Can someone explain Quantum Bayesianism to me?

The latest issue of Scientific American had an article on it, and I’m not sure I even understand what it’s claiming. Superficially it sounds almost like solipsism. About all I understand is that it claims that DeBroglie wave functions are subjective on the part of the observer.

THANK YOU for posting this! I read the same article, and came away with a great big “Huh?”

How does this new (?) approach resolve the double-slit experiment? Aren’t we “really” seeing interference fringes? Those surely aren’t just in our heads.

The approach may be valid, but the article needed a lot more care in explanation!

This is definitely one for Half Man Half Wit, but this is my limited understanding of it:

The basic idea, I believe, is to frame quantum theory as if it were a guide for an observer to bet on the outcome of experiments (of course this is more of an analogy as betting does not actually comes into it). It shares with the Copenhagen interpretation the idea that the important information about a system is not the quantum state itself, but the probabilities of getting different results, but goes further and tries (I say try because it hasn’t been proven that the method it uses works in all cases) to frame the formalism of quantum mechanics in terms of probability, so that the quantum state is merely a useful calculational tool that can in principle be ignored completely (though each allowable probability distribution will be associated with a mixed or pure quantum state).

Obviously there is a heavy emphasis on probability in the approach and probabilities can be subjective. For example let’s say a red and a black dice are thrown and there are two gamblers. Due to a brief slip by the croupier, one gambler knows that one of the dice is a six (but not which one) and the dice are fair, the other simply knows the dice are fair. The probability that the red dice was a six for the first gambler is 6/11, but for the second gambler the probability is 1/6.

QB similarly says that the probabilities as to the outcome of the same experiment may not be the same for two different observers, as for example one observer may’ve conducted a previous experiment which alters their knowledge of the system. As each probability distribution is associated with a quantum state, this makes the quantum state subjective too. In particular this tackles the Wigner’s friend gedanken experiment in a consistent way that doesn’t invoke consciousness, multiple Universes or fundamentally alter quantum theory by invoking spontaneous collapse.

It may seem like solipsism, but a proponent of QB would argue that quantum theory s an observercentric theory as it’s predictions are the probabilities of different results of an experiment from the point of view of an observer, which from a subjectivist Bayesian p.o.v. would be interpreted as the strength of belief of the observer as to each different result. They would also say that given this, you would not necessarily expect to derive the concept of an observer from quantum theory itself.

Okay, thanks for making it perfectly clear.

OK, I’ve gotten this far: Bayesian statistics is one particular school/philosophy of interpreting probability. Quantum mechanics involves the probability of certain measurement outcomes being observed. QB is what you get when you apply the tenets of Bayesian statistics to Quantum mechanics.

Well, I can’t say I’m an expert, but the broad outline—adding to what Asymptotically Fat has already said—is roughly the following:

Probability, in the classical case, can be interpreted in various ways. The most widespread approach is perhaps the frequentist one: probabilities are simply the limit of relative frequencies of certain occurrences. That way, the sentence ‘a fair coin comes up heads with probability 1/2’ means nothing else but that on a sufficiently large number of throws, about half of them comes up heads.

But another interpretation is related to knowledge about something. As a way to illustrate this, one often uses metaphors related to placing bets on outcomes—given what you know about the system, what sorts of bets should you accept? If you believe a coin to be fair, for instance, anything but an even money bet would be stupid; but if you have observed a series of coin throws, and have a reason to believe that it’s biased (say, heads appears more often), you’d be justified in placing higher bets on heads.

Now, quantum mechanics is a fundamentally probabilistic theory: for any given occurrence, it only gives us a certain probability (which may be one). Quantum Bayesianists interpret this as meaning that the quantum state or the wave function, i.e. the mathematical object we use to calculate these probabilities (via a prescription known as Born’s rule), is itself just an encapsulation of our knowledge about the world, and not in itself a kind of ‘thing’ in the world—wave functions don’t describe any real, physical wave (thus, the interpretation is of a kind known as ‘epistemic’, as opposed to the ‘ontic’ kind that take the wave function to be, in some sense, ‘real’). Note that this does not mean that the observed effects aren’t real: after all, those are what we calculate the probabilities of. It’s just an instrumentalist or operationalist take on these phenomena: quantum mechanics doesn’t tell us what happens to produce them, it just provides a recipe to calculate what we should expect to observe.

Specifically, quantum Bayesianism postulates a set of ‘Bureau of Standards’-measurements, and aims to interpret the quantum state as giving the probabilities of their outcomes (though as Asymptotically Fat notes above, it’s not known—though strongly conjectured—whether these special measurements exist in all cases). So, the quantum state is nothing but a list (Schrödinger called it ‘a catalog of our knowledge’) giving the probabilities of making certain observations, i.e. of the standard measurements yielding certain values.

The charm (to its proponents) of this interpretation is the potential solution to several philosophical problems quantum mechanics brings with itself, among them the infamous measurement problem: the question how an indefinite quantum state suddenly upon measurement produces a definite outcome. On a quantum Bayesian interpretation, this is no problem at all: it just encapsulates the fact that when you learn something new, you have to adjust your beliefs. More accurately, in Bayesian inference, you start with ascribing some probability distribution to the system you are considering. Then, upon receiving new data, you change—‘update’—that distribution to reflect this new data (I’ve described this somewhat in detail in this rather lengthy OP). This is a process that is discontinuous and instantaneous, and as such, looks just like the infamous ‘wave function collapse’.

So, to summarize, quantum mechanics is a calculus to make reasonable predictions about measurement outcomes; whenever we learn new stuff, we change our beliefs, and thus, future predictions.

So… is this a theory within physics, or is it a philosophical standpoint about the nature of human knowledge? It doesn’t seem to actually predict anything new. I mean, I could adopt a nihilistic pose and say that since existence is meaningless and ultimately nothing matters, my take on the meaning of quantum physics would be “don’t worry about it”. That’s not particularly useful.

As a non-expert, this sounds like a different statistical framework for hidden variable theories. How does it differ? I thought that local hidden variables have been essentially disproven.

(Being a biologist who wallows in uncertainty and hunches I have a fondness for Bayesian approaches. But I really only know just enough to be dangerous…)

It’s an interpretation, so no, it doesn’t predict anything new. It’s a way to cope with the problems of quantum mechanics, which its proponents claim is more sensible than alternative approaches. Of course, that’ll depend on taste somewhat.

Quantum Bayesianism doesn’t make any kind of ontological statement in itself, i.e. it carries no commitment regarding what actually goes on. To the quantum Bayesianist, what’s real is ultimately just the ‘click’ of a detector (or lack thereof), and quantum mechanics is just a formal tool to predict the statistics of these clicks. There might be some more fundamental theory we don’t know yet (in which case it won’t be a local realistic theory, as you note), but that question is simply left open. If there is some philosophical tendency inherent in the framework, it’s probably roughly the view that absent of measurement, there simply is no fact of the matter regarding ‘what’s really going on’.

The basic idea is to take the rules of Bayesian interpretation along with a philosophically subjectivist interpretation of those rules and then to add further rules that are derived from the formalism of quantum mechanics.

Something human accessible (no offense) from [physics world](http://boards.straightdope.com/sdmb/In less than 100 seconds, Daniel Mortlock ponders whether the quantum wavefunction could be more than a mathematical function.).

Spoiler - that’s sort of a fib, but still worth watching.

Just as a general-purpose reminder, deciding between different interpretations of quantum mechanics is a philosophical matter, not a scientific one. All of the mainstream interpretations produce exactly the same measurable outcomes, and therefore no measurement can prove nor disprove any of them. Since it doesn’t change anything scientifically-speaking, most physicists prefer not to hold to any particular interpretation at all, in what’s sometimes called the “shut up and do the calculations” interpretation.

Now, sometimes thinking about a particular interpretation makes it easier to figure out how to set up a particular calculation (the same calculations can be done in any interpretation; sometimes it’s just easier than others), and in such a case a physicist might temporarily make use of that interpretation, but then might just as easily switch to some other interpretation for some other problem.

Sometimes, also interpretations may suggest or facilitate new technical advances—quantum Bayesianism has been quite fruitful in that regard, providing a quantum analogue to the de Finetti theorem and introducing the notion of symmetric informationally complete positive operator-valued measures (SIC-POVMs), the aforementioned ‘bureau of standards’-measurements whose properties are interesting beyond just this use.

Well, by gum, I’m accepting the Many Worlds interpretation.

Well, by gum, I’m rejecting the Many Worlds interpretation.

Here’s an interesting experiment that apparently creates a 2d visual representation of a hydrogen atom’s electronic states.

Orig. article

Wouldn’t this sort of thing tend to undercut more subjective interpretations?

Generally speaking interpretations of QM do not differ in what they predict for the outcome of experiments as they are interpretations of what the formalism of QM predicts for the outcome of experiments. These results aren’t any different in that respect.

What you are seeing in the images in the first link is the electron density of the screen of a detector (i.e. the number of electrons hitting the screen per unit area) which, due to the experimental set-up, corresponds to a 2-D cross-section of the square-modulus of the wavefunction of an electron in a hydrogen atom.

Well, as the article describes it more specifically:

So aren’t you actually “seeing” the wave function in some meaningful sense?

No more meaningful than I put it: i.e. you are seeing something that is a representation of a cross-section the square-modulus of the (time-independent) wavefunction - which is not surprising at all as the square-modulus of the wavefunction of a single particle is the probability density for a position measurement on that particle.

Uh, ok. I’m sure that couldn’t be any clearer, although I seemed to have no problem understanding the article. Odd.

For anyone who’s interested, Physics World has a much better article on this which I just got to (sorry). It’s not easy reading but they do try to explain things, for example: