Lorentz Transformation from Symmetry of Reference Principle

The Lorentz Transformation is traditionally derived requiring the Principle of Relativity and light-speed universality. While the latter can be relaxed, the Principle of Relativity is seen as core to the transformation. The present letter relaxes both statements to the weaker, Symmetry of Reference Principle. Thus the resulting Lorentz transformation and its consequences (time dilatation, length contraction) are, in turn, effects of how we manage space and time.Comment: 2 page

Crystallization in load-controlled shearing flows of monosized spheres

Identical, inelastic spheres crystallize when sheared between two parallel, bumpy planes under a constant load larger than a minimum value. We investigate the effect of the inter-particle friction coefficient of the sheared particles on the flow dynamics and the crystallization process with discrete element simulations. If the imposed load is about the minimum value to observe crystallization in frictionless spheres, adding small friction to the granular assembly results in a shear band adjacent to one of the planes and one crystallized region, where a plug flow is observed. The ordered particles are arranged in both face-centered cubic and hexagonal-closed packed phases. The particles in the shear band are in between the crystalline state and the fluid state, but the latter is never reached, which results in a large shear resistance. As the particle friction increases, the shear band disappears, and the ordering in the core region is destroyed. A significant portion of the particles are in a fluid state with a zero shear rate, leading to a substantial and unexpected reduction in the shear resistance with respect to the frictionless case. If the imposed load is increased well above the minimum from the onset of crystallization, we observe the formation of one shear band in the core, where the particles are again between the crystalline state and the fluid state, surrounded by two crystallized regions near the boundaries, in which most of the particles are in the face-centered cubic phase and translate as a rigid body with the boundaries themselves. In this case, the macroscopic shear resistance is independent of the particle friction

Relativity principles in 1+1 dimensions and differential aging reversal

We study the behavior of clocks in 1+1 spacetime assuming the relativity principle, the principle of constancy of the speed of light and the clock hypothesis. These requirements are satisfied by a class of Finslerian theories parametrized by a real coefficient $\beta$, special relativity being recovered for $\beta=0$. The effect of differential aging is studied for the different values of $\beta$. Below the critical values $|\beta| =1/c$ the differential aging has the usual direction - after a round trip the accelerated observer returns younger than the twin at rest in the inertial frame - while above the critical values the differential aging changes sign. The non-relativistic case is treated by introducing a formal analogy with thermodynamics.Comment: 12 pages, no figures. Previous title "Parity violating terms in clocks' behavior and differential aging reversal". v2: shortened introduction, some sections removed, pointed out the relation with Finsler metrics. Submitted to Found. Phys. Let

Deriving relativistic momentum and energy

We present a new derivation of the expressions for momentum and energy of a relativistic particle. In contrast to the procedures commonly adopted in textbooks, the one suggested here requires only the knowledge of the composition law for velocities along one spatial dimension, and does not make use of the concept of relativistic mass, or of the formalism of four-vectors. The basic ideas are very general and can be applied also to kinematics different from the Newtonian and Einstein ones, in order to construct the corresponding dynamics.Comment: 15 pages, 2 figure

The minimization of mechanical work in vibrated granular matter

Experiments and computer simulations are carried out to investigate phase separation in a granular gas under vibration. The densities of the dilute and the dense phase are found to follow a lever rule and obey an equation of state. Here we show that the Maxwell equal-areas construction predicts the coexisting pressure and binodal densities remarkably well, even though the system is far from thermal equilibrium. This construction can be linked to the minimization of mechanical work associated with density fluctuations without invoking any concept related to equilibrium-like free energies