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.