Something Rotten in Copenhagen Interpretation

Modern physics is based on the Copenhagen Interpretation CI of the wave function $\Psi$ as solution to Schrödinger's equation as a full description of all of atom physics. For an atomic system consisting of $N$ electrons labeled $n=1,2,...,N$, the (complex-valued) wave function has the form  

• $\Psi (x,t)$

with each electron $n$ being connected to a 3d Euclidean space $E_n$ with coordinates $x_n$ collected as a $3N$-dimensional coordinate $x=(x_1,x_2,...x_N)$ and a common time coordinate $t$. In CI

• $\vert\Psi (x,t)\vert^2$

represents the the possible appearance of an electronic configuration at time $t$ with electron $n$ appearing as a particle at space coordinate $x_n$ for $n=1,2,...,N$. 

More precisely, $\vert\Psi (x,t)\vert^2dx$ is viewed to be the probability of "finding" an electron configuration within the volume $dx$ around $x$ as an act of an Observer, see PS2 below.   

The very rich $3N$-dimensionality of $\Psi (x,t)$ with a unique 3d Euclidean space $E_n$ reserved for each electron $n$, puts CI outside classical deterministic physics taking place in a common shared 3d Euclidean space $E$, and then outside the rationality of the scientific revolution.  

In CI electrons appear in 3d worlds which are entirely separate but also overlap into a common 3d world. This is not easy to grasp and is the root cause of the never-ending debate about the physical meaning of CI with "shut up and calculate" as desperate dictate.  

Schrödinger's equation contains the following elements with $\nabla_n$ gradient with respect to $x_n$:

• Atomic kernels as point charges with corresponding Coulomb kernel potentials.   ( 1)
• $\vert\nabla_n\Psi\vert^2$ as kinetic energy of electron $n$.                                                                       (2)
• Coulomb potential between each pair of electrons $x_i$ and $x_j$ for $i\neq j$.          (3)     

Here (1) acts in a common space $E$ while(2) acts in each separate $E_n$, which is comprehensible but unphysical. But (3) has a double function which is not comprehensible unless you are a believer in CI.   

The total inter-electronic Coulomb potential energy arising from (3) is given by

• $\sum_{i<j}\int\frac{\vert \Psi (x,t)\vert^2}{\vert x_i-x_j\vert}dx$      (EP)

We see here the presence of all the separate $E_n$ but also the shared presence in $\vert x_i-x_j\vert$.

Each electron in CI thus lives in a separate world, but also appears in the separate worlds of all the other electrons. 

This is not possible in a classical deterministic common world, and so CI presents instead a probabilistic world as a World of Possibilities, instead of a classical world of actualities. 

This is a world so rich that even a system with moderate number of electrons, would span more possibilities than the number of atoms in the whole known Universe. To handle this absurdity CI reduces wave functions to be either symmetric or anti-symmetric, but the number of possibilities is still overwhelming.

A symmetric wave function $\Psi (x_1,x_2,...,x_N,t)$ does not change under permutation of variables which in CI is viewed to signify that electrons lack individuality in space and time, and so that the labelling $n=1,...,N$, has no real physical meaning. Yet each electron has its own 3d space and also appears with individuality in space and time in the shared distance $\vert x_i-x_j\vert$ in (EP). 

There is a general agreement that quantum mechanics in the form CI cannot be understood or visualised in some sense, but still serves as the foundation of all electronic technologies of  modern society. 

The basic difficulty of understanding/visualisation comes from the mix of possibility and actuality carried by the wave function: Electrons interact by actualities in space and time involving individuals within deterministic physics, while electrons also appear as possibilities without individuality outside deterministic physics. Understanding the root of a difficulty is the first step to come to grips with it.

Real Quantum Mechanics presents a form of quantum mechanics within the realm of classical deterministic physics which can be understood, and may well serve electronic technology better than CI. Why not give it a try?

PS1 CI connects to the Monadology of Leibniz with monads as simple substances each one within its own 3d space yet with a window open to interaction with other monads. But Monadology is today not viewed to be science because modern physicists cannot understand it.  

PS2 The world of possibilities of CI is not that of statistical mechanics describing a world of most probable actualities. In CI a possibility becomes an actuality in the act of observation by an Observer causing the wave function to collapse, which is maybe the deepest mystery of CI. The role of an Observer is not crucial in classical mechanics nor in statistical mechanics arising from difficulty of observation in classical mechanics.