which, because it is linear, has no singularities. Equation (3) thus is the mathematically consistent form of the Hamilton-Jacobi equation. It is of course the Schrödinger equation. Notice however that the above derivation leaves us no choice in choosing the meaning of ψ: it is necessarily a relative density of trajectories (worlds or universes) amplitude, not a probability amplitude. Similarly, the derivation tells us what is: the strength of interaction between the worlds. It also tells us what a "classical" world is: a trajectory along which the other worlds can be ignored. This can occur only if ∇ 2 R = 0, which has R = constant as the only bounded regular solution. In particular, if V ( x, t) = 0, the classical trajectories are the plane waves, not minimal uncertainty wave packets. Many-Worlds quantum mechanics is thus more general that standard quantum mechanics, because the wave function need not be an element in a Hilbert space, which a plane wave is not. Finally, the derivation tells us why the equations of physics are quantized: to prevent singularities from arising in the laboratory. The Many-Worlds meaning of ψ entails that the Born frequencies are approached in the limit of an infinite number of experiments , .