Gravitational Inverse-square Law Research Articles

Momentum – the Archilles’ Heel of Causality-based Physics

Galileo famously discovered the inverse square law of gravitation on earth and also formulated the concept of momentum as “mv” (mass x velocity) for the dynamics of moving bodies. But the momentum “mv” was at an odd with his inverse square law of “Fee Fall” as pointed out later by G.W. Leibniz, who gave the correct formulation of momentum as “mv^2”. G.W.F. Hegel later showed that the momentum expressed as “mv” is incompatible with what he called, “the laws of absolutely free motion” discovered by Kepler’s three laws of the planetary system. However, in spite of the controversy raised by J. Kepler, Leibniz and Hegel; the continued use of “mv” as the measure of momentum of moving bodies in physics and dynamics since R. Descartes and I. Newton; until now, even after the recognition of the quantum phenomena at the turn of the 20th century; is leading to more and more mysteries and myths; impeding further developments in physics and cosmology. It can now be shown that developments in Quantum electrodynamics and dialectics abolishes any notion of Newtonian mystery of “First Impulse” for matter and motion (momentum) from God. Leibniz’s formulation of momentum as “mv^2” is more appropriate and its use can resolve many of the problems in modern theoretical physics and cosmology; including in extra-terrestrial dynamics of the heavenly bodies and gravitation, electrodynamics and in quantum electrodynamics. The recognition of Leibniz’s vis viva, Hegel’s “absolute dynamics” and momentum as “mv^2” (“mv^3” only for neutral quantum particles like light photons); would represent the end of all mysticism and myths of cosmology, created since Isaac Newton’s “negation” of the Copernican revolution; later reinforced and accentuated by Albert Einstein’s theories of relativity.

Modified Gravitation and Mach's Principle: An Alternative to the Dark Matter and Dark Energy Cosmological Paradigm

The general approach is that all particles with non-null rest mass are subject to the force of gravity through the inverse square law of gravitation, plus an additional term that varies with the comoving distance (UYF-Field). The model is an ΛFRW-Cosmology starting from the modification of the gravity by explicitly incorporating Mach's Principle through an additional term large-scale in the gravitation; the source of this field is the ordinary baryonic matter. It`s deduced from the Matter-radiation decoupling in the early universe. This additional term of gravity UYF result null in the inner solar system, weakly attractive in interstellar ranges, very attractive in ranges comparable to the clusters of galaxies, and repulsive in cosmic scales, in agreement with astronomical and laboratory observables. This term explains dark energy, removes the incompatibility between the density of matter and the flatness of the universe in ᴧFRW-Cosmology; allows the theoretical deduction of the Hubble-Lemaitre Law, between other relevant consequences. Additionally to discuss other relevant astrophysics consequences: Birkhoff Theorem, Virial Theorem, the missing mass of Zwicky, gravitational lenssings, the BAO and the gravitational redshift in AGN, provides an additional contribution for the gravitational redshift that increase the until an factor of ~4, which has resolved the Arp controversy. Also we show the crude explanations of Pioneer anomaly, we obtain as the additional contribution of the acceleration of gravity due to UYF-Field. It is concluded that the dark energy and the missing dark mass can be approached with the usual physics as the large-scale modification of the Gravitation.

A new design for testing the gravitational inverse-square law at the sub-millimeter range with a 32-fold symmetric attractor

Short-range tests of the gravitational inverse-square law are very important for finding new interactions. In order to further improve the constraints on the Yukawa-like gravitational force, we propose a new scheme based on the torsion balance, where the speculative Yukawa-like gravitational force between the pendulum and the attractor is substantially increased by increasing the area of the test mass and the source mass. A dual-compensation design is used to realize a null experiment, which can release the accuracy requirement on some geometric parameters. The calculation result shows that, at the 95% confidence level, the new design can establish the strongest bound on the magnitude α of the Yukawa violation at the range of 40–800 μm with the total error of about 2.0 × 10−17 N m, and improve the previous bounds about one order of magnitude at the length scale λ ≈ 300 μm.

Non-isothermal squeeze film damping in the test of gravitational inverse-square law

For the experiments of testing the Newtonian inverse-square law (ISL) at short range, we have analyzed the residual gas damping effect under the assumption of the temperature of the gas is isothermal (Ke J et al 2020 Class. Quantum. Grav. 37 205008). However, when the test mass squeezes the gas, the temperature of the gas will change accordingly and may cause additional noise. It is essential to study this phenomenon in pursuit of higher precision test of ISL. Here, we discuss the non-isothermal squeeze film damping by using the differential equations of energy conservation and change in molecular density. The results show that this kind of Brownian motion torque noise is larger than that estimated previously and is influenced by the degrees of freedom of molecules. Namely, a larger accessible distance between test bodies is needed in comparison to the internal damping of the pendulum.

Combined Test of the Gravitational Inverse-Square Law at the Centimeter Range.

Experiments measuring the Newtonian gravitational constant G can offer uniquely sensitive probes of the test of the gravitational inverse-square law. An analysis of the non-Newtonian effect in two independent experiments measuring G is presented, which permits a test of the 1/r^{2} law at the centimeter range. This work establishes the strongest bound on the magnitude α of Yukawa-type deviations from Newtonian gravity in the range of 5-500mm and improves the previous bounds by up to a factor of 7 at the length range of 60-100mm.

The Fourier–Bessel expansion: application to experimental probes of gravity and feeble short-range interactions

Two Eöt–Wash torsion balance instruments exploited optimized Fourier–Bessel geometries to test the short-distance properties of gravity and to constrain exotic dipole–dipole and monopole–dipole interactions. We discuss efficient analytic techniques for computing the expected torques in those instruments arising from Newtonian and Yukawa interactions between unpolarized test bodies and dipole–dipole and monopole–dipole torques on polarized test-bodies. We consider systematic effects induced by weak external magnetic fields on the nominally unpolarized test-bodies. We also present a new Fourier–Bessel expansion for inverse-power-law (IPL) potentials and use this to calculate the expected IPL signals in our recent short-distance test of the gravitational inverse-square law. Our results slightly improve limits on inverse-5th-power law potentials.

Edmond Halley's Contributions to Hydrogeology.

Edmond Halley's Contributions to Hydrogeology.

Influence of the residual gas damping noise in the test of the gravitational inverse-square law

Many theories, such as the unification theories that would include gravitation, predict deviations from Newtonian inverse-square law (ISL) at short range. Many high precision experiments have been performed, but additional experiments are still of high scientific importance. Here, we discuss the torque thermal noise caused by residual gas damping, especially the effect of squeeze-film damping, in a proposed ISL experiment at the range of tens of microns. In such experiments, torsion pendulums are usually used to probe the torque interactions between the detector and the attractor, of which the thermal noise should be considered carefully due to the high sensitivity. By introducing a thermal accommodation coefficient, we can accurately model the torque noise of the residual gas damping as a combination of elastic and inelastic collisions. The results show that the noise will increase significantly at short separations between the pendulum and the surrounding components. In particular, when the separation is smaller than 40 μm, the squeeze-film damping may be larger than the internal damping of the pendulum used in present experiments, and become the fundamental limit for the experiments in the shorter range.

Improvement for Testing the Gravitational Inverse-Square Law at the Submillimeter Range.

We improve the test of the gravitational inverse-square law at the submillimeter range by suppressing the vibration of the electrostatic shielding membrane to reduce the disturbance coupled from the residual surface potential. The result shows that, at a 95%confidence level, the gravitational inverse-square law holds (|α|≤1) down to a length scale λ=48 μm. This work establishes the strongest bound on the magnitude α of the Yukawa violation in the range of 40-350 μm, and improves the previous bounds by up to a factor of 3 at the length scale λ≈70 μm. Furthermore, the constraints on the power-law potentials are improved by about a factor of 2 for k=4 and 5.

Weakly bound molecules as sensors of new gravitylike forces

Several extensions to the Standard Model of particle physics, including light dark matter candidates and unification theories predict deviations from Newton’s law of gravitation. For macroscopic distances, the inverse-square law of gravitation is well confirmed by astrophysical observations and laboratory experiments. At micrometer and shorter length scales, however, even the state-of-the-art constraints on deviations from gravitational interaction, whether provided by neutron scattering or precise measurements of forces between macroscopic bodies, are currently many orders of magnitude larger than gravity itself. Here we show that precision spectroscopy of weakly bound molecules can be used to constrain non-Newtonian interactions between atoms. A proof-of-principle demonstration using recent data from photoassociation spectroscopy of weakly bound Yb2 molecules yields constraints on these new interactions that are already close to state-of-the-art neutron scattering experiments. At the same time, with the development of the recently proposed optical molecular clocks, the neutron scattering constraints could be surpassed by at least two orders of magnitude.

Test of higher-derivative gravitational relativistic models with the gravitational inverse-square law experiments

The theory of general relativity has an ultraviolet(UV) problem that can be ameliorated by gravity with higher derivatives. The four-derivative gravity as an effective gravitational theory at UV scalars has two Yukawa-like corrections with parameters ${\ensuremath{\lambda}}_{0}$ and ${\ensuremath{\lambda}}_{2}$. By the analysis of experiments of HUST-2015, Newman's group, lake experiment, and Cassini spacecraft, we obtain the strong-bound regions for these parameters at submillimeter-to-millimeter, centimeter-to-meter, tens-of-meter, and solar-system scales, in which the properties of potential are clearly shown. Recently, the ghostfree and singularityfree gravity, a more potential modified gravity theory, introduces the novel conception of nonlocality. We test the scale of gravitational nonlocality ${\ensuremath{\lambda}}_{\mathrm{m}}l2.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\text{ }\text{ }\mathrm{m}$ by the torsion pendulum experiment HUST-2015. The predicted decaying spatial oscillations are visible meaning possible violation at shorter ranges. Our result provides useful information for gravitational interaction at microscopic ranges.

Constraints on generalized Eddington-inspired Born-Infeld branes

The Palatini $f(|\hat{\Omega}|)$ gravity is a generalized theory of the Eddington-inspired Born-Infeld gravity, where $\Omega_{~N}^{K}\equiv\delta_{~N}^{K}+bg^{KL}R_{LN}(\Gamma)$ is an auxiliary tensor constructed with the spacetime metric $g$ and independent connection $\Gamma$. In this paper, we study $f(|\hat{\Omega}|)$ theory with $f(|\hat{\Omega}|)=|\hat{\Omega}|^{\frac{1}{2}+n}$ in the thick brane scenario and give some constraints on the brane model. We finally found an analytic solution of the thick brane generated by a single scalar field. The behavior of the negative energy density denotes the localization of the thick brane at the origin of the extra dimension. In our braneworld, the warp factor is divergent at the boundary of the extra dimension while the brane system is asymptotically anti$-$de Sitter. It is shown that the tensor perturbation of the brane is stable and the massless graviton is localized on the thick brane. Therefore, the effective Einstein-Hilbert action on the brane can be rebuilt in the low-energy approximation. According to the recent test of the gravitational inverse-square law, we give some constraints on the $f(|\hat{\Omega}|)$ brane.

New bounds on dark energy induced fifth forces

We consider the gravitational Wilsonian effective action at low energy when all the particles of the standard model have decoupled. When the ${\cal R}^2$ terms dominate, the theory is equivalent to a scalar-tensor theory with the universal coupling $\beta=1/\sqrt 6$ to matter for which we present strong lower and upper bounds on the scalaron mass $m$ obtained by using results from the E\"ot-Wash experiment on the modification of the inverse-square law, the observations of the hot gas of galaxy clusters and the Planck satellite data on the neutrino masses. In terms of the range of the scalar interaction mediated over a distance of order $m^{-1}$, this leads to the small interval $4\,\mu m \lesssim m^{-1} \lesssim 68\, \mu m$ within reach of future experimental tests of deviations from Newton's gravitational inverse-square law.

The Copenhagen problem with a quasi-homogeneous potential

The Copenhagen problem is a well-known case of the famous restricted three-body problem. In this work instead of considering Newtonian potentials and forces we assume that the two primaries create a quasi-homogeneous potential, which means that we insert to the inverse square law of gravitation an inverse cube corrective term in order to approximate various phenomena as the radiation pressure of the primaries or the non-sphericity of them. Based on this new consideration we investigate the equilibrium locations of the small body and their parametric dependence, as well as the zero-velocity curves and surfaces for the planar motion, and the evolution of the regions where this motion is permitted when the Jacobian constant varies.

Combined Search for Lorentz Violation in Short-Range Gravity.

Short-range experiments testing the gravitational inverse-square law at the submillimeter scale offer uniquely sensitive probes of Lorentz invariance. A combined analysis of results from the short-range gravity experiments HUST-2015, HUST-2011, IU-2012, and IU-2002 permits the first independent measurements of the 14 nonrelativistic coefficients for Lorentz violation in the pure-gravity sector at the level of 10^{-9} m^{2}, improving by an order of magnitude the sensitivity to numerous types of Lorentz violation involving quadratic curvature derivatives and curvature couplings.

New Test of the Gravitational Inverse-Square Law at the Submillimeter Range with Dual Modulation and Compensation.

By using a torsion pendulum and a rotating eightfold symmetric attractor with dual modulation of both the interested signal and the gravitational calibration signal, a new test of the gravitational inverse-square law at separations down to 295 μm is presented. A dual-compensation design by adding masses on both the pendulum and the attractor was adopted to realize a null experiment. The experimental result shows that, at a 95%confidence level, the gravitational inverse-square law holds (|α|≤1) down to a length scale λ=59 μm. This work establishes the strongest bound on the magnitude α of Yukawa-type deviations from Newtonian gravity in the range of 70-300 μm, and improves the previous bounds by up to a factor of 2 at the length scale λ≈160 μm.

A novel study on Kepler’s law and inverse square law of gravitation

The Udwadia–Kalaba equation is a simple, aesthetic, and thought-provoking description of the world at a very fundamental level. It is about the way systems move. In this paper, we creatively apply the Udwadia–Kalaba approach to study heavenly bodies’ movements (especially on Kepler’s law and the inverse square law of gravitation). In an alternative way, we show that a heavenly body’s motion orbit can be an ellipse, a circle, a hyperbola, or a parabola and show the conservation of angular momentum. Furthermore, by applying the Udwadia–Kalaba approach, we use the constraint of motion orbit (ellipse, circle, hyperbola, or parabola) and the conservation of angular momentum constraint (or energy conservation constraint) and easily verify that any heavenly body’s motion complies with the inverse square law of gravitation. That is, we study Kepler’s law and Newton’s inverse square law in an analytical way, which makes the dynamicist more clear about the way heavenly bodies move and also makes the celestial mechanician more clear about the analytical mechanics (the Udwadia–Kalaba approach). Furthermore, for the students of dynamics and celestial physics, a different unique perspective is provided for them to study. At the end, we present the detailed process of applying the Udwadia–Kalaba approach to two imaginary cases to show its simplicity and efficiency.

Sensitivity Considerations for a Short-range Test of the Gravitational Inverse-square Law

Sensitivity Considerations for a Short-range Test of the Gravitational Inverse-square Law

From Modified Newtonian Gravity to Dark Energy via Quantum Entanglement

Starting from the classical Newton inverse square law of gravitation we arrive at a modified Newtonian gravity in the spirit of the work of Milgrom-Bekenstein pioneering work. This is achieved by injecting the needed quantum mechanical dissection of special relativity into Newton’s law via the modified energy mass relationship which transforms Einstein’s famous formula from a smooth four dimensional space to a rugged fractal-like spacetime manifold. The confidence in the present result stems not only from the consistency of the mathematical scheme but also from agreement with the general direction of cosmological measurements and observations.

PROGRESS IN LABORATORY GRAVITATIONAL EXPERIMENTS IN HUST GROUP

We briefly review recent progress of laboratory gravitational experiments conducted in our group, which include the determination of the gravitational constant G, the test of the gravitational inverse-square law, and the test of the Equivalence Principle.