Bell proved that there is no local hidden variable model that is consistent with quantum theory. He said the same thing as Von Neumann (quantum mechanics can't be understood merely in terms of hidden variables), only more robustly. No new physics was discovered.
No, that's not the whole story. Bell pointed out that Bohm's theory, already known but ignored, is a counterexample to von Neumann's and others' claims on impossibility of hidden variables. He analyzed how that is possible and found out: 1) von Neumann made some unreasonable assumptions in his analysis; 2) the fixation on hidden variables is missing the point; the real surprise is that locality, not theory with hidden variables, is inconsistent with quantum theory. That's quite a discovery.
Wait a minute, my understanding of QM rejects both non-locality and hidden variables. Put it that way however, you kinda have to believe in macroscopic decoherence, that is, Everet's multiverse: there are 2 universes, one in which the cat is dead, and one in which the cat is alive, and observing one universe doesn't rule out the existence of the other. (Similarly, sending a photon (or settlers!) outside of the observable universe doesn't end its existence.)
Non-locality sounds way, way weirder to me than macroscopic decoherence. Stuff like quantum collapse is really an additional, un-falsifiable claim: why the universe would zero-out precisely the stuff that the math says we can't observe?
These two Quanta Magazine articles are probably the most accessible-with-least-compromise articles about the subject, and also include a lot of the history behind it:
It's pretty hard to say anything meaningful about quantum mechanics and above without being precise with the math (case in point, there are so many frustrating examples of people who don't have the math down making statements that aren't consistent with it).
Here's a summary, cause talking about this stuff is fun, with the caveat that it won't
Quantum mechanics in its usual interpretations involves some randomness, where a measurement can give multiple results with different probabilities. The interpretations tell us that this is truly random; that the values are not known until you measure them, and then afterwards they are known and true everywhere.
The obvious objection is "hey, maybe the values were there already, but until we measured them we just didn't know what they were". A theory with this property is called a 'hidden variable' theory.
A 'local' hidden variable is one attached to a particle, such as its velocity. If you measured two entangled particles at the same time that are some difference apart, QM shows us that the results of one can be influenced by the results of the other - for example, if you measure one particle as having a positive spin on the Z-axis, the other would have to have a negative spin, in a certain experiment.
Excluding superluminal communication (one particle did not send a message to the other), we might guess: well, one had spin up and the other had spin down to begin with, and we were just measuring them to find out which one was which.
Bell's Theorem [1] proves (in an experimentally verifiable way) that this is not the case. There is no way that local hidden variables can reproduce the results of quantum mechanics. This is one of the most amazing discoveries of the 20th century, in my opinion.
Nonlocal hidden variables still work, which is what Bohmian mechanics is. You're allowed to say "there is a variable accessible to every measurement that determines what the result of a measurement is. In Bohmian mechanics - which is mathematically equivalent to regular QM, just more complex - there is a 'pilot wave' that is computed from the whole configuration of the universe, and then is used to determine what the spin of a particule is.
Basically you get to pick between nondeterminism (randomness) and a global function that influences everything that's much more complicated.
The theory is appealing to many because it avoids non-determinism. It's unappealing because it's strictly more complicated than the interpretations that don't have this extra object, but predicts nothing beyond them. By Occam's razor it's not as good as the simpler interpretations.
It is appealing to people who really don't want to accept the possibility of randomness in the universe, which I have no problem with. Not that it's not worth time investigating it, because it's interesting.
(Some people think it's not worth splitting hairs over interpretations over QM, because they don't provide falsifiable predictions and so this stuff isn't science but philosophy. I disagree with this. Finding that one explanation is simpler than another is finding something, and constitutes, in my opinion, valid evidence for that explanation in a scientific sense.)
Just to clarify, Bell's result implies that our universe is either lacking locality or counterfactual definiteness. Counterfactual definiteness means that for any measurement you could perform there is a definite fact of the matter of what the result is prior to or without taking the measurement. The Many-Worlds Interpretation is consistent with Bell's result because it lacks counterfactual definiteness -- there's not one result of measurement; there's several results, all real!
It lacks counterfactual definiteness globally, because there's multiple outcomes, not a single fact-of-the-matter. It lacks counterfactual definiteness locally from a subjective perspective due to the seemingly random outcomes.
Isn't multiple correct outcomes still the same thing? Because you can say in advance that all the outcomes will happen, isn't it just another perspective? As a physical entity inside the universe you know that you'll have different copies of you experience a unique outcome each, rather than being able to say "I will experience outcome X".
In other words, you can say what branches will exist but not with certainty say what you'll see as a result for yourself. By the dictionary definition, isn't that still counterfactual correctness? You'll know what happen in advance, because you can calculate the possibilities.
Is the scientific definition strictly in the perspective of a physical observer?
I think we're talking past each other, and there may be some confusion about terminology. I will do my best to try to describe what's going on to the best of my abilities and see whether that answers your questions.
Bell's Theorem (also called Bell's Inequality) starts with assuming that the universe has locality and counterfactual definiteness and yields and inequality concerning correlations between certain measurements. Experiments later conclusively showed that these inequalities are violated in our universe. So, one of the assumptions of locality or counterfactual definiteness does not hold in the universe we live in. Historically, this result was used to discredit and eliminate a class of theories about quantum mechanics called hidden variable theories -- the idea that quantum mechanics is deterministic, and we just haven't delved deep enough to find out what's determining the behavior of particles.
In my opinion it's most useful to think of Bell's result as a proof by contradiction: there are a bunch of assumptions (implicit and explicit) that go into it, and we're left with a prediction that reality violates. Therefore one of the assumptions is wrong, but we don't know which one, and different interpretations of QM will have different answers to this question. In the context of Bell's Theorem, counterfactual definiteness has a specific definition, and that's from the local perspective of an observer observing from within physics, because Bell's Theorem itself implicitly assumes a single universe and goes from there.
Under the Many-Worlds Interpretation, the result of a measurement is that the observer is split, and different copies of the observer will experience all results. This is the global and deterministic view. The local view is that the observer will see one result or the other, and there is simply no fact of the matter as to why the observer sees this particular result instead of the other.
The Many-Worlds Interpretation has some advantages over other interpretations in that it's local, deterministic, and mathematically the simplest. But it rubs a lot of people's intuitions the wrong way because it posits an unbelievable multitude of copies of what we know of as the universe.
It's for comments like this that I bother reading the comments here on HN. Thanks for distilling a complex subject into understandable-to-a-layman terms.
Agreed. I particularly valued this part, which helps me grasp some other content posted here:
"Bohmian mechanics [describes] a 'pilot wave' that is computed from the whole configuration of the universe... a global function that influences everything".
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The theory is appealing to many because it avoids non-determinism. It's unappealing because it's strictly more complicated than the interpretations that don't have this extra object, but predicts nothing beyond them. By Occam's razor it's not as good as the simpler interpretations.
I'm not a physicist, but doesn't classical QM have the problem of the "collapse of the wave function", i.e. "suddenly" Schrödinger's equation does not hold anymore - a problem that the De Broglie-Bohm theory does not have? Shouldn't this be considered as a strong sign against "typical" QM formulations and for the De Broglie-Bohm theory?
The wavefunction collapse is messy and awkward. It's taken as an axiom, basically, in the Copenhagen interpretation. It's not as awkward as introducing another equation and set of rules to skirt around it, as Bohmian mechanics does, in my opinion.
Many-worlds - which starts with being a lot more rigorous about what 'measurement' is (entangled yourself with the system in question) is much simpler than either, I think.
My general impression is that Many-Worlds is getting more popular as physicists make precise how entanglement, measurement, and decoherence exactly work. I think it'll supplant Copenhagen as what we teach in intro classes eventually. But this is just my impression from the physics blogs and papers I've read; I'm not a physicist myself.
Classical QM (Copenhagen, if I'm not mistaken) does have that problem. The collapse is indeed an additional hypothesis done on the part of the wavefunction the math already says we cannot observe. As always, unfalsifiable additional hypotheses are bad.
I can't speak for De Broglie-Bohm, but it would seem that theory also have a similar strike against it: the math is more complex than the equations QM physicists are familiar with. It's just not the simplest theory that fits the observation.
The obvious alternative is to just stick to the math. Problem is, the simplest math that explains our observations implies a universe that forks all the time. For some reason, possibly the intuition of a unique universe, many people cannot accept that.
* caveat that it's not enough information to let you make any concrete predictions
Other afterthought:
The pilot wave model is definitely not directly compatible with relativity, since it purports to have a function 'defined everywhere' at once, and the concept of 'everywhere at a moment in time' doesn't work in relativity. There are apparently methods of working around this, and they're apparently very complicated.
that's not entirely true. Non-einsteinian relativity allows for functions 'defined evewyhere' at once. An example is tangherlini relativity, which allows for anisotropy of the speed of light (and is not inconsistent with contemporary observations IIRC)....
There was a philosophical disagreement at the turn of the century where a bunch of ho-hums (including Einstein) decided to speak for everyone by saying everything here in this reality is discrete and isn't affected by anything anywhere else. A lot of work went into proving this over the last 100 years, with mixed results that just led to more and more testing at higher energy levels. With the Higgs, we started thinking we were "stuck" with our current theories. With the EM Drive, we're seeing things that don't fit in that model.
Going back to when the original disagreement started, there were a few physicists like Bohm and de Broglie who thought there was more than met the eye going on with discrete particles past a certain size limit. Their theories included a medium, or ether, in which all of this exists. To understand it a bit better, you might want to check out the "two slit experiment". There's one on Youtube that covers doing the experiment with photos, electrons, buckyballs and polarized lasers. Basically, when you understand the experimental results, you understand that matter acts like a wave sometimes and a particle others, even at large scales.
Those waves in the two slit experiment are likely responsible for the forces we're seeing in the EM drive. Also, I'm sure I've left out important bits here, but that's the basic idea.
Physics does not seem to operate on conceptually simple terms. Three options, it is simple when approached from some way we have yet to think of. There is some inherent mistake we are making with a huge range of current experiments. Or, as seems most likely the universe operates very differently on different scales making it conceptually difficult to deal with.
Regular QM has non-locality. Entanglement is non-local, at least any way that I've heard it to explain things like delayed choice erasers and the behavior of entangled anyons in confined electron gases. (Anyons (particularly fused anyons) themselves seem to have nonlocal quantum vales assocaited with them.)
So we meet again, SomeStupidPoint. :) I still uphold my claim that regular QM is a local theory and just found time today to reply to your comment on non-locality that you posted a week ago:
Bell's Theorem states that there exists no local hidden variable theory for QM. AFAIK that implies that QM must be non-local because the other possibilities of a local theory can be reduced to a hidden variable theory or have no evidence for them.
Not true. Bell's result precludes local realism. So physics is either not local or lacks realism (counterfactual definiteness). The Many Worlds Interpretation keeps the locality but lacks counterfactual definiteness. The fact that MWI is the only interpretation that manages to hold onto both determinism and locality is what makes it so aesthetically pleasing.
Care to make rigorous how other interpretations require FTL signaling? For that matter, can you actually rigorously explain what it means for worlds to "branch", or why Born probabilities should be interpreted as though they are probabilities in MWI? Saying "all the possibilities actually happen!" doesn't really explain the correlations we actually observe in any interesting way.
You make some good points. Regarding the Born probabilities, the extrapolation of Schroedinger equation to the whole universe seems to make the concept of probability superfluous and the Born rules lose their sense.
