A numerical experiment of ideal stochastic motion of a particle subject to conservative forces and Gaussian noise reveals that the path probability depends exponentially on action. This distribution implies a fundamental principle generalizing the least action principle of the Hamiltonian/Lagrangian mechanics and yields an extended formalism of mechanics for random dynamics. Within this theory,...

This paper presents a theory for the mechanics of beams made of single crystals of shape memory alloys. The behavior of such beams can be quite unexpected and complicated due to the presence and propagation of phase boundaries. It is shown that the usual laws of mechanics do not fully determine the propagation of phase boundaries and that there is a need for additional constitutive information ...

We will demonstrate in this paper that Bell′s theorem (Bell′s inequality) does not really conflict with quantum mechanics, the controversy between them originates from the different definitions for the expectation value using the probability distribution in Bell′s inequality and the expectation value in quantum mechanics. We can not use quantum mechanical expectation value measured in experimen...

In eukaryotic cells, small changes in cell volume can serve as important signals for cell proliferation, death, and migration. Volume and shape regulation also directly impacts the mechanics of cells and tissues. Here, we develop a mathematical model of cellular volume and pressure regulation, incorporating essential elements such as water permeation, mechanosensitive channels, active ion pumps...

Quantum Mechanics and Reality. While quantum mechanics, as presented in physics textbooks, provides us with a formalism, it does not attempt to provide a description of reality. The formalism is a set of rules for computing the probability distribution of the outcome of essentially any experiment (within the realm of quantum mechanics). A description of reality, in contrast, would tell us what ...

In Mod. Phys. Lett. A 9, 3119 (1994), one of us (R.D.S) investigated a formulation of quantum mechanics as a generalized measure theory. Quantum mechanics computes probabilities from the absolute squares of complex amplitudes, and the resulting interference violates the (Kolmogorov) sum rule expressing the additivity of probabilities of mutually exclusive events. However, there is a higher orde...

The initiating explosive devices are prohibited in rock breaking near the goaf of the highly gassy mine. It is effective and applicable to cracking the hard roof with static cracking agent. By testing the static cracking of cubic limestone (size: 200 × 200 × 200 mm) with true triaxial rock mechanics testing machine under the effect of bidirectional stress and by monitoring the evolution process...

Bell’s work [1] led to a revolution in our understanding of Nature. I remember attending my first physics conference on “Microphysical Reality and Quantum Formalism,” in Urbino, 1985. Most of the talks were about Aspect’s experiment [2] confirming the nonlocality of quantum mechanics based on the experimental violations of Bell’s inequalities. Although I did not share the skepticism of many spe...

Bell's inequality is established based on local realism. The violation of Bell's inequality by quantum mechanics implies either locality or realism or both are untenable. Leggett's inequality is derived based on nonlocal realism. The violation of Leggett's inequality implies that quantum mechanics is neither local realistic nor nonlocal realistic. The incompatibility of nonlocal realism and qua...