“Combining Einstein’s General Relativity (everyday-scale physics) with Quantum Mechanics (atomic and sub-atomic physics) would be the long sought ‘Theory of Everything’. So far, the 2 physical realms seem to operate in entirely different ways.”
How does Plank’s Constant fit into this?
Couldn't tell you. Can't even find a clear, straight forward definition of what it is.
"Planck’s constant, (symbol h), fundamental physical constant characteristic of the mathematical formulations of quantum mechanics, which describes the behaviour of particles and waves on the atomic scale, including the particle aspect of light.
The German physicist Max Planck introduced the constant in 1900 in his accurate formulation of the distribution of the radiation emitted by a blackbody, or perfect absorber of radiant energy (see Planck’s radiation law). The significance of Planck’s constant in this context is that radiation, such as light, is emitted, transmitted, and absorbed in discrete energy packets, or quanta, determined by the frequency of the radiation and the value of Planck’s constant.
The energy E of each quantum, or each photon, equals Planck’s constant h times the radiation frequency symbolized by the Greek letter nu, ν, or simply E = hν. A modified form of Planck’s constant called h-bar (ℏ), or the reduced Planck’s constant, in which ℏ equals h divided by 2π, is the quantization of angular momentum. For example, the angular momentum of an electron bound to an atomic nucleus is quantized and can only be a multiple of h-bar.
The dimension of Planck’s constant is the product of energy multiplied by time, a quantity called action. Planck’s constant is often defined, therefore, as the elementary quantum of action. Its value in metre-kilogram-second units is 6.62606957 × 10^−34 joules/second, with a standard uncertainty of 0.00000029 × 10^−34 joules/second.
http://www.britannica.com/EBchecked/topic/462917/Plancks-constant