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Yukawa-Enhanced Di´osi–Penrose Timescale for MAQRO-Like Superpositions

Mustafa Boudjerada

Published Dec 23, 2025• 0 citations
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Abstract

This technical note derives a specific, falsifiable prediction for gravitational decoherence targeting the MAQRO Pathfinder mission parameters ($10^{10}$ amu, 100 nm separation). Using a geometrically motivated scalar-tensor extension ($\beta_{IR} \approx 17.5$), we predict a decoherence time of $\tau \approx 0.94$ seconds. This signal represents a $\sim 600\times$ enhancement over the standard Diósi-Penrose baseline ($\tau \approx 573$ seconds). The derivation uses no free parameters beyond the geometric ansatz and is shown to satisfy all current laboratory fifth-force constraints.

DOI
10.5281/zenodo.18039794

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This technical note derives a specific, falsifiable prediction for gravitational decoherence targeting the MAQRO Pathfinder mission parameters (101010^{10}1010 amu, 100 nm separation). Using a geometrically motivated scalar-tensor extension (βIR≈17.5\beta_{IR} \approx 17.5βIR​≈17.5), we predict a decoherence time of τ≈0.94\tau \approx 0.94τ≈0.94 seconds. This signal represents a ∼600×\sim 600\times∼600× enhancement over the standard Diósi-Penrose baseline (τ≈573\tau \approx 573τ≈573 seconds). The derivation uses no free parameters beyond the geometric ansatz and is shown to satisfy all current laboratory fifth-force constraints.
\This technical note derives a specific, falsifiable prediction for gravitational decoherence targeting the MAQRO Pathfinder mission parameters (101010^{10}1010 amu, 100 nm separation). Using a geometrically motivated scalar-tensor extension (βIR≈17.5\beta_{IR} \approx 17.5βIR​≈17.5), we predict a decoherence time of τ≈0.94\tau \approx 0.94τ≈0.94 seconds. This signal represents a ∼600×\sim 600\times∼600× enhancement over the standard Diósi-Penrose baseline (τ≈573\tau \approx 573τ≈573 seconds). The derivation uses no free parameters beyond the geometric ansatz and is shown to satisfy all current laboratory fifth-force constraints.
This note evaluates Diósi–Penrose gravitational self-energy decoherence for a MAQRO-like superposition using a rigid homogeneous-sphere mass model. For (M=10^{10},\mathrm{amu}) and (s=100,\mathrm{nm}), the Newtonian DP timescale spans (\sim 9)–(100) minutes across representative densities. A Yukawa correction (V(r)=-(Gm_1m_2/r)[1+\alpha e^{-r/\lambda}]) is included by modifying the DP kernel; for (\lambda \gg {R,s}), the timescale reduces approximately by (1+\alpha). For the benchmark ((\alpha,\lambda)=(612.5,20.4,\mu\mathrm{m})), the predicted timescale is (\sim 0.9)–(9.7) seconds.
This note evaluates Diósi–Penrose gravitational self-energy decoherence for a MAQRO-like spatial superposition using a rigid homogeneous-sphere mass model. For (M=10^{10},\mathrm{amu}) and (s=100,\mathrm{nm}), the Newtonian DP timescale lies in the range (\sim 9)–(100) minutes across representative densities. A Yukawa correction (V(r)=-(Gm_1m_2/r),[1+\alpha e^{-r/\lambda}]) is incorporated by modifying the DP kernel; for (\lambda \gg {R,s}), the timescale is reduced approximately by a factor (1+\alpha). For the benchmark ((\alpha,\lambda)=(612.5,20.4,\mu\mathrm{m})), the predicted timescale is (\sim 0.9)–(9.7) seconds.
This note evaluates Diósi–Penrose gravitational self-energy decoherence for a MAQRO-like superposition using a rigid homogeneous-sphere mass model. For (M=10^{10},\mathrm{amu}) and (s=100,\mathrm{nm}), the Newtonian DP timescale spans (\sim 9)–(100) minutes across representative densities. A Yukawa correction (V(r)=-(Gm_1m_2/r)[1+\alpha e^{-r/\lambda}]) is included by modifying the DP kernel; for (\lambda \gg {R,s}), the timescale reduces approximately by (1+\alpha). For the benchmark ((\alpha,\lambda)=(612.5,20.4,\mu\mathrm{m})), the predicted timescale is (\sim 0.9)–(9.7) seconds.
The Zero Constant (Ω0) framework postulates a fundamental drift in vacuum coherence(˙Ω0 ≈5.1 ×10−19s−1) which imposes a temporal limit on quantum superpositions of macroscopic objects. By applying this model to the parameters of the MAQRO space mission (Silica nanospheres), we predict a spontaneous collapse time of Tcoll ≈408 seconds for a 150 nm radius sphere. We explicitly derive the geometric scaling factors consistent with the Penrose-Diósi limit, providing a falsiable signature for near-term space optomechanics.
The sensitivity of current gravitational wave detectors (LIGO, VIRGO, KAGRA) in the low-frequency band (10-40 Hz) is limited by a persistent noise floor. In this Letter, we propose a phenomenological analysis based on the Diósi-Penrose (DP) model of gravitational decoherence. By treating the spatial cutoff parameter Rc as a free variable and fitting the theoretical displacement noise to the observed LIGO O3 sensitivity limit at 30 Hz, we derive a value of Rc ≈ 2.8 × 10^-15 m. This striking coincidence with the nuclear length scale suggests that semiclassical gravity couples to the discrete nuclear mass distribution. We demonstrate that this model correctly predicts the geometric scaling (1/L) observed between LIGO and VIRGO and, crucially, predicts an identical fundamental noise floor for KAGRA despite its different mirror material (Sapphire) and cryogenic operating temperature (20 K). This implies that the observed limit is material-invariant and represents a fundamental property of spacetime granularity interacting with matter.