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How quantum mechanics turned me into a Bayesian

A few elder-statesmen of quantum theory gathered together while a handful of students listened in eagerly. Paraphrasing, one of them—quite seriously—said, “I don’t think any of the interpretations are logically consistent… but there is this ‘transactional interpretation’, where influences come from the future, that might be the only consistent one.” The students nodded their heads in agreement—I walked away.

Bayesianism is (some would say) a radical alternative philosophy and practice for both understanding probability and performing statistical analysis. So, like all young contrarian students of science, I was intrigued when I first found Bayesian probability. But where is the fun in blaming this on my own faults? I’m going to blame someone else—I’m going to blame it on Chris Fuchs.

On two occasions the Perimeter Institute for Theoretical Physics (PI) hosted lectures on the Foundations of Quantum Mechanics. I was lucky enough to be a graduate student in Waterloo at the time. The first, in 2007, was my first taste of the field. It was exciting to hear the experts at the forefront speaking about deep implications for physics andindeed—even the philosophy of science itself. I knew then that this was the area I wanted to work in.

However, I quickly became disillusioned. The literature was plagued by lazy physicists posing as armchair philosophers. There was no interest in real problems—only the pandering of borderline pseudoscience. It’s no wonder—why bother doing hard work and difficult mathematics when peddling quantum mysticism is what gets you press?

I stayed, though, because there were several researchers at PI who seemed interested in solving real, technical problemsand, they were doing so using techniques from another field I had already worked in: Quantum Information Theory. I learned an immense amount from Robin Blume-Kohout, Rob Spekkens and Lucien Hardy while there, but the one who left a lasting impression was Chris Fuchs.

Before we get to Fuchs, though, let’s back up for a momentjust what is this Quantum Foundations thing, and what has it got to do with Bayesianism? As you know, quantum theory dictates that the world is uncertain. That is, as a scientific theory, it makes only probabilistic predictions. Many of the philosophical problems and misunderstandings of quantum theory can be traced back to this fact. Thus, if one really wants to understand quantum theory, one ought to understand probability first. Easy, right?

Nope. As it turns out, more people argue about how to interpret the seemingly simple and everyday concept of probability than do our most sophisticated and complex physical theory. Generally speaking, there are two camps in the interpretations of probability: frequentists and Bayesians. As noted, every student begins as one of the former. It was in 2010 when my conversion to the latter was complete.

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Summary of the interpretations of quantum theory.

In 2010, PI hosted its second course on the foundations of quantum theory. This time around I had a few years of experience under my belt and my bullshit detectors were on high alert. My final assignment was to summarize the course, as shown above. The only lectures that didn’t leave me disappointed where Chris Fuchs’. Because I had been reading up on Bayesian probability anyway, his “Quantum Bayesian” interpretation of quantum theory just clicked.

And it wasn’t just about philosophy. Concurrently, I was taking a great course on Stochastic Processes from Matt Scott. Most of this field takes an objective (frequentist) view of probability. Matt was patient with my constant questions on how to phrase the concepts in terms of the subjective Bayesian view. I was starting to feel a bit overwhelmed with the burden of translating everything to the new framework… then it happened.

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The assignment question was as follows: Show that \int_\infty^\infty p(x_2,x_1;t_2-t_1) d_{x_1} = p(x_2;t_2), the simplest case of the Chapman-Kolmogorov equation. What you were supposed to do is use the Markov property, p(x_2,x_1;t_2-t_1) = p(x_2|x_1;t_2-t_1)p(x_1|t_1), and integrate. It was a straightforward, but tedious, calculation. Here is what I wrote: first  p(x_2,x_1;t_2-t_1) = p(x_1|x_2;t_1-t_2)p(x_2|t_2). Since p(x_1|x_2;t_1-t_2) is a probability, it integrates to 1. Done.

This was seen as unphysical because t_1-t_2 is a negative time. So what?I thoughtprobabilities are not physical, they are subjective inferences. If I want to consider negative time to help me do my calculation, so be it. After all, I considered negative money to get me into university. But what I couldn’t believe is how difficult it was to convince others the solution was correct. It was at that moment I realized how powerful a slight change of view can be. I was a Bayesian.

Just what does a postdoctoral theoretical physicist do all day?

Coffee… mostly, I drink coffee.

A kindergartener once asked me, “why don’t you wear science clothes?” I gathered that she meant a lab coat. Then there is the utter surprise my neighbors show when I tell them—yes—I am on my way to work wearing sandals, shorts and a t-shirt. Take a moment and do a google image search of “scientist”. You have to scroll through several pages before you see a person not wearing a lab coat. So if I don’t wear a lab coat while staring into a beaker as if the colorful liquid inside contained a part of my soul, what do I do all day?

Generally speaking, a postdoctoral researcher (postdoc) is someone at a stage in their academic career between a graduate student and a professor. This usually involves traveling around the world working on short-term contracts. In theoretical physics the typical situation is to move several times over a period of 5–10 years before landing a permanent position as a professor or leave academia for an industry job.

While that sounds kind of horrible, as far as responsibilities go, it’s the best job in the world. I have the freedom of a graduate student, but I don’t have to write exams or engage in any of the administrative duties of a professor. I get to focus on my passion: research.

Now, you might be thinking “wait, pictures of physicists still have lab equipment surrounding them. Presumably, instead of beakers, you still have to be doing something technical with your hands.” No. Let me explain. There are two types of physicists: experimental and theoretical. The distinction is easy to make. Experimental physicists (experimentalists) spend at least some of their time in a lab building devices to probe and test hypotheses about the world. Theoretical physicists (theorists) do not. I am one of the latter.

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OK, so I don’t wear a lab coat, I don’t use beakers, I don’t build anything, I don’t even step foot into a lab, what exactly do I do?

What does the internet say:

Theoretical physicists have a fascinating job that combines observation with mathematics in order to create complex formulas that describe the workings of the universe around us.

Not bad, but still not very illuminating in terms of my day-to-day life. In a business sense, I do create products: journal articles. These are usually 5–15 page papers which summarize a successful result, which can takes months to years to obtain. What they do not contain is any semblance of the blood, sweat and tears which make up the chaotic mess that went into them.

This mess can broken down into four tasks:

  1. Discuss problems with colleagues
  2. Perform mathematical calculations
  3. Read journal articles
  4. Write computer software

I don’t do every task every day, but on average my time is about equally spent on each.

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A day in the life of a postdoctoral theoretical physicist.

Much of every day is spent discussing problems with colleagues. Sometimes I seek advice on the problems I’m working from a co-worker; sometimes I am providing advice to others; and sometimes I am discussing a problem we are jointly working on. These are often brainstorming session which involve scribbling notes on a whiteboard and plenty of coffee.

Next, I perform mathematical calculations. This involves a lot of paper covered in the kinds of symbols pictured above. You’ll notice there is no arithmetic. These are abstract manipulations of symbols according to some rules. The fun part is that I sometimes get to make the rules! Most of the work done in this category gets trashed due to dead ends or errors and the rest gets heavily compressed if and when a journal article is written.

In order to find out what things others have tried and what techniques I can use to solve a problem, I read journal articles written by other scientists. Finding the right articles is a skill on its own given that over 2.5 million scientific journal articles are written each year. Often I find myself skimming over papers, picking out specific pieces. Occasionally, I am asked by a journal to evaluate the scientific merit of another article. This process is called peer review and could very well be the subject of a future post.

Lastly, there is coding. I write computer software that helps answer the scientific questions I have. For example, with my long-time friend and colleague Chris Granade I co-wrote Qinfer, which is statistical software for debugging small quantum computers. You’ll see examples of this and other software projects in future blog posts.

So there you have it. A day in the life of a postdoctoral theoretical physicist.

Quantum Physics for Babies

Why Quantum Physics for Babies? This is the most common question I get and, I must admit, the answer is not as reasoned as you might expect from an academic researcher. But, it is entirely obvious if you know me: it started as a joke.

Though I don’t remember now the exact reason why, in 2013 I wanted to have a prop nerdy baby book. Probably to do something like this:

Initially I had quickly put together a bunch of pages to give it some girth and had it printed by  an online photobook printing company. It didn’t end up looking like a real book. But, my wife and kids liked it enough to encourage me to spend a little more time on the interior.

This time around I was determined to get it printed to look like a real book. Through some online research I came across CreateSpace, which is a self-publishing platform. It was easy enough to upload my files and order a copy for myself  (as the author, I just paid the shipping of $4). It turned out great. My daughter brought it to her preschool class and the teachers were all very excited about it. It was at that point when I clicked the button to have it go live on Amazon.com.

I was surprised that it started selling a few copies per day. Some initial positive reviews prompted me to write more books. I followed Quantum with Newtonian Physics for Babies and Optical Physics for Babies. Over the next few years things were going quite well. I was writing more books in my spare time and they were all selling a few copies per day. I didn’t think it was something I could make a living at, but it paid for coffee anyway. Then this happened:

As it turns out, Mark Zuckerberg is pretty popular. And, although he shared the book as a joke, I received lots of interest following this. I still don’t make a living from the books, but it is kind of fun when all your friends and colleagues think you are famous.

Since then, I’ve written some more books with some ideas that I’m really excited about. Stay tuned to find out more in the coming months.