We propose that Heisenberg's uncertainty principle is a consequence of gravity. While quantum mechanics and gravity are widely considered incompatible, we show that Heisenberg's uncertainty principle, which is a central tenet in quantum mechanics, in fact, arises from non-diminishing finite gravity between a particle and another identical particle. We observe that it is impossible to know the position or momentum of the particle with unlimited precision, unless the gravity is infinite or zero, respectively, between the particles. We derive upper and lower bounds on the uncertainties in position and momentum of the particle, based on the uncertainty principle emerging from gravity. Accordingly, the quantum-classical boundary is identified, beyond which gravity behaves classically.

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.

We propose that what is gravity in curved spacetime yields quantum mechanics in flat spacetime. This implies that if there was no gravity, quantum mechanics would not exist. In other words, the universe is general relativistic, and therefore, classical and local, in curved spacetime, but the same universe is quantum and nonlocal (Newtonian), when projected onto special relativistic flat spacetime. We previously demonstrated how the quantum Schrödinger equation arises from a classical Schrödinger equation, which in turn arises from Newtonian gravity. Here, we illustrate that the classical Schrödinger equation corresponds to Einstein’s field equation of gravity for Schwarzschild metric in curved spacetime. Since the Schwarzschild metric is an exact solution of the vacuum Einstein equation, the Schwarzschild radius is for Ricci flat spacetime but with non-zero Riemannian curvature. It then follows that quantum mechanics arises from this Riemannian curvature of gravity.