Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Technical Note Yukawa-Enhanced Diosi--Penrose Timescale for MAQRO-Like Superpositions

Mustafa Boudjerada

Published Jan 9, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.5281/zenodo.18190605

Related papers

Technical Note Yukawa-Enhanced Diosi--Penrose Timescale for MAQRO-Like Superpositions

Mustafa Boudjerada

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.

•Jan 8, 2026•0 citations

Technical Note Yukawa-Enhanced Diosi--Penrose Timescale for MAQRO-Like Superpositions

Mustafa Boudjerada

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.

•Jan 8, 2026•0 citations

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

Mustafa Boudjerada

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.

•Dec 23, 2025•0 citations

Technical Note MAQRO Prediction

Mustafa Boudjerada

\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.

•Dec 23, 2025•0 citations

Geometry-Only CSL/DP Ratios and the Nonuniqueness of Decoherence Kernels

Randy Davila, Gerard J. Milburn

We study idealized levitated protocols that create spatial superpositions of massive test particles. For each protocol, we compare the dimensionless contrast-loss exponent of mass-proportional continuous spontaneous localization (CSL) with the Diósi--Penrose (DP) self-energy exponent $E_Gτ/\hbar$. We first prove that the point-particle CSL separation kernel has an exact random-unitary realization: Gaussian momentum kicks arriving at Poisson-distributed times produce the same unconditional decay of spatial coherence, although a pure state conditioned on the complete kick record remains pure. The separation kernel alone therefore specifies an operational decoherence law, not the occurrence of objective collapse. We then show that the ratio of the CSL and DP exponents is independent of particle mass and interrogation time. In the point-particle model it depends only on branch separation and an effective distance; for the standard GRW reference parameters, its resolved-superposition crossover is $x_*\approx1.91\,\mathrm{nm}$. For rigid spherical bodies with an arbitrary normalized radial mass profile, total mass, overall density scale, and interrogation time again cancel, leaving a dimensionless geometry factor. The results distinguish three requirements for a decisive experiment: detectable absolute effects, a controlled comparison of CSL and DP scales, and observables capable of discriminating physically different dynamics that share the same ensemble decoherence kernel.

quant-pharXiv:2608.05972•Aug 7, 2026•0 citations

Causal Consistency of Diósi–Penrose Reduction and a Profile-Independent Mass Scale M_P/√2

Taishi Namba

The Diósi–Penrose (DP) model assigns a spatial superposition the lifetime τ_DP = ħ/ΔE_G, computed from the instantaneous Newtonian self-energy difference of its branches. We ask what local relativistic causality adds to this picture. First, in a relativistic scalar-field model of the branch difference, a finite protocol duration T replaces the logarithmic infrared dependence ln(ξ/σ_eff) of static configurations by ln[min(ξ, cT)/σ_eff]; the result is independent of the branch separation ξ only for ξ > cT, whereas laboratory protocols satisfy cT ≫ ξ. Second, defining the causal self-crossing time ⟨t⟩ of a branch from the retarded Green function, we prove that E_self⟨t⟩ = Gm²/c for every regular mass profile. Consequently τ_DP/⟨t⟩ = (m_H/m)² with m_H = M_P/√2 ≈ 15.39 μg, independently of the profile and of the regularization width: above m_H the DP reduction would be completed before the self-energy that drives it is causally established across the branch. We also show that the switch-on action deficit of the branch difference vanishes identically by mass conservation. What happens at m_H depends on whether the branch phase keeps accumulating beyond ⟨t⟩. If it does (H1), the decoherence time crosses over from the DP law ∝ m⁻² to a causally limited ∝ m^(−2/3) at m_H, for every profile. If it does not (H2), the phase acquired per causal interval is exactly (m/m_H)², and m_H acts as a Heisenberg cut. Both hypotheses predict that a superposition with m ≥ m_H and ξ ≫ σ_eff loses coherence within about 2⟨t⟩, while their predictions below m_H differ. All results are reproduced by openly available code (doi:10.5281/zenodo.23064101).

•Sep 30, 2026•0 citations
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.
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 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.
We study idealized levitated protocols that create spatial superpositions of massive test particles. For each protocol, we compare the dimensionless contrast-loss exponent of mass-proportional continuous spontaneous localization (CSL) with the Diósi--Penrose (DP) self-energy exponent EGτ/ℏE_Gτ/\hbarEG​τ/ℏ. We first prove that the point-particle CSL separation kernel has an exact random-unitary realization: Gaussian momentum kicks arriving at Poisson-distributed times produce the same unconditional decay of spatial coherence, although a pure state conditioned on the complete kick record remains pure. The separation kernel alone therefore specifies an operational decoherence law, not the occurrence of objective collapse. We then show that the ratio of the CSL and DP exponents is independent of particle mass and interrogation time. In the point-particle model it depends only on branch separation and an effective distance; for the standard GRW reference parameters, its resolved-superposition crossover is x∗≈1.91 nmx_*\approx1.91\,\mathrm{nm}x∗​≈1.91nm. For rigid spherical bodies with an arbitrary normalized radial mass profile, total mass, overall density scale, and interrogation time again cancel, leaving a dimensionless geometry factor. The results distinguish three requirements for a decisive experiment: detectable absolute effects, a controlled comparison of CSL and DP scales, and observables capable of discriminating physically different dynamics that share the same ensemble decoherence kernel.
The Diósi–Penrose (DP) model assigns a spatial superposition the lifetime τ_DP = ħ/ΔE_G, computed from the instantaneous Newtonian self-energy difference of its branches. We ask what local relativistic causality adds to this picture. First, in a relativistic scalar-field model of the branch difference, a finite protocol duration T replaces the logarithmic infrared dependence ln(ξ/σ_eff) of static configurations by ln[min(ξ, cT)/σ_eff]; the result is independent of the branch separation ξ only for ξ > cT, whereas laboratory protocols satisfy cT ≫ ξ. Second, defining the causal self-crossing time ⟨t⟩ of a branch from the retarded Green function, we prove that E_self⟨t⟩ = Gm²/c for every regular mass profile. Consequently τ_DP/⟨t⟩ = (m_H/m)² with m_H = M_P/√2 ≈ 15.39 μg, independently of the profile and of the regularization width: above m_H the DP reduction would be completed before the self-energy that drives it is causally established across the branch. We also show that the switch-on action deficit of the branch difference vanishes identically by mass conservation. What happens at m_H depends on whether the branch phase keeps accumulating beyond ⟨t⟩. If it does (H1), the decoherence time crosses over from the DP law ∝ m⁻² to a causally limited ∝ m^(−2/3) at m_H, for every profile. If it does not (H2), the phase acquired per causal interval is exactly (m/m_H)², and m_H acts as a Heisenberg cut. Both hypotheses predict that a superposition with m ≥ m_H and ξ ≫ σ_eff loses coherence within about 2⟨t⟩, while their predictions below m_H differ. All results are reproduced by openly available code (doi:10.5281/zenodo.23064101).