A note on the mechanics emerged from systems with a stochastic process of the time variable

Research output: Contribution to journalArticlepeer-review


Stochastic mechanics is an attempt to build a well-defined probabilistic formulation of quantum theory. This formulation proposes a deeper origin for the (non-relativistic) Schrödinger equation using a hypothesis that a massive particle with mass m is influenced by a Brownian motion having a diffusion coefficient of ħ/2m and no friction. However, the hypothetical ether (as suggested by Nelson) that causes such a Brownian motion remains uncleared. While most of the literature on stochastic mechanics follows the original interpretation given by Nelson, we present an alternative interpretation of stochastic mechanics, where the stochasticity of time, and not space, is responsible for the emergence of the quantum particle. In particular, we show that stochastic mechanics (in one dimension) can be deduced by assuming that time is a stochastic process of a universal absolute time. This replaces the proposed ether with a new notion of time for particles in the quantum regime.

Original languageEnglish
Article number128334
JournalPhysica A: Statistical Mechanics and its Applications
StatePublished - 1 Jan 2023


  • Brownian motion
  • Ito process
  • Itô’s lemma
  • Quantum mechanics
  • Stochastic mechanics
  • Time

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability


Dive into the research topics of 'A note on the mechanics emerged from systems with a stochastic process of the time variable'. Together they form a unique fingerprint.

Cite this