The claim about the blue color caused by a relativistic effect in osmium being attributable to the increased mass (inertia, really) of the inner electrons pinned my BS detector. A back-of-the-envelope calculation says the orbital velocity of the innermost electrons is only about c/3. This would result in only about a 6% increase in the inertia of those electrons. There may, indeed be relativistic effects but the simplistic faster means more massive wouldn’t seem to be sufficient explanation.
Edit: The explanation is also a bit glib since adjacent elements are not blue. Rhenium is silvery, as are iridium and platinum. Tungsten’s more gray. None of these come close to blue.
I made an error in estimating the velocity, above. Shoulda used the Uncertainty Principle instead of orbital dynamics. The velocity estimate is closer to c/2, which does cause more significant inertia effects. Nevertheless, adjacent elements aren’t blue even though the same velocity estimate applies so the explanation has to be far more complicated.
The spectral absorption (and hence perceived colour) of bulk metals is a baroquely complicated business. We can usually ignore it as a matter of visual appearance since most metals absorb outside the human visual range and hence reflect all visual wavelengths about the same and appear “silvery”. But for those which do absorb visual wavelengths, such as copper, gold, and (to a lesser extent) osmium, there’s a lot going on.
Here is a 1986 paper from the Soviet Journal of Experimental and Theoretical Physics, “The structure of the energy bands and optical absorption in osmium” [PDF] which gets into the weeds for the case of osmium. Basically, while the electron shell structure of the atom is the root cause of the absorption, the behaviour of a large ensemble of atoms in bulk metal depends upon the conduction bands of the free electrons and the “interband optical conductivity”, whatever that is. This, in turn, is affected by the crystal structure of the metal, and behaves differently for cubic lattice metals such as gold and those with a hexagonal lattice like osmium. Further, the absorption of a hexagonal lattice metal may be anisotropic and different depending upon the polarisation of light.
While relativistic effects shift the energy levels of electrons in the atom (particularly the s orbitals, whose probability density function is concentrated near the massive nucleus), that is only one contributor to the absorption and colour of bulk metal.