Dear Janko,
Thanks for the links. I read Holger Lyre. He is a profound connoisseur of Weizsäcker. I will read the other links as well. I find them very interesting.
For the derivation of my equation (1) the starting point is a radical atomism that states, that all known physical objects can be decomposed into qbits. This is logically true. Why this should make sense physically should be explained. I haven't found a concise answer to that, except Wheelers "there is no law". The claim is that the 3 dimensionality of the spin observable of the qbit having the same dimensionality of the physical space is not merely a coincidence, but that the second can be derived from the first.
A von Neumann can be described as follows: Let a qbit state be in a superposition c1|1>+c2|2> and the measurement system be in a state |0>. After the measurement the qbit will be entangled with the measurement system: c1|1>|m1>+c2|2>|m2> . It is also called a non demolition measurement, since if we repeat the same measurement we would get the same result. This is for a discrete time. The interaction s switched on for a certain time and then switched off again. For continuous time the following measurement scheme gives a von Neumann measurement. Let |1> and |-1> be the eigenstates of the 3rd Pauli matrix s3 , p3=-id/dx3 and the Hamiltonian H=s3p3 and let f(x3) be a wave packet peaked around 0.Then
(c1|1>+c-1|-1>) f(x3) --> c1|1> f(x3 - t) + c-1|-1> f(x3+t)
where f(x3 - t) is peaked at the location t and f(x3+t) at the location -t.
The problem with this measurement is that the interaction Hamiltonian is chosen in a way to get the measurement in the 3-direction. So the direction of the measurement comes in externally. In a closed description of the measurement the interaction Hamiltonian should be SU(2) symmetric and the decision on the direction should be done in the measurement system. This can be made SU(2) symmetric if we take H=si pi where we sum over the indices i=1,2,3. The initial state of measurement system can be chosen so that in the 3-direction is peaked around 0 and pi=0 for I =1,2. The Schrödinger equation becomes
id/dt g(x1 , x2 , x3 , t) = si pi g(x1 , x2 , x3 , t) = - i si d/dxi g(x1 , x2 , x3 , t)
which is actually the Weyl equation for the right handed Weyl spinor g. With the opposite sign in H we get the left handed Weyl spinor.
Comment:
1. One should show, that this Hamiltonian is somehow unique and that it is not possible to get an SU(2) invariant Hamiltonian for a finite dimensional measurement system.
2.This procedure does not at all resolve the measurement problem. It postulates merely an iterative method how to get interactions from a quantum object.
3.The Weyl spinor I got might not yet be an elementary particle and xi not yet our physical space. (see my answer Jeffrey Michael Schmitz's comment)
4.I like to think that every qbit carries its own measurment system. But how connect them together. Rovellis article might help.
5.How to continue?