Is Length Meaningless on the Planck-Scale?

Growing up, I had always heard about the Planck length was physically interpreted as being something like "the length at which our concept of length breaks down".

Here I'll talk only about the Planck length and not the Planck time, though these ideas apply to it just as much.

The Common Interpretation

Here is what Wikipedia currently says about the physical interpretation of the Planck length:

Snapshot of Wikipedia taken November 2nd

The smallest possible length? How does that make any sense? It baffled me when I was younger. How could a length define when the notion of length no longer worked? When you measured something just larger than the Planck length, your measurements would work, but try and measure something smaller than that and it would no longer work? This doesn't make much sense as a hard-and-fast line. Supposing it was a blurry effect didn't help: how could the effect be blurry, but the number be so well-defined? Couldn't we measure the "blurriness", and wouldn't that be the most interesting part? Was length "pixelated"?

Something like this train of thought bothered me, and I think it highlights just what is so absurd about the typical physical interpretation of this concept. How could one define the point at which a particular concept no longer made sense to use, when the definition of that point used that concept? It's as if someone temporarily decreed that no one was allowed to use calendar measures of time anymore. When asked when the decree would no longer be in effect, they would look silly if they said "two weeks from now".

What I think

So that's why the common interpretation is rubbish. Utterly unhelpful. The better interpretation of the Planck length is that it refers to when many of our physical theories begin to break down. This is very different. We can, and do, continue to use the concept of length well beyond the limit of the Planck length. The notion of space and dividing that space into points, lines, and distances are the mathematical basis for our physical theories. But while they are fundamental to the physical theory, they are not exactly "part of it" since they can be used meaningfully in the exact same way in many other contexts.

And that's exactly what we do. We use these concepts in quantum mechanics for different purposes, but they are nonetheless the same concepts. The concept of distance is unaltered at that scale, it's our classical theories that no longer work. And part of our classical theory is the notion that physical matter is made up of particles and those particles have locations. At the Planck scale, it doesn't really make sense anymore to ask where a particle is, since that is the scale at which their location begins to be indeterminate.

And that indeterminacy is definitely part of physics. When it's said that a particle has an indeterminate location, it doesn't mean that we simply cannot determine it's location. It means that that location is not determinate. It's location is blurry. This is what is significant about the Planck scale; the concept of length is still just as meaningful, it's just that physical particles no longer have well-defined locations. That indeterminacy is well-defined, actually. It's worth pointing out that physical quantum waves are not indeterminate at that scale; they are perfectly well defined at that scale.

What I Think: Gleiser's on the Theory of Everything

I read an interesting NPR Opinion Piece written by Marcelo Gleiser. Go read it. In it he argues against pursuing a so-called "Theory of Everything", or TOE for short. It makes several good points.

First off, he's right that a TOE would not actually be a theory of everything. Rather, it would be a theory of everything that is considered the most fundamental building blocks of the physical universe. This leaves out a lot of stuff, like nearly everything in day to day life.

Second, he's also right to link the desire for unity to Judeo-Christian monotheism. This may seem like an odd idea nowadays since religion and science are seen as opposing sides of a dichotomy (they aren't). Though it may seem counterintuitive, historically these ideas come from the same source. In addition, monotheism and the search for scientific unity get support in similar ways. Science is often thought of as becoming unified in the "mind of God".

Ceteris Paribus

But there is one point that he makes that I think is not quite right. He argues that the TOE doesn't make sense, but I would disagree with this. This idea comes from his argument that theories will always be incomplete.

"A physical theory can only be proved wrong, never right, at least in any permanent sense. This is because every theory is necessarily incomplete, always ready for updates as we learn more about the physical world. What we can say about Nature depends on how we measure it, the precision and reach of our instruments dictating how 'far' we can see. As a consequence, no theory that attempts to unify current knowledge can be seriously considered a 'final' theory or a TOE given that we can't ever be sure that we aren't missing a huge piece of evidence."

Essentially, he's arguing that a TOE is impossible because all theories will always be incomplete. That is to say, there will always be some relevant data missing if we try and use it to explain everything.

But this is just an uninteresting feature of induction itself. No inductive inference can ever be proven true in the exact sense of a deductive statement. Inferences can only be stronger or weaker, never "proven".

This is not what prevents us from having a TOE, however. If a theory is shown to be sufficiently strong, then we say it is true. This is what we mean when we say that classical mechanics or relativity is true. It's certainly not true in the deductive and exact sense, but that doesn't mean it isn't true in a different sense.

Is Gleiser committed to the idea that our greatest scientific theories are not true? That is to say, not true in any sense of the word? I would hope not, because that argument showing that any TOE cannot be true necessarily also proves that any theory cannot be true necessarily. Regardless of whether or not this is the correct way to think of scientific theories (it's not), it clearly is not an idea in favor of his argument since it would admit that a "true TOE" is not any more or less sensible than the truth of any other scientific theory.

Outside influences may not integrate into theory

Gleiser's argument still allows the possibility of formulating a theory that could explain any sort of circumstance, had we enough data about that circumstance. And that is exactly what a TOE would supposedly do. It would allow us to explain anything we wanted, so long as we had enough information about it.

It is this idea about a TOE that is actually wrong. For a theory to work in the world there must not be any relevant outside influences acting on the system that is being studied. For physics, these are often things like thick shielding so as to prevent radiation or other similar influences. Making the theory work means making sure no influences like this could affect the system. Without these shielding conditions, our best theories could only come up with 'educated guesses' at best.

So how to make sense of these outside influences? Most who give it some thought might think that these outside influences could be understood within the theory if we knew enough about them.

Here's a mental picture: some scientists are studying fluid dynamics of a substance that is not well understood. If someone breaks the shielding conditions by reaching into an apparatus and waving their hand around, sufficiently disrupting the experiment, we might say that we could in principle factor their influence into the theory if we only knew the exact motions of their hand, etc.

This may be true, but it misidentifies the problem. The problem is not the fact that there is not enough information, but that the information we have is not the right kind. Presumably, we could learn many things about how this person waved their hand in the apparatus, like why they did it or the sensations they felt on their hand when they did it. None of these facts would be helpful, however. We would need to have the right kind of info: we would need to know the exact motion of their hand in the apparatus and the material properties of their hand, etc.

This is why a TOE is such an absurd notion: outside influences on a system might not make sense in the theory.

This is not to say that a TOE is impossible. It may be possible, but it seems highly unlikely we will find one. More importantly, however: searching for such a vain and unlikely scientific theory is very likely to hurt our efforts to understand less "symmetric" or "beautiful" phenomena. Not every scientific discoveries are "beautiful", but this does not make them insignificant by any stretch of the imagination. We should not spend our time seeking out these ideal theories when our attention is best put into doing what science does best: helping us to understand the world around us.


(It should be noted that this discussion is based heavily on the ideas found in Nancy Cartwright's book, The Dappled World.)

Survey of Quantum Interpretations

When I was writing my senior thesis about quantum mechanics I began to wonder which interpretations were most and least popular. My professor found this illuminating survey taken in July of 2011 at the conference named Quantum Physics and the Nature of Reality. In attendance were 33 individuals, most of whom were affiliated with physics, while a small handful were associated with math or philosophy. The study is by Maximilian Schlosshauer , Johannes Kofler, and Anton Zeilinger.

The poll is interesting to sort through. It is by no means a completely representative sample of all thinkers in the whole world, but it is sizable and professional enough to be taken seriously. It as good looking and informative graphics as well a solid statistical analysis.

Here is the link. I highly recommend checking it out yourself.

• Interestingly, they were highly divided over the nature and solution of the measurement problem. Nearly equal split of support between different answers.
• A majority of experts optimistically predicted we would have a "working and useful" quantum computer in 10 to 25 years and no one thought it would take longer than 50 years. Very few comparably think it will happen before ten years from now.
• Copenhagen is the most popular interpretation. I think that this is still an unclear result, though, since it is not always clear what the Copenhagen interpretation is. The second most popular were information-based interpretations, and I'm not entirely sure what those are. I would have guessed many-worlds would be second, but it was in a relatively close third.
• Apparently most of them thought that personal philosophical prejudice played a large part in choice of interpretation. This isn't too surprising: most of the time when one is heavily informed on a topic and debates that topic with others one is very likely to become frustrated with their views, regardless of how informed they are. While some might think this suggests that viewpoints are inherently about nothing more than our preferences, I don't think that's the right conclusion. While that could be true, I think that it suggests that smart people who strong opinions just have more opportunities to come up with excuses as to why others don't accept (their obviously true) views on some matter.
• Very few people thought we would stop having conferences devoted to quantum foundations in the future. A great many thought we would. My guess is that we will, but they will be of a completely different nature. Instead of trying to figure out the "right answer" where the focus is on debating which is best, conferences in the future will be more of a "marketplace of ideas". My reasoning: the "right answer" is not obvious to the experts now so it would definitely not be obvious to most people in the near future. Even if we discover the "right answer" in 50 years, that doesn't mean it will be commonly accepted or taken seriously. Future conferences will probably not continue to focus on sorting things out and will instead be about exploring cool ideas. I like the authors' take on this:

"Among the different interpretive camps, adherents of objective (physical) collapse theories were the only group to believe, in significant numbers, that in fifty years from now, there will likely be still conferences devoted to quantum foundations. So perhaps this reflects the fact that those who pursue collapse theories tend to view quantum theory as an essentially unsatisfactory and unfinished edifice requiring long-term modification and construction efforts. Vice versa, it may be a sign that those who regard such efforts as unnecessary or even misguided are optimistic that the remaining foundational problems, whatever they may be, will soon be resolved."

• I find it interesting that most of the correlations found in the data mostly just show logical conclusions. Not too surprising since the survey-takers are all thinkers by profession.
• The largest consensus on a question was about quantum information, where a relatively large majority agreed that it "is a breath of fresh air for quantum foundations". I'm not entirely sure what quantum information is, so I'm surprised it has been such a big deal and I haven't heard much about it.

Measurement

What exactly is "measurement"? It's a confusing question in the context of the philosophy of quantum mechanics. Confusing enough to warrant a short discussion about it.

Two Meanings

There are several different things the word could mean. The first means about the same thing as "observe". It is used to speak about the steps of an experimental setup we take to determine the state of a system or some specific property or aspect of its state. This is on par with our common-sense use of the term, like "measuring" the length of something by using a yard stick.

This first meaning also refers to when we measure something indirectly, like measuring the height of a tree by measuring its shadow and the angle the sun's rays make at the tip of the shadow. Knowing those two things you could use trigonometry to figure out the tree's height.

The second meaning is specific to the context of the philosophy of quantum mechanics. Here, "measurement" is typically meant to refer to something that happens to a quantum system in superposition. This system is put into an experimental setup that determines the state or some property of the system in such a way that it is no longer in a superposition. When a system goes from being in a superposition state to a mixed state, that is called "collapse", so this second meaning can be said to mean about the same thing as "measurement with collapse".

The Confusion Begins

What is tricky is this second meaning. It seems to indicate that there is something about observing quantum systems in superposition that will cause them to change, or "collapse". What causes this collapse, and how should we understand it?

Well the first confusion to dispel is that quantum mechanics does not show that the world around us is affected by our observations of it. This is a philosophical view (roughly, this is "idealism") which may or may not be compatible with quantum mechanics, but quantum mechanics does not in any way require this view.

One might think that it does because one conflates the two meanings of "measurement" above. In other words, one could say: 'every time we observe something, isn't some part of the universe collapsing?' The answer to this would be an unequivocal no. The world does not collapse around us because nearly nothing in our daily observable lives is in a superposition. Though material objects around us may be constituted of atoms with quantum wave functions, the superpositions associated with those atoms will have entirely unobservable effects on our lives in all but the most absurd situations.

In other words, chairs do not cease to exist in a determinate way when we leave the room as a result of quantum mechanics for a very simple reason: quantum mechanics has absolutely no say in the state of the chair. One could certainly argue that the chair does not exist when we leave the room, but quantum mechanics does not support this claim. One would have to argue this on philosophical grounds.


This discussion will be continued...

Schrödiner's Cat: Explain Live I'm Five

Recently I answered a thread on Reddit. Someone asked for the Schrödinger's cat thought experiment to be explained to them "like they were five" (basically, just use simple language and simple terms to explain something complicated). I was happy with the result, so I thought I'd share it.

******

Schrödinger's cat is really strange, and that is the way it is meant to be. Schrödinger thought about this to try and make quantum mechanics seem just too weird to accept. He was wrong, though: quantum mechanics is true. So now we have a story that sounds really weird but actually reveals something hard to understand.

Matter is a Wave

The easy understand part: if you shrink down really tiny, all of matter looks like waves. These aren't sound waves or water waves, though they sometimes act similarly.

Imagine making a splash in a pool and looking at it from the side. You will see a little wave go to the left and one will go to the right. Matter looks kinda like that sometimes: a little bit of the splash goes to the left and little goes to the right. This state is called a superposition.

Now here's the weird part: even when there is only one particle, it still behaves this way. "Splash" this one particle, and it wiggles to the left, and wiggles to the right. One might ask: which way did it actually go? Well, it did not go to the left, and neither did it go to the right. It didn't literally go both directions, it just went the direction you go when you go left and right at the same time. It wiggles in both directions because it is in a superposition.

My Brain Hurts

This is weird. Lots of smart people did not like this. It made their brains hurt and they were unhappy with the idea. "How can something be in two places at once?" they would ask. Schrödinger asked this as well. He was a smart man, though, and came up with a story to help him argue.

He asked "If a particle in a superposition can move in two directions at once, then couldn't a cat in a superposition be both dead and alive at the same time?" Obviously, this made quantum mechanics sound silly.

Quantum Mechanics: Not Silly

But these people were wrong: quantum mechanics is not as silly as it sounds, it is just really really hard to understand. When a particle wiggles both left and right, it would be wrong to say that it "went to the left". It would also be wrong to say that it "went to the right". That is because it did not wiggle in only one of those directions: it wiggled in both directions because it was a wave.

Still Confused?

You might still wonder: how can something be in more than one state at once?

The answer is that it was not in several different states, it was only in one state, a superposition state. Remember, we know that the quantum wave did not go to the left AND to the right, it wiggled in both directions. It did not become two waves moving away from each other, it was still just one wave spreading apart.

You should know that no one has done this experiment with a cat. It turns out to be something that is very very hard to do. It is hard to visualize also. But the cat is made up of atoms that can wiggle in two directions. One of those directions might make the cat die, and the other direction will let the cat live. The cat is somehow in a superposition state of alive and dead. When we open the box, the cat stops wiggling and we see either an alive or a dead cat. How exactly it stops wiggling and how it becomes only one or the other is something very smart people argue about, so don't worry about that part yet.

If it seems really confusing, that is because it is.

Quantum Mechanics and Consciousness

There are many different interpretations about how quantum mechanics and consciousness are related, but they fall into one of two categories:

1. consciousness is the cause of some physical or non-physical effect ("mind makes matter")
2. or consciousness is the effect of a quantum mechanical process ("matter makes mind").

The first category I call quantum-intentional interpretations. These interpretations include the many-worlds interpretation as well as the sort featured in this xkcd comic:

http://xkcd.com/1240/

The second category of ideas basically argues that consciousness can somehow be explained with a quantum mechanical understanding of the brain. Basically, the brain is in some way a quantum computer and this gives rise to consciousness in some way. This sort of interpretation is discussed quite well in a short question-answering blog entry on Scott Aaronson's blog.

Essentially, he cites a thought experiment by David Chalmers' and argues that quantum mechanics could not solve what is called the "Hard Problem of Consciousness". Aaronson then goes on to argue that, while there is no evidence to disprove the claim, there currently is no good reason to believe that our brains are quantum computers in any hugely significant way.

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.