I introduce a novel realistic, stochastic approach to quantum mechanics by extending the recently proposed grabit formalism \cite{braun_stochastic_2022} to two Twin Worlds. According to the picture developed, we live at the intersection of two worlds with identical stochastic laws of evolution. Our World is limited to that intersection, and only coincidence events from the two Twin Worlds, post-selected automatically by our restriction to the intersection, have physical reality in Our World. This fully reproduces standard non-relativistic quantum mechanics, including Born's rule and the violation of Bell's inequality. I derive the stochastic evolution equation in each Twin World that fully reproduces Schrödinger's equation for an arbitrary number of particles with arbitrary interactions, and demonstrate that hall-mark quantum effects such as tunnling are correctly reproduced.

quant-pharXiv:2603.14464Mar 17, 20260 citations

Epilogue

Shan Gao

In this book, I have argued that the wave function in quantum mechanics is real, and it represents the state of random discontinuous motion (RDM) of particles in three-dimensional space. Moreover, this picture of quantum ontology is complete in accounting for our definite experience, but it requires that the quantum dynamics be revised to include a stochastic, nonlinear evolution term resulting from the RDM of particles. Obviously I took a road less traveled by researchers in the foundations of quantum mechanics. In order to convince more readers that this road is deserved to be taken, I will review the main results of this book and discuss them in a broader context. The starting point of my road is protective measurements (Chapter 1). In 1993, this new method of measurement in quantum mechanics was discovered (Aharonov and Vaidman, 1993; Aharonov, Anandan, and Vaidman, 1993). Distinct from conventional projective measurements, protective measurement is a method for measuring the expectation value of an observable on a single quantum system. By a series of protective measurements, one can even measure the wave function of a single quantum system. Therefore, besides the Born rule for projective measurements, protective measurements provide another, more direct connection between the wave function and results of measurements, which is not probabilistic but definite. It can be expected that a definite connection between the wave function and results of measurements is more important for understanding the meaning of the wave function and searching for the ontology of quantum mechanics. However, it seems that this connection provided by protective measurements is still less well known today, and its significance has not been fully realized by most researchers, either. The first stop on my road is the reality of the wave function (Chapter 4). It is correct to say that protective measurements alone do not imply the reality of the wave function. An additional connection between the state of reality and results of measurements is needed.

Cambridge University Press eBooksJan 1, 20170 citations