A procedure is given for the transformation of quantum mechanical operator equations into stochastic equations. The stochastic equations reveal a simple correlation between quantum mechanics and classical mechanics: Quantum mechanics operates with “optimal estimations,” classical mechanics is the limit of “complete information.” In this connection, Schrödinger's substitution relationsp x → -iħ ∂/∂x, etc, reveal themselves as exact mathematical transformation formulas. The stochastic version of quantum mechanical equations provides an explanation for the difficulties in correlating quantum mechanics and the theory of relativity: In physics “time” is always thought of as a numerical parameter; but in the present formalism of physics “time” is described by two formally totally different quantities. One of these two “times” is a numerical parameter and the other a random variable. This last concept of time shows all the properties required by the theory of relativity and is therefore to be considered as the relativistic time.
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Neumann, M. A probabilistic analysis of the difficulties of unifying quantum mechanics with the theory of relativity. Found Phys 8, 721–733 (1978). https://doi.org/10.1007/BF00717502
- Quantum Mechanic
- Classical Mechanic
- Mechanical Operator
- Probabilistic Analysis
- Present Formalism