  A nonrelativistic Hamiltonian describing interaction between a mechanical
degree of freedom and radiation pressure is commonly used as an ultimate tool
for studying system behavior in opto-mechanics. This Hamiltonian is derived
from the equation of motion of a mechanical degree of freedom and the optical
wave equation with time-varying boundary conditions. We show that this approach
is deficient for studying higher order nonlinear effects in an open resonant
opto-mechanical system. Opto-mechanical interaction induces a large mechanical
nonlinearity resulting from a strong dependence of the power of the light
confined in the optical cavity on the mechanical degrees of freedom of the
cavity due to coupling with electromagnetic continuum. This dissipative
nonlinearity cannot be inferred from the standard Hamiltonian formalism.
