I don’t know whether I’d consider myself a “fan” of any particular interpretation, but I think Quantum Bayesianism ranks highly in terms of the insight it sheds into the nature of quantum theory. I’d be interested in discussing or reading about the Bayesian interpretation in more detail, as I haven’t had too much exposure besides Fuchs et al’s papers and a couple of conference talks. For example, what is your take on the recent PBR theorem concerning the ontology of the quantum state, and would this depend on whether your Bayesianism is objective or subjective?
Do you have any resources you’d particularly recommend?
My own brief summary of the subject is in an nLab article. (This is a math/physics wiki, and I assumed that the reader already knows quantum mechanics, at least up to the point of knowing what a density matrix is and what it’s good for.) There are references there, but you’ll notice that they’re all linked from the History section. (Part of the point of that section is to make it clear that the idea predates Caves, Fuchs, et al, although they certainly deserve credit for making it prominent.) I don’t know any over-all exposition that I really like, although I will always like the one cited as Baez 1993, which is where I learnt about it (and in fact where I first learnt about density matrices). That article doesn’t say ‘Bayesian’, but as I was already a Bayesian when I read it, and since I knew Baez to be a Bayesian, I naturally interpreted it so. If you interpret the probabilities in a different way, then you’ll get a very different interpretation of quantum mechanics as a result!
Someday I want to write something for beginners, at the level of Eliezer’s essays here (and in fact probably post it here too), but I haven’t done that yet! Until then, Baez’s piece is at the right level, but it doesn’t address the things that LessWrongers specifically would want to see.
I’d like to try and flesh out the difference between your personal interpretation and (for example) QBism. In your nLab article you describe an objective Bayesian is someone who “who naturally thinks of Bayesian probabilities as reflecting knowledge rather than belief, betting commitments, etc”. This suggests that it has to be knowledge about something; about some objective ontological process I assume. Is this ontological process still somehow “quantum” in nature? Is it perhaps a hidden variable of some kind? You didn’t reply to my previous question about the PBR theorem, which seems relevant since it places strong restrictions on hidden-variable-type psi-epistemic interpretations of quantum theory. I’d be very interested in hearing a response to that if you have the time.
Sorry, I forgot to answer you about PBR. I agree with Matt Leifer’s analysis. Briefly: it’s a fine theorem, and it’s good that they proved it, but it shouldn’t surprise anybody, and it doesn’t rule out any of the interpretations that people actually advocate.
As for my interpretation, I don’t have any problems with Caves, Fuchs, and Schack’s comprehensive 2001 paper on the subject (this is not their first 2001 paper, which was more about a technical result and vaguer on the interpretation). This paper writes extensively about states of knowledge. But since then, Fuchs has criticized that phrasing as insufficiently Bayesian (by which he really means insufficiently subjectivist). Quantum States: What the Hell Are They? at his website covers this, although it’s hard to read. As you can see from the dates, he had these thoughts pretty early on. Anyway, if the original 2001 papers define the orthodoxy for the Bayesian interpretation, then I am an orthodox quantum Bayesian, and Fuchs is the heretic.
Knowledge of what? Fuchs says knowledge of (or beliefs about, etc) the conesequences of one’s interventions in a system; one can also say (which may be same thing) knowledge of the outcomes of further measurements. I would use more realist language: knowledge of the physical observables. If you try to build an ontological model in which each observable has an associated actual value and the results of measurements are determined by these values, then you’ll have a hard time with that; but that’s not what I want to do. An observable O does not (necessarily) have an actual value, but it has potential values (comprising its spectrum), and I have knowledge about O that can be summarized as a probability distribution over these potential values.
To clarify: do you believe that there is something ontological in the system which is assigning probabilities of measurement outcomes in some way, when you make a measurement of the obervable O?
Probabilities aren’t ontological; they’re epistemological. I agree with everything that Eliezer writes about that, probabilities are in the map, etc.
But remove that word; there is something ontological that assigns measurement outcomes when I make a measurement. Or to keep it simpler: when I make a measurement, the measurement outcome is ontological.
A belated thank you for your replies. I feel like I’m starting to get the hang of what it means to take seriously the idea that probabilities are epistemological. It’s difficult, moving between papers espousing differing interpretations, because their very language tends to presuppose some ontological commitment or other.
I don’t know whether I’d consider myself a “fan” of any particular interpretation, but I think Quantum Bayesianism ranks highly in terms of the insight it sheds into the nature of quantum theory. I’d be interested in discussing or reading about the Bayesian interpretation in more detail, as I haven’t had too much exposure besides Fuchs et al’s papers and a couple of conference talks. For example, what is your take on the recent PBR theorem concerning the ontology of the quantum state, and would this depend on whether your Bayesianism is objective or subjective?
Do you have any resources you’d particularly recommend?
My own brief summary of the subject is in an nLab article. (This is a math/physics wiki, and I assumed that the reader already knows quantum mechanics, at least up to the point of knowing what a density matrix is and what it’s good for.) There are references there, but you’ll notice that they’re all linked from the History section. (Part of the point of that section is to make it clear that the idea predates Caves, Fuchs, et al, although they certainly deserve credit for making it prominent.) I don’t know any over-all exposition that I really like, although I will always like the one cited as Baez 1993, which is where I learnt about it (and in fact where I first learnt about density matrices). That article doesn’t say ‘Bayesian’, but as I was already a Bayesian when I read it, and since I knew Baez to be a Bayesian, I naturally interpreted it so. If you interpret the probabilities in a different way, then you’ll get a very different interpretation of quantum mechanics as a result!
Someday I want to write something for beginners, at the level of Eliezer’s essays here (and in fact probably post it here too), but I haven’t done that yet! Until then, Baez’s piece is at the right level, but it doesn’t address the things that LessWrongers specifically would want to see.
I’d like to try and flesh out the difference between your personal interpretation and (for example) QBism. In your nLab article you describe an objective Bayesian is someone who “who naturally thinks of Bayesian probabilities as reflecting knowledge rather than belief, betting commitments, etc”. This suggests that it has to be knowledge about something; about some objective ontological process I assume. Is this ontological process still somehow “quantum” in nature? Is it perhaps a hidden variable of some kind? You didn’t reply to my previous question about the PBR theorem, which seems relevant since it places strong restrictions on hidden-variable-type psi-epistemic interpretations of quantum theory. I’d be very interested in hearing a response to that if you have the time.
Sorry, I forgot to answer you about PBR. I agree with Matt Leifer’s analysis. Briefly: it’s a fine theorem, and it’s good that they proved it, but it shouldn’t surprise anybody, and it doesn’t rule out any of the interpretations that people actually advocate.
As for my interpretation, I don’t have any problems with Caves, Fuchs, and Schack’s comprehensive 2001 paper on the subject (this is not their first 2001 paper, which was more about a technical result and vaguer on the interpretation). This paper writes extensively about states of knowledge. But since then, Fuchs has criticized that phrasing as insufficiently Bayesian (by which he really means insufficiently subjectivist). Quantum States: What the Hell Are They? at his website covers this, although it’s hard to read. As you can see from the dates, he had these thoughts pretty early on. Anyway, if the original 2001 papers define the orthodoxy for the Bayesian interpretation, then I am an orthodox quantum Bayesian, and Fuchs is the heretic.
Knowledge of what? Fuchs says knowledge of (or beliefs about, etc) the conesequences of one’s interventions in a system; one can also say (which may be same thing) knowledge of the outcomes of further measurements. I would use more realist language: knowledge of the physical observables. If you try to build an ontological model in which each observable has an associated actual value and the results of measurements are determined by these values, then you’ll have a hard time with that; but that’s not what I want to do. An observable O does not (necessarily) have an actual value, but it has potential values (comprising its spectrum), and I have knowledge about O that can be summarized as a probability distribution over these potential values.
To clarify: do you believe that there is something ontological in the system which is assigning probabilities of measurement outcomes in some way, when you make a measurement of the obervable O?
Probabilities aren’t ontological; they’re epistemological. I agree with everything that Eliezer writes about that, probabilities are in the map, etc.
But remove that word; there is something ontological that assigns measurement outcomes when I make a measurement. Or to keep it simpler: when I make a measurement, the measurement outcome is ontological.
A belated thank you for your replies. I feel like I’m starting to get the hang of what it means to take seriously the idea that probabilities are epistemological. It’s difficult, moving between papers espousing differing interpretations, because their very language tends to presuppose some ontological commitment or other.