Many theoretical models have been developed to explain the rapid acceleration to relativistic energies of electrons that form the Earth's radiation belts. However, after decades of research, none of these models has been unambiguously confirmed by comparison to observations. Proposed models can be separated into two types: internal and external source acceleration mechanisms. Internal source acceleration mechanisms accelerate electrons already present in the inner magnetosphere (L < 6.6), while external source acceleration mechanisms transport and accelerate a source population of electrons from the outer to the inner magnetosphere. In principle, the two types of acceleration mechanisms can be differentiated because they imply that different radial gradients of electron phase space density expressed as a function of the three adiabatic invariants will develop. Model predictions can be tested by transforming measured electron flux (given as a function of pitch angle, energy, and position) to phase space density as a function of the three invariants, ¿, K, and Φ. The transformation requires adoption of a magnetic field model. Phase space density estimates have, in the past, produced contradictory results because of limited measurements and field model errors. In this study we greatly reduce the uncertainties of previous work and account for the contradictions. We use data principally from the Polar High Sensitivity Telescope energetic detector on the Polar spacecraft and the Tsyganenko and Stern <1996> field model to obtain phase space density. We show how imperfect magnetic field models produce phase space density errors and explore how those errors modify interpretations. On the basis of the analysis we conclude that the data are best explained by models that require acceleration of an internal source of electrons near L* ~ 5. We also suggest that outward radial diffusion from a phase space density peak near L* ~ 5 can explain the observed correspondence between flux enhancements at geostationary orbit and increases in ULF wave power.