Mechanical surface tension governs membrane thermal fluctuations.

We use analytical considerations and computer simulations to show that the membrane spectrum of thermal fluctuations is governed by the mechanical and not the intrinsic tension. Our study highlights the fact that the commonly used quadratic approximation of the Helfrich effective Hamiltonian is not rotationally invariant. We demonstrate that this nonphysical feature leads to a calculated mechanical tension that differs dramatically from the correct mechanical tension. Specifically, our results suggest that the mechanical and intrinsic tensions vanish simultaneously, which contradicts recent theoretical predictions derived for the approximated Hamiltonian.