Stochastic mechanics and quantum theory (original) (raw)
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Stochastic Models of Quantum Mechanics — A Perspective
AIP Conference Proceedings, 2007
A subjective survey of stochastic models of quantum mechanics is given along with a discussion of some key radiative processes, the clues they offer, and the difficulties they pose for this program. An electromagnetic basis for deriving quantum mechanics is advocated, and various possibilities are considered. It is argued that only non-local or non-causal theories are likely to be a successful basis for such a derivation.
The stochastic nature of physics
The stochastic nature of quantum physics can best be comprehended by shifting to another space-progression model. This other model is called a paginated space-progression model and uses a universe wide time clock that ticks synchronously at the location of all observable items/events. As a consequence this model proceeds with universe wide progression steps from each static status quo to the next one. A straight forward consequence is that the whole universe is recreated at every progression step. This recreation is used to explain the stochastic structure of elementary particles.
Quantum Mechanics as a Classical Theory XIV: Connection with Stochastic Processes
1996
In this paper we are interested in unraveling the mathematical connections between the stochastic derivation of Schrödinger equation and ours. It will be shown that these connections are given by means of the time-energy dispersion relation and will allow us to interpret this relation on more sounded grounds. We also discuss the underlying epistemology. 1
Fluctuations and Noise Letters, 2016
By means of the examples of classical and Bohmian quantum mechanics, we illustrate the well-known ideas of Boltzmann as to how one gets from laws defined for the universe as a whole to dynamical relations describing the evolution of subsystems. We explain how probabilities enter into this process, what quantum and classical probabilities have in common and where exactly their difference lies.
Is quantum mechanics equivalent to a classical stochastic process?
Physical Review A, 1979
The authors analyze the connection between the theory of stochastic processes and quantum mechanics. It is shown that quantum mechanics is not equivalent to a Markovian diffusion process as claimed in recent papers. The origin of a possible confusion about this question is clarified. The authors further demonstrate that there does not even exist a non-Markovian process equivalent to quantum mechanics.
Quantum mechanics as a statistical theory: a short history and a worked example
arXiv: Quantum Physics, 2018
A major question in our understanding of the fabric of the world is where the randomness of some quantum phenomena comes from and how to represent it in a rational theory. The statistical interpretation of quantum mechanics made its way progressively since the early days of the theory. We summarize the main historical steps and then we outline how the randomness gains to be depicted by using tools adapted to Markov processes. We consider a model system corresponding to experimental situations, namely a single two-level atom submitted to a monochromatic light triggering transitions from the ground to the excited state. After a short summary of present quantum approaches, we explain how a general "kinetic-like" Kolmogorov equation yields the statistical properties of the fluorescent light radiated by the atom which makes at once Rabi oscillations between the two states, and random quantum jumps with photo-emission. As an exemple we give the probability distribution of the ti...
Stochastic phenomena in physics
Acta Applicandae Mathematicae, 1983
The basic concepts of stochastic variables and their characterization by stochastic differential equations, diffusion equations and path integrals are reviewed. Applications of stochastic processes are then outlined for problems in optics, spin diffusion, random potentials in solids, and quantum mechanics.