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Schrödinger Equation from Gravity
  • Shibdas Roy
Shibdas Roy
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Abstract

We propose that Schrödinger equation in quantum mechanics is a consequence of gravity. We derive the quantum Schrödinger equation for a gravitational wave from classical gravity, and accordingly present a classical Schrödinger equation in spacetime for the gravitational wave. We notice that the quantumness of Schrödinger equation arises from non-zero finite gravity of the classical Schrödinger equation in spacetime, by treating time separately from space at small enough scales compared to the actual masses. In other words, (mass-) energy curves spacetime, and the curvature of spacetime, in turn, gives rise to the quantum nature of the energy. We also observe that the wavefunction in Schrödinger equation corresponds to the state of the energy of a flat closed spacetime system and has non-zero fluctuations even when the masses are zero. These quantum vacuum fluctuations of a flat spacetime evidently arise only from the temporal profile of the wavefunction. Besides, our result naturally explains why the square of the magnitude of the wavefunction represents the probability of finding a given body at a spatial location upon position measurement.