Schr\"odinger's Cheshire Cat: A tabletop experiment to measure the Di\'osi-Penrose collapse time and demonstrate Objective Reduction (OR)

For nearly 100 years, the paradox of Schr\"odinger's Cat has remained unresolved. Why does the world we live in appear classical despite being composed of quantum particles governed by the Schr\"odinger wave equation? Lajos Di\'osi 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 Di\'osi-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.