What are the scientific arguments against decoherence? What do up-to-date theoreticians think?
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.
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.
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 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.
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.
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.
If you're not familiar with these terms I can explain.
Edit: Just to be clear, I'm aware that Bell's theorem says that QM must either break locality or realism, but I don't really understand why it can't break locality. While incredibly inconvenient, wouldn't that solve the problem? Again, I realise I'm naive, so I don't actually suppose my line of reasoning is correct ;-)
This makes no sense unless the speed of light is a fundamental physical constant, so that motion in general depends on the speed of light, which is what special relativity postulates.
Now there are ways to have a special kind of non-locality that do not violate special relativity - you can have phenomena that happen at infinite speed, but only if they do not carry mass or energy or any information at all. The common interpretation of wave-function collapse is an example of such a phenomenon.
I'd also note that the famous E=mc^2 is also a limit on speed, since kinetic energy (mv^2/2) is part of the total energy of an object.
I think that may be the reason it's not very popular: ok, so we've got these faster-than-light pilot waves, but we can't actually use them to do anything faster than light. They're just there for bookkeeping. (That said, Many Worlds suffers from the same problem, but it's very popular. They're two different ways of slicing up the same equation. You pick whichever one suits you.)
If the simplest and most consistent math is a non-physical pilot wave, I don't think this really matters if it lets you calculate something more easily or correctly. I don't personally know how to use them (my five QM courses used traditional techniques) but if they give useful results it hardly matters if they're "real".
My good friend did his undergraduate thesis by noticing that Clebsch–Gordan coefficients could be used to describe grain boundary orientations in polycrystalline materials. Doesn't mean grain boundaries have spin. It's just math that was convenient and worked well.
That said, physics advances do sometimes come from asking "What if X is real?" The positron and electron spins are both poster children for that. Instead of just shutting up and calculating, people focused on the part of the calculation that seemed to imply the existence of an unobserved thing. We could, in fact, have kept going with a physics in which positrons were merely calculation conveniences; that physics is valid. But we might not have discovered the Standard Model that way.
So I'm of two minds... and in a lot of ways, I'm not really entitled to be of any minds, since my formal education stopped at undergrad, and I'm no longer capable of doing even that much math. I get leery when people with even less education want to "understand" without doing any of the math, because I fear that the best of explanations will only mislead them.
It's not like it is exclusive, everyone thinks a bit different thankfully. Like your example of the positron and electron seems fine; math and experiment in a cycle of discovery. You wouldn't know to look for a positron if you didn't study the electron experimentally and try to come up with some math for it.
The big problem with infinite speeds is that, somewhat like superdeterminism, they mean that you can't do fully controlled experiments. If effects can propagate at infinite speeds, the whe universe has an impact on any experiment, including the state of your measuring apparatus and so on. That doesn't make them impossible, but it explains why they are disliked in theories.
\* even with Newtonian physics, the universal attraction of any object does have non-0 values everywhere, but we know that the influence is negligible. However, with global hidden variables, the speed a billiard ball will take when I hit it may depend on the size of a planet in a different galactic cluster.
Every experiment does depend on the entire state of the universe, even in QM, but those influences are typically small due to symmetries. At the quantum level, many of these symmetries no longer apply.
In any case, quantum field theories are good at predicting stuff but almost certainly not descriptions of the true fundamental dynamics of the universe, given their known and relatively well understood divergences.
I disagree, with the following example to back up why I believe it is less weird.
Superdeterminism can mean that faraway events can be correlated by a common ancestry. For instance: if you suddenly create a massive object, it will attract massive objects indiscriminately spherically; most points in space will be eventually affected, and so, they all are limited in the space of possibilities, no matter whether you can actually detect gravity.
In the case of quantum mechanics, there may well be some currently-undetectable field similar to the gravitational one, which is very chaotic at a nanoscopic level, but that is severely constrained in the shape it can form, even across large distances.
It is similar to how a large-space LCG (the PRNG) may look extremely random, but if you plotted consecutive numbers as coordinates across the complete cycle, you would get a lattice. Locally chaotic, but globally constrained.
On the other hand, non-locality means superluminar information, which really breaks the common understanding of spacetime and of causality.
I'm listening to the Into to QM course from mit's open courseware [0] and I have to say that QM represents a complete break with the classical past, not because of a scientist's ambition or a quirk of history, but because the experimental evidence demands it. The evidence results in a few postulates, and QM is really the only theory that satisfies the postulates, in the sense that any theory that satisfies those postulates will look like Schroedinger's eq. The story is not over at all, we're still very much at the beginning of understanding it.
[0] https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-s...