Geometric Justification of the Fundamental Interaction Fields for the Classical Long-Range Forces

Abstract

Based on the principle of reparametrization invariance, the general structure of physically relevant classical matter systems is illuminated within the Lagrangian framework. In a straightforward way, the matter Lagrangian contains background interaction fields, such as a 1-form field analogous to the electromagnetic vector potential and symmetric tensor for gravity. The geometric justification of the interaction field Lagrangians for the electromagnetic and gravitational interactions are emphasized. The generalization to E-dimensional extended objects (p-branes) embedded in a bulk space M is also discussed within the light of some familiar examples. The concept of fictitious accelerations due to un-proper time parametrization is introduced, and its implications are discussed. The framework naturally suggests new classical interaction fields beyond electromagnetism and gravity. The simplest model with such fields is analyzed and its relevance to dark matter and dark energy phenomena on large/cosmological scales is inferred. Unusual pathological behavior in the Newtonian limit is suggested to be a precursor of quantum effects and of inflation-like processes at microscopic scales.

On the relation of the lunar recession and the length-of-the-day

“…The result is a velocity dependent extra term κ 0 v with κ 0 = 1/t. Recently, similar term was derived as a result of un-proper time parametrization (Gueorguiev and Maeder 2021). Krizek et al (2015) are emphasizing that there is no reason that the dark energy responsible for the accelerated expansion does not manifest itself in galaxies and in the Solar System as well.…”

Symmetries for Nonconservative Field Theories on Time Scale

“…We can discuss the case of a simple relativistic engine made of two current loops of arbitrary geometry, in which we shall consider the mechanical momentum and energy gained by the engine [25]. Extending this theory to the gravitational field on a time scale, we could calculate the interaction field Lagrangians for the electromagnetic and gravitational interactions [26]. Next, we can look for analogies between the Fibonacci sequence and certain spatially homogeneous and isotropic universes in Friedmann-Lemaitre-Robertson-Walker cosmology on time scales [27].…”

An Alternative Explanation of the Orbital Expansion of Titan and Other Bodies in the Solar System

“…In this section we discuss how non-conservation effects could be due to the use of unproper time parametrization and can be controlled by a parameter κ 0 . The un-proper time parametrization leads to fictitious acceleration proportional to the velocity of a body of the form κ 0 v [20]. Similar acceleration term is also present in the week field limit of the SIV theory [38,39].…”

“…Note that when expanded in powers of v/c the force effect is of 3rd order in v/c. If this additional acceleration is assumed to be the fictitious acceleration due to un-proper time parametrization, see equation ( 21) of [20], then for a two-body system, like the one shown in Fig. 1, we can estimate the value of the proportionality parameter κ 0 in a t = κ 0 v to be κ 0 ≈ G M γ 2 R 2 c .…”

“…Nevertheless, tidal effects and random impacts do affect the parts of the particular planetary system. For example, in the Earth-Moon system the leading effect is the loss of rotational kinetic energy E ∝ Iω 2 (see (23) of [20]) that results in Ė/E ≈ 2 ω/ω = −2 Ṫ /T , where ω is the Earth rotational rate 2π/T . By ( 13) and ( 14) the leading term in the angular momentum (see (24) of [20]) is the Moon orbital momentum L 2 = 27.92 • 10 33 kg m 2 /s which is a factor of 4.8 bigger than Earth rotation momentum L 1 = 5.86 • 10 33 kg m 2 /s.…”