Effect of inertial mass on a linear system driven by dichotomous noise and a periodic signal

A linear system driven by dichotomous noise and a periodic signal is investigated in the underdamped case. The exact expressions of output signal amplitude and signal-to-noise ratio （SNR） of the system are derived. By means of numerical calculation, the results indicate that （i） at some fixed noise intensities, the output signal amplitude with inertial mass exhibits the structure of a single peak and single valley, or even two peaks if the dichotomous noise is asymmetric; （ii） in the case of asymmetric dichotomous noise, the inertial mass can cause non-monotonic behaviour of the output signal amplitude with respect to noise intensity; （iii） the curve of SNR versus inertial mass displays a maximum in the case of asymmetric dichotomous noise, i.e., a resonance-like phenomenon, while it decreases monotonically in the case of symmetric dichotomous noise; （iv） if the noise is symmetric, the inertial mass can induce stochastic resonance in the system.

Classical Theory of Advance of Perihelion of Mercury with Velocity Dependent Inertial and Gravitational Masses

It is shown that Mercury's motion of the perihelion around the Sun, which is believed to be explicable quantitatively only by general relativity, can be fully understood within the frame of the dynamics of special relativity. It is only necessary to take into consideration the relativistic dependence of the planet's inertial and gravitational masses on its velocity (relative to the Sun) in the conservation equations for energy, and linear and angular momenta in the gravitational field. The physical Problem is reduced to a singular, nonlinear differential equation, which is solved numerically for the planet Mercury. The advance of the perihelion of Mercury is shown to be = 42.087' for a period of 100 years, which is in agreement with the as- tronomical observations and the result (by analytical approximations) of general relativity.

From Dirac’s Aether to the Dirac Equation

In 1951, Dirac proposed a formalism for a Lorentz invariant Aether with a vacuum state that contains all possible velocity states at each space-time point. Dirac showed no explicit path from the Aether towards the Quantum Mechanics. In this paper, we demonstrate that Dirac’s proposed Aether can be described by a lattice of possible events in space-time built in the local Lorentz frame. The idealised case of single velocity state leads to the famous Dirac equation for a plane wave state and is compatible with quantum statistics. On the lattice, possible space-time events are connected by the Dirac spinors which provide the probability of observing an event. The inertial mass of a particle is shown to be equivalent to the density of possible events on the lattice. Variation of the lattice density of events modifies the metric and provides a space-time curvature leading to the Hilbert action associated with general relativity. In classical limit, the perturbation in the density of possible events of the Aether is proportional to the Newtonian gravitational potential.

Effect of inertia mass on the stochastic resonance driven by a multiplicative dichotomous noise

A stochastic system driven by dichotomous noise and periodic signal is investigated in the under-damped case.The exact expressions of output signal amplitude and signal-to-noise ratio（SNR） of the system are derived.Numerical results indicate that the inertial mass greatly affects the output signal amplitude and the SNR.Regardless of whether the noise is symmetric or asymmetric,the inertial mass can influence the phenomenon of stochastic resonance（SR） of the system,leading to two types of resonance phenomenon：one is coherence-resonance-like of the SNR with inertial mass,the other is the SR of the SNR with noise intensity.

Gravity as a Unified Force

A model universe is hypothesized where gravity is developed to take on the qualities of electrostatics. This necessarily breaks the Einstein Equivalence Principle where gravitational and inertial mass may vary. We are told that gravity and electromagnetism were unified in the earliest moments of the universe. Perhaps they are still unified today and the EEP is broken at the small scale. This paper shows a possible way how. For simplicity Newtonian Mechanics [1] are used throughout which means that formulae are only valid in the low mass, low speed limit. For high mass or high speed please refer to General Relativity [2]. Gravity is developed in the following sections: 1) Model A is attractive;standard physics. 2) Model AB is attractive/repulsive;Hermann Bondi [3];3) Model ABCD is likes vs opposites;non-standard physics. Also discussed is a new way of looking at Electron-Positron annihilation.

Physics of Clocks in Absolute Space-Time

20th century physics experimentally established beyond doubt the fact that moving clocks read differently from “static” clocks. This fact is typically interpreted as support for special relativity. On the other hand, the same century produced proof that clocks at various locations in the gravitational field also read differently, and this fact is explained by general relativity, which is, in general, not Lorentz transformable. This paper establishes a common framework for the physics of clocks in these different situations.

Gravitational Space-Time Curve Generation via Accelerated Charged Particles

A force with an acceleration that is equal to multiples greater than the speed of light per unit time is exerted on a cloud of charged particles. The particles are resultantly accelerated to within an infinitesimal fraction of the speed of light. As the force or acceleration increases, the particles’ velocity asymptotically approaches but never achieves the speed of light obeying relativity. The asymptotic increase in the particles’ velocity toward the speed of light as acceleration increasingly surpasses the speed of light per unit time does not compensate for the momentum value produced on the particles at sub-light velocities. Hence, the particles’ inertial mass value must increase as acceleration increases. This increase in the particles’ inertial mass as the particles are accelerated produce a gravitational field which is believed to occur in the oscillation of quarks achieving velocities close to the speed of light. The increased inertial mass of the density of accelerated charged particles becomes the source mass (or Big “M”) in Newton’s equation for gravitational force. This implies that a space-time curve is generated by the accelerated particles. Thus, it is shown that the acceleration number (or multiple of the speed of light greater than 1 per unit of time) and the number of charged particles in the cloud density are surjectively mapped to points on a differential manifold or space-time curved surface. Two aspects of Einstein’s field equations are used to describe the correspondence between the gravitational field produced by the accelerated particles and the resultant space-time curve. The two aspects are the Schwarzchild metric and the stress energy tensor. Lastly, the possibility of producing a sufficient acceleration or electromagnetic force on the charged particles to produce a gravitational field is shown through the Lorentz force equation. Moreover, it is shown that a sufficient voltage can be generated to produce an acceleration/force on the particles that is multiples greater than the speed of light per unit time thereby generating gravity.