A bus ride with quantum trajectories

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I wrote this piece for "Birth of an Idea".

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(https://arxiv.org/abs/1504.00308)

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Some time in around February 2015 I was wrestling with a problem to do with dark matter. Together with some colleagues, I wanted to simulate galactic structure formation including the wave-like effects present when the dark matter is composed of a condensate of ultra-light particles. In this case, you can’t use “out of the box” computer codes, because these “N-body simulations” treat dark matter as a collection of particles interacting only via Newtonian gravity, and cannot model the wave-like effects and interference that I was interested in seeing.

I knew that other people were able to simulate the type of dark matter I was interested in using something called the “Gross-Pitaevski-Poisson equations”, which treat dark matter as a field instead of as a particle. But I didn’t want to solve these equations. I wanted to solve something much closer to the standard N-body simulations, so I could build on all the work and understanding we have in that field already rather than having to start from scratch.

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Well, I was taking an over night bus from Toronto to New York city, which I did about once a month at that time. It was cold outside, I had my music on, and I was bundled up in the semi-darkness with a hip flask of Canadian Rye, and a book about quantum mechanics. 

I’m a cosmologist, and I hadn’t had to think about quantum mechanics since early on in my PhD. I was reading this book, trying to understand where the Gross-Pitaevski equations came from, and how they were related to other descriptions of quantum mechanics. I was reading around somewhat haphazardly, searching in the dark for some answers, but also enjoying the journey, and the opportunity to revisit some classic physics.

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Then I started coming across a whole new way of looking at the problem that I was unaware of before. 

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This approach, which was hardly new to anyone but me, involves describing quantum mechanics (and by extenstion, the Gross-Pitaevski equations without gravity) as a set of statistical distributions, fluid equations, and forces. 

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This was just what I was looking for, because it meant that with an almost trivial generalisation of the textbook quantum mechanics description, I could adapt this language to the galaxy formation problem. The description in terms of fluids and forces mapped perfectly into the standard way to describe dark matter in simulations, and the wavelike effects of the Gross-Pitaevski equations could be modelled with a modification to the usual gravitational force law.

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What I had been exploring with my colleagues already were fudges and approximations. Guesses at a force law modification that would approximate the wave-like effects. But here, staring at me from the page of a textbook, was the exact answer: no approximations necessary!

Sitting on that dark bus, reading a textbook almost for leisure to catch up my quantum mechanics knowledge, I’d stumbled across the solution to all my problems. I quickly scribbled down the ideas to email to my colleagues in the morning, and set to work chasing through strings of references.

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Like I said, the ideas themselves weren’t new, but sometimes even a Eureka moment of finding the right part of the literature, the right signpost, can be exhilarating. And these moments often take place in out-of-the-ordinary environments, when we’re not expecting them.

Knowing that moments like this can happen is a joy, and reminds me that science is a creative and non-linear process. That we can be working at any time, with problems ticking over in the background before Eureka strikes.