A formulary for the application of the Di ósi-Penrose criterion to solids in quantum superpositions is developed, which takes the solid's microscopic mass distribution (resulting from its nuclei) and its macroscopic shape into account, where the solid's states can differ by slightly different positions or extensions of the solid. For small displacements, smaller than the spatial variation of the solid's nuclei, the characteristic energy of the Di ósi-Penrose criterion is mainly determined by the mass distribution of the nuclei. For large displacements, much larger than the solid's lattice constant, the solid can be idealised as a continuum, and the characteristic energy depends on the solid's shape and the direction of the displacement. In Di ósi's approach, in which the mass density operator has to be smeared, the solid's microscopic mass distribution plays no role. The results are applied to a special single-photon avalanche photodiode detector, which interacts as little as possible with its environment. This is realised by disconnecting the detector from the measurement devices when it is in a superposition, and by biasing the photodiode by a plate capacitor, which is charged shortly before the photon's arrival. For a suitable choice of components, the detector can stay in a superposition for seconds; its lifetime can be shortened to microseconds with the help of a piezoactuator, which displaces a mass in the case of photon detection.1 My official last name is Wiese. For non-official concerns, my wife and I use our common family name: Quandt-Wiese.

A new approach to wavefunction collapse is proposed. The so-called Dynamical Spacetime approach enhances semiclassical gravity and enables it for an explanation of wavefunction collapse by postulating that the spacetime region on which quantum fields exist and on which the wavefunction's evolution can be regarded is bounded towards the future by a spacelike hypersurface, which is dynamically expanding towards the future. Collapse is displayed in the way that the wavefunction's evolution becomes unstable at certain critical expansions of spacetime, at which it reconfigures via a self-reinforcing mechanism quasi-abruptly to an evolution resembling a classical trajectory. Thereby, spacetime geometry changes in favour of the winning state, which causes the path of the other state to vanish by destructive interference. This mechanism for collapse can explain the quantum correlations in EPR experiments without coming into conflict with relativity and the Free Will theorem. The Dynamical Spacetime approach is mathematically formulated on basis of the Einstein-Hilbert action and predicts for the Newtonian limit the same lifetimes of superpositions as the gravity-based approaches of Di ósi and Penrose. A second important feature of the Dynamical Spacetime approach is its capability to forecast reduction probabilities. It can explain why all experiments performed so-far confirm Born's rule, and predict deviations from it, when solids evolve into three-state superpositions. The basics needed for the derivations in this paper are developed in Part 1 by an analysis of semiclassical gravity.

A new approach to wavefunction collapse is prepared by an analysis of semiclassical gravity. The fact that, in semiclassical gravity, superposed states must share a common classical spacetime geometry, even if they prefer (according to general relativity) differently curved spacetimes, leads to energy increases of the states, when their mass distributions are different. If one interprets these energy increases divided by Planck's constant as decay rates of the states, one obtains the lifetimes of superpositions according to the Di ósi-Penrose criterion and reduction probabilities according to Born's rule. The derivation of Born's rule for two-state superpositions can be adapted to the typical quantum mechanical experiments with the help of a common property of these experiments. It is that they lead to never more than two different mass distributions at one location referring e.g. to the cases that a particle "is", or "is not", detected at the location. From the characteristic energy of the Di ósi-Penrose criterion, an action is constructed whose relativistic generalisation becomes obvious by a decomposition of the Einstein-Hilbert action to the superposed states. In Part 2, semiclassical gravity is enhanced to the so-called Dynamical Spacetime approach to wavefunction collapse, which leads to a physical mechanism for collapse.

A phenomenological model for the calculation of reduction probabilities of a superposition of several states is presented, which bases only the idea that quantum state reduction has its origin in a physical interaction between the states. The model is explicitly worked out for the hypothesis of gravity-induced quantum state reduction. It agrees for typical quantum mechanical experiments with the projection postulate and predicts regimes in which other behaviour could be observed. For verification a feasible quantum-optical experiment is proposed. An outlook on the possible role of state reduction for biology is given by exemplarily discussing mutation effects of bacteria.

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