Amateur thoughts on QM theory at celestial scale Some amateur scientist asked me that why can't one just simply apply the entire theory of QM at atomic scale to "quantize" celestial system with a different choice of $\hslash$, which he believed can be used to understand celestial orbital configurations, for example, the "discrete" distances from various Solar System objects to the sun, and to somehow "unify" the fundamental forces.
Well I'm pretty sure this has been done before and must turn out to be mathematically invalid. However, can anyone give me some intuitive arguments (not too technical) about why this would not work at all.
 A: The constant $\hbar$ may be defined in one of several ways that are ultimately equivalent. For example, it's the quantum of the angular momentum. The orbital angular momentum is a multiple of $\hbar$ while the spin is a general integer multiple of $\hbar/2$.
The $\hbar$ is the commutator $[x,p]/i$ or, equivalently, $\hbar/2$ is the right hand side of the uncertainty relationship $\Delta x \cdot \Delta p \geq \hbar/2$. 
The constant $\hbar$ is the ratio between the energy and frequency of photons – and any other particles with an underlying wave, for that matter: $E=\hbar\omega$.
$(2\pi\hbar)^N$ is the volume of a single "phase cell" with a single discrete state in what classically looks like the $2N$-dimensional phase space.
$2\pi \hbar$ is the minimal positive additive change of the action that doesn't change the physics at all.
I could continue for hours. The mathematics of quantum mechanics may be used to show that all these definitions and many others are actually equivalent.
Whatever definition we use, we may actually more or less "directly" measure how large $\hbar$ is in any units we like, and in the SI units, for example, it is equal to $1.054\times 10^{-34}\,{\rm J}\cdot {\rm s}$. It just can't be anything else just like $\pi$ cannot be $73$.
A related problem – it's really the same problem – is that the specific quantum effects are negligible for the Solar System and the Solar System almost exactly obeys the laws of classical physics that don't depend on any $\hbar$. For large systems like that, the dependence on $\hbar$ simply disappears so the right description obviously cannot depend on any (much higher) value of $\hbar$.
Quantum mechanics still affects lots of things and questions about the Solar System – for example, the inner dynamics of every single atom in the Solar System – but it can't affect the motion of planets' centers of mass in the same way as it does electrons because the value of $\hbar$ is and has to be a universal constant of Nature (there's one Schrödinger's equation for Nature, for example, and it therefore has one $\hbar$) and its value is such that the quantum effects are strong and self-evident for the smallest elementary objects such as elementary particles and not for composite objects like celestial bodies.
