The Measurement Problem

Alright, let's talk about the measurement problem! This is defined by different thinkers in different ways, so it isn't always clear how we should talk about it.

This is how I have chosen to state the measurement problem, and it is admittedly arbitrary. Every interpretation chooses a different gripe to have about the measurement problem, and will likely formulate the problem in a way that makes their gripe, and subsequent solution, most obvious.

I don't aim to avoid bias in my formulation, I just want to define the problem in the biggest possible strokes that make sense to me. That is to say, I want a formulation of the measurement problem that most clearly frames the issues being debated and allows interpretations to be categorized and their relationships understood quickly.

The Measurement Problem

Some variables:
Let's call the observing mind of the scientist "O",
the macroscopic-sized measuring apparatus "A",
and the quantum state of the system being studied "Q".

The measurement problem could then be stated as three propositions which cannot all be true. One of these must be false.

1. Under the right conditions, A can be in the same quantum state Q as a microscopic-sized system; the size of the apparatus does not matter. Q can be a superposition state.
2. O directly perceives the world. This means that if it perceives the state of A, it perceives its state as exactly what it is.
3. A superposition state represents multiple realities, or a reality that is indeterminate between multiple realities. Minds cannot exist in multiple realities, so O cannot perceive or otherwise interact with A if it is in state Q.

This particular way of formulating the measurement problem has the strength of relative generality, but has the flaw of being fairly abstract and difficult to grasp without some explanation. So, let's look at each part more closely.

'A can be in state Q'

This is the least controversial of the three. Basically, it says that the laws of quantum mechanics are true in the scientific sense. It is the one claim that is a posteriori, meaning it can be verified empirically. Specifically, this means two things: 

a) Large macroscopic sized objects can follow quantum laws under the right conditions.

This is a point that could be brought under debate. Could it be that a relatively large-sized object like a cat actually cannot be brought to a quantum state so that it would behave as quantum mechanics would predict? Or is there some sort of physical effect that prevents that from happening? Some interpretations argue that there is an effect like this.

b) Quantum states can be superpositions.

This is a fundamental part of quantum mechanics. It would be difficult for an interpretation to deny this. Since superposition states are so effective at explaining quantum phenomena, denying this would mean completely denying that quantum mechanics is true in even an approximate sense and that we need to start from scratch.

Accepting this statement does not mean that one believes quantum superposition states must be real things that exist in the world, which is a much more controversial statement. Nor does it mean that a quantum state must be interpreted as a literal physical state. Many interpretations would argue that quantum states should not be considered real physical states because there is some better notion of state out there that we have not yet discovered. These interpretations would still have to admit that the notion of quantum states and the notion that those quantum states can be in a superposition state, however those two things are to be understood, are essential in empirically successful quantum mechanics.

Like I said, this statement is the least controversial.

'O directly perceives the world'

This is a metaphysical statement. Essentially, this statement boils down to whether or not we perceive reality as it really is, or if reality is there is an aspect of reality we fundamentally cannot perceive.

The famous philosopher Immanual Kant introduced the notion of transcendent that is used in modern philosophy. It refers to something that is essentially beyond human experience. Does an interpretation allow for a transcendent reality? If so, that interpretation would deny this statement.

This is important to include because it establishes whether or not it would allow for there to be some kind of "hidden reality" of the metaphysical kind. For example, the multi-universe interpretation allows for possible worlds that are beyond our perception because we are trapped in our own possible universe.

I would think that many would find no problem in denying this proposition. Some interpretations accept this statement, and some don't, and it is a good proposition to use to divide and begin to categorize interpretations.

'Superpositions represent multiple realities'

This is where the problem comes into full form. Superpositions are the linear combination of two other quantum states. That is to say, add two quantum states and you get a superposition. Since superpositions are just this kind of mathematical combination of two other states, it seems natural to assume that they should be interpreted as representing both states in some way. 

Perhaps it is an indeterminate state that ceases to become one reality until collapsed. Perhaps it is a dual existence, one that represents both realities existing at the same time until it is required to be one or the other. Whatever the case, this statement says that it cannot represent just one determinate state.

And because of this dual existence, this is a problem for how we should understand what perception of a superposition should look like. Excluding weird and unhelpful ideas, we don't typically think of our minds as existing in multiple realities. Since this is the case, these extra realities have to be shed somewhere between the physical superposition and our mind's perception of it.

Many would lump the notion of superpositions representing multiple realities in with the baggage associated with quantum mechanics. I don't do this because it is useful to separate this a priori claim from the a posteriori claims of the first statement. It's a statement about how to understand the significance of the superposed quantum state, not a matter of the predictions made using it, though the latter can inform the former.

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So that is how I like to phrase the measurement problem. It is simple enough to grasp, while still showcasing many of the concerns interpretations try to address.

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.

What is realism anyway?

I know when I first started studying quantum mechanics and the topic of realism in it, I had to spend some time trying to figure out what the heck realism actually meant. It is a topic that is in some ways quite natural, but figuring out how anyone could genuinely disagree about this was confusing for a while. Here is what I learned about the distinction between realism and anti realism, scientific or otherwise. 

Of course, if the distinction between realism and anti-realism is to be worth anything, it has to actually make sense on a basic level and be a view that people actually could conceivably hold. Understanding the view of anti-realism can give insight into realism.

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The disagreement between these two views is about ontology; it's a disagreement about what exists. Sometimes people use realism to signify the view that certain things exist and that this constitutes an explanation for certain phenomena. This is wrong: realism does not by itself provide an explanation. Much more is needed for an actual explanation than just what exists in an experimental situation. Especially in physics: one could express this by saying that the math has to work out as well. This is a blunder committed by some advocates of the Many-worlds interpretation. The interpretation is presented as a fix for quantum weirdness simply by supplying the right ontology, but this is misguided. For the many-worlds interpretation to be true, it must work out in the details, not just its ontological commitments. 

Ontology, by itself, is not an explanation; theory is.

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That being said, ontology is a very robust way to divide and categorize different theories. Every theory admits of a certain "cast of characters" that it uses in theorizing. For example, classical mechanics has equations like "F=ma", which use the terms "force", "mass", and "acceleration". These terms can be used across different equations, and so long as the circumstances are the same, they can be used interchangeably in different theoretical equations. The "m" in "F=ma" and "p=mv" both stand for mass, and can refer to the same thing in the right circumstances.


Since this "cast of characters" of abstract terms are what the theory uses to describe a given experimental setup, they form the vocabulary that we use to describe the world in that theory. Different theories may have some abstract terms in common (like Newtonian and Quantum mechanics both use Hamiltonians), but they will still have abstract terms that do not overlap. This is a good way to show that two different forms of theorizing truly are parts of separate theories: their "cast of characters" are not the same.

Since different theories use different vocabularies to describe the world, this implies that they can admit different ontologies. That is to say, different theories describe different ontologies because they describe the world in different ways. The same can be said of philosophical interpretations of a physical theory. For this reason, ontology is a good topic to use to distinguish different interpretations of quantum mechanics.

This should be understood with two grains of salt, however: 1. ontology is not always the best way to distinguish interpretations and 2. not all interpretations disagree on ontologies, yet I would be inclined to say they are different theories (for example, some interpretations disagree on empirically-verifiable grounds.

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So what would an opponent of realism have to say that would make sense? They'd say that while of course we have the impression of real persisting objects in the world around us, these impressions (or certain ones) are best explained in terms of some mechanism other than real existing objects.

For example, it's possible all of the impressions of physically existing things we perceive come from some extra-physical being called God, and no physical thing actually exists. (This is roughly a view that the famous philosopher Berkeley argued for).

Or maybe we are simply brains in vats, hooked up to some elaborate machinery that gives us the impressions that we are in the physical world? (This is probably a much more palatable version to contemporary readers.)

In both of these examples, our perceptions are not caused by what we would naturally think they are caused by. Instead, there is another explanation, and this explanation pictures reality differently. Anti-realism is a claim that what we perceive is best explained by an idea which does not admit of the existence of some thing.

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There's something else we can say about this alternate explanation. Not only is it asserted to be a better explanation, it is purported to be a better explanation of our impressions. If the anti-realist explanation is true, then it will bridge the gap between the impression as experienced and the explanation of that impression. This results in the meaningfulness of the words we use to describe the reality being replaced being undermined in a special way. If this anti-realist explanation is true, we would be able to exactly define the meaning of the words we used to describe the now-replaced ontology, and we'd be able to exactly define them in terms of how we came to know them. The meanings of the words we used would be definable through their epistemology.

That is far from clear, so imagine this example: there is someone permanently plugged into a realistic simulation of the outside world who was aware that this was the case. This person wanted to study how this simulation worked (and let's assume that he/she could genuinely understand it). Let's call this interested mind the 'matrix scientist'. Presumably, this matrix scientist would be able to figure out, in ideal circumstances, what sorts of mechanisms in the simulation were in action when he/she observed something, even though he/she was never taken out of the realistic simulation.

So let's say that this matrix scientist was trying to understand his/her own sense of smell, and the matrix produces this sensation through two distinct programs. You could even imagine this is a hardware difference, where these two aspects of smell run on two physically separate machines. The important point is that there are two distinct causal processes for producing the scientist's sense of smell. Let's call them process A and process B.

The matrix scientist could study these different processes and learn their differences, their similarities, how they work together, etc. Even after learning all about them, however, that textbook knowledge he/she had would still not count, strictly speaking, as knowledge of the unreality of his/her sense of smell. After all, that knowledge has not yet been connected to his/her perception of smell. In order to do that, the matrix scientist would have to be able to describe his/her sense experiences of smell in terms of these processes. Suppose process A controlled the smell of crayons, and everything else was controlled by process B. The matrix scientist might at some point smell crayons, and because he/she knows that this is a result of process A, he/she could say "process A is occurring" just as easily as he/she might say "I smell crayons". The matrix scientist could go on to do this with all aspects of his senses, given enough information about the causal forces that give rise to his/her sensations. The end result of this is a language which can be used to describe all aspects of the reality of perception without using any sensory concepts like "smell".

What this elaborate example is meant to illustrate is that, in order for some natural notion of reality (like sensory reality) to be replaced with another notion of what is real, we have to have ways of describing our old reality in terms of the new.

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So at the end of the day, anti-realism is a commitment to the following:

1. There may be some realist explanation of our impressions, but the anti-realist thinks that there is a better explanation that does not use the disliked ontological concept.

2. Our sense impressions can be completely described in terms of this alternate causal process. 

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.