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Quantum mechanics is the square root of a stochastic process

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arxiv 1201.5091 v2 pith:JOHWGPF7 submitted 2012-01-24 math-ph math.MPquant-ph

classification math-phmath.MPquant-ph
keywords processstochasticbrownianmechanicsmotionquantumrootsquare
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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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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Quantum Systems as Indivisible Stochastic Processes

    quant-ph 2025-07 reject novelty 3.0 of 10

    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 an...

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