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Quantum mechanics teaches us what the physical meaning of action really is.phase
Action is really a phase of a complex amplitude. One cycle of action
corresponds to h = 6.626 x 10^(-34) J*s and an action of one radian of
angle corresponds to h_bar = 1.0546 x 10^(-34) J*s. The extent that one
wants to think of angles as dimensionless is the extent to which action is
also fundamentally dimensionless.
David Bowman