John Denker's question about gravity prompted my thinking about what other concepts have some type of duality. My first finding was kinetic energy.
In classical mechanics, we often use the equation E = K + U, with E being total (mechanical) energy, K being kinetic and U being potential energies. Hence, classically, K = E-U. We also, classically, determine K = (mv^2)/2 = (p^2)/2m, or with SR K=mc^2(gamma -1). All 3 are positive definite, and everyone is happy.
In QM, with the time independent SWE, <psi|(E-U)|psi> = -(hbar^2)/2m <psi|psi''>, and we allow the quantity (E-U) to be negative (barrier penetration) and when it is we say it's "classically forbidden." Is it proper to also call this occurrence of (E-U) kinetic energy, and that it is negative? I generally do, and I even mention that while classical or SR kinetic energies are positive, QM kinetic energies can have negative values. Does someone have a vocabulary for this that avoids negative K?