Understanding the well-documented differences between Greenland and Antarctica's paleoclimate proxy time series in terms of the dynamic processes connecting the two Polar Regions would help develop a quantitative theory of polar climate teleconnections. Multiple conceptual models have been proposed to explain the polar climate time series relationship, and to extend Greenland climate records based on the much longer records from Antarctica. Here we compare the most relevant conceptual models proposed to characterize inter-polar teleconnections associated with these time series. We show that the polar synchronization model, which proposes that the climates of the Polar Regions were phase synchronized over most of the last ice age, shows better overall skill across the range of parameter space under test and provides a physical explanation of the polar teleconnection as the mutual synchronization of two nonlinear, coupled oscillators. Phase synchronization results when two or more nonlinear oscillators couple (in this case the two polar climates coupled through the ocean and atmosphere) and therein adjust their (initially different) natural rhythms to a common frequency and constant relative phase. Detailed analyses presented here show that the polar synchronization is a reliable framework to support further studies of polar climate teleconnections.