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.
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.
