I have been trying to work out how to prove theat Quatum Superposition is contradictory rather than just contraintuitive, as claimed in the propaganda put out by the QS evangelists. One of the difficulties is that their arguments are actually rather vauge when you try to analyse them.
What is worse is that if you accept the QS contradiction, then any resulting contradictions simply become "evidence" to support the original position.
I think I have managed to identify the central flaw in their argument. As the QS argument is actually an argument by analogy, it has to be approached the same way:
If we apply the same logic to solving a simple equation that the Copenhagen Interpretation of Quantum Mechanics applies to solving the Wave Equation, we would conclude that an unknown point on a line is a superposition of all points on the line, which would then collapse to a single point when solve the equation.
Stating this in Set Theory form, they claim that an unresolved solution to an equation is the set of all possible solutions, which then collapses to being one member of the set when the equation is solved.
This is clearly wrong - while the unresolved solution can be any one of the possible solutions in the set, it remains a solution and does not become the set (I am ignoring cases where the solutions are also sets).
While a line can be considered to be the superposition of all points on the line, it is incorrect to claim that an unknown point on a line is the superposition of all points on the line. A point is a point, while a line is a set of points.
Going back to QS, it is clear that they are treating the unresolved Quantum State of an electon as being the set of all its possible states. This is contradictory.
In the point on the line example, the superposition of all the solutions is the line. If my logic is correct, then it may also be possible to identify what the superposition of all electron quantum states really applies to. Obviously it is something to do with all possible states of electron "orbitals" around an atom rather than an individual electron.
Can anyone see any holes in this, or a better way of stating it?
