A gravity-induced approach to wavefunction collapse based on semiclassical gravity is enhanced by the hypothesis of a temporally expanding spacetime, which leads to a collapse model that can resolve the conflict between quantum nonlocality and relativity. It is postulated that the spacetime region on which the evolution of the state vector exists is bounded towards the future by a border that is dynamically moving towards the future, and at which the state vector must fulfil a boundary condition. Wavefunction collapse is represented in such a way that the evolution of the state vector changes abruptly at critical spacetime expansions to an evolution resembling a classical trajectory. This can explain the correlations in EPR experiments without coming into conflict with relativity, since the evolution of the state vector before and after the abrupt change is governed solely by local physical laws. This model leads to the same lifetimes of superpositions as the gravity-based approaches of Diosi and Penrose, and is characterised by the facts that energy is conserved at collapse and that the reduction point in time does not vary statistically. Some unique features of the model are that it naturally leads to stochastic behaviour and that it can predict reduction probabilities. It explains why all experiments performed so far behave in agreement with Born's rule, due to a property that they have in common. This gives rise to new experiments for checking Born's rule, which can be realised in the short term.
A gravity-induced approach to wavefunction collapse based on semiclassical gravity is enhanced by the hypothesis of a temporally expanding spacetime, which leads to a collapse model that can resolve the conflict between quantum nonlocality and relativity. It is postulated that the spacetime region on which the evolution of the state vector exists is bounded towards the future by a border that is dynamically moving towards the future, and at which the state vector must fulfil a boundary condition. Wavefunction collapse is represented in such a way that the evolution of the state vector changes abruptly at critical spacetime expansions to an evolution resembling a classical trajectory. This can explain the correlations in EPR experiments without coming into conflict with relativity, since the evolution of the state vector before and after the abrupt change is governed solely by local physical laws. This model leads to the same lifetimes of superpositions as the gravity-based approaches of Diosi and Penrose, and is characterised by the facts that energy is conserved at collapse and that the reduction point in time does not vary statistically. Some unique features of the model are that it naturally leads to stochastic behaviour and that it can predict reduction probabilities. It explains why all experiments performed so far behave in agreement with Born's rule, due to a property that they have in common. This gives rise to new experiments for checking Born's rule, which can be realised in the short term.
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 Diosi 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 Diosi-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 Diosi-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.
According to Penrose, the fundamental conflict between the superposition principle of quantum mechanics and the general covariance principle of general relativity entails the existence of wavefunction collapse, e.g. a quantum superposition of two different space-time geometries will collapse to one of them due to the ill-definedness of the time-translation operator for the superposition. In this paper, we argue that Penrose's conjecture on gravity's role in wavefunction collapse is debatable. First of all, it is still a controversial issue what the exact nature of the conflict is and how to resolve it. Secondly, Penrose's argument by analogy is too weak to establish a necessary connection between wavefunction collapse and the conflict as understood by him. Thirdly, the conflict does not necessarily lead to wavefunction collapse. For the conflict or the problem of ill-definedness for a superposition of different space-time geometries also needs to be solved before the collapse of the superposition finishes, and once the conflict has been resolved, the wavefunction collapse will lose its physical basis relating to the conflict. In addition, we argue that Penrose's suggestions for the collapse time formula and collapse states are also problematic.
We propose a novel semiclassical mechanism to unify quantum mechanics and general relativity, where wave function collapse in a superposition state induces a rapid change in the energy-momentum tensor, triggering spacetime dynamics that propagate at the speed of light. Unlike models assuming superposed spacetimes, we posit that the superposition yields a single, continuous classical spacetime driven by the expectation value of the energy-momentum tensor. Upon collapse, the abrupt shift modifies the spacetime metric via Einstein's field equations, respecting causality. We explore this for a particle in a spatial superposition, propose detailed experimental designs with numerical simulations of gravitational perturbations, address potential theoretical challenges, and discuss implications for existing quantum-gravity theories. This framework offers a pathway to reconcile quantum and gravitational dynamics without quantizing spacetime, with testable signatures in future experiments.
According to Penrose, the fundamental conflict between the superposition principle of quantum mechanics and the principle of general covariance of general relativity entails the existence of wavefunction collapse, e.g. a quantum superposition of two different space-time geometries will collapse to one of them due to the ill-definedness of the time-translation operator for the superposition. In this paper, we argue that Penrose's conjecture on gravity's role in wavefunction collapse is debatable. First of all, it is still a controversial issue what the exact nature of the conflict is and how to resolve it. Secondly, Penrose's argument by analogy is too weak to establish a necessary connection between wavefunction collapse and the conflict as understood by him. Thirdly, the conflict does not necessarily lead to wavefunction collapse. For the conflict or the problem of ill-definedness for a superposition of different space-time geometries also needs to be solved before the collapse of the superposition finishes, and once the conflict has been resolved, the wavefunction collapse will lose its physical basis relating to the conflict. In addition, we argue that Penrose's suggestions for the collapse time formula and the preferred basis are also problematic.
An experiment for checking the Dynamical Spacetime approach to wavefunction collapse is proposed. The Dynamical Spacetime approach predicts deviations from Born's rule, when a solid evolves into a three-state superposition, and when the displacement between the superposed states is, at the reduction point in time, significantly larger than the spatial variation of the solids nuclei, being typically on the order of a tenth of an Angstroem. The solid is brought into the three-state superposition by splitting a photon into three beams and by detecting it in each beam by avalanche photodiodes, which displace the solid at different distances with the help of a piezoactuator. The challenge of the experiment is the precise prediction of the setup's reduction point in time to ensure a sufficient separation between the states at this point in time. This is addressed by avoiding interactions of the setup with the environment during superposition, and by a precise calculation of the setup's reduction point in time with the help of a formulary for the Diosi-Penrose criterion for solids in quantum superpositions. Since the measurement of reduction probabilities is not disturbed by state decoherence, the experiment can be performed at room temperature. The quantitative analysis demonstrates that the predicted increase of the reduction probability of one state by a factor of 1.5 with respect to Born's rule can be measured by a few hundred statistically significant measurements.