The tyranny of reciprocal space

I was again thinking about why it can be difficult to explain some solid-state physics ideas to the lay public, and I think part of the problem is what I call the tyranny of reciprocal space.  Here's an attempt to explain the issue in accessible language.  If you want to describe where the atoms are in a crystalline solid and you're not a condensed matter physicist, you'd either draw a picture, or say in words that the atoms are, for example, arranged in a periodic way in space (e.g., "stacked like cannonballs", "arranged on a square grid", etc.).  Basically, you'd describe their layout in what a condensed matter physicist would call real space.  However, physicists look at this and realize that you could be much more compact in your description.  For example, for a 1d chain of atoms a distance a apart from each other, a condensed matter physicist might describe the chain by a "wavevector" k = 2 \pi/a instead.  This k describes a spatial frequency; a wave (quantum matter has wavelike properties) described by cos kr would go through a complete period (peak of wave to peak of wave, say) and start repeating itself over a distance a.   Because k has units of 1/length, this wavevector way of describing spatially periodic things is often called reciprocal space.  A given point in reciprocal space (k_x, k_y, k_z) implies particular spatial periodicities in the x, y, and z directions.

Why would condensed matter physicists do this - purely to be cryptic?  No, not just that.  It turns out that a particle's momentum (classically, the product of mass and velocity) in quantum mechanics is proportional to k for the wavelike description of the particle.  Larger k (shorter spatial periodicity), higher momentum.  Moreover, trying to describe the interaction of, e.g., a wave-like electron with the atoms in a periodic lattice is done very neatly by worrying about the wavevector of the electron and the wavevectors describing the lattice's periodicity.  The math is very nice and elegant.  I'm always blown away when scattering experts (those who use x-rays or neutrons as probes of material structure) can glance at some insanely complex diffraction pattern, and immediately identify particular peaks with obscure (to me) points in reciprocal space, thus establishing the symmetry of some underlying lattice.

The problem is, from the point of view of the lay public (and even most other branches of physics), essentially no one thinks in reciprocal space.  One of the hardest things you (as a condensed matter physicist) can do to an audience in a general (public or colloquium) talk is to start throwing around reciprocal space without some preamble or roadmap.  It just shuts down many nonexperts' ability to follow the talk, no matter how pretty the viewgraphs are.  Extreme caution should be used in talking about reciprocal space to a general audience!  Far better to have some real-space description for people to hang onto.