Spekkens' 'Toy Theory' Part 2: Epistemic vs. Ontic

I don't like the dichotomy of 'epistemic vs. ontic'. It's helpful in certain ways, but it ultimately is a false dichotomy.

'Ontic' here loosely refers to interpretations that treat the quantum state as a real physical entity. This is the same as 'realism', but that term is ambiguous so it isn't necessarily a bad thing that there is this redundancy. The opposite of an ontic interpretation is a non-realist interpretation--one that takes the quantum state to not be a real entity itself. A non-realist interpretation is a position about explanation. It holds that there is a different explanation of events that is better than the realist explanation, and that these explanations cannot both be true.

'Epistemic' here refers to interpretations that take the quantum state to be 'states of belief about the system', which is horribly confusing. I don't like this definition. Belief doesn't actually factor into physics like this, so something is not right here. 

Let's consider another term instead: probabilistic. The term 'epistemic' pretty much refers to an explanation that is probabilistic. With phase space probability distribution in classical thermodynamics, there is some collection of outcomes which are not known deterministically in advance, but we can write up a function which will hold true of the distribution of outcomes we see. Regardless of whether or not each individual outcome is able to be found deterministically, we can use a probability distribution to understand the whole collection of outcomes. This is a probabilistic physical prediction, and Spekkens is simply arguing that a quantum state is just the same kind of thing as this phase space distribution. 

The tricky thing about all of this is that there's an assumption that these probabilistic (epistemic) theories are non-real theories, but that simply isn't the case. What makes these probability distrutions true are "chance set-up" situations. There has to be something that sets up the distribution to be predictable by a probability distribution. If there is no chance set-up, there's no reason to believe that a probabilistic prediction will be true. Nancy Cartwright writes much better than I about this aspect of probabilistic laws (1999). These chance set-ups, then are the description of the world that physics brings. Probability distributions are not lacking in ontological committments, since they require that the world be set up in this certain way. Maybe this is a less satisfying ontological claim than one about the existence or non-existence of something, but it undoubtedly is an ontological claim that physics makes.

So probabilistic (epistemic) theories are not necessarily non-real about quantum states. They are only non-real if they provide an alternate explanation for quantum effects compared to the the interpretation of quantum mechanics which takes quantum states to be real entities. Spekkens argues that there is alternate explanation that is better, we just don't know it yet. But he has no reason to argue that this is actually true. Remember, the 'Toy Theory' does not actually replace quantum mechanics in explanatory power. At best, it gives an account for what the new explanation would look like, but this is not enough to claim that interpretations that take quantum states to be real are incorrect. 

In fact, Spekkens seems to overlook the possibility that quantum mechanical theorizing is in some ways epistemic and that the wave function is also a real physically existing thing. This is the view I like best. In a sense, it's not quantum mechanics that has failed to understand some phenomena, but really it is classical mechanics that has failed. Classical mechanics asks where a particle is, and only gets a probability distribution, which quantum mechanics gives. What is obviously in partial belief (and probabilistic) is our knowledge of particle positions, so this is in a sense uncontrovertably epistemic. But, at the same time, what provides the probability distributions accurately? Quantum mechanics does.

Spekkens asks us to look for a third theory which can explain why our knowledge of particle positions seem to always be in partial belief, and therefore probabilistic, but the answer is something more obvious than what he proposes. In fact, quantum mechanics is a theory which correctly describes the real world, and provides correct probability distributions for our lack of knowledge of the positions of particles. 

Update: Upon reflection, I realize that this treatment of the dichotomy is not entirely fair to it. I think that the point I made here is still valid, I just don't think the case is closed on this dichotomy. It's absolutely a false dichotomy; there is just more to say about it that is less dissmissive. I'll write up another post soon...

Spekkens' 'Toy Theory'

I just read the paper about Spekkens' 'Toy Theory' of quantum mechanical phenomena. I had heard about this paper from the interview with Fuchs, where the paper is cited as being a support of the quantum bayesianism interpretation. I was not disappointed. This essay is awesome, and I think it is going to be seen as one of the most influential papers in in recent history. 

You should go read it here.

That's not to say that I think it is right in what it argues. Far from it, I think that the essay is fundamentally mistaken in many ways, though it is a smart and insightful fresh take on the subject. I think that there is much to learn from it, despite being at heart incorrect.

The paper's main goal is is argue that quantum states are epistemic and not ontic. Essentially, this is a claim against the realist interpretation of quantum mechanics. Ontic, here means that it is a theory which describes real objects in the world in a reliable way. The opposite of this is to claim that, though it enjoys predictive success, quantum mechanics at its base does not exactly describe the world. It is only a phenomenological theory, in a sense. It gives a scientist the means to predict how the world will behave, but it does so in a kind of incidental way. Phenomenological theories do not give causal accounts of why things behave the way they do, just a way to know what they will do. These types of theories are missing the causal mechanism that explains what happens.

Get it? Toy theory?

The alternative is epistemic, which is a version of non-realism that is plausible for quantum mechanics. Essentially, it claims that quantum states are not physical states, but are rather states of lack of information. Instead of encoding something about the world, the superposition of Schrödinger's cat just describes the information that we are lacking: the life or death state of the cat. Epistemic interpretations of quantum mechanics argue that quantum mechanics does not describe the real world, just a kind of lack of information about the world. Quantum Bayesianism is one of the more well known epistemic interpretations of quantum mechanics. 

This distinction between epistemic and ontic interpretations is a false dichotomy: it's not necessary that an interpretation fall into either of these categories. Furthermore, the dichotomy has a latent presupposition, but that is the subject of a later post.

Quantum states come in two different varieties: 'pure' and 'mixed' quantum states. A 'pure' q-state is essentially just a a quantum system described by one state vector in a superposition. 'Mixed' states are when a quantum system is described by multiple state vectors. A common view of many philosophers of science is that pure q-states are ontic, while mixed q-states are considered epistemic since they are just states of incomplete knowledge about what pure state a system is in. Spekkens argues that both pure and mixed q-states, however, are epistemic.

He claims that the epistemic view of q-states is superior to ontic view because certain phenomena like interference, noncommutivity, entanglement, no cloning, teleportation, etc. are mysterious in the ontic view seem natural in the epistemic view.

The success of this argument is a mixed one. On the one hand, this toy theory is useful for understanding some aspects of quantum phenomena. I think that it indeed is useful precisely because there is something true to it.

But I don't think Spekkens' claim is, strictly speaking, a fully true one. While it can be used for insight, the toy theory does not replace quantum mechanics in predictive power. This is why his argument is misleading: the toy theory cannot account for the list of phenomena above. For example, you cannot apply the toy theory alone to the situations which give rise to quantum interference phenomena. Quantum mechanics is capable of making empirical predictions, but the toy theory simply piggy-backs on those predictions.

This means that the toy theory is not a replacement of quantum mechanics in any way. This should be a red flag: scientific endeavors aim for predictive power. The 'toy theory' may be a strong philosophical aside, but it clearly requires another step backwards in understanding before we can go forwards.

Quantum Bayesianism: Reaction to an Interview Part 1

In researching Quantum Bayesianism (or QBism for short) I found a fascinating interview piece online. It is a series put to the Quantum Bayesian (QBian?) Christopher A. Fuchs. While the interview is part of a book which features similar figures being asked the same questions, this interview is offered in whole for free online. I highly recommend you check it out.

Interview with a Quantum Bayesian

The following are some of my thoughts on QBism after reading the interview. ( I should note that since Fuchs is not representative for all QBians everywhere, these should just be considered impressions of QBism and not necessarily correct of all versions of QBism.) This is a continuation of my first post about QBism.

Realism and Anti-Realism

The most basic way to put QBism is that it is anti-realist about quantum states (q-states) but realist about everything else that is uncontroversially considered real in contemporary physics.

One way to explain what it means to be anti-realist about something is to say that it means one believes something is an aspect of mind and not of the world. This is not the best way, however, since delving into the philosophy of science and perception shows that this distinction is not nearly as clear as one hopes. Regardless, it is accurate to say that QBism argues that q-states are expressions of our beliefs about a quantum system and not an expression of any particular part of the system itself.

The most helpful way to think about realism and anti-realism is that it has to do with the meaning of entity-terms. Entity terms are those that we use to refer to things. Typically, an entity-term refers to something which exists. Examples of these from classical physics are "the planet Mars" or "a mass on a low-friction cart". Sometimes, however, we can use an entity term to refer to something that does not exist, however. An example of this from physics both classical and quantum is the "Del operator" (∇), which is considered only functional in use. It is a mathematical and conceptual tool and not a representation of nature (though we use it in multivariate calculus which helps us calculate things that do represent nature).

An anti-realism view of certain entity-terms would try and provide epistemic definitions for those entity-terms. This means that every situation where the offending entity-term is used can be replaced with some sufficiently long sentence describing what it means. For example, since the Del operator is used functionally, one could replace any instance of the use of it as a term with a long explanation of the mathematical role that it plays. This epistemic definition of Del operator would be considered complete because it is not considered real.

Entity-terms which we see as referring to real aspects of the world are not allowed to be constricted in this way. Though it may seem philosophically annoying, if we think of something as referring to an existing thing we must allow the term to be flexible so as to accommodate unforeseen behaviors exhibited by the real object.

Realism and Lack Thereof in QBism

All that to say, QBism considers q-states to not be real things because they can be defined as being functionally defined through the irreducible probabilities associated with them. QBism essentially argues that every q-state can be epistemically defined through the Generalized Born Interpretation. Fuchs says:

"A quantum state just is a probability assignment."

Fuchs says that he attended a conference where it was discussed what kind of linguistic classification q-states should have. In other words, are they nouns, verbs, adjectives, etc.? His answer was they are exclamations (or, more specifically, expletives). This is an absurd answer, but it should illustrate that Fuchs seeks to eliminate any talk which uses q-states.

Q-States cannot be Exclamations

The significance behind saying something is an exclamation should be immediately obvious to anyone who has taken a course in meta-ethics or has researched non-cognitivism. Non-cognitivism holds that moral sentences cannot be true or false, they are only an expression of an attitude, like "Ouch!" or "Hey!" These sentences are not considered true or false.

Sentences which use quantum states cannot possibly be exclamations because they are true or false. When a physicist uses quantum mechanics to describe a physical system he typically begins by assigning it a quantum state, and he can be mistaken or correct about the quantum state he assigns.

It should be noted that saying a q-states are a nouns does not commit one to any metaphysical view about them. Entity-terms that we do not consider actually real are still nouns. For example, one can say metaphorically that "a feeling of dread hung in the air". One can be committed to this dread not literally existing but regardless one will still use the word "dread" as a noun.

Implications of QBism's Anti-Realism

Quick question: why does science work so well? How come these weird concepts science uses can be interpreted by humans and used to manipulate the world so reliably? The easiest answer to this question: the weird concepts of science actually describe the world around us and not simply some aspect of our mind.

Anti-realist views about an aspect of science have the disadvantage of not being able to account for why those concepts are so successful at manipulating the world. Since QBism argues that q-states are not physically real things, then it must admit that it is a huge unexplained mystery as to how quantum mechanics can be used so effectively.

Surprisingly, I found this embraced by Fuchs in the interview. He says that this is the most pressing question of quantum mechanics: "Why the quantum?" (how it is possible that it works so well?). Though this is a solid argument against QBism, this shows that it is obviously no nail in the coffin. For Fuchs, it is not a problem because he sees no other interpretation of quantum mechanics as being sufficient for understanding quantum mechanics in a way that makes sense, therefore "why the quantum?" is just as much a mystery for them as well. (Whether or not he is right in this judgment is another issue entirely, but I will not deal with that here.)

For Fuchs, the ideal resolution of this is when two things are achieved:

1. All discussion of q-states is eliminated or sufficiently accounted for with epistemic definitions of meaning.
2. After reformulating quantum mechanics in this way, scientists discover what it is actually about. That is to say, it comes to light what aspects of the world quantum mechanics truly describes.

This should seem to be obviously a great deal of work to justify something simple: how an extremely useful and well-understood theory is successful in manipulating the world. Instead of simply saying "it describes the world" we must instead shrug our shoulders and then offer the above game plan to understand it. But like I said, this is no death blow to QBism, which suffers no contradiction by agreeing with this picture of quantum mechanics.

(More thoughts to come...)

Correction: In the first draft I referred to the Hilbert space as an example of an entity-term in quantum physics that is not considered "real" (by which I mean "actually existing", and not "number which could be complex but lacks an imaginary value"). Upon reflection, I think that this most likely an incorrect assumption on my part, since it seems to correspond to quantum systems and represents the possible outcomes of measurements on those systems. I'll have to look into it more to figure it out.For now, however, I replaced any mention of "Hilbert space" with mention of the "Del operator", which I am sure is functionally defined. It's kinda cheating since it is a mathematical term, but it gets the point across.

Quantum Bayesianism Interpretation

Recently I picked up the June 2013 issue of Scientific American and read an interesting article about the quantum Bayesianism interpretation of quantum mechanics. I have not studied this interpretation at all, and the article piqued my interest, so I decided to look into it. Here are some of my initial reactions to the interpretation after looking into the commentary N. David Mermin's commentary about the topic.

Resources:
Commentary by N. David Mermin

Sci Am Article

Bayesian Probability

Quantum Bayesianism is one of the latest interpretations that has taken a swing at making sense of quantum mechanics, a subject that is notoriously difficult to make sense of. It seems to be based around extending certain notions found in the subjective Bayesian interpretation of probability.

The subjective Bayesian interpretation of probability, as I understand it, is something like this: Probability is not something that is intrinsically inherent in any system; it is simply a judgment of how likely that thing is going to happen.

This is in contrast with the Frequentist interpretation of probability, which says that probability is some intrinsic property of a situation, which can be determined through many trials. For example, we know that the probability of flipping a coin and having it land on heads or tails is 50/50 because we are able to perform many trials. Flipping a coin many times will yield an equal number of heads as tails, if the coin is a fair one.

Both the Bayesian and the Frequentist interpretations will agree that flipping a fair coin a great number of times will result in an even distribution: this is uncontroversial. The disagreement is that the Frequentist argues that this is what defines the probability of something happening in any given situation. A statement of probability has meaning because if we were to perform many trials in the same situation we would see a ratio develop. In this way, the Frequentist interpretation of probability claims that probability ascribes a value that is inherent to some situation.

In contrast, the subjective Bayesian interpretation of probability says that we should not think of probabilities as something inherent to an object or system. Instead, they are aspects of our belief about the object or system.

Relevance to Quantum Mechanics

I am not interested in delving much further into this debate in the philosophy of mathematics since it is not relevant to our discussion on quantum interpretations. The important thing to pull from the above is the last bit: Bayesianism considers probability to be an aspect, not of some object or system, but of our belief about that object or system. In this way, Bayesianism claims that probability is inherently subjective.

This is relevant to quantum mechanics because one of the first attempts to make sense of quantum states has stuck around. This is the generalized Born interpretation, and it states that:

"If the state of the system is |α⟩, then the probability that a measurement finds the system in a state |β⟩ is |⟨β|α⟩|2" (Ohanian 1990 p.102)

This means that we make sense of quantum states by thinking of them as probabilities that the quantum system will be “measured” to be in some other state.

Quantum Bayesianism has connected this notion to the subjective Bayesian interpretation of probability. It says that because quantum states are defined using probabilities, this means that they are inherently subjective. That is to say, they are aspects of our beliefs about the world and not aspects of the world itself.

“Since quantum states determine probabilities, if probabilities are indeed assigned by an agent to express her degree of belief, then the quantum state of a physical system is not inherent in that system but assigned by an agent to encapsulate her beliefs about it. State assignments, like probabilities, are relative to an agent.” (Mermin Physics Today 2012, p.8)

The Quantum Bayesianism Interpretation

Quantum Bayesianism, or QBism for short, claims to solve different paradoxes of quantum mechanics. For example, Schrödinger’s cat does not describe a cat that is both dead and alive at the same time. The cat is described by a quantum state, which is nothing more than a subjective description; it doesn’t describe the actual cat. If we were to actually open the box the cat is clearly either alive or dead.

Furthermore, QBism says that looking in the box does not cause the cat to become either dead or alive. Other interpretations, such as the multi-worlds interpretation, would claim that measuring the cat would cause its wave function to collapse. QBism argues that collapse is not a change of state in the system, but in our information about the system; therefore there is no need for multiple universes or other metaphysical postulations.

“Collapse” is still a meaningful word to QBism, but it signifies the change in a quantum state and not a change in the system itself.

Metaphysical Claims

QBism may appear initially to be claims about mathematical probabilities, but it is truly a metaphysical claim. QBism relies on the distinction between mind and matter. That is to say, we can identify things which are part of the world outside of our minds, and we can also identify things which are part of our mind and do not exist in the world. For example, a hallucination is an example of something that is in our minds but obviously does not exist in the world.

The central claim of QBism is, of course, that quantum states fall into that second category: they are part of minds and not part of the world.

This is a problem, however. QBism will have trouble answering the question “does quantum mechanics describe the world outside of our minds?” We are compelled to answer: “it describes some part of it, yes”, but QBism would lack the ability to make that claim. Remember, if quantum states do not describe the world, and are really part of our minds, it is not clear how quantum mechanics describes the real world that is outside of our heads.

Proponents of QBism could claim that quantum mechanics describes the world outside of our minds; they simply would have no basis for this claim. They would have to claim that quantum mechanics describes the world in some objective way that we simply do not understand yet. This is counter to our intuition that we have good reason to believe that quantum mechanics describes the world, and not simply an aspect of our minds.

The obvious alternative is that quantum mechanics describes nothing more than some part of our minds. All of this business of wave functions and evolution of the state vector are nothing more than inventions of our minds that have no bearing on external reality. This would lead to a kind of quarantined idealism for specifically quantum states. I feel as if this is a rather counterintuitive and controversial claim, so I guess that most proponents of QBism would advocate the former realism.

A Return to Schrödinger’s Cat

Perhaps an example is in order? Imagine the case of Schrödinger’s cat again. QBism has good reason to argue that a cat is not both dead and alive at the same time. They could say that it is in a superposed state, but they would have to qualify this and say that this only means that we are able to ascribe certain probabilities to it and that it is not a state that the cat is in.

QBism would then have difficulty saying anything about the cat. On the one hand, I have seen it written that QBism says that the cat can be considered either dead or alive; we simply do not know which.

“[Quantum Bayesianism] says that of course the cat is either dead or alive (and not both). Sure, its wave function represents a superposition of alive and dead, but a wave function is just a description of the observer’s beliefs.” (Baeyer SciAm June 2013, p.49)

The problem with this is that the statement “the cat is actually either dead or alive when it is described by quantum mechanics as being in a superposition” is not true! Superposition accounts for interference effects, whereas classical states cannot.

For this reason, QBism fails to explain how quantum states seem to describe the behavior of the system while failing to actually describe reality outside of our minds.

Strengths of the Interpretation

Let me end on a positive note about the interpretation. Though it fails to give an adequate account of some basic questions we might have about quantum mechanics (such as “how does quantum mechanics describe the world?” and “what state is Schrödinger’s cat actually in, if not a superposition?”), it is a surprisingly sophisticated interpretation.

I think that it zeroes in on good questions that should be asked in examining quantum interpretations. We should be taking a second look at the probabilistic nature of quantum mechanics and asking questions about the generalized Born interpretation.

In addition, N. David Mermin’s commentary of QBism outlines the problem of interpreting quantum mechanics as one of a “split” between classical and quantum mechanics. This is a step towards phrasing the debate as one about the inability to translate between two contradictory theories. This is a more advanced way to tackle the problem as compared to some others (such as worrying about the role of the “mind” and “observer”). I am not sure if this is unique to Mermin’s commentary or if it is a feature of literature about QBism as a whole. Regardless, I think that QBism seems to be an especially strong theory when viewed under the light of this particular way of phrasing the debate.

In addition, QBism holds a rather robust objection to the claim that choice of measurement basis affects reality and that consequently the mind of the observer is necessarily part of quantum mechanics. It denies that superpositions represent multiple realities, and that therefore collapsing superpositions constitute a change in possible reality. This, I think, is the right objection to the claim.

So on the whole, I found quantum Bayesianism to be a much more sophisticated interpretation than I initially anticipated. I do think that it fails to account for the reality that quantum mechanics describes, as I detailed above. I will continue to look into the interpretation.