How To Make An Electron Seem Lighter Than It Is

Some of the electrons in this semiconductor may behave like they have a smaller mass. Source: Shutterstock

I’ve been largely silent here because classes are in session and I have an impending deadline for a book, so time for blogging is rather scarce. I don’t want to let the site go completely dark, though, and a post last week by fellow Forbes blogger Jillian Scudder provides a great opportunity for a quick post about some physics that ought to be more widely known.

The post in question is a response to a reader asking about a well-known feature of relativity, namely the increasing resistance to acceleration as the speed of an object increases. This is the same sort of behavior that you would expect from a higher-mass object (though for technical reasons physicists tend not to talk about “relativistic mass” any more), so the particle “looks like” it’s gotten heavier.

This naturally leads to the reader question answered in that post, namely:

Speed can make objects act as if they have more mass, but can you ever make an object appear to have less mass?

The answer given is “no,” and that’s perfectly true… in the context of macroscopic objects moving in free space. Which is the primary domain of interest for astrophysics. If you take a more expansive view of physics, though, it’s perfectly possible to create a scenario in which an electron behaves as if it has a lower mass, provided you do it inside a material.

This goes back to something I got from a very cool talk by Jimmy Williams of the University of Maryland a couple of years ago, that put condensed matter physics into a very interesting context. Williams noted that when you start to consider the electrical characteristics of materials– how easily electrons move around in response to applied fields– you can do surprisingly well with the simplest, stupidest model you might want to imagine, namely one where the electrons move freely inside the material, and don’t interact with each other. This works great, giving you good quantitative agreement with experiments, provided you slightly modify the properties of the electron. Instead of using the free-space electron mass and charge that you can find on the inside back cover of any physics textbook, you use an effective mass and an effective charge for the carriers, that differ from the free-space values.

This is a remarkable coincidence– given the complicated interactions of uncountably huge numbers of particles inside a macroscopic chunk of stuff, you wouldn’t necessarily expect them to all combine in a way that produces such a simple result. This surprising result drives a lot of work in one particular subfield of condensed matter physics, where people use the observation that natural materials create situations where electrons seem to have different properties, and try to engineer new substances to push those effective properties to extreme values.

And in that context, it’s perfectly possible to create a situation where an electron has an effective mass smaller than the free-space mass. In fact, if you just look up effective mass on Wikipedia like a lazy sophomore, most of the values listed are lower than the free-space mass.

This sort of work is also done within one of my favorite subfields of atomic physics, namely cold-atom analogues of condensed-matter systems (I wrote a ebook about this area for <em, though I didn’t talk about effective mass). Cold atom systems have the additional advantage of allowing you to look at behavior that happens much too quickly to see in real solids, as seen in this 2013 paper from Toronto (arxiv version). And there’s been very recent work claiming the creation of a negative effective mass (arxiv version), though there’s also been a lot of argument about that description.

Now, you might object that this isn’t “really” a change in the mass of an electron. But this description is ultimately derived from exactly the same sort of measurement that leads you to say that the mass of an object increases in relativity: you apply a force, measure an acceleration, and apply Newton’s second law to infer a “mass.” So I would argue that it’s exactly as accurate to talk about electron mass decreasing inside a solid as to talk about electron mass increasing in a particle accelerator.

Of course, it’s not nearly as much fun to think about effective properties of subatomic particles down inside a solid as the effective mass of a macroscopic object moving through space at high speed. If you want to make something look lighter, though, that’s the way you have to do it: start with an electron, stick it inside a solid, and let condensed matter physics do the rest.

Chad Orzel is a physics professor, pop-science author, and blogger. His latest book is Eureka: Discovering Your Inner Scientist (Basic Books, 2014).

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