Superposition as the Collapse of Quantum Mechanics

Today Quantum Mechanics is still viewed to be as weird and strange as at its formation 100 years ago, evidenced in a large number of books like this undergraduate text by Travis Norsen:

• Foundations of Quantum Mechanics An Exploration of the Physical Meaning of Quantum Theory  

The book presents three basic problems:

1. Measurement Problem 
2. Locality Problem
3. Ontology Problem 

along with “solutions” in the form 

• Copenhagen Interpretation 
• Pilot Wave Theory
• Many Worlds Theory
• Collapse Theory

none of which is considered to be satisfactory. The net result for the undergraduate student is frustration from confusion, at least this is my reaction. 

All Problems 1-3 connect to the the fundamental postulate of QM as 

• Multi-d linear Schrödinger equation in non-physical configuration space.  (S)

This is an ad hoc model derived from formal mathematics without real physics in physical 3d space. Solutions to (S) are referred to as wave/state functions typically denoted by $\Psi$. A consequence of the linearity of (S) is superposition: If $\Psi_1$ and $\Psi_2$ solve (S), so does the linear combination

• $\Psi = c_1\Psi_1 + c_2\Psi_2$,

for any coefficients $c_1$ and $c_2$. Typically, $\Psi_1$ and $\Psi_2$ are eigenstates with different energies. This is the Schrödinger Cat in the Box, which can be in superposition of eigenstates of being alive and dead. Strange QM Cat. 

The Measurement Problem concerns the collapse of the wave function $\Psi =  c_1\Psi_1 + c_2\Psi_2$ by observation/measurement into one of the eigenstates $\Psi_1$ and $\Psi_2$ with probability given by the cofficients $c_1^2$ and $c_2^2$, that is upon opening the box discovery of an alive or dead cat with a certain probability.

But the Measurement Problem is unresolved despite 100 years of massive efforts by the sharpest brains. It is reasonable to suspect that this problem is not well formulated. The suspicion goes the the idea of superposition build into (S) as a formal equation in configuration space without physics. 

What forces us to insist that (S) is the foundation of atomistic mechanics? The standard answer is that this is the best we have, even if it leads into an abyss of contradictions. Here RealQM offers an alternative. 

To give perspective on superposition in a linear equation, let is consider the simple case of a vibrating string with the vibration as a linear combination of a ground state and higher harmonics as eigenstates with larger eigenfrequencies, resulting from plucking the string thus exciting all harmonics. But as we listen to a vibrating string the higher frequencies fade away and what remains is only the basic harmonic. This is because the vibrating string equation is not fully linear and so carries some damping increasing with frequency (see above picture).

In the setting of an atom the basic harmonic corresponds to the ground state with minimal energy, which is not radiating and thus can sustain over time, while the eigenstates with higher energies are all radiating and thus can only sustain under exterior forcing. This is how the spectrum is generated. An atom without exterior forcing will thus remain in its ground without collapse.  

The atom in ground state is thus fully deterministic, just as the basic harmonic of a vibrating string.  Higher harmonics have to be excited by exterior forcing, like plucking the string in some specific way, and

the resulting state is then deterministically determined by the forcing. Every time you pluck the same way,

the same sound is produced. The spectrum of an atom always comes out the same way fully deterministic.

The spectrum shows itself under exterior forcing, not by stochastic collapse of wave functions.  

We understand the idea of a linear Schrödinger wave equation (S) allowing sustained superposition over time and only collapsing into an eigenstate under observation, brings a whole battery of problems which have shown to be unresolvable. We are forced to seek to replace (S) with a physical model, possibly in the spirit of RealQM.

We note that computational techniques to find solutions to (S) like Density Theory or Hartree-Fock Slater Determinants effectively reduce (S) to a non-linear deterministic system in 3d like RealQM. 

I have asked Travis Norsen for a comment on this post.