For nearly 100 years, the paradox of Schrödinger's Cat has remained unresolved. Why does the world we live in appear classical despite being composed of quantum particles governed by the Schrödinger wave equation? Lajos Diósi and Roger Penrose propose the wavefunction collapses because it describes two incompatible space-times, demonstrating an inconsistency between quantum mechanics and general relativity. To avoid this paradox, collapse must occur within Heisenberg's time-energy uncertainty limit. Subatomic particles with low mass, and correspondingly low energy, collapse in years, while superposed cats would collapse almost instantaneously. We propose a table-top experiment to put two small mirrors into superposition and observe them collapse in a time consistent with the Diósi-Penrose model. We employ two techniques to perform this experiment in ambient laboratory conditions. Most experiments separate a small mass by a large distance. In contrast, we displace a large mass by a small distance where the self-energy follows an inverse square law with correspondingly high collapse times. We further use a symmetrical apparatus, where a break in symmetry indicates collapse independent of decoherence.
For nearly 100 years, the paradox of Schrödinger's Cat has remained unresolved. Why does the world we live in appear classical despite being composed of quantum particles governed by the Schrödinger wave equation? Lajos Diósi and Roger Penrose propose the wavefunction collapses because it describes two incompatible space-times, demonstrating an inconsistency between quantum mechanics and general relativity. To avoid this paradox, collapse must occur within Heisenberg's time-energy uncertainty limit. Subatomic particles with low mass, and correspondingly low energy, collapse in years, while superposed cats would collapse almost instantaneously. We propose a table-top experiment to put two small mirrors into superposition and observe them collapse in a time consistent with the Diósi-Penrose model. We employ two techniques to perform this experiment in ambient laboratory conditions. Most experiments separate a small mass by a large distance. In contrast, we displace a large mass by a small distance where the self-energy follows an inverse square law with correspondingly high collapse times. We further use a symmetrical apparatus, where a break in symmetry indicates collapse independent of decoherence.
Probing gravity-related decoherence with a 16 μg Schrödinger cat state
The Schrödinger equation predicts the validity of the superposition principle at any scale, yet we do not experience cats being in a superposition of "dead" and "alive" in our everyday lives. Modifications to quantum theory at the fundamental level may be responsible for the objective collapse of the wave function above a critical mass, thereby breaking down the superposition principle and restoring classical behavior at the macroscopic scale. One possibility is that these modifications are related to gravity, as described by the Diósi-Penrose wavefunction collapse model. Here, we investigate this model using experimental measurements on the decoherence of a Schrödinger cat state of a mechanical resonator with an effective mass of 16 micrograms.
For a century, the Quantum Measurement Problem (Schrödinger's Cat paradox) has remained suspended between two untenable extremes: the subjective Copenhagen postulate (which requires an external "conscious observer" to trigger non-unitary wavefunction collapse) and the Everettian Many-Worlds interpretation (which postulates an unobservable exponential branching of the universe into dim_C H = 2^N → ∞ orthogonal copies). Meanwhile, continuous gravitationally induced collapse models of the Diósi–Penrose (DP) type without an information-capacity threshold predict continuous Brownian heating of nuclear matter and spontaneous X-ray Bremsstrahlung, which has been experimentally refuted by underground germanium detectors at Gran Sasso LNGS (Donadi et al., Nature Physics 17, 74, 2021). Building upon our demonstration that gravitation is not a fourth fundamental quantum force mediated by elementary gravitons but the macroeconomic Clausius equation of state (δQ = T_Unruh dS_ent) and Sakharov induced elasticity (G_emerg = 6.674254 × 10^-11 m^3 kg^-1 s^-2, DOI: 10.5281/zenodo.23524205) of the three gauge forces SU(3)C × SU(2)L × U(1)Y, here we resolve the Quantum Measurement Problem across 1,360 degrees of freedom (NDF = 1,354, χ^2/NDF = 0.9160). We prove that quantum collapse is an objective geometric phase transition governed by the finite information capacity of the positive Grassmannian Gr+(4,53) (3.58 GB VRAM) and the tetravalent paraconsistent sink L4 (2^28 = 268,435,456 complex states in 2.147 GB VRAM). We establish four foundational milestones: (1) Finite Positroid Information Capacity (C_Positroid = 196) and Mesoscopic 1RSB Threshold (M_crit = 2.10 × 10^9 Da), proving that the 292,825 Plücker minors Δ_I(C) > 0 enforce a 1-step replica-symmetry-breaking (1RSB) overlap gap at packing fraction η_1RSB = 0.949939 (0.12σ), setting the critical collapse mass at Δx = 100 nm to log10(M_crit/Da) = 9.322126 (0.01σ) and refuting Everettian unitary branching (H2) at 1398.5σ; (2) Exact Resolution of the Gran Sasso Underground X-Ray Anomaly (13993.2σ Refutation of Unthresholded DP H3), showing that for 73Ge nuclei (72.92 Da ≪ M_th = 5.70 × 10^10 Da), the 1RSB activation factor is Θ_1RSB(Ge) = e^-196 = 7.5558 × 10^-86, yielding identically zero spontaneous X-ray emission Γ_X-ray = 0.000000 counts kg^-1 day^-1 (0.00σ); (3) Complete Concordance with Vienna Macromolecular Interferometry (C60 to 25 kDa) and Blind Prediction for MAQRO, reproducing V/V_QM = 1.0000 across all subcritical experiments while predicting an abrupt visibility drop to V = 0.5692 at 2.10 × 10^9 Da and V = 0.0000 at 10^10 Da; and (4) First-Principles Derivation of Born's Quadratic Rule (β_Born = 1.999996, 0.06σ) via Cauchy–Binet and L4 Dialeteia Sink Absorption, proving that P_k = |Δ_Ik(C)|^2 / det(CC^†) ≡ |c_k|^2 is an exact Itô martingale on Gr+(4,53) while off-diagonal coherence is absorbed into Node 0 (01 ∨_k 10 = 11) with exact extended trace conservation Tr(ρ_collapsed) + N_sink^(L4) ≡ 1.000000.
The Diósi-Penrose model states that the wave function collapse ending a quantum superposition occurs due to the instability of coexisting gravitational potentials created by distinct geometric conformations of the system in different states. The Heisenberg time-energy principle can be invoked to estimate the collapse time for the energy associated with this instability, the gravitational self-energy. This paper develops atomistic models to calculate the Diósi-Penrose collapse time. It applies them to a range of systems, from small molecules to large biological structures and macroscopic systems. An experiment is suggested to test the Diósi-Penrose hypothesis, and we critically examine the model, highlighting challenges from an atomistic perspective, such as gravitational self-energy saturation and limited extensivity.
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.
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.
Physical systems to exist in multiple states simultaneously. While standard quantumtheory permits superposition to persist indefinitely in the absence of mea-surement or environmental decoherence, this work proposes that superpositionstates possess an intrinsic temporal constraint. We argue that quantum super-position cannot remain stable forever and that every superposed system ischaracterized by a finite lifetime, beyond which the superposition inevitablybreaks down and the wave function collapses into a single definite state. Thisproposed time-limited superposition introduces an objective mechanism for wave-function collapse that does not rely on observation or classical interaction.Conceptual arguments, mathematical considerations, and potential experimentalimplications are discussed, including connections to macroscopic quantum lim-its, decoherence timescales, and fundamental temporal structure. If validated,this framework would offer a new perspective on the measurement problem andsuggest that time itself plays an active role in determining quantum outcomes.This perspective is conceptually related to objective collapse models such as theGhirardi–Rimini–Weber (GRW) theory and Penrose’s gravitationally inducedcollapse, while differing in that the collapse mechanism proposed here arisesfrom an intrinsic temporal instability of superposition rather than stochastic orgravity-driven effects.