Collapse theories stand in opposition to many-world theories, in that they hold that a process of wavefunction collapse curtails the branching of the wavefunction and removes unobserved behaviour. Objective collapse theories differ from the Copenhagen interpretation in regarding both the wavefunction and the process of collapse as ontologically objective. The Copenhagen interpretation includes collapse, but it is non-committal about the objective reality of the wave function, and because of that it is possible to regard Copenhagen-style collapse as a subjective or informational phenomenon. In objective theories, there is an ontologically real wave of some sort corresponding to the mathematical wave function, and collapse occurs randomly (“spontaneous localization”), or when some physical threshold is reached, with observers having no special role.
See: “Meaning of the wave function”, Shan Gao:
As we think, the Schrödinger equation of a charged quantum system under an external
electromagnetic potential already provides an important clue. The equation is …
where m and Q is respectively the mass and charge of the system, ϕ and A are the
electromagnetic potential, V is an external potential, h is Planck’s constant divided by 2π , c is the speed of light. The electrostatic interaction term Qϕψ (x,t) in the equation seems to
indicate that the charge of the quantum system distributes throughout the whole region where its wave function ψ (x,t) is not zero. If the charge does not distribute in some regions where the wave function is nonzero, then there will not exist any electrostatic interaction there. But the term Qϕψ (x,t) implies that there exists an electrostatic interaction in all regions where the wave function is nonzero. Thus it seems that the charge of the quantum system should distribute throughout the whole region where its wave function is not zero. Furthermore, since the integral Q x t dx 2 ψ (x ,t ) is the total charge of the system, the charge density distribution in space will be 2 Qψ (x,t) . Similarly, the mass density can be obtained from the Schrödinger equation of a
quantum system with mass m under an external gravitational potential …
The gravitational interaction term mV (x,t) Gψ in the equation also indicates that the (passive gravitational) mass of the quantum system distributes throughout the whole region where its wave function ψ (x,t) is not zero, and the mass density distribution in space is 2 mψ (x,t) .
The above result can be more readily understood when the wave function is a complete
realistic description of a single quantum system as in many-worlds interpretation and dynamical collapse theories. If the mass and charge of a quantum system does not distribute as above in terms of its wave function ψ (x,t) , then other supplement quantities will be needed to describe the mass and charge distributions of the system in space, while this obviously contradicts the premise that the wave function is a complete description. In fact, the dynamical collapse theories such as GRW theory already admit the existence of mass density (Ghirardi, Grassi and Benatti 1995).
Since many years I have been thinking about the ‘particle-wave duality problem’. It occurs that all the problem was in properly understanding/interpreting the Schroedinger wave equation…
OK, thanks to Shan Gao. I.V.