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.

Quantum-Intentional Interpretation

In my post on quantum mechanics and consciousness I mentioned a category of quantum interpretations that I call "quantum-intentional interpretations". I defined these as any interpretation that holds that consciousness can be a cause of physical quantum effects.

I want to revise this definition slightly, however. I was conflating two types of ideas. Exactly what aspect of consciousness is acting as a cause? There are two obvious ways of thinking of it:

1. Passive: conscious perception causes physical change.
2. Active: conscious decision of the way in which a quantum system is measured brings about a physical change.

(There may be more ways of thinking about this, but this seems exhaustive me.)

Obviously, the second is more appropriately called the quantum-intentional interpretation since it deals with the intentions of the quantum physicist. I want to use this as the new definition of the term. Interpretations that fall into first of the above distinction should be called quantum-observational interpretations.

There are a couple of reasons I accidentally conflated these two categories. The first is that my understanding of perception is that it needn't be understood as passive. That is to say, any passive description of perception could be phrased so as to be an active description. This is not an immediately obvious point, however. In addition, it's not clear whether or not this is actually true, much less whether or not I am justified in assuming it. Arguing this point would not be important for the discussion, so it is best to avoid implicitly assuming it.

There is a very good reason to make this distinction: one of these two interpretations is very easily refuted. It is easy to show that the quantum-intentional interpretation is plainly ridiculous.

The second is that the quantum-intentional interpretation was just so plainly false. But first, let's see what the most compelling argument in favor of it looks like.

Arguing in Favor of the Quantum-Intentional Interpretation

The technical term for the way a quantum state is measured is called the basis. When one measures a quantum state, one must measure it with respect to basis.

A loose analogy would be to think of the coordinate grid you overlay on top of some two dimensional plane you want to measure. If you want to mathematically describe a coordinate direction, it must be described in terms of a coordinate system. This coordinate system can be changed at will, and there is established mathematics to describe the way in which the math will change as a result. 

Similar to how a coordinate overlay defines what coordinate directions one can use to describe a direction, basis defines the types of measurements we can make on a system. Changing the basis one measures in will change the way a quantum state will be measured and what the outcome will be.

In fact, for every quantum superposition, there is a basis in which to measure it such that it does not behave like a superposition and there will be no probabilistic outcome.

So the question is: if we are able to affect the superposition simply by the way in which we choose to measure it, does that intentional decision change reality? It would seem to be compelling to say yes. After all, a scientist could choose to measure something in one basis rather another, and this decision has made a real change in the stuff itself.

The Quantum-Intentional Interpretation is False

So why is this so ridiculous? That's because it's a category error (you know, that same distinction that has made dualism so passé in contemporary philosophy). There are different kinds of causes, and intentions are the wrong kind of cause to truly act as the kind of explanations we want them to be.

First, a joke. One is touring a physics lab when you see an elaborate device with pieces all around the room. You are intrigued, so you ask what it does. The physicist giving your tour begins to explain each part of the device. Each step it goes through is more elaborate than the next, and it all seems to rely on mechanisms that are being studied elsewhere in the lab, but you can't figure out which part is specifically being studied. At the end of the physicists explanation, you vaguely understand the way every part functions and how they all interact with each other, but you still cannot figure out what is being studied with this device. You ask "what do you study with this device?" In reply, the physicist just laughs and says: "we don't study anything with this device, it's just an elaborate Rube Goldberg device for making coffee."

The physicist has, in a sense, answered your question. He explained what device did in terms of all of the physical workings that are involved in its functioning. The explanation that satisfied you, however, was an explanation about the intentions of those who built the device: the device is for making coffee. The joke, obviously, is that the physicist offered the physical explanation instead of the one that was most helpful. Anyone who has dealt with physicists, or similar creatures, can tell you that this not an unrealistic situation.

When we give an explanation, we can give different kinds of causal explanations. Sometimes a certain kind of causal explanation is, strictly speaking, not an adequate explanation for a question, even if it is not a, strictly speaking, incorrect causal explanation.

When scientist designs a device to measure some quantum state, of course the intentions of the scientist play a factor in how the device ends up behaving. But when a scientist is trying to understand some physical system, they are looking for a physical cause. If someone were to ask why a quantum state is showing the behavior that it is upon measurement, saying that a scientist intentionally designed the apparatus to measure in a certain basis, this would not be an adequate explanation, regardless of whether or not it is a true explanation in some sense. The physicist is looking for a physical cause, and intentions are not a physical cause.

So yes, the intentional choice of measurement basis does, in a sense, cause reality to change. However, that cause is not a physical cause, and would be an inadequate kind of explanation for a physicist studying 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...

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.