The stochastic-quantum correspondence rewrites any quantum unitary as a matrix of squared entries, making quantum systems formally equivalent to indivisible stochastic processes, but the equivalence is definitional and the unitarity claim overreaches.
Quantum mechanics is the square root of a stochastic process
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We prove a theorem showing that quantum mechanics is not directly a stochastic process characterizing Brownian motion but rather its square root. This implies that a complex-valued stochastic process is involved. Schr\"odinger equation is immediately derived without further assumptions using It\=o integrals that are properly generalized. Fluctuations in space arise from a Brownian motion and the combined effect of a stochastic process with a symmetric Bernoulli distribution typical of tossing a coin.
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Quantum Systems as Indivisible Stochastic Processes
The stochastic-quantum correspondence rewrites any quantum unitary as a matrix of squared entries, making quantum systems formally equivalent to indivisible stochastic processes, but the equivalence is definitional and the unitarity claim overreaches.