Velocity dependent inertial induction

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Inertial induction is a dynamic model of gravitation interaction based on a modification of Newton’s laws. In the model, the interactive force may depend not only on the relative positions of two interacting bodies, but also on acceleration and velocity.

Sciama "On the origin of inertia"

In 1953, in order to express Mach’s Principle in quantitative terms, Cambridge University physicist Dennis W. Sciama proposed the addition of an acceleration-dependent term to the Newtonian gravitation equation.... Sciama’s acceleration-dependent term was $F=G\frac{m_A{m}_B\mathbf{𝐚}}{r{c}^2}$ where $r$ is the distance between the particles, $G$ is the gravitational constant, $\mathbf{𝐚}$ is the relative acceleration and $c$ represents the speed of light in vacuum.

This model was applied to determine the resistive force offered by a particle of gravitational mass $m_g$ (due to its interaction with the matter present in the rest of the universe according to Mach’s Principle) when it is accelerated at the rate $\mathbf{𝐚}$. The objective was to discover whether this acceleration-dependent force becomes $-m_g\mathbf{𝐚}$. The result was a force approximately equal to $-0.1m_g\mathbf{𝐚}$ when the estimated values of the mass–energy density of the universe, the velocity of light, $G$ and the observed size of the universe were inserted. The result was intriguing, but an exact equivalence between the inertial and gravitational masses of a particle cannot be achieved without extreme fine-tuning of the various quantities involved, which raises philosophical questions.

Extension of Inertial Induction

In 1984 Amitabha Ghosh, then at IIT Kanpur, proposed adding a velocity-dependent term to the static Newtonian term and Sciama’s acceleration-dependent term. Thus the total force between two particles becomes as follows:

$\mathbf{𝐅}=-{\widehat{\mathbf{𝐮}}}_r\frac{G{m}_A{m}_B}{r^2}-f(\theta ){\widehat{\mathbf{𝐮}}}_r\frac{G{m}_A{m}_B}{c^2{r}^2}{v}^2-f(\varphi ){\widehat{\mathbf{𝐮}}}_r\frac{G{m}_A{m}_B}{c^{2}r}a$

Note that in the detailed equation the effect of the angles of $\mathbf{𝐫}$, $\mathbf{𝐚}$ and $\mathbf{𝐯}$ was taken into account as $f(\theta )=\cos \theta |\cos \theta |$ and $f(\varphi )=\cos \varphi |\cos \varphi |$ where $\cos (\theta )={\widehat{\mathbf{𝐮}}}_r.{\widehat{\mathbf{𝐮}}}_a$ and $\cos (\varphi )={\widehat{\mathbf{𝐮}}}_r.{\widehat{\mathbf{𝐮}}}_v$, with ${\widehat{\mathbf{𝐮}}}_r,{\widehat{\mathbf{𝐮}}}_a,{\widehat{\mathbf{𝐮}}}_v$ being the unit vectors along $\mathbf{𝐫}$, $\mathbf{𝐚}$ and $\mathbf{𝐯}$. When the total force on a particle of gravitational mass $m_G$ due to the interaction with the matter present in the rest of a quasi-static, infinite, non-evolving, homogeneous universe was calculated, a new force law was found. One feature of the law is that $G$ is not a constant, but instead depends on the distance as $G=G_0\exp (-\kappa \frac{r}{c})$, where $\kappa$ is extremely small. The new force law that emerged is

$\mathbf{𝐅}=-m_G\mathbf{𝐚}-m_G[\frac{\kappa v^2}{c}]\widehat{{\mathbf{𝐮}}_{\mathbf{v}}}$

where $\kappa =\sqrt{\pi \rho G_0}$, $\rho$ being the average mass-energy density of the universe, and $G_0$ the local value of the gravitational coefficient. The value of κ is found to be about $1.2\times 10^{-18}{s}^{-1}$. The second term represents a cosmic drag acting on all moving bodies opposing the velocity. It was argued by Ghosh that a mean rest frame of the quasi-static infinite homogeneous universe exists, and the velocity is measured in this frame of reference.

New Force Law

Equation (2) represents a new force law that is derived from gravitational interaction. The exact equivalence between gravitational and inertial masses emerges as a natural consequence, without the need for any fine-tuning. The velocity-dependent term yields a feedback effect that obviates the need for any fine-tuning among the various parameters. The exponential decrease of $G$, suggested by Laplace in the 19^th century [16], removes the gravitational paradox.

Cosmic Drag

When this force law is applied to photons travelling from distant galaxies, it is found that the wavelength decreases due to the cosmic drag, and a cosmological redshift of the photons occurs, given by the relation

$z=\exp \frac{\kappa r}{c}-1$

This implies an equivalent Hubble constant of magnitude not very different from the present estimate of approximately 50 km s⁻¹ Mpc ⁻¹. Thus the observed cosmological redshift is accounted for without cosmological expansion, while the theoretical magnitude matches well with the observed value. Moreover, because cosmic drag entails no scattering or blurring, it does not suffer from the drawbacks of some other energy depletion mechanisms. Ormaston has hypothesized that velocity-dependent inertia may account for size reduction in quasars caused by extreme rotation velocities, resulting in "aberration redshift".

Local and Universal Interactions

Application of inertial induction theory to universal interactions results in an exact equivalence of gravitational and inertial mass of a particle, as well as the observed cosmological red-shift without universal expansion. The validity of the theory has been tested through application to the effects of local interactions, involving both interaction of light with matter, and matter-to-matter interactions. The results have not only matched the observations but have also been able to resolve a number of mysteries. Finally, it must be emphasized that the proposed model yields correct quantitative results in many different cases of a widely varying nature, and yet does not entail any free adjustable parameters. The only quantities involved are $G_0$, $c$ and $\rho$, all of which have well-defined values. Various applications of the theory are listed below.

1. Universal Interaction: The following results are obtained – (i) The exact equivalence of the gravitational and inertial mass; (ii) Newton’s force law along with a small cosmic drag on moving objects; (iii) Exponential decrease of $G$ with distance and elimination of the gravitational paradox when an infinite universe model is assumed; (iv) The gravitational potential energy of a particle with mass $m$ comes out as $-\frac{4}{3}m{c}^2$; (v) Cosmological red shift in a quasi-static non-expanding universe
2. Local Interaction of Light and Matter: In this category the results obtained are as follows – (i) An excess redshift of light grazing massive bodies explains the excess redshift of photons emitted from the solar limb; (ii) Excess redshift of photons grazing a massive object; (iii) Elimination of the mass discrepancy problem in white dwarfs; (iv) Determination of true velocity dispersions in clusters of galaxies and elimination of the need for a large amount of dark matter; (v) An explanation of the annual and daily fluctuating components of the Pioneer 10 anomaly
3. Local Interaction of Matter with Matter: The velocity-dependent inertial induction of this type led to the following results – (i) Secular retardation of the Earth without the tidal friction phenomenon and secular acceleration of Phobos; (ii) Matter distribution in spiral galaxies leading to flat rotation curves; (iii) The transfer of solar angular momentum and solution of the angular momentum problem of the solar system ; (iv) Elucidation of the unexplained excess orbital decay of LAGEOS I

Precession of Mercury's Perihelion

When the theory was applied to investigate the motion of Mercury, an unexpected result emerged. It was found that a reasonable amount of oblateness of the Sun may be present. Consequently, there is no need to assume the value of J₂ to be extremely small, i.e., near zero. In view of the axial spin of the Sun, it is quite reasonable that J₂ has some finite, though very small, magnitude

Secular Retardation of Mars's Rotation

The Rotation and Interior Structure Experiment (RISE) is sensitive enough to detect tiny changes in the rotation rate of Mars, translating into a variation in the length of its days. In addition to seasonal rotation changes due to variations in ice cap formation, RISE may also detect a secular retardation of Mars’s rotation predicted by the velocity-dependent inertial induction theory. On this theory, the planet Mars is expected to decelerate over the long term at a rate on the order of 1 x 10⁻²² rad s⁻². RISE may be able to detect a secular retardation on the basis of a few years’ data.

Proposal for a Direct Test

A modified version of the Michelson–Morley experiment has recently been suggested in order to directly detect the existence of velocity-dependent inertial induction. In this experiment, a difference between the redshifts of photons moving in the horizontal and vertical directions over an identical distance might yield a directly measurable effect due to inertial induction.

References

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