How certain are we at this point, that there are no hidden variables in quantum mechanics?
I'm asking because I read an article a while ago about some advances in higher-dimensional math that turned out to simplify certain quantum mechanical computations [1]. And it got my hopes up that we might eventually see quantum mechanics explained this way - e.g. as a projection/cross-section of higher dimensional phenomena into our 3D/4D reality. That the "weirdness" of QM could be explained by the effects happening in higher dimensional space. But from our perspective those would be hidden variables, so I'm curious whether we've been able to rule those out completely, or only partially?
I just want to correct some comments that say we are certain there are no local variables and that they have been ruled out experimentally.
This is false information and even Bell himself knew it:
"There is a way to escape the inference of superluminal speeds and spooky action at a distance. But it involves absolute determinism in the universe, the complete absence of free will."
Regarding unfalsifiable, from [0] "If engineers ever succeed in making such quantum computers, it seems to me that the CAT is falsified; no classical theory can explain quantum mechanics." By "such quantum computers" he means computers that can run Shor's algorithm. "...but factoring a number with millions of digits into its prime factors will not be possible – unless fundamentally improved classical algorithms turn out to exist."
Or right in the page I linked: "This makes it possible to construct a local hidden-variable theory that reproduces the predictions of quantum mechanics, for which a few toy models have been proposed."
From Wikipedia about superdeterminism:
"By postulating that all systems being measured are correlated with the choices of which measurements to make on them, the assumptions of the theorem are no longer fulfilled"
By assuming superdeterminism you can indeed construct a valid local hidden variable theory. But there is no way you can say superdeterminism is by itself a local theory, and no physicts will call it so. It's as far from "local" theory as possible, it's actually global.
So, what is supposed to be wrong with "the complete absence of free will"?
It reads like some sort of religious objection. If the data leads you there, you go there.
Sabine, particularly, goes there. Apparently there are no actual problems with giving up the illusion of "free will", whatever the hell it was supposed to mean in the first place.
Distaste seems pretty rich coming from people promoting MWI.
Chess is superdeterministic as all the moves are known in advance, but free will is still there. The "reality" might be such a superdeterministic playground that simply tells what the possible next moves are, while the players keep a pointer to one "chess" position and advance it one step at a time with their free will.
iirc local hidden variables have been ruled out experimentally. global hidden variables have not, and form the basis of Pilot Wave Theory, but pilot waves have a lot of unresolved issues, and there's no full theory that explains what MWI and Copenhagen do.
I think, ultimately, there are only 3 possible explanations for the paradoxes of the quantum world. 1) superdeterminism (everything including our choices in quantum experiments today were fully determined at the instant of the Big Bang), 2) something "outside" our observable reality acting as a global hidden variable (whether something like the bulk in brane cosmology or whatever is running the simulation in simulation theory) or 3) emergent spacetime (if space and time are emergent phenomena then locality and causation are not fundamental).
Until it's "Bell's Law", I think we should consider quantum mechanics a statistical approximation. Every time QM is questioned people point to Bell's Theorem and challenge anyone to disprove it, when it seems to me that it is QM which is making extraordinary claims that require extraordinary evidence. Every theory of physics has at one point been "the ultimate", and they have all been replaced by better theories as our ability to investigate has expanded.
The only claims QM make is about probabilities of measurements, and you can verify these experimentally, as we did, repeatedly. You are free to interpret these as many universes, pilot waves, or fairies playing tricks on scientists, suit yourself.
But we know for sure if it's fairies (or any other hidden variables) - they have to conspire globally. Cause otherways the experimental results couldn't happen the way they did cause fairies in place X wouldn't know which way to nudge the results to be consistent with the way fairies in place Y nudged them.
No. Local hidden variables can not explain experimental results of QM without implying something many people find distasteful. But no one has demonstrated any objective reason why that distaste has anything to do with the universe or its laws.
So, another way to say it is local hidden variables do explain experimental results of QM if you are willing to accept the implications, none of which contradict observation.
There is this essentially religious notion of "free will" that physical theories have been obliged to preserve, for no objective reason. Hidden variables are inconsistent with experiment only if you demand "free will" be preserved.
You call an interpretation you don't like "nonsense". But calling a thing nonsense is not a way to refute it. Relativity was nonsense, once. Can you devise an experiment that may produce results inconsistent with the interpretation?
That's the same argument every model has made for the history of science, but :shrug:. The value of a model is its predictive capability. Thinking any one to be absolute truth blinds us from progress.
I'm asking because I read an article a while ago about some advances in higher-dimensional math that turned out to simplify certain quantum mechanical computations [1]. And it got my hopes up that we might eventually see quantum mechanics explained this way - e.g. as a projection/cross-section of higher dimensional phenomena into our 3D/4D reality. That the "weirdness" of QM could be explained by the effects happening in higher dimensional space. But from our perspective those would be hidden variables, so I'm curious whether we've been able to rule those out completely, or only partially?
[1] https://www.quantamagazine.org/physicists-discover-geometry-...