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We hypothesize that an agent that can look around in static scenes can learn rich visual representations applicable to 3D object tracking in complex dynamic scenes. We are motivated in this pursuit by the fact that the physical world itself is mostly static, and multiview correspondence labels are relatively cheap to collect in static scenes, e.g., by triangulation. We propose to leverage multiview data of \textit{static points} in arbitrary scenes (static or dynamic), to learn a neural 3D mapping module which produces features that are correspondable across time. The neural 3D mapper consumes RGB-D data as input, and produces a 3D voxel grid of deep features as output. We train the voxel features to be correspondable across viewpoints, using a contrastive loss, and correspondability across time emerges automatically. At test time, given an RGB-D video with approximate camera poses, and given the 3D box of an object to track, we track the target object by generating a map of each timestep and locating the object's features within each map. In contrast to models that represent video streams in 2D or 2.5D, our model's 3D scene representation is disentangled from projection artifacts, is stable under camera motion, and is robust to partial occlusions. We test the proposed architectures in challenging simulated and real data, and show that our unsupervised 3D object trackers outperform prior unsupervised 2D and 2.5D trackers, and approach the accuracy of supervised trackers. This work demonstrates that 3D object trackers can emerge without tracking labels, through multiview self-supervision on static data.