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arXiv:1701.00355

Experimental proposal for the Dynamical Spacetime approach to wavefunction collapse

Garrelt Quandt-Wiese

Published Jan 2, 2017• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.1701.00355

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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.
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.
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 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 novel approach for measuring wavefunction collapse is proposed which, unlike interferometric measurements, is not affected by decoherence. A mirror of a Michelson interferometer is transferred into a quantum superposition, where the decay of the mirror superposition is measured by the fact that it affects the probability of detecting photons in the interferometer. The experiment can be realised with currently available technology for photon generation and detection and is suitable for testing collapse models, which is shown by calculating the expected outcomes for the gravity-based models of Diósi and Penrose.
We propose a threshold-based physical framework for quantum state reduction in which wave function collapse occurs when the accumulated interaction action between a quantum system and a measurement environment exceeds a critical threshold of order Planck's reduced constant (Ac∼ℏA_{c}\sim\hbarAc​∼ℏ). The model introduces a nonlinear collapse boundary governed by invariant accumulated interaction action, predicting a sigmoidal collapse law. We demonstrate compatibility with Born-rule statistics and show that the Diósi-Penrose gravitational collapse timescale emerges as a special case in the static gravitational Hamiltonian limit. The theory predicts experimentally distinguishable deviations from exponential decoherence.
This paper presents a geometric framework for objective wavefunction collapse that addresses core challenges in quantum foundations. We develop a complete mathematical formulation using the Riemann sphere as the natural state space for two-level quantum systems. The theory provides explicit dynamical equations for collapse as a deterministic geometric flow, resolves the preferred-basis problem through environmental coupling, derives the Born rule statistically from the uniform Fubini–Study measure, and explains the system-size dependence of collapse via a mass-squared scaling of the collapse rate. The parameter λ0 = (6.0 ± 2.0) × 10−16 s−1 (referenced to 1 atomic mass unit) yields precise, falsifiable predictions—from electrons maintaining coherence for over 1016 years to 1 kg objects collapsing in 0.27 µs. These predictions are consistent with all current experimental bounds from LIGO, molecular interferometry, and optomechanics. By grounding collapse in the intrinsic geometry of quantum state space, our approach avoids ad hoc modifications to quantum dynamics and offers a mathematically natural resolution to the measurement problem.