Bicycling and Quantum Measurement
Humble-bragging about bike rides made (even) dorkier
My goal for today is to write the absolute dorkiest thing you are likely to read about bicycling in 2022. That’s a high bar to clear, I know, but I think we can do it.
Some background first: When we bought our house, a couple of miles from campus, I bought a mountain bike with the intention of riding it to work in nice weather. I’ve never been terribly good about doing that, but for a while in the 2006-7 sort of range I got into riding long-ish distances for exercise. Mostly on the Mohawk-Hudson bike trail and on various and sundry surface streets. I got out of the habit after SteelyKid was born in 2008 (followed by The Pip in 2011), but picked it up again after SteelyKid learned to ride. The Pip learned to ride a bike in early 2020— one of the last mask-less trips I took to Target was to pick up the one bike of an appropriate size that they had— and biking has been a godsend during the harder bits of the pandemic. It’s perfect socially distant exercise— outdoors, and at such a speed that even if you pass people, you’re only sharing air for a second or two.
The kids haven’t continued to be enthusiastic about biking, but I still go out a fair bit, trying to ride in when I need to go to campus for relatively sedate activities (i.e., not to play hoops), and riding loops on weekdays just for exercise. I have turned into the sort of person who says “I have a Zoom call in an hour, that’s enough time to get in eight miles,” a development that would have been a severe shock to 19-year-old me. If you follow me on social media, you’ve seen a bunch of these Strava screengrabs:
I’ve been doing a lot of biking this year— the weather has been unusually cooperative, and I’m also making an effort to lose a bit of weight, so have been less of a slacker than some other times. One of the cool results of this, as I noted on Twitter last week, is a feeling like I “leveled up”:
As I went on to note in the thread, this is mostly an illusion, in a way that also works as a kind of illustration of projective measurement in quantum mechanics.
So, what do I mean by that? Well, what’s actually going on here as that as I bike more and more, my general level of fitness increases in a fairly continuous way, sort of like the blue line in this (totally fake) graph:
While that’s the key underlying phenomenon, the quasi-objective measurement available to me is the gear setting at which I can comfortably cruise on the bike. That’s discrete— the bike ccan only work when the chain is on one of the eight gears on the back wheel— so looks more like the red curve in the graph above. At some point, my fitness improves to a point where it’s comfortable to ride along at the next gear up, and that feels like “leveling up,” even though it’s just a reflection of a slower, continuous improvement.
What does this have to do with quantum physics? One of the most famous philosophical difficulties with the problem is the “measurement problem,” which has a very similar character. The wavefunction describing a quantum system, the thing we use to calculate the probability of a given measurement outcome, evolves in a smooth and continuous way, like the blue curve in the above. This corresponds to a slowly increasing probability of being in one state rather than the other. The act of measuring, on the other hand, is discrete: when you measure the state of the system, you get one and only one answer, which has to match one of the allowed states of the system. Following the measurement, the system is 100% in the state that was just measured— in quantum jargon, it has been “projected” onto the relevant state— and the continuous evolution resumes.
The various “interpretations” of quantum physics— Copenhagen, Many-Worlds, QBism, etc.— are at some level just stories that we tell about what happens during that measurement process. They’re offering different explanations about how that continuously evolving probability turns into a discrete measurement result, and people get very invested in these, leading to lengthy and sometimes acrimonious arguments.
The actual process involved is an unquestionable empirical fact, though, well established through innumerable experiments. My favorite of these is probably the “Quantum Zeno Effect,” which uses this projective measurement to change the evolution of the system. The name comes from one of Zeno’s paradoxes, which purport to show the impossibility of motion— one of the most famous versions says that you can’t get anywhere, because to go some distance you first have to go to the halfway point, and then half of the remaining distance, and then half of that last quarter, and so on. Each of those steps takes some time, and there are an infinite number of them, so motion is impossible.
With regard to motion in general, physicists tend to regard this as solved with the invention of calculus, and respond to any attempt to bring it up as a serious issue in the manner of Diogenes the Cynic: by standing up and walking away. Quantum measurement allows you to do a kind of active version of this, though: if you have a system that’s slowly moving between one of two possible states, measuring the state at some intermediate point will project it to one or the other. If you make the measurement at a point where the probability of having changed states is low, the most likely result is to send the system back to the start. If you keep making measurements after short intervals, you can keep re-setting the state, and end up keeping it from ever changing.
The classic demonstration of this is a 1990 paper by Wayne Itano, Dan Heinzen, John Bollinger, and Dave Wineland at NIST in Boulder (thanks to that affiliation, the PDF is freely available). They took a bunch of beryllium ions held in a trap and exposed them to light that would push them from one state to another, with the probability of being found in the other state increasing like a sine function— exactly the blue curve in my fake data above. This process is very well understood, and has a 100% probability of moving all the ions from the initial state to the final state in a particular amount of time, which they confirmed experimentally.
Then they made measurements at intermediate times by shining a different color of light on the ions, which would be absorbed by one state and not the other. Any ions that absorbed a photon would quickly re-emit one that could be detected, returning to the absorbing state. It would then absorb-and-emit again, repeating this cycle at a rapid pace. This makes the total amount of light detected after the pulse a fairly direct measurement of the number of atoms in the absorbing state, which also projects all those atoms into that state, in keeping with quantum rules.
They used this to measure the probability of ending up in the intended final state after one full cycle— which, remember, ought to be 100% in the absence of measurements— as a function of how many times they measured the state during the slow evolution process. The results look like a set of bar graphs:
(There are two of these because one looked at the probability of starting in state 1 and ending in state 2, the other of starting in state 2 and ending in state 1.) These clearly show the probability dropping off as the number of measurements increases, exactly as predicted for the Quantum Zeno Effect. Each measurement re-starts the process for some fraction of the atoms, and more frequent measurements make that fraction larger. With frequent enough measurements, you can extend the transition process almost indefinitely.
This is a really cool result, one of my favorites from quantum optics because it’s so clean and unambiguous. This is also featured in a dialogue from my first book, which I turned into a video way back in 2009 (reading the dog’s part in a silly voice):
(They re-did the cover a few years later, so the image you see in the video is not the cover you’ll get today…)
It’s also sorta-kinda the same thing that’s going on with my “level up” feeling on the bike: a smooth and continuous evolution has been turned into a discrete step by a process of measurement. And that, I hope, is the dorkiest bike story you’ll read this year…
Now that I’m basically out of the book-publicity cycle, I’m going to try to put more science-y content here. I don’t know how well that’s going to work, but if you’d like to encourage that, here’s a button:
(Paid subscriptions are particularly encouraging, though not strictly necessary…) If you have questions or would like some point clarified, or just want to remark on the late, great Emmy, Queen of Niskayuna, the comments will be open: