Quantum Bayesianism

The QBist aim is not to provide an ontological description of the universe. Rather, it is to persuade you that whatever such a description is, quantum theory ain't it.

"The professed goal is to strip away all those elements of quantum theory that can be interpreted in subjective, agent-dependent terms. The hope is that whatever remains will hint at something essential and objective about nature."

- Schlosshauer (https://arxiv.org/pdf/1405.2390.pdf)

I've read the quantum theoretic parts of the sequences: Eliezer doesn't really make a case for why Born probabilities arise. Indeed this is one of the major open problems with the MWI.

Quantum Bayesianism

Depends what you mean by "about". The (strong) Qbist perspective is that probabilities, including those derived from quantum theory, represent an agents beliefs concerning his future interactions with the world. If you're looking for what these probabilities tell us about the underlying "reality" then that's an open question, which Fuchs et al are still exploring.

16y

I am. It seems to me that if quantum mechanics is about probabilities, then
those probabilities have to be about something: essentially, this seems to
suggest that either the underlying reality is unknown, indicating that quantum
mechanics needs to be modified somehow, or that Qbism is more like an
"interpretation of MWI", where one chooses to only care about the one world she
finds herself in.

Quantum Bayesianism

A Qbist would say they represent the map. The complex vector formalism of quantum theory is simply a convenient/elegant manual for predicting the outcomes of one's future interactions with nature. It may be able to tell us something about the territory, but is not the territory itself.

06y

Do you see how that's not an answer? Why do they work?
A solipsist/Parmenidean theory of reality would need to add another theory, or a
copy of all the evidence, in order to make predictions. It would be simpler to
drop the solipsism and just state the part of the theory that does the work
(which would be our account of reality). Eliezer makes the case that something
like a wavefunction exists, and the splitting of 'worlds' somehow gives rise to
the Born probabilities.

The File Drawer Effect and Conformity Bias (Election Edition)

I'd be grateful if someone could give/suggest a reason for the downvotes.

57y

I'd guess it's a combination of several things:
First, you're not really adding anything to the overall debate (why the polls
were wrong). Second, your post is mostly about politics, and how those of the
party you disagree with is evil (or at least engages in ethically questionable
behavior). Third, your bias is evident (Why do you doubt the left-leaning
newspaper wouldn't engage in character attacks - as written, it comes off as
little more than "My side is better than their side, and wouldn't resort to such
tactics").
Don't stress the voting too much, though. It doesn't mean "You've done something
wrong" (in general), it means "I don't want to see this kind of thing". Look at
what you've posted - if you care what other people want to see - and don't write
that kind of thing anymore. That, of course, depends on being able to tell what
it is you've actually done.

The File Drawer Effect and Conformity Bias (Election Edition)

Whilst the BBC may lean towards the left and be a powerful organisation, I doubt that the effect it had was anywhere near as great as the combined forces of the Daily Mail, The Sun, the Daily Telegraph, and The Times. These newspapers, which account for a huge percentage of the UK's circulation, conducted what I can justifiably describe as a co-ordinated campaign of vitriolic rhetoric against the Labour party and Ed Miliband's character. It's telling that 2 of the 4 are owned by Rupert Murdoch, who has a lot to gain from a continued Conservative government... (read more)

07y

I'd be grateful if someone could give/suggest a reason for the downvotes.

[LINK] The Wrong Objections to the Many-Worlds Interpretation of Quantum Mechanics

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.

And the Winner is... Many-Worlds!

As far as I can tell, all he does in his experiment is label one of a pair of electrons as the "Observer" and exclaim that Many-World has been proven because this "Observer" electron enters into a superposition with the other electron. The problem is that literally every other interpretation of quantum theory would make the same predictions for this experiment, however you label the electrons.

[LINK] The Wrong Objections to the Many-Worlds Interpretation of Quantum Mechanics

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?

07y

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.

[LINK] The Wrong Objections to the Many-Worlds Interpretation of Quantum Mechanics

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... (read more)

[LINK] The Wrong Objections to the Many-Worlds Interpretation of Quantum Mechanics

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.

07y

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'.

[LINK] The Wrong Objections to the Many-Worlds Interpretation of Quantum Mechanics

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 pr... (read more)

07y

Sorry, I forgot to answer you about PBR. I agree with Matt Leifer's analysis
[http://mattleifer.info/2011/11/20/can-the-quantum-state-be-interpreted-statistically/]
. 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 [http://arxiv.org/abs/quant-ph/0106133] 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
[http://www.perimeterinstitute.ca/personal/cfuchs/] 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.

[LINK] The Wrong Objections to the Many-Worlds Interpretation of Quantum Mechanics

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?

17y

My own brief summary of the subject is in an nLab article
[http://ncatlab.org/nlab/show/Bayesian+interpretation+of+quantum+mechanics].
(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 [http://math.ucr.edu/home/baez/week27.html], 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.

[LINK] The Wrong Objections to the Many-Worlds Interpretation of Quantum Mechanics

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.

07y

First, condescending snark? Seriously?
Second, now I'm really confused. In what way can't QM be the fundamental
ontology of the universe?

[LINK] The Wrong Objections to the Many-Worlds Interpretation of Quantum Mechanics

That experiment sounds very problematic to me. He says "After you measure the electron’s spin about the x-axis, have someone fully reverse the physical evolution.... Such reversal would be applied to everything: the electron, the equipment, and anything else that’s part of the experiment.".

There is no explanation of the mechanics of how he thinks such a time-reversal could be implemented. We simply don't have the fine control over the quantum state of the entire measurement apparatus. In fact, the very assumption that quantum theory is even the t... (read more)

[LINK] The Wrong Objections to the Many-Worlds Interpretation of Quantum Mechanics

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 Le... (read more)

07y

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.)

47y

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.

The Dilemma: Science or Bayes?

This comment is old, but I think it indicates a misunderstanding about quantum theory and the MWI so I deemed it worth replying to. I believe the confusion lies in what "World" means, and to whom. In my opinion Everrett's original "Relative-State Formalism" is a much better descriptor of the interpretation, but no matter.

The distinct worlds which are present after a quantum-conditional operation are only distinct worlds according to the perspective of an observer who has engaged in the superposition. To an external observer, the system... (read more)

A new derivation of the Born rule

As I understand, it's less of a problem for a hardline Copenhagen interpretation because no definite ontological status is assigned to the wavefunction, or indeed the collapse of the wavefunction. CI can roughly be paraphrased as

"Consider this set of rules for predicting experimental outcomes. Look how well it works! Of course, we're not asserting anything about actual reality here".

One of those rules is the Born rule. Another is the fact that physical transformations correspond to unitary maps on the Hilbert space. All of them are postulated, an... (read more)

The Dilemma: Science or Bayes?

I'd like to know what you're implying with this post, but I'm unable to make a confident guess. Are you claiming that this WP quotation has something to do with many worlds?

[Link] Quantum theory as the most robust description of reproducible experiments

I wonder if you would apply the same criticism to so-called "derivations" of quantum theory from information theoretic principles, specifically those which work within the environment of general probabilistic theories. For example:

http://arxiv.org/abs/1011.6451 ; http://arxiv.org/abs/1004.1483 ; http://arxiv.org/abs/quantph/0101012

The above links, despite having perhaps overly strong titles, are fairly clear about what assumptions are made, and what is derived. These assumptions are more than simply uncertainty and robust reproducibility: e.g. on... (read more)

08y

I have no problem with alternative derivations of quantum theory - if they are
correct! But the framework in this paper is too weak to qualify. Look at their
definition of 'category 3a' models. They are sort of suggesting that quantum
mechanics is the appropriate prediction calculus or framework for reasoning, for
anything matching that description.
But in fact category 3a also includes scenarios which are completely classical.
At best, they have defined a class of prediction calculi which includes quantum
mechanics as a special case, but then go on to claim that this definition is the
whole story about QM.

08y

There is nothing special about complex numbers in quantum mechanics. You can get
rid of them by adding an extra dimension to the Hilbert space.

Academic Cliques

I am reminded of a series of documents uploaded to the arxiv earlier this year, each one reporting the results of a survey taken at a distinct conference, and supposedly revealing a "snapshot" of the participants' atitudes towards foundational issues (such as interpretations). Although the first document seems to be making some fairly strong claims about academic consensus, the following two are a little more conservative. The final one says something very similar to the original post here; their results suggest that,

'there exist, within the broa... (read more)

The QBist stance is that we "know" very little about the underlying reality. One of the only things that Chris Fuchs is willing to accept as an objective property of a quantum system is its Hilbert space dimension.

I doubt it's sensible to talk about an interpretation of MWI. MWI says that the wavefunction is a real physical object and wavefunction splitting is something that's genuinely physically occurring. QBism denies that the wavefunction is a real physical object.