The resistivity of La$_{1-x}$Sr$_x$MnO$_3$ cannot be explained by the double exchange model alone. A. J. Millis, P. B. Littlewood, and B. I. Shraiman argue that the model is incompatible with experimental data and propose that strong electron-phonon interactions, arising from Jahn-Teller splitting of the Mn$^{3+}$ ion, play a crucial role. The system is described by a Hamiltonian that includes the double exchange interaction and core spin coupling. The model is solved to show that the calculated conductivity and resistivity disagree with experimental results. The discrepancy is attributed to additional physics, such as polaron effects due to strong electron-phonon coupling. The authors suggest that the Jahn-Teller splitting is significant and that the magnetic transition temperature is much higher than observed, indicating the need for additional physics. They also show that the calculated resistivity is too small and has incorrect temperature and field dependence, suggesting that polaron effects are responsible for the discrepancy. The paper concludes that the double exchange model is insufficient and that a more comprehensive theory is needed to explain the observed properties of La$_{1-x}$Sr$_x$MnO$_3$.The resistivity of La$_{1-x}$Sr$_x$MnO$_3$ cannot be explained by the double exchange model alone. A. J. Millis, P. B. Littlewood, and B. I. Shraiman argue that the model is incompatible with experimental data and propose that strong electron-phonon interactions, arising from Jahn-Teller splitting of the Mn$^{3+}$ ion, play a crucial role. The system is described by a Hamiltonian that includes the double exchange interaction and core spin coupling. The model is solved to show that the calculated conductivity and resistivity disagree with experimental results. The discrepancy is attributed to additional physics, such as polaron effects due to strong electron-phonon coupling. The authors suggest that the Jahn-Teller splitting is significant and that the magnetic transition temperature is much higher than observed, indicating the need for additional physics. They also show that the calculated resistivity is too small and has incorrect temperature and field dependence, suggesting that polaron effects are responsible for the discrepancy. The paper concludes that the double exchange model is insufficient and that a more comprehensive theory is needed to explain the observed properties of La$_{1-x}$Sr$_x$MnO$_3$.