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24 pages, 333 KB

Open AccessArticle

Is Gravity Truly Balanced? A Historical–Critical Journey Through the Equivalence Principle and the Genesis of Spacetime Geometry

by Jaume de Haro and Emilio Elizalde

Symmetry 2025, 17(8), 1340; https://doi.org/10.3390/sym17081340 - 16 Aug 2025

Cited by 3 | Viewed by 2324

Abstract

We present a novel derivation of the spacetime metric generated by matter, without invoking Einstein’s field equations. For static sources, the metric arises from a relativistic formulation of D’Alembert’s principle, where the inertial force is treated as a real dynamical entity that exactly compensates gravity. This leads to a conformastatic metric whose geodesic equation—parametrized by proper time—reproduces the relativistic version of Newton’s second law for free fall. To extend the description to moving matter—uniformly or otherwise—we apply a Lorentz transformation to the static metric. The resulting non-static metric accounts for the motion of the sources and, remarkably, matches the weak-field limit of general relativity as obtained from the linearized Einstein equations in the de Donder (or Lorenz) gauge. This approach—at least at Solar System scales, where gravitational fields are weak—is grounded in a new dynamical interpretation of the Equivalence Principle. It demonstrates how gravity can emerge from the relativistic structure of inertia, without postulating or solving Einstein’s equations. Full article

(This article belongs to the Special Issue Mathematics: Feature Papers 2025)

13 pages, 3041 KB

Open AccessArticle

Thermal Lens Measurements of Thermal Expansivity in Thermosensitive Polymer Solutions

by Vincenzo Ruzzi, Stefano Buzzaccaro and Roberto Piazza

Polymers 2023, 15(5), 1283; https://doi.org/10.3390/polym15051283 - 3 Mar 2023

Cited by 5 | Viewed by 3212

Abstract

The weak absorption of a laser beam generates in a fluid an inhomogeneous refractive index profile acting as a negative lens. This self-effect on beam propagation, known as Thermal Lensing (TL), is extensively exploited in sensitive spectroscopic techniques, and in several all-optical methods for the assessment of thermo-optical properties of simple and complex fluids. Using the Lorentz–Lorenz equation, we show that the TL signal is directly proportional to the sample thermal expansivity

α

, a feature allowing minute density changes to be detected with high sensitivity in a tiny sample volume, using a simple optical scheme. We took advantage of this key result to investigate the compaction of PniPAM microgels occurring around their volume phase transition temperature, and the temperature-driven formation of poloxamer micelles. For both these different kinds of structural transitions, we observed a significant peak in the solute contribution to

α

, indicating a decrease in the overall solution density—rather counterintuitive evidence that can nevertheless be attributed to the dehydration of the polymer chains. Finally, we compare the novel method we propose with other techniques currently used to obtain specific volume changes. Full article

(This article belongs to the Section Polymer Analysis and Characterization)

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18 pages, 3045 KB

Open AccessArticle

A New Compartmentalized Scale (P_N) for Measuring Polarity Applied to Novel Ether-Functionalized Amino Acid Ionic Liquids

by Xu Zheng, Chun Guo, Wenqing Wu and Jing Tong

Molecules 2022, 27(10), 3231; https://doi.org/10.3390/molecules27103231 - 18 May 2022

Viewed by 2454

Abstract

Functionalized and environmentally friendly ionic liquids are required in many fields, but convenient methods for measuring their polarity are lacking. Two novel ether-functionalized amino acid ionic liquids, 1-(2-methoxyethyl)-3-methylimidazolium alanine ([C₁OC₂mim][Ala]) and 1-(2-ethoxyethyl)-3-methylimidazolium alanine ([C₂OC₂mim][Ala]), were synthesized by a neutralization method and their structures confirmed by NMR spectroscopy. Density, surface tension, and refractive index were determined using the standard addition method. The strength of intermolecular interactions within these ionic liquids was examined in terms of standard entropy, lattice energy, and association enthalpy. A new polarity scale, P_N, is now proposed, which divides polarity into two compartments: the surface and the body of the liquid. Surface tension is predicted via an improved Lorentz-Lorenz equation, and molar surface entropy is used to determine the polarity of the surface. This new P_N scale is based on easily measured physicochemical parameters, is validated against alternative polarity scales, and is applicable to both ionic and molecular liquids. Full article

(This article belongs to the Section Physical Chemistry)

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20 pages, 6183 KB

Open AccessArticle

Micro Satellite Orbital Boost by Electrodynamic Tethers

by Peter Yao and Timothy Sands

Micromachines 2021, 12(8), 916; https://doi.org/10.3390/mi12080916 - 31 Jul 2021

Cited by 11 | Viewed by 4963

Abstract

In this manuscript, a method for maneuvering a spacecraft using electrically charged tethers is explored. The spacecraft’s velocity vector can be modified by interacting with Earth’s magnetic field. Through this method, a spacecraft can maintain an orbit indefinitely by reboosting without the constraint of limited propellant. The spacecraft-tether system dynamics in low Earth orbit are simulated to evaluate the effects of Lorentz force and torques on translational motion. With 500-meter tethers charged with a 1-amp current, a 100-kg spacecraft can gain 250 m of altitude in one orbit. By evaluating the combined effects of Lorenz force and the coupled effects of Lorentz torque propagation through Euler’s moment equation and Newton’s translational motion equations, the simulated spacecraft-tether system can orbit indefinitely at altitudes as low as 275 km. Through a rare evaluation of the nonlinear coupling of the six differential equations of motion, the one finding is that an electrodynamic tether can be used to maintain a spacecraft’s orbit height indefinitely for very low Earth orbits. However, the reboost maneuver is inefficient for high inclination orbits and has high electrical power requirement. To overcome greater aerodynamic drag at lower altitudes, longer tethers with higher power draw are required. Full article

(This article belongs to the Special Issue Space Robotics)

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17 pages, 5362 KB

Open AccessArticle

Numerical Analysis of Radiation Effects on Fiber Optic Sensors

by Sohel Rana, Harish Subbaraman, Austin Fleming and Nirmala Kandadai

Sensors 2021, 21(12), 4111; https://doi.org/10.3390/s21124111 - 15 Jun 2021

Cited by 15 | Viewed by 5029

Abstract

Optical fiber sensors (OFS) are a potential candidate for monitoring physical parameters in nuclear environments. However, under an irradiation field the optical response of the OFS is modified via three primary mechanisms: (i) radiation-induced attenuation (RIA), (ii) radiation-induced emission (RIE), and (iii) radiation-induced compaction (RIC). For resonance-based sensors, RIC plays a significant role in modifying their performance characteristics. In this paper, we numerically investigate independently the effects of RIC and RIA on three types of OFS widely considered for radiation environments: fiber Bragg grating (FBG), long-period grating (LPG), and Fabry-Perot (F-P) sensors. In our RIC modeling, experimentally calculated refractive index (RI) changes due to low-dose radiation are extrapolated using a power law to calculate density changes at high doses. The changes in RI and length are subsequently calculated using the Lorentz–Lorenz relation and an established empirical equation, respectively. The effects of both the change in the RI and length contraction on OFS are modeled for both low and high doses using FIMMWAVE, a commercially available vectorial mode solver. An in-depth understanding of how radiation affects OFS may reveal various potential OFS applications in several types of radiation environments, such as nuclear reactors or in space. Full article

(This article belongs to the Special Issue Optical Fiber Sensors in Radiation Environments)

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8 pages, 1704 KB

Open AccessArticle

Performances of PMMA-Based Optical Fiber Bragg Grating Sensor in Extended Temperature Range

by Wei Zhang and David J. Webb

Photonics 2021, 8(6), 180; https://doi.org/10.3390/photonics8060180 - 23 May 2021

Cited by 5 | Viewed by 3742

Abstract

PMMA based optical fiber Bragg grating (POFBG) sensors are investigated in an environmental chamber with controlled temperature and relative humidity at temperature extended to 70 °C. At below a critical temperature of 50 °C the POFBG sensor exhibits good linearity and sensitivity for both temperature and humidity sensing. Nonlinear responses are observed at higher temperature, giving rise to varying, reduced magnitudes of sensitivities. An important feature of POFBG humidity sensing is observed at above critical temperature where the POFBG humidity sensitivity turns from positive to negative. A theoretical model based on Lorentz–Lorenz equation is presented to estimate the dependence of POFBG refractive index on temperature and relative humidity. The experimental results qualitatively agree with the theoretical analyses. Full article

(This article belongs to the Special Issue Advancements in Fiber Bragg Grating Research)

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68 pages, 498 KB

Open AccessArticle

Maxwell–Lorentz Electrodynamics Revisited via the Lagrangian Formalism and Feynman Proper Time Paradigm

by Nikolai N. Bogolubov, Anatolij K. Prykarpatski and Denis Blackmore

Mathematics 2015, 3(2), 190-257; https://doi.org/10.3390/math3020190 - 17 Apr 2015

Cited by 7 | Viewed by 9062

Abstract

We review new electrodynamics models of interacting charged point particles and related fundamental physical aspects, motivated by the classical A.M. Ampère magnetic and H. Lorentz force laws electromagnetic field expressions. Based on the Feynman proper time paradigm and a recently devised vacuum field theory approach to the Lagrangian and Hamiltonian, the formulations of alternative classical electrodynamics models are analyzed in detail and their Dirac type quantization is suggested. Problems closely related to the radiation reaction force and electron mass inertia are analyzed. The validity of the Abraham-Lorentz electromagnetic electron mass origin hypothesis is argued. The related electromagnetic Dirac–Fock–Podolsky problem and symplectic properties of the Maxwell and Yang–Mills type dynamical systems are analyzed. The crucial importance of the remaining reference systems, with respect to which the dynamics of charged point particles is framed, is explained and emphasized. Full article

(This article belongs to the Special Issue Mathematical physics)

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