Conventional tracking paradigm takes in instantaneous measurements such as range and bearing, and produces object tracks across time. In applications such as autonomous driving, lidar measurements in the form of point clouds are usually passed through a "virtual sensor" realized by a deep learning model, to produce "measurements" such as bounding boxes, which are in turn ingested by a tracking module to produce object tracks. Very often multiple lidar sweeps are accumulated in a buffer to merge and become the input to the virtual sensor. We argue in this paper that such an input already contains temporal information, and therefore the virtual sensor output should also contain temporal information, not just instantaneous values for the time corresponding to the end of the buffer. In particular, we present the deep learning model called MULti-Sweep PAired Detector (MULSPAD) that produces, for each detected object, a pair of bounding boxes at both the end time and the beginning time of the input buffer. This is achieved with fairly straightforward changes in commonly used lidar detection models, and with only marginal extra processing, but the resulting symmetry is satisfying. Such paired detections make it possible not only to construct rudimentary trackers fairly easily, but also to construct more sophisticated trackers that can exploit the extra information conveyed by the pair and be robust to choices of motion models and object birth/death models. We have conducted preliminary training and experimentation using Waymo Open Dataset, which shows the efficacy of our proposed method.