What is controversial is what you mean by a "clear link." Who decides what forms this link must take, and when is it clear versus murky? I would say that MWI does have a clear link-- they say closed systems (and systems whose only external interactions can be treated as specified rather than self-consistently evolving, as with a potential function) evolve by the Schroedinger equation, and that when an observer (or apparatus) becomes part of that system in ways that are not being tracked in detail, the Born rule applies for attributing the measure of the various outcomes the apparatus might be considered to follow when all that missing information is not being tracked. That seems like a clear link to me, even though it doesn't explain the Born rule any better than CI does. If MWI users want a better explanation of the Born rule, it's not because they have to have one to make MWI a valid interpretation, it's that they need one to make MWI a new theory that could potentially make different predictions and guide us into seeing how to test those differences. Successful testing would then make MWI a clearly superior theory, rather than just an alternate interpretation.Yes, in order for a conceptual model to qualify as an interpretation of a theory, we must establish a clear correspondence between the elements and features of the model and the empirical content of the theory, which is generally expressed in mathematical terms. I wouldn’t have thought this was controversial.
The point is, only better predictions are demonstrable, not better interpretations. I would argue that anyone who sees a link, and uses it when they write down the equations, is following their interpretation without any need to demonstrate that their interpretation leads to those equations because interpretations always fall short of doing that. Interpretations are fundamentally subjective, and fundamentally ad hoc.
Sure, but those are formulations, meaning they are equations. We can all agree on the equations of quantum mechanics, they're in the textbooks. What you are saying is that a valid interpretation of a given formulation must demonstrate a correspondence with that formulation. You are in effect asking for the postulates of the formulation to follow from the interpretation! That never happens, it would be backward. We don't interpret Newton's laws as forces on particles, and that gives us F=ma, we start with the formulation (F=ma) and interpret the meaning of the letters. The interpretation gives us a sense of cognitive resonance when we write those letters down, that's all it does. People who use the MWI interpretation get that sense of cognitive resonance when they write the equations of quantum mechanics, so they are using an interpretation-- they can no longer demonstrate that the equations they are writing down somehow follow from that interpretation than you can demonstrate that F=ma follows from the concept of pushing on particles.For example, there is no difficulty translating between a force/vector formulation of mechanics to a Lagrangian formulation. This is a perfectly well defined correspondence. No problem at all.
To elaborate, let's say I am a strict "shut up and calculate" empiricist. I say that F=ma is just some mathematical symbols used to translate between the outcomes of experiments. I have my initial data, and my calculated prediction, and I compare that to some final data. That's it, no forces, no particles, nothing-- just letters and data. Further, I claim that this is all anyone can ever demonstrate that the physicist is actually doing. The rest is just some kind of self-delusion they carry in their minds, a bunch of interpretations that fail the very test you have put to them-- that they must establish a clear correspondence to the letters in the formulae. If I say that no such clear correspondence is possible because there's no such thing as any of those make-believe notions like forces or electrons, there is not a single thing you can do to demonstrate that I am wrong. If physics really stuck to what is demonstrable, then it would involve no interpretations of any kind. That's what "shut up and calculate" really means-- all interpretations are invalid at the level of demonstrability. So we either stick to that, or we take the alternate approach of recognizing from the start that interpretations are not demonstrable, and use them to get that sense of cognitive resonance that we crave.
There is no other mathematics associated with their model-- they don't have a model. They have an interpretation of the exact same mathematics. If they had any different mathematics, or anything that was demonstrably a different model, then it would be a different theory. If it makes all the same testable predictions, then it is the same theory, and any differences in how it is imagined is just an ontological difference, a purely philosophical difference. This is the only way to enforce a line between science and philosophy.So hopefully we agree that an advocate of MWI is entitled to make that kind of calculation. But they never do. Instead, they use the von Neumann recipe, and they justify this use by claiming that the mathematics associated with their model reduces to the von Neumann recipe (at least for all practical purposes). But does it?
If those mathematics are different, then what is the difference? I think we agree that if you look over the shoulder of an MWI proponent as they solve some problem on a quantum mechanics final exam, you are not going to have the slightest idea if they are an MWI proponent or a CI proponent. So I reject the idea that there is a "mathematics of MWI", if there were you could point out on their paper "that's where they used the mathematics of MWI." There won't be such a place.We have two mathematical formalisms, and a claim that one entails the other. This is easy to confirm in the case of force/vectors versus Lagrangian, but not nearly so easy to confirm for the mathematics of MWI and CI.
So you are claiming that the reason for this is they were really using CI, not MWI, they only deluded themself into thinking they were using MWI, but in fact the mathematics they did use is only consistent with CI. CI has now claimed the quantum mechanics theory, from your perspective, so of course MWI must be wrong if it isn't allowed to use quantum mechanics. But then you have to point to the place where they used an equation that was not consistent with MWI. That would have to be the Born rule-- you are claiming MWI has no Born rule. But it does-- it just uses the Born rule postulate to determine the measure of the probabilities that associate with the fragmented "worlds."
Note that is just exactly what CI would do, and for no better reason, the only difference would be that the CI user would be imagining in their head, when they write down the Born rule, that this corresponds to the entire reality. The MWI user imagines it corresponds to a "world." The answer to the final exam question, the "empirical content", is exactly the same either way-- nowhere in that correct solution will we ever see what is going on in the imagination of the testtaker, we just don't get to see the interpretation because it was never anything but a source of cognitive resonance that might have helped them imagine what the letters they were writing down mean. Since the letters are the same, they translate immediately across interpretations, and no one is the wiser. Much like the word "red" we use when we are describing our experience of color.
The von Neumann recipe is a postulate of MWI just like it is a postulate of CI, all that is different is what that is imagined to mean. The MWI user thinks the Born rule means something different, and might someday yield to some deeper derivation as a result, but they still use it all the same-- begrudgingly. Just like how someone might use F=ma begrudgingly even if they believe the real ontology is least action-- they know that F=ma makes equivalent predictions to any approach that would fit in their ontology, so they use it, even though it is not in their ontology. Same for the Born rule.We lack any demonstration that the axioms of MWI (whichever version you prefer) actually do lead to the von Neumann recipe, even just "for all practical purposes".
I believe that is because they are talking about something different from what you are. They want something more from MWI than just another valid interpretation of QM! They want it to guide them to some deeper message that QM is trying to tell them, something CI is not hearing, but there's no way to demonstrate it is really doing that, until MWI (or CI) inspires some new theory that is actually different from QM and makes some testable prediction that has been verified.This is why so many volumes have been filled by people striving to establish that correspondence, or at least to make it more plausible. I get the impression that you would advise them to stop wasting their time, because you think it has already been sufficiently established. But I suspect that even most advocates of MWI would not agree with that, and certainly the critics would not agree.
It includes a very important change-- I have stricken out your objective requirement for "demonstrably clear connection" in favor of the purely subjective criterion that it "uses the same mathematics but imagines that it means something different." Sort of like how, if you watch someone solve an F=ma problem, you never have any idea what they imagine that "F" means.Actually I agree with your standard, i.e., an interpretation needs to "give us a sense that we understand the meanings of the operations we are carrying out". That's essentially a paraphrase of my criterion.
Yes, we differ on what requirements we need to satisfy to claim we have an understanding. Let me give an example. Let's say someone back in the day of Newton, let's call him Jim, was told about F=ma and how great it works, and Jim said he will be happy to use F=ma, but he just can't interpret it as forces that are pushing on things. Jim has a philosophical objection to the idea that objects can really have that kind of power over each other, they are just dumb inanimate objects. Instead, all agency must stem from nature herself, and nature must create in some sense the "best of possible worlds". So Jim imagines that objects follow F=ma not because there really are forces on them, but because nature is finding some kind of extremum in some quantity that has not yet been discovered. Jim interprets the "F" as just an illusion of the presence of a force, he feels the F is emergent from some effort by nature to find an extremum. It doesn't matter that Jim cannot say what that extremum is, it's just an interpretation of the meaning of F, based on his philosophical priority that everything that happens must trickle down from nature herself, nothing can be what one object is doing to another because objects don't have that ability.I think we differ only in having different ideas about what it takes to "give us a sense that we understand" something. For me, I don't have that sense unless I can see how the terms of my equations correspond to the features of the conceptual model in some definite way.
So then, you come along and say Jim's interpretation is not valid because he can't say what is being minimized. But he says he doesn't need to, it's just what he's imagining when he writes down "F". All the same, he's motivated to try and figure out an extremum principle that could generate the same equation, and he eventually finds action, and then he goes on to use that in deriving relativity and quantum mechanics-- which actually are new theories in which minimizing action has some greater importance than just F=ma. You can say that only then has his interpretation become valid, but he says no, that was only when it became powerful. That's what MWI proponents are trying to do (and similarly for some CI proponents, like Fra)-- they are trying to make the interpretation powerful instead of just passively valid. Power is the only thing that is demonstrable.
MWI isn't really a model, but I agree that these are obstacles for MWI to become powerful. Still, shouldn't we look under every stone? You don't need to put your own stock in that avenue, but it's best if someone tries it.Yes, I only mention it to emphasize that the task of reconciling the MWI model with our actual computational physics is even more challenging than just the non-relativistic version might suggest, so we are very far from being able to really justify MWI as a viable model.
Yes, the deviation does constitute a signature, collapse constitutes a signature that the observer (or his proxies) have become part of the system and the Schroedinger equation only applies when no measurement is occuring (in CI, where the truth must result from that interaction, rather than preside in spite of it).So if v does not interact with anything in a way that leaves a signature or trace, is that a strong enough condition to say that v(t) evolves in accord with Schrodinger’s equation? If not, wouldn’t the deviation itself constitute a signature?
You are asking Clifford to have a new theory of gravity, not an interpretation of Newton's gravity. An interpretation would go like "the reason all objects follow the same paths in space and time under gravity is because gravity is nothing but a redefinition of the meaning of an inertial path." That's it, that's all one would need to say, it's an interpretation of mg = ma by cancelling the m's and writing it a-g=0. There is no requirement to provide any equation to support that interpretation other than that.Well, if someone like William Kingdon Clifford, who vaguely imagined that gravity might be interpreted as curvature of space, had written F=mg and claimed that this equation was consistent with his conceptual model of gravity, he would indeed have been lying, because he could not establish that correspondence.
True, but Einstein was not credited with finding a new interpretation, he found a new theory. I would say a better analogy to a new interpretation was D'Alembert's. He replaced F=ma by F-ma=0 and interpreted ma as some kind of inertial force, then he said that the principle is that all forces always balance. He never provided any reason that there ought to be some inertial force called ma, he just asserted that one could look at Newton's laws that way.It was Einstein’s great achievement to show – explicitly – precisely how the 4-dimensional tensor equations of his metrical theory of spacetime curvature actually do reduce to the simple Newtonian scalar equations in the lowest order approximation.
That's all MWI is doing-- saying you can look a different way at the postulates of QM, and even though you still use the same postulates, you think they carry a different message (like D'Alembert thinking the message is that forces are always in balance, we live in a balanced universe). It is only the ontology that is different, not the mathematics. When the mathematics is demonstrably different, you have a new theory.
Then why doesn't CI have to start with the observer and show how making an observation collapses into an eigenstate? If CI is allowed to assert the Born rule by fiat and interpret what is real is what happens on the observer end of that mathematical description, then MWI is allowed to assert the Born rule by fiat and interpret whas is real is what happens on the wavefunction end of that mathematical description. It is only if someone wants to argue that MWI is a different theory, or a superior interpretation at least, that they would need to do what you ask. They would like to do it, no doubt, but failing to do so does not render the interpretation invalid, and more than failing to account for why the Schroedinger equation applies to unobserved wave functions if it is their collapse that is real renders CI invalid (which anti-CI people claim all the time).You need to start with the wave function and Hamiltonian and initial conditions of the entire universe (none of which are knowable), and then show how the Schrodinger evolution of this wave function, taking decoherence into account, leads (at least approximately) to the time-asymmetrical behavior and empirical content represented by the von Neumann recipe.
Not quite, what I would do is say that I see no personal value for me in the interpretation that you suggest. But if a thousand theoretical physicists interpreted quantum mechanics the way you were describing, and achieved some cognitive resonance by doing so, I would probably have to conclude I couldn't find any value because I simply didn't understand the interpretation you were suggesting.If I tell you I can parse the equations of quantum mechanics from contemplation of my dog Smithers, you would dismiss my claim out of hand – and rightly so.
I have to to use it myself, but I don't have to convince others. One can point to a problem with an interpretation without concluding that the interpretation is invalid, because validity of an interpretation is not demonstrable, it is highly subjective.So you can’t maintain the position that you will accept any claim that any model represents a legitimate interpretation of any theory. You do have standards, i.e., you require some rational basis for thinking the model really is a representation of the theory.
That means the interpretation doesn't work for you-- you see those conditions as a stretch. Others don't think quantum mechanics could work as well as it does if those things weren't true. Myself, I'm agnostic about it-- I don't see the point in building a world view that involves those things being true, but I don't think interpretations are for building world views. I think an interpretation is nothing other than a way of thinking about a theory, a way to get the theory to show you a different angle of itself.You are convinced that if someone actually could make sense of the Hilbert space and Hamiltonian of the entire universe, and if they could somehow divine the initial conditions of a universal wavefunction, such that, subject to the Hamiltonian under the Schrodinger equation (or, better, it’s relativistic counterpart) it leads to suitable time-asymmetric evolution, and that the result, taking decoherence into account, would yield something whose components or projections into some suitable sub-spaces, selected, combined, and arranged in some suitable order, would reduce in some approximation to the usual equations of quantum mechanics. To you this is sufficiently self-evident that you’re willing to take it as given. It isn’t that self-evident to me.