$t$. At large times the smaller spheres continue to move, but they stop contributing to $g^{(1s)}(q,t)$ or to the nominal $\langle (\Delta x)^{2}\rangle$ from eq \[eq:meansquare2\].

Experiment thus demonstrates that neither eq \[eq:gaussianform\] nor eq \[eq:g1ssimple\] is generally valid for probe diffusion in complex fluids. Even in a Newtonian fluid, a model system in which $g^{(1s)}(q,t)$ does not decay exponentially in time does not follow eqs \[eq:g1swrong\] and \[eq:meansquare2\], a result that is exactly as required by Doob’s theorem. Interpretations of quasielastic scattering spectra for probes in complex fluids, based on the Gaussian approximation of eq \[eq:g1swrong\], are therefore incorrect. Interpretations of spectra of probes in complex fluids in terms of particle displacements are properly based on eq \[eq:g1sanddisplacements\], which correctly reflects the non-Gaussian displacement distribution function of real probes.

Interpretations of Quasielastic Scattering Spectra \[sectioninterpretations\]
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First, every single physical $g^{(1s)}$ viewed only as a function of $t$ corresponds to a system in which the mean-square particle displacement increases linearly with time. However, the correspondence is not unique. The same $g^{(1s)}(q,t)$ may also correspond to systems in which particle thermal motions are more complex. In consequence, from a $g^{(1s)}(q,t)$ measured over a full range of times and a single 