Gravity and Inertia in the Vethathirian Model of Universe G.Alagar Ramanujam, Uma Fitzcharles Vethathiri International Academy Chennai, India

Introduction: Gravity was the first discovered force, but remains least understood. A careful reexamination of Newton’s and Einstein’s concepts of gravity reveals that mass remains undefined in both. It is precisely for this reason that gravity is still not fully and properly understood. Our approach is to define mass in terms of its causative (kinematic) factors and thereby we reach a deeper understanding of gravity. This work is based on axioms originally given by Shri Vethathiri Maharishi and is therefore called the “Vethathirian Model of the Universe”.

Basic Axioms of the Model The Newtonian mechanics is well-known to be based on four independent entities – space, time, matter and energy. In Einstein’s theory space and time were unified by the Lorentz transformation and energy and matter were unified by the famous relation E = Mc2. Thus while Newton worked with four independents, Einstein worked with two independents (spacetime and matter-energy). Following this trend, in the present work complete unification is achieved by identifying space as the unitary entity with the following properties, expressed as the Basic Axioms of the Model [1,2,3,4]. 1. Space is the all-pervading substance inherent with all-potential energy and consciousness; it has the property of self-compression and surrounding pressure. 2. Self-compression results in the formation of spinning quanta of space termed “formative dust”. Due to the spin, every dust (or group of dust formed by surrounding pressure) is a source of repulsion. The first statement above describes the built-in mechanism of space to transform into the fundamental particles of which further structures are made. This built-in mechanism is postulated here as the self-compressive nature of space. The second statement deals with the nature of the repulsive forces operating between any two systems.

is that it defines matter, energy and time as the manifestations of the space itself. The entire universe is of, by and in space. Let us briefly discuss the interpretation of inertia by Galileo, Newton and Mach. Galileo interpreted inertia of matter as the resistance that a body would give to a force applied on it. Following Galileo, Newton obtained the inertia of a body as a constant of proportionality between a force applied on it and acceleration thus produced. Hence, Newton considered the mass of a body to be absolute. Mach challenged the absoluteness of inertia of the body and argued that inertia of the body is a measure of its interaction with ambient matter and hence depends on the configuration of matter surrounding the body. Vethathirian Model modifies the Mach principle to become as follows: The inertia of a body is due to the effect on it by the self-compressive nature of space, and also due to its interaction with surrounding matter. Let us consider first the effect of the compressive force on a given particle ‘A’, in the absence of any other surrounding matter. If ‘C’ is the constant compressive force exerted on the particle ‘A’, and ‘R’ represents the repulsive force of the particle due to its spin, then

Concept of Inertia in Vethathirian Model ( C - R ) = UIA (1) The essential feature of the Vethathirian Model

represents the net gripping force acting on the particle. The greater the value of UIA, the greater would be the difficulty for an applied force to move the particle. This difficulty is interpreted classically as the inertia of the particle. We call the inertia UIA the intrinsic inertia of the particle A. Further, there is an effect of surrounding matter on the inertia of the above particle A. The surrounding matter is a collection of spinning particles. Of them, let us consider the effect of a single particle B on A. Considering A and B as a system, the compressive nature of space acting on the system as a whole tends to minimize the distance between A and B. The mutual repulsion between A and B, due to their spins, tends to increase the distance between them. This gives an interaction between A and B, resulting in a kind of dynamic equilibrium. Due to this interaction let f(C,R) represent the effect of B on A. The effect of f(C,R) gives an inertia to A which we call the extrinsic inertia of A due to B. Extending this principle, due to every other particle of the surrounding matter there is an effect on the inertia of A. The sum of these effects on A, i.e. Σf( C,R) = UEA , is the extrinsic inertia of A due to the entire surrounding matter. Hence the total inertia of the particle A is given as: UTA = UIA + UEA UTA = (C-R) + Σf( C,R) (2) UTA of the body corresponds to its inertial mass. Vethathirian Law of Gravity The law of gravitation: F = GMm/r2 is a great gift of Newton to the world; it has had tremendous impact on our culture and civilization. This profound formula has certain limitations too: for example, Newton assumes “action at a distance” which in turn implies infinite velocity. Later, it was contradicted by special relativity, which puts a limit on the speed of communication. A deep look into the formula F = GMm/r2 reveals that it is deduced from Kepler’s empirical laws but not derived from basic axioms, as admitted by Newton himself. The derivation of Newton’s formula from basic axioms remains a great challenge over the past 350 years, and here we have addressed that challenge.

As an application of our basic axioms, we study the interaction between the sun and the planets. This study leads to a formula which we call “Vethathirian Law of Gravity”, and after a suitable approximation the same reduces to Newton’s law of gravity. We consider a test particle (p) of unit area at a distance ‘r’ from the sun with an orbital velocity ‘v’. The compressive force acting on every unit area of the imaginary sphere of the radius r is converging toward the centre of the sun. As r decreases, the surface area over which the compressive force acts decreases and hence the compressive pressure due to space increases. Let Cs represent the compressive pressure on the surface of the sun. Then the compressive pressure on the test particle at a distance r is given by 4πR2Cs/4π r2 or R2Cs/ r2 , where R is the radius of the sun. Let Rs be the outward flux per unit area of the surface of the sun. The total outward repulsive flux from the sun spreading radially outward is 4πR2 Rs. As r increases, the repulsive flux per unit area decreases and is given by 4πR2 Rs/4πr2 or R2 Rs/r2. Due to the net compressive force ( Cs – Rs)R2/r2 , the column of the free particle medium between the unit area of the test particle p and the sun’s surface gets compressed. Due to this compression, the column (comprising the mutually repulsing free particles) manifests a reaction which acts on p, pushing it away from the sun. Let K be the mean reactive repulsive force on the particle due to the mutually repelling free particles present per unit length of r. Then Kr gives an effective repulsive force on the particle. Hence, the magnitude of the net centripetal force (F) on the particle is given by, F = R2 Cs/r2 – R2 Rs/r2 – Kr (3) =( Cs – Rs ) R2 / r2 – Kr Since ( Cs – Rs ) is the net gripping force per unit area of the surface of the sun, the total net gripping force on the sun is 4πR2 (Cs – Rs). This total net gripping force is the cause for the resistance that any applied force on the sun

meets with, and this resistance is taken as the inertia of the sun. In the case of Sun, if M is its mass M = β 4πR2(Cs – Rs) (4) Combining eq (4) and (5) we have F= ( 1/ β 4π ) M/ r2 – Kr

Discussion The significance of eq.(3) of this paper is that it expresses the centripetal force F in terms of the contributing forces. This is in sharp contrast to the approach of Newton wherein he expressed the force F in terms of the masses and to the approach of Einstein wherein he wrote his field equations in terms of parameters of the curvature of space.

Denoting the constant ( 1/ β 4π ) as G, we have F(r) = GM/r2 – Kr (5) Eq.(5) is called the Vethathirian law of Gravity. The first term on the right hand side of eq. (5) is the Newtonian law of Gravity asserting that the centripetal force on p is directly proportional to the mass of the sun and inversely proportional to the square of the distance r of p from the sun and the second term is an additional one that our approach gives. For events at the terrestrial level the term Kr is negligible, and when it is thus neglected we get back Newton’s law of Gravity. Newton’s Law of Gravity Derived A derivation of a well known formula by a fresh set of axioms has great significance: it demonstrates not only the relative validity of the past but also the enlarged validity of the present. It is gratifying to note that we are able to get back Newton’s law of Gravity as a component of our expression for gravitational force. A look at our eq.(3) reveals that it contains the action at a distance concept of Newton through the term C, and the travelling wave concept of Einstein through R. The term C is rather indicative of ‘action at distance’ but with a more profound implication: as the compressive force on p is due to space, such a force is everpresent on p no matter where the particle p is located in space. Thus there is no “travel” involved for the compressive action; in other words, gravity does not travel. The flux represented by R in eq.(3) emanates from the sun and takes a certain time to travel and reach the particle p. It must be stressed here that what is travelling is not compressive gravity but the repulsive flux.

To begin from a basic unitary state and to identify that as the source of all physical phenomena essentially represents a unified approach. The Vethathirian Model begins from the radical Beginning – the single entity, space. Space itself transforms into the universe; by selfcompression space becomes particles. The spin of a particle produces in space a radially outward repulsive flux which we call magnetic wave. By the interaction of the compressive and the repulsive forces innumerable systems are formed. As Newton believed space to be nothing but a passive, empty background, he had no option but to attribute both the properties of inertia and gravity to the mass of the particle. He was forced to introduce two masses for the same particle -- inertial mass and gravitational mass -the first one as a measure of its resistance to an applied force and the second as its strength to attract other particles. However, in our model (C – R) appears as inertial effect in eq.(2), and the same appears in eq.(3) as the gravitational effect of the same particle. As (C – R) changes, the inertial effect and the gravitational effect change correspondingly. This is our version of the “principle of equivalence”, which Newton admired as a “God-given gift” and which Einstein exploited to formulate his General Theory of Relativity. Application of Vethathirian Law of Gravity in Cosmology The factor Kr in Eqn. 5 has significant implications in cosmological studies. As already mentioned, since K is extremely small at the terrestrial level the Kr term then becomes negligible, but at cosmological distances the Kr term is effective. We show below how Eqn.5 coupled with Hubble’s Law leads to the Friedmann cosmological equation with cosmological

constant (Λ). It is noteworthy that Newton’s law of gravity cannot lead to the Friedmann equation with cosmological constant, and in Einstein’s theory of gravity the cosmological constant Λ had to be introduced in an ad hoc way. Significantly, in our theory, the Friedmann equation with cosmological constant is the natural consequence of our axioms. By Vethathirian Law of Gravity we have: F = G M/r2 – Kr Integrating the above equation we get an expression for the potential V (r) as: V (r) = - 2 GM/r – Kr2/2 By the law of conservation of energy, we have ½ v2 - 2 GM/r – Kr2/2 = C (constant) Introducing the velocity-distance law of Hubble, i.e. v = Hr, expressing M as 4/3π r3 ρ and introducing the scale factor R, for distances at different epochs as r = r0 R, and rearranging, we get: H2 = 16 π G ρ/3 + K/2 + 2C/ r02 R2 This is the Friedmann cosmological equation with cosmological constant, expressed in different notations.

Conclusion In the Vethathirian Model we have derived an equation for the inertia of a body and derived Newton’s law of gravity from our axioms. As mass remains still undefined in conventional science, and Newton’s law of gravity still remains only deduced from Kepler’s law, our derivation of an equation for mass and our derivation of Newton’s law of gravity without using Kepler’s law, are both important contributions to the growth of science. It is again highly significant that our axioms lead to the Friedmann cosmological equations with cosmological constant and thereby give an explanation for the source of the so-called ‘dark energy’. Science progresses only through constant review and updating. The necessity to revise or update a given theory may arise from new experimental results or from the demands of aesthetic or philosophic logic. Instances of both

of these are abundant in the history of science. Vethathirian Model is another instance of the latter case. Vethathirian Model begins from the radical Beginning itself, and hence has a philosophic base. Contemporary science rather begins from the stage of fundamental particles without sufficient knowledge as to the essential nature of these particles. The fact that the Vethathirian Model begins with and consistently proceeds from the radical, primordial state -- the space ¬-- is its strength and gives us a holistic perspective. Only a holistic theory can be profound enough to reveal the fundamental Truth and it is in this context that Vethathirian Model is significant and valuable. It is not a superficial modification of Newton’s or Einstein’s concepts, but a radically different theory which has finally brought monism into scientific thinking and thereby Effect is seen as inherent and inseparable from its Cause. It all began with Tycho de Brahe, a great experimentalist of the sixteenth century. His lifelong rigorous observations of celestial objects produced an ocean of data. From these heaps of numbers Kepler carved out a set of empirical laws known as Kepler’s laws of planetary motion. Using these laws Newton deduced his law of gravity in terms of masses. Then came Einstein: he was the first to attribute a role for space for understanding gravity. He considered space as the transmitting agency of gravitational interaction between two bodies. From Einstein, we now come to Vethathiri Maharishi who asserts that gravity is the inherent property of the space itself. The journey of mankind to understand the source of gravity reaches a decisive stage in the Vethathirian concept of space. References 1. Vethathiri Maharishi, Unified Force, Vethathiri Publications, 1996 2. Vethathiri Maharishi, Gravity of Gravity, Vethathiri Publications, 2002 3. Proceedings of the Seminar on Vethathirian Concepts of Gravity and Cosmology, Aliyar, India, Jan.,2003 4. G.Alagar Ramanujam, Uma Fitzcharles, K.Perumal; Wide Spectrum, Coimbatore, 2004