Speed and distance dependence of non-contact quantum friction
In plain words
Two smooth surfaces sliding past each other without touching might still feel a drag from quantum fluctuations of the field between them, even at zero temperature. Most theories predict a tiny nonzero drag, but they disagree on how it depends on speed and distance, and no experiment has detected it.
Precise statement
Two planar half-spaces with dielectric response $\varepsilon(\omega)$ at gap $d$, moving parallel with constant velocity $v << c$, at $T = 0$ and in vacuum. Quantity: the lateral force $F_x(v, d)$ and its exponents at small $v$ (for Drude metals treatments give $F_x \sim v^{3} / d^{n}$, with $n$ and prefactors differing between formalisms, and some model treatments find zero). An answer is the $T = 0$ exponents and prefactor of $F_x(v, d)$ agreed across macroscopic-QED formalisms for dissipative media, plus a measurement of a velocity-dependent drag separated from thermal and electrostatic contributions.
What would settle it
A derivation of $F_{x}(v, d)$ at $T = 0$ accepted across competing formalisms, and a measurement with an atom, nanoparticle or tip moving near a surface that isolates the quantum term.
Status in the literature
No observation exists; the zero-temperature result was disputed by Philbin and Leonhardt (2009) and answered by Pendry (2010), and the scaling still differs between treatments.