The Spell of QM

Experiments spell doom for QM

The Schrödinger equation for the Hydrogen atom solves the eigenvalue problem in the real-valued wave function $\Psi (X)$ depending on a 3d spatial variable $X$:

• $(-\frac{1}{2}\Delta - V)\Psi = E\Psi$   (Q)

where $V(X)=\frac{1}{\vert X\vert}$, with normalisation 

• $\int \Psi^2 (X) dX = 1$.

The equation (Q) is formally derived from a classical one-particle Hamiltonian $H(x,p)$ with $x$ a 1d particle position variable and $p=\dot x =\frac{dx}{dt}$ corresponding momentum, of the form 

• $H(x,p)=\frac{1}{2}p^2 - W(x)$      (C)

where $W(x)$ is a potential depending on position $x$. We see that (Q) corresponds to formally replacing $p$ by $i\nabla\Psi$ and $W(x)$ by $V\Psi$. Really strange!

Here (C) represents a classical problem in a 1d position variable $x(t)$ depending on time $t$, while (Q) is a partial differential equation for a function $\Psi (X)$ of a 3d space variable $X$. The formality takes us from an ordinary differential equation in real-valued function $x(t)$ depending on time $t$ as the equations of motion for (C), to a partial differential equation pde in 3d space for $\Psi (X)$. We see that the point position $x$ is formally expanded to a function $\Psi(X)$ depending on 3d space variable $X$. (Q)  thus can be seen as a formal expansion from point to full 3d space. 

The Schrödinger equation (Q) can be directly formulated as a classical partial differential equation in a function $\Psi (X)$ with $\Psi^2(X)$ representing charge density with the Laplacian $\Delta$ forcing $\Psi(X)$ to spread out away from the kernel at $X=0$. So for the one-electron atom of Hydrogen (Q) is a pde of classical form in 3d. Schrödinger was very happy with this model since the eigenvalues of (Q) perfectly matched with the observed spectrum of Hydrogen. The first step into modern physics was a complete success and expectations quickly mounted. 

But how to generalise (Q) to atoms with with $N>1$ electrons? The classical formulation (C) could directly be extended to $N$ particles simply by letting the position variable represent $N$ different particle positions with corresponding momenta. That would correspond to expanding from one to $N$ position coordinates as the subject of classical Lagrangian mechanics. Doing the same thing in (Q) would bring in a full 3d coordinate system for each electron altogether a pde in $3N$ space dimensions. This was what Schrödinger did and so was QM born from a formal generalisation of classical mechanics with a mysterious replacement of momenta by $i\nabla$ acting in $3N$ space dimensions, and then formed into a canon named Copenhagen Interpretation CI filling text  books. 

But the generalisation of (Q) for the Hydrogen atom was done through a purely formal process without physical meaning and the struggle to give meaning has not been successful. Schrödinger gave up in despair leaving the scene to Bohr.

RealQM offers a different generalisation of (Q) into a model with physical meaning. With the renewed interest into the foundations of QM motivated by the 2022 Nobel Physics Prize, I hope that RealQM can attract some attention. RealQM has a direct deterministic physical meaning free of the statistics of the CI. Why not give it a try?  

It is truely amazing the foundations of QM are still hotly debated 100 years after QM was created by Schrödinger and Heisenberg and then canonised by Bohr and Born into an abstract recipe to make statistical predictions of outcomes of experiments with attempts by Bohm, Bell and Everett to give physical meaning to the abstractions which did not bring clarity. 

The hype today is to build a quantum computer capable of computational simulation of quantum systems by building the quantum computer to mimic the quantum system, that is making the quantum computer simulate itself. This is like thinking of yourself when you are thinking of yourself, in order to figure out what you are thinking about yourself...  

Adam Becker gives in What Is Real?: The Unfinished Quest for the Meaning of Quantum Physics

the following summary as of 2018:

• So what is real? Pilot waves? Many worlds? Spontaneous collapse? 
• Which interpretation of quantum physics is the right one? 
• I don’t know. Every interpretation has its critics (though the proponents of basically every non-Copenhagen interpretation are usually agreed that Copenhagen is the worst of the lot). 
• Somehow, something is going on in the world that is related to the mathematics of quantum physics.
• There is a correct interpretation, though it may not be any of the ones that we have yet. 
• Simply dismissing the quantum world as a convenient mathematical fiction means we aren’t taking our best theories of the world seriously enough, and we are hobbling ourselves in the search for a new theory.
• Stating that the conclusions of the Copenhagen interpretation are “inevitable” or “forced upon us by the mathematics of the theory” is simply wrong. 
• It is not true that it’s meaningless to talk about reality existing independently of our perceptions, that we must think of the world solely as the subject of our observations. 
• Solipsism and idealism are not the messages of quantum physics.

This is a disappointing result after 100 years of apparently fruitless quest into the foundations of QM as the show piece of modern physics. But this reality is unacceptable and as a cover-up the Nobel Prize in Physics 2022 is given to "ultimate verification of (foundations of) QM":

• The founding fathers of quantum mechanics were well aware of its potentially revolutionary physical and philosophical implications, and held very different, and sometimes bluntly contradictory, views on the subject. 
• Indeed, the overwhelming empirical evidence in the realms of atomic and optical physics was, to most practitioners, confirmation of the potent predictive power of quantum mechanics. 
• Others saw them as fundamental discoveries about the nature of physical reality, providing an ultimate verification of quantum mechanics in a regime that is far removed from classical laws and reasoning.

PS1 The question What Is Real? directly confronts our daily life: What are the foundations of human society, what is true, what is fake, is Big Brother real and what are His plans, what is freedom of thought, why are we freezing, who will survive, what is information, what is desinformation, what is the value of classical laws and reasoning...?? 

PS2 Travis Norsen gives in Foundations of Quantum Mechanics a critical analysis in Chapter 5 The Ontology Problem of giving a physical meaning to the $3N$-dimensional wave function of CI:

• Perhaps we can thus summarize “the ontology problem” as follows: in quantum mechanics, there simply is nothing in the theory other than the wave function with which to describe the physical state of a microscopic system; but it simply is not clear how the wave function might be understood as describing some material structures in three-dimensional physical space. Put simply, it is just not at all clear, from the mathematical formulation of the theory, what sort of physical things quantum mechanics might be about.

This Ontology Problem (about what is?) was apparent from start to both Lorentz, Einstein and Schrödinger and the problem remains today, despite 100 years of efforts to sweep it under the rug.