Sleeping Beauty and Quantum Mechanics

This is a repost of an article I wrote in 2014.  Note that Sean Carroll also wrote about this, and he’s an author of the cited paper.

My newest favorite philosophical dilemma is the Sleeping Beauty problem.  The experiment goes as follows:

1. Sleeping Beauty is put to sleep.
2. We flip a coin.
3. If the coin is tails, then we wake Sleeping Beauty on Monday, and let her go.
4. If the coin is heads, then we wake Sleeping Beauty on Monday.  Then, we put her to sleep and cause her to lose all memory of waking up.  Then we wake her up on Tuesday, and let her go.
5. Now imagine Sleeping Beauty knows this whole setup, and has just been woken up.  What probability should she assign to the claim that the coin was tails?

There are two possible answers.  “Thirders” believe that Sleeping Beauty should assign a probability of 1/3 to tails.  “Halfers” believe that Sleeping Beauty has gained no new relevant information, and therefore should assign a probability of 1/2 to tails.  The thirder answer is most popular among philosophers.

This has deep implications for physics.

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Magic-Angle Graphene Superconductors

A couple weeks ago, there was an exciting discovery in my (former) field of research. It was found that if you take two layers of graphene, and rotate one of the layers by a “magic angle” of 1.1°, then you can create a superconductor.

Some brief background on superconductors. A superconductor is a kind of material that conducts electricity with zero resistance. That means you could transport electrical power without any energy loss. Or you could create so much electrical current that it creates a powerful magnet (used in MRI machines). Superconductors also have special magnetic properties that allow for magnetic levitation (used in maglev trains). But superconductors need to be cooled below a certain temperature to work, otherwise they’re just ordinary materials.

As of 1957, physicists have a working theory of superconductors, but the theory only explains certain varieties of superconductors, called conventional superconductors. Magic-angle graphene is an unconventional superconductor.

So, why would you ever try rotating two layers of graphene? Graphene is simply a layer of carbon atoms that form a hexagonal pattern. If you overlay two hexagonal patterns with a bit of rotation, you create what’s called a Moiré pattern.

Two hexagonal grids, one rotated by 10 degrees, form a moire pattern when overlaid.

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Things I liked about grad school

To cap off my series on why grad school sucks, I’d like to talk about some of the things I did, after all, like about the experience. This will be more personally focused, and may describe aspects of grad school that other people would miss out on, or dislike.

I can read papers

I started out this series by talking about how physics talks are really bad.  Even now after finishing a PhD, I find that most talks are still incomprehensible. In contrast, I feel pretty good about my improved ability to read papers.

Note, the best way to understand more physics presentations, is to understand when a presentation is best skipped, and it’s the same way with papers. A lot of skill in reading technical papers comes from knowing when to skip a paper, or when to skip large sections of it. But also, as I got further in my Ph.D., there were fewer sections that I needed to skip, and I could return to old papers and understand them better. Some of my most satisfying experiences were going beyond mere reading, being able to critique papers in detail.

This ability extends beyond my own field of study, to other fields of physics, and to other disciplines entirely. I’ve mentioned before, I’ve read scholarly papers in math, psychology, sociology, gender studies, and law. Of course, some disciplines are more difficult than others.

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Is grad school doing what you love?

Many people place a special value on “doing what you love”. Should you become a corporate tool, or a real-life scientist? “You should do what you love” is the reply. And it’s a reply that is detached from any real cost-benefit analysis. Like, maybe you only sorta love being a real scientist, and maybe you don’t love the working conditions of a scientist, and maybe the salary of a corporate tool is so much higher that it enables you to do other things that you love. But you can’t make a snappy motto out of such considerations.

The problem with “doing what you love” is that it doesn’t come for free. If academic institutions need a certain number of grad students,* then they need to provide incentives for just enough people to apply. “Doing what you love” is one incentive, and it takes the place of other incentives that academic institutions could have offered instead. In other words, they don’t need to pay you well, or treat you well. However much grad students are willing to tolerate in order to do what they love–that’s how much they end up having to tolerate.

*I’m only talking about Ph.D. students and not Masters students. I’ve never heard anyone describe a Masters degree as doing what you love.

In economic terms, we can speak of the “marginal” grad student (a concept similar to the “swing voter”). For the marginal grad student, the expected costs and benefits are exactly equal, such that the decision to go to grad school could go either way. It may be that the marginal grad student thinks they would love being a scientist, but this is exactly offset by the costs. So for some people, grad school may be a good deal. But the deciding factor is not merely whether you love grad school, it’s whether you’d love it more than the marginal grad student.

Beyond that, I think even the marginal grad student is getting a bad deal. The marginal grad student expects they would love grad school, but ends up loving it less than they predicted.

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On work hours in academia

Since I’m looking for jobs, I need a little elevator speech for why I chose to leave academia. “The attitude in academia, is that you’re doing extremely important work, and it’s the passion of your life, and therefore you should be willing to accept terrible work conditions. I would rather have a less glamorous job about actually helping people in my immediate surroundings, instead of slaving towards a distant ideal.” How’s that sound? Eh, maybe.

Poor working conditions are hard to quantify, but one thing we can quantify are the work hours. How many hours do academics work? If the titles of news articles are to be believed, you do not need to work 80 hours a week. The title is hilarious because it suggests some people really do work 80 hours, but it’s just unnecessary. But yes, people tend to overestimate their work hours, and studies suggest that it’s really 50-60 hours a week on average for faculty. But how’s that for an absurd standard? Instead of arguing that we should be working only 40 hours like a normal job, people instead have to argue that the 80-hour week is a myth–or at the very least, unnecessary. This also tells me that even when people work 50-60 hours, they feel like they’re working 80, that everyone around them is working 80, and/or that their colleagues and students should be working 80.

Even when academics argue for a 40 hour work week, the main argument is that you can be just as productive in shorter hours. I appreciate that this is the argument people need to make. But now that I’m on the outside, I can finally say, fuck y’all. Forget productivity. How about being humane to your workers? I don’t know that much about the history of labor rights, but my understanding is that the 40-hour work week was a greater step forward for humanity than any of that stuff I did with superconductors.

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Luck in grad school

I am continuing my blogging series on why grad school sucks.  This series has only had one entry so far, in which I talk about how bad physics talks are, and how this worsens impostor syndrome.  Today I will talk about how scientific success is based on luck.

If you have ever read any popularizations of science, you’ve likely heard that many scientific discoveries are made by serendipity.  This makes sense, because if a discovery isn’t a big surprise, then it’s not much of a discovery, is it?

We have one of these stories in the field of superconductivity too.  Kamerlingh Onnes is credited with the discovery of superconductivity in 1911.  But that’s not what his work was really about.  His real accomplishment was being the first person to liquefy helium.  He just tried cooling a bunch of things, and that’s how superconductivity was discovered.  That’s serendipity!  Kinda?

The thing is, serendipitous discoveries might make for a fun story, but it’s garbage to actually live through.  If you go to grad school, will you hit upon something truly interesting?  Or will you just produce a bunch of unremarkable studies that nobody cares about?  Nobody knows!  But your career success depends on it!

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One: the universe’s favorite digit

This is a repost of an article I wrote way back in 2011.  I’m still proud of figuring this one out.

Out of all the digits, from zero to nine, one is the most common.  This has to do with the log scale.

The log scale captures an important fact that is true of many quantities in life.  Take money for instance.  If you have one dollar, then earning another dollar is great because you’ve doubled your money!  If you have a million dollars, earning another dollar does not make much of a difference.  Small changes matter less the more you already have.

This is true on a log scale too.  On a log scale, 1 is the same distance from 2 as 100 is from 200.  The higher you go up, the more the numbers all get smooshed together.  What does that mean for the digits from zero to nine?

A picture of a log scale, highlighting the regions that have 1 as their first digit (eg 1-2 and 10-20)

In the above picture, I show a log scale.  And on that scale, I highlighted in blue all the regions where 1 is the first digit of the number.  You should see that the blue regions cover more than one tenth of the log scale.  In fact, they cover about 30%.  And so, if we pick numbers randomly on the log scale, about 30% of those numbers will have 1 as their first digit.

Just for fun, let’s apply this concept on the fundamental constants of nature.  I will compare two hypotheses: [Read more…]