Related papers: Hamiltonian equations and inertial mass increase
According to Einstein, the trajectory of a particle that is predicted by special relativistic mechanics is well approximated by the trajectory predicted by Newtonian mechanics if the particle speed is low, i.e., much less than the speed of…
At the beginning of the 20th century the classical electron theory (or, perhaps more appropriately, the classical electromagnetic mass theory) - the first physical theory that dared ask the question of what inertia and mass were - was…
Some of the possible consequences of a generalized uncertainty principle (which emerges in the context of string theory and quantum gravity models as a consequence of fluctuations of the background metric) are analyzed considering the case…
A argument is described for how deformed or doubly special relativity may arise in the semiclassical limit of a quantum theory of gravity. We consider a generic quantum theory of gravity coupled to matter, from which we use only the…
Beginning with a relativistic action principle for the irrotational flow of collisionless matter, we compute higher order corrections to the Zel'dovich approximation by deriving a nonlinear Hamilton-Jacobi equation for the velocity…
The classical motion of spinning particles can be described without employing Grassmann variables or Clifford algebras, but simply by generalizing the usual spinless theory. We only assume the invariance with respect to the Poincare' group;…
We show that in complete agreement with classical mechanics, the dynamics of any quantum mechanical wave packet in a linear gravitational potential involves the gravitational and the inertial mass only as their ratio. In contrast, the…
The renaissance of General Relativity witnessed considerable progress regarding both understanding and justifying Einstein's equations. Both general relativists and historians of the subject tend to share a view, General Relativity…
The Newton equation describing the particle motion in constant external field force on canonical, Lie-algebraic and quadratic space-time is investigated. We show that for canonical deformation of space-time the dynamical effects are absent,…
To address the observation of Max Born (M. Born 1969) that the Newton's second law can emerge from a purely statistical perspective, we derive the evolution equation about the statistical distribution for dilute gas based solely on…
The equations of motion describing all physical systems, except gravity, remain invariant if a constant is added to the Lagrangian. In the conventional approach, gravitational theories break this symmetry exhibited by all other physical…
We propose a conservative two-dimensional particle model in which particles carry a continuous and classical spin. The model includes standard ferromagnetic interactions between spins of two different particles, and a nonstandard coupling…
We investigate the possibility of extending Newton's second law to the general framework of theories in which special relativity is locally valid, and in which gravitation changes the flat Galilean space-time metric into a curved metric.…
In the pilot-wave theory of quantum mechanics particles have definite positions and velocities and the system evolves deterministically. The velocity of a particle is determined by the wave function of the system (the guidance equation) and…
Several new ideas related to Special and General Relativity are proposed. The black-box method is used for the synchronization of the clocks and the space axes between two inertial systems or two accelerated systems and for the derivation…
The Standard Model (SM) ascribes the observed mass of elementary particles to an effective interaction between basis states defined without mass terms and a scalar potential associated with the Higgs boson. In the relativistic field theory…
A major consequence of special relativity, expressed in the relation $E_0 = m c^2$, is that the total energy content of an object at rest, including its thermal motion and binding energy among its constituents, is a measure of its inertia,…
It has been suggested that the recent acceleration of the expansion of the Universe is due a modified gravitational action consisting of the Einstein-Hilbert term plus a term proportional to the reciprocal of the Ricci scalar. Although the…
The vectorial velocity is given as a function of the position of a particle in orbit when a Newtonian central force is supplemented by an inverse cubic force as in Newton's theorem on revolving orbits. Such expressions are useful in fitting…
We discuss two applications of Riccati equation to Newton's laws of motion. The first one is the motion of a particle under the influence of a power law central potential $V(r)=k r^{\epsilon}$. For zero total energy we show that the…