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Classical theories are useful approximations of quantum theories.
"Particles do not follow trajectories. They are described by wavefunctions but under appropriate circumstances the constructive interference of the phases of the wavefunction will single out a path which we call a classical trajectory. The Hamilton-Jacobi Equation is just the lowest-order Schrodinger equation if we use the ansatz in Eq. (2.1). The ¨ mysterious procedure in Hamilton-Jacobi theory — of differentiating the solution to Hamilton-Jacobi equation and equating it to a constant — is just the condition for constructive interference of the phases of waves differing slightly in the parameter E. The procedure based on Hamilton-Jacobi theory works in classical mechanics because it is supported by the Schrodinger equation"
See also: Decoherence and the Transition from Quantum to Classical—Revisited by Zurek and The quantum-to-classical transition and decoherence by Maximilian Schlosshauer