

 

[Ken G]

Correction -- it's not an empirical fact until we find a way to prove or disprove it. Theory-making is part of what makes it science. Without the theory-making, you're doing nothing more than collecting a bunch of anecdotal tales.

It's not a question of either/or, you need to be doing both to be doing science. You need to be unifying the results of empirical tests in a way that is itself testable. If you are not doing any part of that, you are not doing science, you are simply cataloging (in the first case) or storytelling (in the second).

And, for the record, the testability of any hypothesis requires an ontology -- you can't test a hypothesis unless you have some means of connecting the hypothesis with the results of your experiment.

That sure doesn't sound like "an ontology" to me, a "model" does that fine. Do you think a model is the same as an ontology? If so, we have no disagreement on the physics, though a bit of a disagreement on the language.

Specifically, my evaluation that Ken G simultaneously makes a lot of metaphysical assertions while dismissing other metaphysical arguments on the grounds that they are merely metaphysics.

An accusation that I refuted forthwith. Please cite a "metaphysical assertion" that I have made to support your contention that the term was appropriate. I claim to do nothing but refer to the defining principles of the scientific method, and I have seen you cite no counterexamples in any of my statements.

 

[peter0302]

Correction -- it's not an empirical fact until we find a way to prove or disprove it. Theory-making is part of what makes it science. Without the theory-making, you're doing nothing more than collecting a bunch of anecdotal tales.

No, no, no, that's not right. There is a difference between a scientific theory and a non-scientific hypothesis. A scientific theory is one that can be _tested_ using the tools of science, the scientific method. Non-scientific speculation is a hypothesis that may fit the facts but makes no predictions different from any other such hypothesis. It is, fundamentally, the same as a religious belief - the difference, thankfully, is that people don't tend to build churches or launch wars over them. But, just like a religious belief, an interrpetation is an explanation for phenomina that cannot be tested or disproven. It's not a scientific theory.

And, name calling is name calling. It's an ad hominum attack and it's inappropriate, especially given that Ken's posts were objective and appropriate.

 

[pellman]

OK, then getting back to the OP, the MWI is exactly the same as looking at a superposition state from the outside. So saying that we have "many worlds" when the scientist is part of the system is exactly that same as saying a photon in a double slit experiment is part of "many worlds" which we are observing from the outside.

Ok, Ken, I 'll take one more stab it. I haven't understood your posts so far, so all I can do is try to explain my understanding again and see if you can tell me where I'm going wrong.

I don't know what probabilities can mean apart from relative frequencies. (I know there are some other theories of probability; I'm just not familiar with them.) So in the standard explanation, the amplitudes modulus-squared are the relative frequencies of the associated eigenvalue in the limit of many observations. In my second example,

|\psi\rangle = \sqrt{\frac{1}{1000}}|A\rangle + \sqrt{\frac{999}{1000}}|B\rangle

according to the usual textbook explanation, after many experiments, the ratio of acutal B results to A results should approach 999:1.

However, if in each individual observation both A and B occur and coexist as a superposition, then a meta-observer who is "outside"--by which, I think we mean someone who can "see" the whole wavefunction and not just one element in the superposition--will see exactly one A result and one B result from every experiment. The ratio of As to Bs is 1:1, no matter what the amplitudes are.

If I am wrong, please explain in what sense the B results occur 999 times as often as the As.

 

[Ken G]

I don't know what probabilities can mean apart from relative frequencies.

I'm sorry I didn't catch this question before. I think this is the problem right here. In MWI, probabilities are to be interpreted more as weights than as frequencies. I'll expound.

However, if in each individual observation both A and B occur and coexist as a superposition, then a meta-observer who is "outside"--by which, I think we mean someone who can "see" the whole wavefunction and not just one element in the superposition--will see exactly one A result and one B result from every experiment. The ratio of As to Bs is 1:1, no matter what the amplitudes are.

True-- the frequency of appearance of A and B is not predictive of anything in MWI. What is predictive is the amplitudes-- if you are the "outer observer" and you want to take your calculation and use it to predict whether you'll open the box and see A or open the box and see B, it doesn't matter how many terms in your expansion contain A or B, what matters is the amplitudes. I think a way to say that is, MWI suffers from a problem of "dissipating probability", if you like-- the branches become less and less likely. So to interpret them as "many worlds", you have to renormalize the probability of each branch to get it back to 1 (a "world" needs to be conceived as if it had probability 1, internally-- I think that's what is bothering you). What you need to do to renormalize that probability will tell you the probability that that will be the "world" you observe if you step into the box. So that's not an issue of frequency, it's more like renormalized weights.

You could think of it like throwing darts at a dartboard. Maybe there are two circles on the board, one large and one small. The relative frequency of the circles is 1:1, but their "weight" is more like their surface area, and the latter, not the former, will determine the likelihood of hitting them with a dart. An ant on one circle, and an ant on the other, might know which circle they are on, so say they have certainty 1 of being on that circle no matter what its area is, but that's not the predictive issue for hitting that circle with a dart.

 

[reilly]

When we look at cloud or bubble chamber measurements, we see trajectories. And these trajectories, say in a magnetic field, are governed by normal temporal unitary transformations -- in scattering theory we should use wave packets, cf. Goldberger and Watson, Scattering Theory. And so, initial and final states are asymptotic to localized trajectories with reasonably sharp momentum; and the whole process of scattering or particle production is governed by QM.

We make a measurement by examining the trajectories; and clearly under these particular circumstances our measurements can only modify the observer's information; the trajectories are written in stone - or bubbles, as you wish. Our knowledge changes; collapses from a set of possibilities to a single outcome, and that collapse is indeed governed by a unitary transformation, that describes the rods and cones,neurons.

Why, in such a case, invent an MWI-type interpretation that, necessairily requires an uncountable number of possibilities, hence apparently, an uncountable number of universes. Keep this up and you will get to ALEPH1 to the ALEPH1 universes(and on an on), a very nasty number. That is, MWI seems to ascribe a reality to QM derived probability trees; and these grow big real fast, and to the point where it is not at all clear that we have the mathematics, nor any language to describe such a situation.

I just don't see any advantage to building a highly complex structure, particularly when , in my opinion, there are vastly more simple interpretative approaches, some of which have survived for several hundred years, and are still used extensively in practical probability and statistics.

As I think about this, I'm curious to see an example of a "non-unitary" measurement -- all measuring devices are governed by the physics we all know and love.

I do not get MWI at all, it makes no sense to me. I would appreciate a simple minded explanation, that could give some understanding. MWI is an approach to which some very bright and able people have subscribed. Even though I tend to discount all of MWI, there must be things that if I get them will reduce my lack of comprehension.

Regards,
Reilly Atkinson

 

[confusedashell]

Reilly, if I don't remember wrong your a copenhagenist right?

I reject MWI, but agree with it's objectivism and realism so I support Bohm's interpretation, you might want to check that out.

As for MWI: it simply states wave functions are all that exists. Makes no sense.

 

[peter0302]

There is definitely no consensus on what the probabilities mean, but I would look at it this way.

Let's say you start out with two possible spin states for a particle A, + or -. Say the wavefunction is

|Psi A>=.436|+> + .9|->

Now as we all know, the universe continues to evolve after the split, and particle A will continue to interact with other things. Well, the amplitude of the different probabilities of + or - for A will carry through with the rest of the universe as the universe evolves. So when the next experiment comes along:

|Psi B>=.8|+> + .6|->

And A and B eventually interact, the continued universal wavefunction of the system becomes:

|Psi A,B> = .3488|A+,B+> + .2616|A+,B-> + .72|A-,B+> + .54|A-,B->

So with the wavefunction continually evolving, the odds from the original experiment (the odds of A being + or -) carry through as well, and, after a long while, will be reflected in the number of universes in which A is + and the number in which it is -.

I think a good way of looking at it is imagine that you're randomly jumping into all the different quantum realities like Mr. Worf did in one episode of Star Trek. If you had a quantum experiment whose outcome was 75% + and 25% -, 75% of the time you jumped you'd be in a universe where the outcome was +, and 25% 0f the time you'd jump into a universe where the outcome was -, and those odds will be determined by the original wavefunction describing that experiment.

Does that help or make sense to anyone besides me?

 

[JesseM]

As I think about this, I'm curious to see an example of a "non-unitary" measurement -- all measuring devices are governed by the physics we all know and love.

Don't you assume that when you make a measurement, it projects the quantum state of the system onto an eigenstate of whatever you're measuring? And unlike in classical probability you can't assume that this just represents a change in your knowledge rather than a physical change, that would suggest a hidden-variables theory where the system already had a definite value for that variable even before you measured it.

 

[Ken G]

And unlike in classical probability you can't assume that this just represents a change in your knowledge rather than a physical change, that would suggest a hidden-variables theory where the system already had a definite value for that variable even before you measured it.

I would say that measurement represents both a physical change, and a change in our knowledge (the latter change being different if we look or not, the former being the same either way), because the process involves both elements and a great deal of confusion stems from requiring it to be one or the other. To me it makes sense to say that the part that is a physical change involves whatever is the physical coupling to the measurement (say, the interactions that make the bubbles), and the part that is a change in information is when the physicist interprets those bubbles in terms of a solution of some equation involving a wave function. Why can't the measurement be physical but the wave function changes be changes in information? The fact that two people, with different information, can use two different wave functions and still conclude that quantum mechanics is working perfectly is a very telling fact, in my view.

 

[peter0302]

I would say that measurement represents both a physical change, and a change in our knowledge

Well, when you measure the state of an entangled particle, information about the twin certainly changes, but is there a physical change in the twin as well? That's why I find great difficulty saying that a measurement is always a physical change.

 

[JesseM]

I would say that measurement represents both a physical change, and a change in our knowledge (the latter change being different if we look or not, the former being the same either way), because the process involves both elements and a great deal of confusion stems from requiring it to be one or the other.

Well, perhaps I should have said that the projection onto an eigenstate cannot be imagined to be purely a change in knowledge in exactly the same manner as changes in subjective probability due to measurement in classical probability. If it were, that would imply that even when the particle is not being measured, it is "really" in one eigenstate or another at all times, with probability equal to the square of the amplitude that its current state assigns to each eigenstate, and measurement just reveals this preexisting truth (if that were the case, why would measurement of which slit the particle goes through in the double-slit experiment affect the probability distribution on the screen?)

 

[Ken G]

Well, when you measure the state of an entangled particle, information about the twin certainly changes, but is there a physical change in the twin as well?

No, there is no physical change in the twin, because there is no interaction with it. That's why someone who does not know about your measurement will never find any contradictions in their quantum mechanics, as a result of not knowing that information.

 

[Ken G]

Well, perhaps I should have said that the projection onto an eigenstate cannot be imagined to be purely a change in knowledge in exactly the same manner as changes in subjective probability due to measurement in classical probability.

Had you said that, it would be true, but all it would be saying is that classical systems respond in a more robust way to couplings to classical measuring devices than do delicate and fragile quantum systems-- a fact that should hardly surprise anyone with the hindsight of quantum mechanics yet seems to continually do so.

 

[JesseM]

Had you said that, it would be true, but all it would be saying is that classical systems respond in a more robust way to couplings to classical measuring devices than do delicate and fragile quantum systems-- a fact that should hardly surprise anyone with the hindsight of quantum mechanics yet seems to continually do so.

But here you have to draw a boundary between "classical systems" and "quantum systems", rather than treating everything using the same quantum laws as reilly was suggesting when he said 'As I think about this, I'm curious to see an example of a "non-unitary" measurement -- all measuring devices are governed by the physics we all know and love.' If you do try to assign a wavefunction to the combined system of the measuring device and the particle being measured, then although you can assign amplitudes to various outcomes after the measuring device does its stuff, if you assume this system is just like any other quantum system then you can't assume the measuring device has "really" found one outcome or another and that if you later measure the measuring device's records, you are merely discovering a preexisting truth. This is just another way of stating the Schroedinger's cat paradox of course, replacing the cat with the measuring device and replacing the fact of the cat being alive or dead with the measuring device's recordings.

Basically, I think the motivation for the MWI is just to treat all systems with a uniform set of laws at all times, without the need for any external observer to measure the system, and to try to make these uniform laws differ as little from the standard textbook laws as possible.

 

[Ken G]

But here you have to draw a boundary between "classical systems" and "quantum systems"

Not in any "real" sense I don't, it's all in how I choose to treat them. I can treat a quantum system classically, if I'm willing to get lots of wrong results along with the right ones, and I can treat a classical system quantum mechanically, if I'm willing to squint my eyes and pretend a bowling ball is a "particle". It's all up to me and my objectives.

If you do try to assign a wavefunction to the combined system of the measuring device and the particle being measured, then although you can assign amplitudes to various outcomes after the measuring device does its stuff, if you assume this system is just like any other quantum system then you can't assume the measuring device has "really" found one outcome or another and that if you later measure the measuring device's records, you are merely discovering a preexisting truth.

Actually, you can assume that, because you cannot be derailed by coherences in classical systems (that's what defines classical systems). You make no errors at all, in the sense that none of your predictions prove false. You just don't surround it with such a formal exoskeleton of untestable axioms.

This is just another way of stating the Schroedinger's cat paradox of course, replacing the cat with the measuring device and replacing the fact of the cat being alive or dead with the measuring device's recordings.

Right-- and recall that Schroedinger introduced that paradox on the grounds that you could treat the cat as alive or dead, to discredit the idea that you could not-- quite the irony.

Basically, I think the motivation for the MWI is just to treat all systems with a uniform set of laws at all times, without the need for any external observer to measure the system, and to try to make these uniform laws differ as little from the standard textbook laws as possible.

I agree, that is what is behind it. But to me, that's taking science outside its own definitions, and telling reality that it must be the way we like to imagine it. Countless times we have ended up with egg on our faces doing precisely that, so why pretend we know it now? Just treat it like an optional and untestable picture, that admits certain mathematical niceties but does not reflect some of our most basic perceptions of reality. Until we have a working model of what a "self" is, we should expect surprises.

 

[JesseM]

Not in any "real" sense I don't, it's all in how I choose to treat them. I can treat a quantum system classically, if I'm willing to get lots of wrong results along with the right ones, and I can treat a classical system quantum mechanically, if I'm willing to squint my eyes and pretend a bowling ball is a "particle". It's all up to me and my objectives.

But you're talking about what you can do in practice, I'm talking about the more theoretical problem of picking a set of laws such that we can imagine a universe described exactly by those laws, such that what would be seen by an observer in that model universe would look no different than anything we see in actual experiments.

Actually, you can assume that, because you cannot be derailed by coherences in classical systems (that's what defines classical systems). You make no errors at all, in the sense that none of your predictions prove false. You just don't surround it with such a formal exoskeleton of untestable axioms.

You can assume it in practice, but only because in practice you have an informal understanding of the difference between "classical" and "quantum" systems, although no such boundary follows directly from quantum laws themselves. The quantum laws don't give you a basis for saying that for some quantum systems, the square of the amplitudes just represents a probability that the system was in that state before measurement, while for others the square of the amplitudes does not represent any preexisting probabilities.

Right-- and recall that Schroedinger introduced that paradox on the grounds that you could treat the cat as alive or dead, to discredit the idea that you could not-- quite the irony.

In principle QM predicts that you could still see interference effects here, if the cat was perfectly isolated from the external environment and "opening the box" involved measuring every single particle that makes up the cat and the rest of the stuff inside the box that was interacting with it. In practice this would be too difficult, although if quantum computing goes anywhere we might eventually be able to simulate some simplified version of a multiparticle "cat" system which is isolated from the external environment and therefore behaves in a quantum manner before it's measured.

I agree, that is what is behind it. But to me, that's taking science outside its own definitions, and telling reality that it must be the way we like to imagine it. Countless times we have ended up with egg on our faces doing precisely that, so why pretend we know it now? Just treat it like an optional and untestable picture.

Maybe it depends if you see physics more as a set of recipes for making predictions, or as an attempt to create a self-contained mathematical model of the universe whose predictions can be compared with the real world around us. Certainly taking any given successful model too seriously has left scientists with egg on their faces, but at the same time, I think a lot of good theoretical insights have been inspired by physicists who try to go beyond merely predicting the results of current experiments, and who instead try to find elegant mathematical models that give them a "bird's eye view" of a complete universe described by the model's laws, with experimenters and measuring devices just being part of the model (take Einstein's work on general relativity, for example). And I think if you want to do quantum cosmology you're really forced to think about what it would mean to describe an entire self-contained universe using quantum laws, with no external measuring-devices.

Anyway, my main point was just to respond to reilly's comment that 'As I think about this, I'm curious to see an example of a "non-unitary" measurement -- all measuring devices are governed by the physics we all know and love.' Do you agree with this comment? Can we make sensible predictions if we assume measuring devices are governed by precisely the same laws as quantum ones, without adopting some MWI type viewpoint?

 

[Hurkyl]

I do not get MWI at all, it makes no sense to me. I would appreciate a simple minded explanation, that could give some understanding.

I will try to restate a short description of how I understand it.

QM gives us a state space (which is usually presented as a Hilbert space), and the dynamics of how a state evolves over time. MWI says "that's it". All this talk about worlds and splitting universes is just an attempt to make a qualitative description of elements in a Hilbert space, and of how they evolve over time.

In the famous entangled photon thought experiment, once Alice measures her photon as spin up, MWI says that if you try to compute "the probability that Bob measures spin down", it will be 50%. However, MWI says that's probably not what you meant to compute -- you probability meant to compute "the probability that Bob measures spin down, given that Alice measured spin up", which will be 100%.

Our knowledge changes; collapses from a set of possibilities to a single outcome, and that collapse is indeed governed by a unitary transformation

To the best of my knowledge, this is (generally) wrong -- collapsing to a single outcome is an honest-to-goodness irreversible process (it's not merely a process statistically unlikely to reverse), even when you take the environment into account. Therefore, it cannot be described by a unitary transformation. To get an actual unitary transformation, you have to invoke decoherence -- the relative state of the system evolves into a statistical mixture of all outcomes. (The state of the system+environment is still pure, though, assuming it started pure) (Decoherence is not possible without interacting with the environment)

 

[Hurkyl]

That sure doesn't sound like "an ontology" to me, a "model" does that fine. Do you think a model is the same as an ontology? If so, we have no disagreement on the physics, though a bit of a disagreement on the language.

That sounds right -- in every context I've cared about where I've seen the word "ontology" used (and given a coherent description), it has appeared operationally equivalent to the notion of an "interpretation" from model theory.

 

[Hurkyl]

Countless times we have ended up with egg on our faces doing precisely that, so why pretend we know it now?

We shouldn't pretend we "know it now" in the absolute sense. We should pretend we "know it now" in the empirical sense -- it is the theory (and interpretation) best supported by the results of our experiments. (except, of course, we don't have to pretend)

 

[Ken G]

That sounds right -- in every context I've cared about where I've seen the word "ontology" used (and given a coherent description), it has appeared operationally equivalent to the notion of an "interpretation" from model theory.

Then I propose we simply stick to the word "model", a well known concept in science, rather than introduce extraneous philosophical notions like "existence" and "ontology". According to what you are saying here, the latter adds nothing to the well-known use in science of models, and it certainly is easily mistaken for making claims about existence.

 

[Ken G]

We shouldn't pretend we "know it now" in the absolute sense. We should pretend we "know it now" in the empirical sense -- it is the theory (and interpretation) best supported by the results of our experiments. (except, of course, we don't have to pretend)

Again, then let's just agree to say "we have a model or a theory"-- the lack of any pretense is more obvious in that statement than in any other I can imagine. This all relates to MWI, because MWI is not a model, nor a theory-- the model or the theory does not require the additional postulate you mentioned above (the "that's it" postulate). The model or theory is perfectly satisfied with "we have no idea if a wave function is appropriate for a system when we cannot use that wave function to do science". Indeed, had I said to a Newtonian-era physicist that "we need not assert that a particle has a location to any greater precision than we can actually do science on", they would likely have accused me of being too lazy or obstinate to accept that an obvious aspect of sensible axioms is that particles do have exact positions even if we can't do science on them. Indeed, that's precisely the mindset that caused such a stir in the 1920s. The lesson still isn't learned.

For example, in the empirical definition you state here, the term "interpretation" has no place, because there is no basis for saying an interpretation is "best supported" by experiment-- other than the interpretation that says what you are interpreting is what you are experimenting on (i.e., CI). MWI extends the interpretation to include things that are not being experimented on (analogous to the exact position of a particle in Newtonian physics), blithely assuming it can account for that which is not being accounted for, and settling for consistency when it should be striving for demonstrability.

Of course, any individual can say "MWI is just an interpretation, a picture I use when I set up the equations, I'm not claiming any of these things actually exist outside my head", but that is not generally how people talk about it, and indeed there are some people in the "quantum myth 1: wave/particle duality" thread who very much seem to view that general type of scientifically responsible approach as "mere memorization" exhibiting "positivist tunnel vision". I don't really blame them-- there is a tremendous lure to take our physics more seriously than is really responsible, and history has shown that over and over.

 

[Hurkyl]

Again, then let's just agree to say "we have a model or a theory"

Now I remember why I don't use the word "model" -- it has multiple meanings. In the model theoretic sense: a theory is simply a collection of statements made in an abstract language (i.e. a theory is pure syntax), a structure is some 'thing' in which the abstract language can be interpreted (i.e. it gives the semantics), and a model is simply a structure that satisfies (the interpretations of) axioms of the theory.

What a physicist calls a theory really consists of three parts:
(1) A mathematical theory
(2) An interpretation of that theory in the 'universe'
(3) Empirical evidence supporting the claim that the universe is a model of the mathematical theory

Well, (3) isn't part of the physical theory, but it's a requirement for calling it a physical theory.

 

[Ken G]

What a physicist calls a theory really consists of three parts:
(1) A mathematical theory
(2) An interpretation of that theory in the 'universe'
(3) Empirical evidence supporting the claim that the universe is a model of the mathematical theory

Well, (3) isn't part of the physical theory, but it's a requirement for calling it a physical theory.

I basically agree, but I have a few modifications to that scheme. [2] should not say "an interpretation", it should say "a set of interpretations that are equivalent with respect to application of the theory to the observations, chosen entirely by the preference of the practitioner". One does need that to know how to apply [1], but one does not need to see any particular interpretation as integral to the theory, nor does one need to think that any interpretation describes reality (a problem with how many people talk about MWI). Also, note that in [3] you refer to the universe as a model of the theory, but in fact the theory is a model of the universe. That kind of inversion of what is real, and what is in our heads, is precisely my "beef" with MWI.

 

[Hurkyl]

Also, note that in [3] you refer to the universe as a model of the theory, but in fact the theory is a model of the universe.

Only if you make a fallacy of equivocation. As I said, I am using the word "model" in the model theoretic sense -- a model of a theory is, by definition, an interpretation for which the axioms of the theory are valid. In this sense, nothing can be a model of the universe, because the universe is not a theory. But we can ask if a particular the universe is a model of a theory (under a chosen interpretation). More generally, we can apply statistical inference to experimental results to assign degrees of confidence¹ to statements of the theory, and use the given interpretation to translate back into the universe in order to make predictions.

1: Or, to sidestep the whole 'a priori' issue, we can simply look at the Bayes factors, rather than trying to derive a posteriori confidence.


Incidentally, I note the Wikipedia page on the meaning of the word that you're using (i.e. not the model-theoretic kind) explicity states that models have ontologies.