Think of it this way - decoherence depends on regions of the wave function more or less becoming isolated from one another in such a way that the results of experiments for classical things in those regions match our results. The wave function is still fundamental, but classical physics emerges as a limit.

The problem with decoherence is that the underlying physics of the wave function is still profoundly non-local in the sense that regions of the wave function don't have a simple relationship with regions of physical space.

And yet, classically, the notion of locality pertains precisely to physical space and is deeply related to fundamental physics. In fact, locality is still fundamental to the formulation of quantum mechanical theories, even if the quantum mechanical description ends up having some non-local features. And there isn't any philosophical or physical intuition that resolves this disconnect.

Decoherence has a variety of other philosophical issues. In particular, it requires that we accept the idea of the wave function (something we never see or interact with directly, for which we have no direct evidence) as fundamental and real AND that we take our day to day experiences, upon which all of our physical sciences are based, as derived, perhaps even, in important ways, not really real. In any case, the actual theoretical terms in which decoherence actually resolves the measurement paradox aren't fully understood either mathematically or in terms of the fundamental ontological status of things.

Thank you for this very well articulated response.

I don't see why locality is a requirement. What is it that makes a theory with particles being points in a six-dimensional position-momentum space acceptable, but particles being complex-valued functions over a three dimensional space unacceptable?

> it requires that we accept the idea of the wave function (something we never see or interact with directly, for which we have no direct evidence) as fundamental and real AND that we take our day to day experiences, upon which all of our physical sciences are based, as derived, perhaps even, in important ways, not really real.

I see no issue in pure quantum states being fundamental. Our day to day experiences are not compatible with a number of things we hold to be true. Take the physics of fluids for example, it suggests that liquids are infinitely dividable, which we know to be false. In that sense, fluid physics is decidedly not real. But it can also be derived as a very good approximation of the underlying reality on larger scales, similarly to how classical theories are good approximations of the underlying quantum reality on larger scales.

I do realize that my interpretation requires decoherence to work such that the pure quantum states reduce to ones that are well approximated by classical theories, and I'm not sure if we have evidence that decoherence works this way.

No mainstream physicist really objects to decoherence - it is obvious. But just decoherence doesn’t give you single outcomes - it gives you many worlds.

And people do debate how to derive our single world experience from many worlds. It can’t be done without more assumptions.

Many in this field do accept it, but say the other worlds are not real (QBism, dBB).

But that position is philosophically weak, so those against many worlds still look for alternatives.

Decoherence does not give you Many Worlds, or at least not unless you interpret it that way.

Decoherence or more strongly environmental super-selection from something like electromagnetic scattering, results in a Classical probability distribution over the macroscopic observables or more accurately renders the algebra of classical properties Boolean. This means there is no interference between the terms and the probabilities are simply ignorance of facts which have occurred.

Once this superselection process has occurred the mathematical structure of macroscopic observables is just as it is in classical statistical mechanics. There's no need to read this as multiple worlds, although you can if you want to. If interference terms persisted you might have more of a case for Many Worlds. Even then though there are other ways of reading the formalism.

I think when you add in the word "experience" you turn the physics problem into a philosophical one, and every pragmatic scientist wanders off to work on something else. Many worlds is totally sufficient for every question except for the nature of consciousness, and there are some very good reasons to believe that consciousness is non-empirical.

I don't see many-world arising from decoherence, please elaborate.

Decoherence doesn't give you single outcomes, but it gives you a classical probability distribution (like an enthropic ensemble) over pure quantum states, with the pure quantum states having reduced coherence (i.e. they 'look classical').

Classical probability distributions are nothing new, we don't need a many worlds interpretation to explain the butterfly effect.

Quantum states with a small amount of residual superposition also seem fine to me, as long as you are willing to accept that the world is ultimately quantum and not classical. That we don't see any quantum effects in daily life is just because the scales are too small, similar to how we don't observe relativistic effects because the scales are too large, or how we don't observe the atomicity of water. But in all these cases we can do experiments to reveal the true nature.

So during decoherence you don’t have classical worlds - the probabilities interfere so you can’t ignore the other terms. Over time that interference reduces, but as you say never disappears completely.

But at no point does one world even approximately emerge - it’s always many. I can say only the one I experience is real, but there’s no justification for it.

Your main problem though is thinking classically - you can't justify your theory by saying it can be reduced (after an infinite amount of time) to an old way of thinking. Classical probability is fraught with issues; just saying it’s always been acceptable isn’t true nor a rational argument.

What are the issues with Classical probability relevant to accepting there being a single world?

But, uh, a single world experience is trivially compatible with many worlds — in every world, the human is in a pure state that corresponds to a normal human experience of continuously living in a single world. If we don't require the conscience to be a single supernatural entity that flows along the timeline, selecting a world to visit at every branching point, then... that's it? Nothing else that still needs to be explained?

I apologize for the naivite of my line of thinking but wouldn't the locality of Relativity slot in at that point? Other realities could all be real, but only a subset could be real/accessible from the perspective of a given measurement device. As a guy who reads popular books on the subject to fall asleep, that seems like the obvious place for the two theories to couple. What am I missing?

Decoherence on its own still has a basis problem. You need superselection to reduce that to one basis. However this has been shown long ago (1980s) so in essence decoherence + superselection does solve these problems.

If you're not familiar with these terms I can explain.

There's intuition built on copenhagen interpretation, like probabilities and such, and people want to elaborate on that intuition.