Where Quantum Mechanics Went Wrong

One of the many traumas of modern physics, maybe the most severe, is the lack of convincing physical meaning of the wave function $\Psi$ of standard quantum mechanics stdQM. Despite 100 years of brooding by Science Titans, it is still a mystery. How can it be? What went wrong?

Let us recall that stdQM arises as a formality without physical meaning starting  from a classical Hamiltonian function for a collection of $N$ unit point masses with positions $x_i$ for $i=1,...,N$, and potential energy $V(x_1,....,x_N)$ of the form

• $\sum_{i=1}^N\frac{1}{2}p_i^2 + V(x_1,...,x_N)$                     (1)

where $p_i=\frac{dx_i}{dt}$ is momentum (velocity), as total energy as kinetic energy plus potential energy. The Hamiltonian thus depends on positions and velocities of a collection of particles roaming over $3N+3N$-dimensional position-momentum configuration space. 

From this classical mechanics model stdQM comes out by formally replacing momentum $p_i$ by the gradient operator $\nabla_i$ acting on $x_i$-coordinates (multiplied by the imaginary unit $i$) to arrive at a quantum mechanical Hamiltonian operator of the form 

• $\mathcal{H} = -\sum_{i=1}^N\frac{1}{2}\nabla_i^2+\mathcal{V} =  -\frac{1}{2}\Delta_i + \mathcal{V}$   (2)

where $\mathcal{V}$ is a potential operator, acting on wave functions $\Psi (x_1,...,x_N)$ depending on $N$ three-dimensional spatial coordinates $x_1,...,x_N$, altogether $3N$ spatial coordinates as a formal analog to configurations space.   

This means that stdQM from its very beginning was formed as a formality without physics since replacing kinetic energy $\frac{p_i^2}{2}$ by the differential operator $-\frac{1}{2}\nabla_i^2$ lacks physics.  Thus the physics of (2) remained to be invented, and that showed to be beyond human capacity.  Even worse, $\Psi$ is uncomputable on present day computer for $N>3$ and on any thinkable computer for $N>10$.

RealQM presents a different story with a different wave function representing a sum of non-overlapping electronic charge densities with direct physical meaning depending on a common single spatial coordinate, thus computable for any $N$.

This simply means that the non-overlapping point masses of (1) are replaced with distributed non-overlapping (charge) densities in a common 3d Euclidean space $R^3$carrying a form of compression energy measured by the gradient $\nabla$ acting on $R^3$. This makes perfect sense from a classical continuum physics sense, while introducing $\nabla_i$ lacks physical meaning and so poses unresolvable questions blocking progress.

If physical meaning of the wave function $\Psi$ of stdQM is still evading, and in addition $\Psi$ is uncomputable, why not start from computable physics instead of magical formality, as in RealQM?  

PS Listen to Peter Woit giving his view on what is wrong with modern physics including in particular string theory, which despite the fact that it does not work still is propagated by leading theoretical physicists like Ed Witten. If leading modern physicists are not willing to accept the fact that string theory does not work, maybe the situation is the same with stdQM? If the $\Psi$ of stdQM is uncomputable, then it is impossible to decide between right and wrong, and then wrong must be rule in science.