Tabletop Quantum Gravity: Feasible via Matter-Wave Interferometry and Optomechanics — E8 Intelligence Research

FINDING: Tabletop experiments for quantum gravity are now feasible using matter-wave interferometry and optomechanical systems, potentially enabling direct observation of quantum gravitational effects at low energies. | MATH: Key constants: Planck length \( l_P = √ G/c^3 ≈ 1.616 × 10⁻³⁵ \, m \); Planck mass \( m_P = √ c/G ≈ 2.176 × 10⁻⁸ \, kg \); Newton's constant \( G ≈ 6.674 × 10⁻¹¹ \, m^3 kg⁻¹ s⁻² \). The experiment probes the quantum superposition of masses, with phase shift \(Δ φ ∝ G m_1 m_2 t^3 / d^3\) (the "T-cubed" scaling from Penrose–Folman). | CONNECTION: The T-cubed scaling involves a cubic time dependence, which resonates with cubic lattice symmetries (e.g., simple cubic, body-centered cubic) common in crystallography. The ratio of Planck length to typical experimental scales (\(~ 10⁻¹⁰ \, m\)) is \(~ 1.6 × 10⁻²⁵\), far from g Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com