Re: [Phys-l] Quantum of action

[David Bowman <David_Bowman@georgetowncollege.edu>]

Regarding JD's interpretation of the physical meaning of Planck's Constant:

> ...
> Executive summary:  In phase space, Planck's constant is the area 
> per /basis/ state, for any given basis.  It is not the quantum of
> action, and it is not the quantum of energy. 
> ...

I agree with JD that h happens to be the mean area occupied per basis state in phase space.  This shows up quite nicely when those states are given their Wigner function representation as real-valued (but not necessarily positive definite) phase space functions.

But I've always considered the actual deeper *meaning* of Planck's constant as it actually being a unit *conversion factor* not all that unlike the causal speed limit c being a conversion factor between intervals of spacetime denominated in temporal units and those denominated in spatial units.  In the particular case of Planck's Constant h-bar is the conversion factor between an elapsed action for some classical path in phase space and the corresponding phase shift in radians of the superposed quantum amplitude of that path between the initial and final states.  Whereas h is the conversion factor between elapsed action along a path and the number of full cycles of phase shift of superposed quantum amplitude.  The factor of 2*[pi] between h-bar and h reflects the fact that there are 2*[pi] radians of phase in a full cycle of phase.  This identification of h/h-bar as conversion factors between elapsed action and complex phase angle shows up most strikingly in the Feynman path integral formulation of quantum mechanics.

In short, in SR c tells us that there are 299792458 m of spacetime in 1 s of spacetime, and in QM h-bar tells us that there is 1.054571726(47)x10^-34 J·s of action in a radian of quantum phase shift and h tells us there is 6.62606957(29)x10^-34 J·s of action in a full cycle of quantum phase shift.

David Bowman