You may be interested in (if you haven’t already encountered) the “QBist” interpretation espoused by Fuchs, Mermin, Schack and others. Here are links to some appropriate papers by Fuchs, who in my opinion expresses the position most eloquently and efficiently:
I personally see QBism as quite a natural extension of classical Bayesianism to quantum mechanics, and I am surprised that it is not discussed at all in this community. Given the interest that Less Wrong members have in quantum theory and its foundations, I can only surmise that this niche is due to some kind of idolization of Eliezer and his views. I am somewhat placated by your inclusion of Kent’s paper in your list of coherent anti-MWI arguments, although I would love to see more of the genuine academic debate surrounding the interpretation and foundations of quantum theory faithfully reflected in this forum.
QBism is less an egocentric model of the universe, more an egocentric interpretation of quantum theory. It doesn’t say that we cannot have an ontological model of the universe; it says that quantum theory ain’t it.
However, I appreciate that this probably won’t help with your lack of interest. Best of luck with everything.
I meant the second. If that is the point of the papers, then I guess that’s fair enough, but, well, I don’t anticipate that their argument is going to be valid. I’ll go and read it; no need to summarize.
First paper,
The trouble with all these interpretations [Bohm, spontaneous collapse, WMI] as quick fixes for Bell’s hard-edged remark is that they look to be just that, really quick fixes.
I recognize that this is subjective and fuzzy, but… no? Bohm looks like an incredibly… well, I won’t get into that, but it doesn’t seem to me like a quick fix. Spontaneous collapse, okay, I grant that one. MWI doesn’t seem like a quick fix in any sense either.
Their world purports to have no observers, but then it has no probabilities ei- ther. What are we then to do with the Born Rule for calculating quantum probabilities? Throw it away and say it never mattered?
No, that’s silly.
It is true that quite an effort has been made by the Everettians to rederive the rule from decision theory.
Yes, that was silly. But that’s hardly the strongest argument that could or has been made. You don’t get to pick your opponents’ arguments like that. The way Decision theory is used when I’ve seen it is: any structure which is formally equivalent to a decider is a decider, and QM has such structures.
No amount of sophistry can make “decision” anything other than a hollow concept in a predetermined world.
… No, that’s stupid. No amount of sophistry can make predetermination relevant to the meaningfulness of ‘decision’. And of course the relevance of this argument is dependent on taking the argument for probability-in-MWI to be strictly dependent on the applicability of decision theory in a particular way which is not the way it’s actually being used. In particular, by the time you ascend the level of abstraction enough for decision theory to be relevant, you’re past the point at which predetermination has fallen away and you’re dealing with an effectively non-predetermined system.
And then he just goes off and makes an argument that the theory is information about the state, not the state itself. But… … … if it successfully models your information about a thing, then the thing acts consistently with the model, which means you’re also modeling the thing. There are theorems that constrain the ontology given these observations, and it basically boils down to ‘QM is super legit’.
I agree with you up until your last paragraph: the strength of Fuchs’ papers are not in their direct criticism of Everettian interpretations (Kent’s papers are a lot better at that).
For your last paragraph, I think Fuchs would take umbrage at the idea that you are necessarily “modeling the thing” when you assign a quantum state to a given system. I don’t think he believes that systems have a “true ontic state” of which quantum states are representative. Rather, the quantum state is merely a representation of an agent’s beliefs about the future outcomes of their interventions/measurements into the universe. Nevertheless, Fuchs claims to be a scientific realist.
I’m deliberately using the word “think” a lot here because I’m not confident of relaying Fuchs’ views faithfully (this isn’t directly my area of research). I haven’t adopted a QBist interpretation (or any other), but from what I’ve read I feel it’s worth serious discussion.
You also mentioned theorems constraining ontology. You may be interested in Fuchs’ take on Bell’s Theorem: http://arxiv.org/pdf/1311.5253v1.pdf . I have been to a talk where he explains why the PBR theorem doesn’t impact his interpretation, although the details evade me (and I can’t find anything written about it by him online).
I’m also a fan of the Bayesian interpretation of quantum mechanics (and I’ve said so here a couple of times). I try not to say ‘Quantum Bayesianism’, because it seems to me that Fuchs has run with that term in directions that I don’t necessarily want to go. (I’m an objective Bayesian, while Fuchs is a subjective Bayesian, and that’s just the start.) Some fans of Everett avoid the term ‘many worlds’ and cringe at some of the writings of David Deutsch, for similar reasons.
All of which is to say that if a hard-headed rationalist thinks that Fuchs is saying crazy things, run it against your model of a classical Bayesian saying similar things, and see if maybe it’s the interpretation of Bayesianism that you object to rather than the interpretation of quantum mechanics, and adjust accordingly. (Of course, this doesn’t help if you’re not a Bayesian in the first place, but Bayes is more sacred here than Everett.)
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.
You may be interested in (if you haven’t already encountered) the “QBist” interpretation espoused by Fuchs, Mermin, Schack and others. Here are links to some appropriate papers by Fuchs, who in my opinion expresses the position most eloquently and efficiently:
http://arxiv.org/abs/1003.5209
http://arxiv.org/abs/1311.5253
http://arxiv.org/abs/quant-ph/0205039
I personally see QBism as quite a natural extension of classical Bayesianism to quantum mechanics, and I am surprised that it is not discussed at all in this community. Given the interest that Less Wrong members have in quantum theory and its foundations, I can only surmise that this niche is due to some kind of idolization of Eliezer and his views. I am somewhat placated by your inclusion of Kent’s paper in your list of coherent anti-MWI arguments, although I would love to see more of the genuine academic debate surrounding the interpretation and foundations of quantum theory faithfully reflected in this forum.
Just from reading the abstract, I’m not interested in an egocentric model of the universe. Ontology doesn’t follow the same rules as epistemology.
QBism is less an egocentric model of the universe, more an egocentric interpretation of quantum theory. It doesn’t say that we cannot have an ontological model of the universe; it says that quantum theory ain’t it.
However, I appreciate that this probably won’t help with your lack of interest. Best of luck with everything.
First, condescending snark? Seriously?
Second, now I’m really confused. In what way can’t QM be the fundamental ontology of the universe?
I’m not sure how to interpret your question.
If you’re asking:
“What is the case against the MWI interpretation of quantum theory?”
then I would probably cite difficulties in explaining why our branch’s history appears to be Born-rule typical as a major argument.
If instead you’re asking:
“What is the case for a non-ontological interpretation of the wavefunction?”
then the best I can do is attempt to summarise the arguments put forth in the above papers.
I meant the second. If that is the point of the papers, then I guess that’s fair enough, but, well, I don’t anticipate that their argument is going to be valid. I’ll go and read it; no need to summarize.
First paper,
I recognize that this is subjective and fuzzy, but… no? Bohm looks like an incredibly… well, I won’t get into that, but it doesn’t seem to me like a quick fix. Spontaneous collapse, okay, I grant that one. MWI doesn’t seem like a quick fix in any sense either.
No, that’s silly.
Yes, that was silly. But that’s hardly the strongest argument that could or has been made. You don’t get to pick your opponents’ arguments like that. The way Decision theory is used when I’ve seen it is: any structure which is formally equivalent to a decider is a decider, and QM has such structures.
… No, that’s stupid. No amount of sophistry can make predetermination relevant to the meaningfulness of ‘decision’. And of course the relevance of this argument is dependent on taking the argument for probability-in-MWI to be strictly dependent on the applicability of decision theory in a particular way which is not the way it’s actually being used. In particular, by the time you ascend the level of abstraction enough for decision theory to be relevant, you’re past the point at which predetermination has fallen away and you’re dealing with an effectively non-predetermined system.
And then he just goes off and makes an argument that the theory is information about the state, not the state itself. But… … … if it successfully models your information about a thing, then the thing acts consistently with the model, which means you’re also modeling the thing. There are theorems that constrain the ontology given these observations, and it basically boils down to ‘QM is super legit’.
I agree with you up until your last paragraph: the strength of Fuchs’ papers are not in their direct criticism of Everettian interpretations (Kent’s papers are a lot better at that).
For your last paragraph, I think Fuchs would take umbrage at the idea that you are necessarily “modeling the thing” when you assign a quantum state to a given system. I don’t think he believes that systems have a “true ontic state” of which quantum states are representative. Rather, the quantum state is merely a representation of an agent’s beliefs about the future outcomes of their interventions/measurements into the universe. Nevertheless, Fuchs claims to be a scientific realist.
I’m deliberately using the word “think” a lot here because I’m not confident of relaying Fuchs’ views faithfully (this isn’t directly my area of research). I haven’t adopted a QBist interpretation (or any other), but from what I’ve read I feel it’s worth serious discussion.
You also mentioned theorems constraining ontology. You may be interested in Fuchs’ take on Bell’s Theorem: http://arxiv.org/pdf/1311.5253v1.pdf . I have been to a talk where he explains why the PBR theorem doesn’t impact his interpretation, although the details evade me (and I can’t find anything written about it by him online).
I’m also a fan of the Bayesian interpretation of quantum mechanics (and I’ve said so here a couple of times). I try not to say ‘Quantum Bayesianism’, because it seems to me that Fuchs has run with that term in directions that I don’t necessarily want to go. (I’m an objective Bayesian, while Fuchs is a subjective Bayesian, and that’s just the start.) Some fans of Everett avoid the term ‘many worlds’ and cringe at some of the writings of David Deutsch, for similar reasons.
All of which is to say that if a hard-headed rationalist thinks that Fuchs is saying crazy things, run it against your model of a classical Bayesian saying similar things, and see if maybe it’s the interpretation of Bayesianism that you object to rather than the interpretation of quantum mechanics, and adjust accordingly. (Of course, this doesn’t help if you’re not a Bayesian in the first place, but Bayes is more sacred here than Everett.)
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.