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.

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.