> "That is because it is not the case that measurements have one outcome. Measurements appear to have one outcome from the perspective of a given classical observer [but actually have none]"
is a big claim, but it lacks "overwhelming evidence". Quantum theory self-consistency is a problem worthy of investigation, but achieving self-consistency is only one of the many possible valid results. This result is not needed as much as many people seem to think; certainly not as much as to reify psi function above objective results of measurements and claim the quoted part. It is a methodological error; instead of shaping the theory around the measurement results, it is rejecting the fact that those measurement results exist.
> The Born rule (which, it must be stressed, is not fundamental, but only apparent from the point of view of any given observer) follows from that, not mathematically but logically
I skimmed the paper [2] but found no such thing there. Could you locate it in more precisely or elaborate on the idea? All these kinds of proofs from algebraic formalism seem to achieve is something like "if Born's rule would not be true, we would have problems with the theory" which is not very interesting; we have some big problems with the theory even without decoherence.
> it is rejecting the fact that those measurement results exist
Well, sort of. I prefer to think of it as replacing one explanatory hypothesis with a superior one, one that is actually consistent with the evidence. To wit:
The observation that requires explaining is that classical measurements are consistent across space and time.
The usual explanation for this is that a classical objective reality exists, and that measurement faithfully reflects the state of this reality. This is a plausible explanation. Einstein believed it. But Bell's theorem and subsequent experiments show it to be false.
The correct explanation is that classical correlation emerges from the Shroedinger equation alone. There is no objective classical reality. If there were, it would be possible to construct a local hidden variable theory consistent with all observations. But it's not so there isn't.
It is only because our subjective experience is (necessarily) classical that we find all this hard to accept.
> I skimmed the paper [2] but found no such thing there. Could you locate it in more precisely or elaborate on the idea?
> But Bell's theorem and subsequent experiments show it to be false.
I think this is an unfounded conclusion. Sure, Bell's theorem and the experiments it inspired did make lots of contribution to investigation of these foundational problems.
But Bell's theorem is about a specific class of probabilistic descriptions. It does not rule out "classical objective reality" unless you restrict meaning of this term so much as to achieve that. Bell himself and many other people who studied the theorem insisted that the theorem is about local hidden variable models, as opposed to nonlocal models. Nothing general is implied about "objective reality".
On the experimental side, I am not aware of any experiment that had ruled out objective reality. How would you even test such a nebulous concept experimentally? We can test only specific predictions.
> Nothing general is implied about "objective reality".
I disagree. The fact that nature cannot be described by any local hidden variable theory tells you a lot about the nature of reality. There is a real difference between quantum randomness and classical ignorance, and so there is a real difference -- one which you can experimentally measure -- between a particle whose position you don't know because you haven't looked at the result of a measurement, and a particle whose position you don't know because it hasn't been measured at all. It is still, perhaps, debatable whether that difference lies in the particle or in you. But if you want to argue that the difference lies in the particle then the burden is on you to provide an account of when and how the transition happens. No one has succeeded in this, and it's not for want of trying.
> The fact that nature cannot be described by any local hidden variable theory tells you a lot about the nature of reality.
If assumed to be true, it means one has to use non-local models such as the quantum theory. Those do not explicitly deny objective reality. Perhaps by "objective reality" you actually mean non-contextual hidden variable theory (a theory that assigns well-defined values to all quantum observables at all times). Then yes, those are incompatible with quantum theory predictions. But I would not use the term objective reality. It is unclear and too general.
> there is a real difference -- one which you can experimentally measure -- between a particle whose position you don't know because you haven't looked at the result of a measurement, and a particle whose position you don't know because it hasn't been measured at all.
Indeed, but this difference has nothing to do with objective reality, and everything to do with the actions of the experimenter or apparatus. In the first option, there is interaction with the particle but experimenter ignores it, and in the second, there is no interaction with the particle. Of course the two situations are different and can result in different results of other measurements.
I am not denying objective reality, I am denying objective classical reality. There is an objective reality, but it is quantum.
> the actions of the experimenter or apparatus
You are missing the point. Before you can talk about "the actions of the experimenter or the apparatus" you have to tell me what an experimenter or an apparatus is. AFAICT, these are classical objects. But theory tells us, and experiment confirms, that classical objects do not actually exist. So why do they appear to exist? And the answer to that is: decoherence/QIT. The classical world is an illusion, an approximation. A very good approximation, but an approximation nonetheless.
If you have a better theory, you should publish it.
> Before you can talk about "the actions of the experimenter or the apparatus" you have to tell me what an experimenter or an apparatus is.
This is a very common error of armchair worldview building. Experiment-based sciences such as physics do not work exclusively that way; we can make progress without being so ambitious as to describe and exhaust the whole world in a single scheme. There are things in the real world that have no useful definition or model in physics, such as matter, or experimenter, or apparatus, or measurement. And this is fine, because we know them by experience, and the subject of the investigation is usually something else and rather more specific.
> But theory tells us, and experiment confirms, that classical objects do not actually exist.
Which theory, which experiment? The studies in quantum foundations showed that explaining expensive experiments with light and particles in the classical terms is hard, and some naive intuitive models, surprisingly, are not consistent with quantum theory. This is very far from "classical objects do not exist". They can easily exist, just with properties that are contextual and interactions that are non-local. And those are categories we are aware of; the possibilities are endless.
If you're thinking about the Everettian viewpoint where indeed no classical objects exist, this is just one possible theoretical scheme of thinking, not an experiment-based physical theory. There is Bohmian mechanics, where particles do exist. There are other theories where particles do exist.
> If you have a better theory, you should publish it.
A better theory in place of "classical objects don't exist" is "don't try to explain the whole world with a single scheme". There is the statistical interpretation due to Einstein, Ballentine and the Bohmian viewpoint which get us useful models and predictions in the realm of atomic physics. There is the classical theory, which gets us understanding of civil engineering, Earth-scale events and celestial mechanics. There is the general theory of relativity, which gets us accurate description of gravity. None of these overlap very well. Neither is explained by Everettian viewpoint.
> Experiment-based sciences such as physics do not work exclusively that way; we can make progress without being so ambitious as to describe and exhaust the whole world in a single scheme.
Nope The object of the game in the physical sciences is reductionism. Reducing the number of explanations required to account for observations is the definition of progress.
> "don't try to explain the whole world with a single scheme"
That's not a theory. That's throwing in the towel.
> "That is because it is not the case that measurements have one outcome. Measurements appear to have one outcome from the perspective of a given classical observer [but actually have none]"
is a big claim, but it lacks "overwhelming evidence". Quantum theory self-consistency is a problem worthy of investigation, but achieving self-consistency is only one of the many possible valid results. This result is not needed as much as many people seem to think; certainly not as much as to reify psi function above objective results of measurements and claim the quoted part. It is a methodological error; instead of shaping the theory around the measurement results, it is rejecting the fact that those measurement results exist.
> The Born rule (which, it must be stressed, is not fundamental, but only apparent from the point of view of any given observer) follows from that, not mathematically but logically
I skimmed the paper [2] but found no such thing there. Could you locate it in more precisely or elaborate on the idea? All these kinds of proofs from algebraic formalism seem to achieve is something like "if Born's rule would not be true, we would have problems with the theory" which is not very interesting; we have some big problems with the theory even without decoherence.