We observed single molecules of fluorescently labeled double-stranded (ds) λ DNA held in an antiBrownian electrokinetic trap. From the measured density fluctuations we extract the density-density response function of the molecule over times >4.5 ms and distances >250 nm, i.e., how a perturbation in density in one part of the molecule propagates through the rest of the molecule. We find a nonmonotonic radial dependence of the relaxation time. In contrast with earlier measurements on freely diffusing dsDNA, we observe clear signs of internal hydrodynamic interactions.Thermal fluctuations agitate molecules in solution over a broad range of times and distances. By passively watching the shape fluctuations of a thermally driven biopolymer, one can infer properties of the underlying interactions that determine the motion.Dynamic light scattering (DLS) and fluorescence correlation spectroscopy (FCS) each probe specific low-dimensional correlation functions of the shape fluctuations; these can be compared to predictions of Rouse, Zimm, or other hydrodynamic models [1]. The two techniques are complementary in that DLS probes fluctuations at a fixed k vector and FCS at a fixed position vector. Both techniques are also limited in the time scales they can probe: very fast fluctuations occur over distances too short to be detected optically, and very slow fluctuations are masked by translational diffusion.DLS has been used to measure the few longest relaxation times of DNA, and much theory has been devoted to predicting scattering functions for different polymer models [2,3]. FCS has also been used to probe the dynamic fluctuations of fluorescently labeled DNA [4,5]. Recently Shusterman and co-workers [6] probed the dynamics of the end monomer in single-stranded (ss) and double-stranded (ds) DNA using FCS. They observed Zimm dynamics in the ssDNA, but, surprisingly, Rouse dynamics in the dsDNA on time scales <10 ms. In contrast, the translational diffusion of dsDNA obeys Zimm scaling to high accuracy [7]. Shusterman et al. argued that a semiflexible partially draining polymer should show Rouse dynamics on short time scales and Zimm dynamics on long time scales. However, the observation times required to detect Zimm dynamics in dsDNA are longer than can be achieved with FCS.Here we directly measure the underlying time-dependent conformations of individual dsDNA molecules over times >4.5 ms and distances >250 nm. FCS-like and DLS-like correlation functions are special cases of the density-density covariance obtained from our data. Our experiment lacks the short-time resolution of DLS and FCS, but probes long-time dynamics (milliseconds to seconds) that are masked by translational diffusion in the other techniques. The data presented here provide the first detailed spatial picture of the fluctuating dynamics within a single conformationally relaxed polymer molecule. To study a single molecule in equilibrium, one would like to eliminate the motion of the center of mass (c.m.), without affecting internal motions. We used ...