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Register a new userA simple way of unifying the formulas for the Coulombs law and Newtons law of the universal gravitation: An approach based on membranes
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Added by
Luis Enrique Gomez Armas
Publication date
2021
fields
Physics
and research's language is
English
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In this work, a new approach is presented with the aim of showing a simple way of unifying the classical formulas for the forces of the Coulombs law of electrostatic interaction ($F_C$) and the Newtons law of universal gravitation $(F_G)$. In this approach, these two forces are of the same nature and are ascribed to the interaction between two membranes that oscillate according to different curvature functions with the same spatial period $xipi/k$ where $xi$ is a dimensionless parameter and $k$ a wave number. Both curvature functions are solutions of the classical wave equation with wavelength given by the de Broglie relation. This new formula still keeps itself as the inverse square law, and it is like $F_C$ when the dimensionless parameter $xi =274$ and like $F_G$ when $xi = 1.14198$x$10^{45}$. It was found that the values of the parameter $xi$ quantize the formula from which $F_C$ and $F_G$ are obtained as particular cases.
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Recent cosmological data for very large distances challenge the validity of the standard cosmological model. Motivated by the observed spatial flatness the accelerating expansion and the various anisotropies with preferred axes in the universe we examine the consequences of the simple hypothesis that the three-dimensional space has a global R^2 X S^1 topology. We take the radius of the compactification to be the observed cosmological scale beyond which the accelerated expansion starts. We derive the induced corrections to the Newtons gravitational potential and we find that for distances smaller than the S^1-radius the leading 1/r-term is corrected by convergent power series of multipole form in the polar angle making explicit the induced anisotropy by the compactified third dimension. On the other hand, for distances larger than the compactification scale the asymptotic behavior of the potential exhibits a logarithmic dependence with exponentially small corrections. The change of Newtons force from 1/r^2 to 1/r behavior implies a weakening of the deceleration for the expanding universe. Such topologies can also be created locally by standard Newtonian axially symmetric mass distributions with periodicity along the symmetry axis. In such cases we can use our results to obtain measurable modifications of Newtonian orbits for small distances and flat rotation spectra, for large distances at the galactic level.
We present a new approach to quantum gravity starting from Feynmans formulation for the simplest example, that of a scalar field as the representative matter. We show that we extend his treatment to a calculable framework using resummation techniques already well-tested in other problems. Phenomenological consequences for Newtons law are described.
Misinterpretations of Newtons second law for variable mass systems found in the literature are addressed. In particular, it is shown that Newtons second law in the form $vec{F} = dot{vec{p}}$ is valid for variable mass systems in general, contrary to the claims by some authors that it is not applicable to such systems in general. In addition, Newtons second law in the form $vec{F} = m vec{v}$ -- commonly regarded as valid only for constant mass systems -- is shown to be valid also for variable mass systems. Furthermore, it is argued that $vec{F} = m vec{v}$ may be considered as the fundamental law, alternatively to $vec{F} = dot{vec{p}}$. The present work should be of direct relevance to both instructors and students who are engaged in teaching and/or learning classical mechanics in general and variable mass systems in particular at a middle- to upper-level university physics.
Under certain conditions usually fulfilled in classical mechanics, the principle of conservation of linear momentum and Newtons third law are equivalent. However, the demonstration of this fact is usually incomplete in textbooks. We shall show here that to demonstrate the equivalence, we require the explicit use of the principle of superposition contained in Newtons second law. On the other hand, under some additional conditions the combined laws of conservation of linear and angular momentum, are equivalent to Newtons third law with central forces. The conditions for such equivalence apply in many scenarios of classical mechanics; once again the principle of superposition contained in Newtons second law is the clue.
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