Quantum games

Last March, I attended the APS March Meeting, which is the largest annual physics conference in the country (and perhaps world?). During the conference, one of the particularly memorable sessions was about quantum gamification, making games using concepts from quantum physics.

Quantum games are an interesting concept, because usually “physics-based games” are only based on classical physics, specifically gravity and collision. The point of having a physics-based game is to have a relatively complex system where you don’t need to teach players every single detail, because they already have an intuition for how gravity and collision work. But obviously, when it comes to quantum physics, players don’t have an intuition, thus the physics must serve some other purpose.

In most of these games, the nominal purpose is either (a) teach physics, or (b) use player data to help physicists. Although I get the sense that the nominal purpose is not always the true purpose. I’m not that confident in the value of collecting player data, and suspect that the true purpose is more about public outreach. And some of the “outreach” projects kinda felt like they were just a way for physicists to do something fun. Well, whatever persuades people to give you grant money.

Anyways, let’s check out some of these games.

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How peer review works

Even if you’ve never been involved in scientific research, you’re probably aware that it involves a process called “peer review”. I want to take a minute to explain how this actually works. This is based on my personal experience, although I think much of it generalizes to other academic fields, including those outside of science.

1. Sending to referees

It starts with the submission of a manuscript to a journal. A lot of work has already gone into the manuscript, including input from collaborators and colleagues, but this is where peer review formally begins.

The journal assigns the manuscript to an editor, and then the editor chooses a few (usually 3) referees to look at the paper. Now, choosing referees can be quite difficult, because they need to be close enough to the field that they can understand and critique the manuscript. In fact, it’s common for referees to decline, because they think the manuscript is too far outside their field. And yet, referees can’t be so close that they’re direct competitors. Authors typically provide a list of competitors to the editor to avoid conflict of interest (or even worse, theft of ideas). But editors aren’t required to follow this advice, and authors never know because they don’t know the names of the referees.

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Physics and p-values

In science, there is something called the “replicability crisis”–the fact that the results of most studies cannot be replicated. This appears to mainly come from psychology and medicine, where meta-studies have found low replicability rates. But it likely generalizes to other scientific fields as well.

At least, when people talk about the replicability crisis, they definitely seem to believe that it generalizes to all fields. And yet, one of the most commonly discussed practices is p-hacking. Excuse me, folks, but I’m pretty sure that p-hacking does not generalize to physics. In my research, we don’t calculate p-values at all!

(Background: p-hacking is the problematic practice of tweaking statistical analysis until you get a p-value that is just barely low enough to technically count as statistically significant. FiveThirtyEight has a neat toy so you can try p-hacking yourself.)

Here I speculate why p-values rarely appear in physics, and what sort of problems we have in their place.
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Stabilizing an inverted pendulum

Like many physicists, I have a fondness for simple physical systems that behave in unexpected ways. Here’s a demo known as “Kapitza’s pendulum”.

For those who didn’t watch the video, it shows an ordinary pendulum attached to a motor. Then the motor starts moving up and down 58 times per second. While the motor is running, the pendulum stands upright, and stays upright even when knocked to the side.

Kapitza’s Pendulum is easily understood by anyone with a degree in physics. But for everyone else, here’s an explanation that could be understood with high school physics.

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Meaning of “theory” in science and pop-science

In science, a theory is “a well-substantiated explanation of some aspect of the natural world that is acquired through the scientific method and repeatedly tested and confirmed”–according to Wikipedia. This is frequently contrasted with the colloquial meaning of “theory”, which usually refers to something speculative and unconfirmed. It is suggested that in a scientific context, it is more appropriate to refer to a speculative idea as a “hypothesis”.

However, in my experience as a physicist, this is not how the word “theory” is used in practice. Generally, the word “theory” is contrasted with “experiment”, describing the kind of work rather than the quality of the work. Since theories are carefully crafted by experts, it is fair to say that they are more than mere speculation, but that doesn’t mean that every theory has been thoroughly tested and confirmed. Some theories are untested, some theories are in direct competition with other equally viable theories, some theories intentionally model things that do not presently exist, and some theories are just poorly crafted.

So, basically, Wikipedia–and most dictionaries as well–appear to be in conflict with my understanding as a fluent speaker of English physics. That probably means there’s some bad lexicography going on.
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The PBR Theorem explained

The PBR theorem is another theorem of quantum mechanics, which could go alongside Bell’s Theorem and the Kochen-Specker Theorem.  I wrote this explanation in 2011, before the paper was officially published in Nature.  Since then, it’s been recognized as a moderately important theorem, and it has been named after its three authors (Pusey, Barrett, and Rudolph).  But at the time I didn’t really know whether it would become important.

There’s a new paper on arxiv called “The quantum state cannot be interpreted statistically“.  It has a theorem which proves that, given a few basic assumptions, the quantum state (ie the wavefunction) must be real, rather than a merely statistical object.  Nature has an article which mostly just harps on how “seismic” the paper is. 

Nature (correction: the article’s author, not Nature itself) compares its importance to Bell’s Theorem, which is a very important result indeed from 1964.  Bell’s theorem proved that if there were “hidden variables” underneath the quantum state, then entangled particles must be communicating with each other faster than light.  I’ve explained Bell’s theorem in the past.

I felt the news coverage left a lot of unanswered questions.  What do they even mean by the “statistical interpretation” of quantum mechanics?  Roughly how is it proven?  What is the difference between this and Bell’s theorem?  I found the answers in the arxiv print, and will attempt to summarize them.

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Kochen-Specker Theorem explained

I previously explained Bell’s Theorem, which is a “no go” theorem of quantum mechanics. In brief, Bell’s Theorem proved in 1964 that any hidden variable interpretation of quantum mechanics must be nonlocal.

Of course, you may be thinking, maybe the world just is nonlocal, and that hidden information is being passed around faster than light. Unfortunately, there’s another major theorem which makes hidden variable theories even more unpalatable. In 1966-1967, the Kochen-Specker Theorem proved that any hidden variable interpretation must be contextual.

To understand the meaning of “contextual”, suppose we have a quantum cat, and the cat has many possible states. It could be awake or asleep. It could be happy or unhappy. Or the cat could be none of those things because it is dead. Now suppose there are two possible measurements, which answer the following questions:

(1) Is the cat awake, asleep, or dead?
(2) Is the cat happy, unhappy, or dead?

This is a quantum cat, so you can only choose one of the two measurements. However, even if you can’t make both measurements experimentally, you might reasonably expect that the outcomes of the two measurements are related to each other.  Specifically, if measurement (1) would find a dead cat, then so would measurement (2), and vice versa. This assumption is called non-contextuality. This cannot be true of hidden variable interpretations of quantum mechanics! Such theories must be contextual.

Figure 1: ambiguous catFig. 1: Cat of ambiguous state.  Credit: Visentico / Sento

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