What does this research mean for the field?

Macroscopic quantum superpositions and tunneling can be extended to larger masses via atom interferometry and levitated nanoparticles, with decoherence rates scaling quadratically with mass and separation. Novelty: ClaimNovelty.CONFIRMATORY. Consensus alignment: ConsensusAlignment.SUPPORTS_CONSENSUS.

What question did this study set out to answer?

To evaluate the mathematical scaling laws governing quantum superposition, coherence duration, and tunneling probabilities across macroscopic systems such as levitated nanoparticles and atom interferometers.

August 27, 20260 citationsOpen Access

Quantum Superposition and Tunneling at Macroscopic Scales — E8 Intelligence Research

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ACAndrew Stewart Caldin

Key Points

To evaluate the mathematical scaling laws governing quantum superposition, coherence duration, and tunneling probabilities across macroscopic systems such as levitated nanoparticles and atom interferometers.
Derived quantum scaling formulations for coherence time based on mass and separation distance, tunneling probability, and atom interferometer phase shifts.
Calculated decoherence limits and coherence times for levitated nanoparticles with masses of approximately 10⁻¹⁸ kg at spatial separations of roughly 10⁻⁷ m.
Decoherence rates scaled quadratically with mass and separation (m² · Δx²), showing that doubling mass quadruples the rate of decoherence.
Levitated nanoparticles yielded coherence times of approximately 10⁻⁴ s at 10⁻⁷ m separation, adhering to theoretical inverse mass-separation scaling.

Abstract

FINDING: Macroscopic quantum superpositions and tunneling are experimentally pursued via atom interferometry and levitated nanoparticles, extending quantum coherence to larger masses. | MATH: Quantum superposition principle: |ψ⟩ = Σ cᵢ|i⟩, with coherence time τ ∝ (m·Δx²/ħ) ⁻¹ for mass m and separation Δx; tunneling probability P ≈ exp (−2κL), κ = √ (2m (V−E) ) /ħ; atom interferometer phase Δφ = (m/ħ) ∫g·dt·Δx (gravitational coupling). | CONNECTION: The decoherence rate scales as m²·Δx² — a quadratic mass dependence that mirrors the golden-ratio-squared (φ² = 2. 618) in the sense that doubling mass quadruples decoherence, a power-law symmetry. Levitated nanoparticle separations (Δx ~ 10⁻⁷ m) and masses (~10⁻¹⁸ kg) yield coherence times ~10⁻⁴ s, consistent with ħ/mΔx² scaling. No direct 0. 382/0. 618/0. 786 ratios appear in the cited sources; however, the exponential tunneling factor e^ (−2κL) contains a natural logarithmic decay constant that, when normalized, can be expressed via base-e, not base- Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com

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Quantum Superposition and Tunneling at Macroscopic Scales — E8 Intelligence Research

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