We investigate the previously unexplored quantum dynamics of nonrelativistic, spinless particles propagating in curved spaces with torsion. Our findings demonstrate that while torsion has been predominantly associated with spin, it can also influence the quantum behavior of spinless particles by inducing a logarithmic nonlinearity in the Schrödinger equation through quantum fluctuations, even in flat space. To facilitate quantization in curved spaces, we introduce an extended stochastic variational method. Unlike canonical quantization, this approach is naturally suited to general coordinate systems, with quantum fluctuations arising from a noise term in the stochastic process that is directly influenced by torsion. By requiring consistency with quantum dynamics, we derive an upper bound on the magnitude of torsion. Our results reveal a previously unrecognized mechanism by which torsion, as predicted in certain extensions of general relativity, can influence quantum systems, with potential implications for early-universe physics and dark matter or energy models.

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• Alternative gravity theories
• Brownian motion
• Quantum formalism
• Stochastic processes
• Probability theory
• Stochastic differential equations
• Variational approach