GENERAL THEORY OF TIME - Gravitation And Universal Rhythm


Jitendra Kumar Barthakur
14 March 2005


Copernicus had the vision of earth rotating round the sun. Kepler, Galilei and Newton presented to science the theory of curved path of planetary movement, attraction between bodies and the laws of planetary rotations. Newton provided mathematical elegance to mechanics and optics. This logical process of providing a language to the physical forces ended with the posterity claiming that Riemannian geometry had created gravitation.

Considering that a freeze-decay of atoms below 0 K and a few other conditions of the physical world can lead to dissipating free particles and sub-particles into space, it is possible to visualise that the dissipated matter might reassemble finally to form star, and before that happened, the free atoms and ions could surround stars and galaxies causing or explaining the well known situations like bending of light rays near massive bodies and a few other things.

Also the freeze-decay develops a theory of universal rhythm to explain foundational links and base of the physical world in the Euclidean space.


Nicolus Copernicus of Poland (Born in 1473) is considered to be a principal renaissance thinker of Europe. In his path breaking 1543 A.D. book in Latin (the title has been translated as "On the Revolutions of the Celestial Spheres") that was published in 1547, Copernicus had proposed that earth moved around a stationery sun. It is called the heliocentric or sun-centric system. The belief that sun moved around a stationery earth is called geocentric system or the "Ptolemic System". The heliocentric system raised con-troversies. It had a scholarly acceptance only about half a century later through its modification and expansion of the scope as suggested by Johannes Kepler of Germany (1571-1630) in his two new planetary laws that were announced in 1609.


In formulating two of his three laws, Kepler had substantially used the data collected mainly by Tycho Brahe of Denmark (1546-1601). Brahe had endeavoured to reject the work of Copernicus as well as the older, geocentric, version of the planetary system to suggest yet another system of his own, which, however, did not survive the scrutiny of the scholars. Kepler had intrinsically ended the standoff against the heliocentric system, though not very well, or successfully. Not yet. It would finally take about a century and half and the brilliance of Sir Isaac Newton of England (1642-1727) to blunt the resent-ment against the objectionable idea that earth was not the centre of the universe.

Kepler's third law is one amongst several others; and it was announced in 1618. The three laws of Kepler, all of them are empirical, may be stated thus: (1) Planets move around sun in elliptical orbits. Sun occupies one of the two focii of the ellipse. (2) The line drawn from the sun to the planet sweeps out equal areas in equal times. (3) The square of the time of orbiting the sun by the planet is proportional to the cube of its mean distance from the sun.

For the purpose of this article, it is interposed that neither the "area" nor the "time" in Kepler's second law may acquire zero values because a "stationary state" of the planet in relation to the sun is not defined; and they can never be negative because the planets are always on motion in the same direction relative to the sun. The "time" in the third law is the "conscious time of observation" of the general theory of time, which can never be zero or negative. Also, the fractioning of an "instant", the smallest part of conscious time, is not allowed - the Finite Foundation of Mathematics of Change (which is described in this web site) prohibits it. It is the change, the motion of the planets, that is encoded in Kepler's laws. When instant is duration, the unit of area and its components like length and breadth also correspond to units; or, in other words, planetary movement is understood in quanta that is dependent upon the stage of refinement that the process of observation demands.


Kepler worked without a telescope. Galileo Galilei of Italy (1564 - 1642), a mathematician, astronomer and physicist, who was the contemporary of Kepler and a genius by any standard, was the first to use a telescope in astronomical observations. What Galileo saw and derived were of astounding interests: All planets moved around the sun, Milky Way was a collection of stars, surface of the moon had mountains and valleys, earth reflected light and shined like all other planets, Jupiter had several moons, Venus showed phases, sun had sun-spots, sun had rotation, earth's revolution around the sun was not regular and it wobbled as it moved; and several other never-before-known facts surfaced. Galileo firmly held that the path of revolution of earth around the sun was circular; and thereafter, following the rejection of the first law of Kepler, he neglected the residual works of Kepler. Galileo understood the principle of inertial law of nature and that the notion of "natural" motion was connected with "force" and "time", the motion of falling object acquired constant acceleration, the "go" of a falling object from "rest" was proportional to the square of the time of "fall". Thus, it can be said that Galileo had conceived the principles of the first two well-known laws of Newton, years before Newton was born.

Galileo's life was controlled by the orthodoxy of Catholicism and at times, that orthodoxy apprehended that Galileo menaced the Faith "much more than Luther and Kelvin put together". Galileo's scientific quest was seized by the hurdles placed before him when his mind was at its the most productive stage; and he was condemned to live under the condition of house arrest for the last eight years of his life. Yet the principal instigators against him were his fellow mathematicians who could not bear him professionally, and not the clergy. The time of his existence was wrong: It was when the ecclesiastical authority in Rome had become intolerant because of the rise of Protestantism and they could not afford to be expansive; or they thought that they could not let mathematicians alone without hurting the organisation or impeding raising of "good" mathematics. [Such things happen even now in different form. Example: Questioning the special theory of relativity may invite intellectual peril.]


Sir Isaac Newton had the benefit of learning, while young, about the discoveries of Copernicus, Kepler, Galileo and the rationality of Rene Descarte of France (1596-1650) who is considered the father of modern philosophy - a deeply religious man who dared and risked contradicting the prevailing ideas. Newton authored in 1687, one hundred and forty years after Copernicus had published his famous treaties on planetary movement and about eighty years after Kepler had announced his first two laws of planetary movements, the most important book of science ever written, Philosophiae Naturalis Principia Mathematica, which contained the laws of motion, theory of gravitation, along with the accompanying theory of tides and precession of equinoxes. In 1704, Newton authored another very important book, Opticks, which contained the theory of light, calculus and the results of other mathematical researches. In his 1687 book, Newton had defined "momentum" being proportional to velocity. The "constant term" of the relationship was given a definite scientific identity, "mass". The momentum of a body, a vector, equals the product of its mass and velocity. Then, in his three famous laws he defined "force" thus: (1) Momentum of an object is constant unless external force acts on the object - law of inertia. The next law says that (2) change in momentum observed during an interval of time, "this instant", equals the force that acts on the object at rest or constant motion just "before this instant", in the "last instant", to change the status of rest or uniform motion between the "last instant" and "this instant". [The words in italics have been added for serving the purpose of this article. Force is not understood unless the state of inertia changes; so, force also cannot be infinitely divisible and comes in units that relate to units of "before" and "after" of a unit of conscious time.] The third law is (3) for every action there is an equal and opposite reaction - "action" and "reaction" are forces. Before "action" is the state of continuation or existence in an open interval, inertia, when no force was applied but that state was conducive to the application of a particular form of force, named "action". The "after" of that "inertial state" is the definitude of application of "action" in "this instant". Action induces sameness in resistance in the "next instant", "reaction". When "action" overcomes "reaction", the "change" of observation takes place.

The experiments conducted by Galileo had led to the anticipation of the first two laws of Newton; but it was Newton who had stated them without flaw. Galileo had related the reality of the physical world as established by experiments in his anticipations. There are experiments - actual observations - that had existed and later covered by the mathematical elegance of the laws of Newton. That is the in-built strength of the laws of Newton. All experiments use conscious time; and in a "stream of conscious time", time-frame, the smallest parts are always durations, instants, and the dimension of an instant depends upon the refinement in observation that is required by the experiment at hand: millisecond for a flying bullet, second for a flying bird, nine months for pregnancy to end with the birth of a fully grown bonny baby.

Newton had used lots of mathematical abstractions in his works for providing solutions to the observational realities. As for example, the idealism of conics is used to bring solutions to the problems of planetary orbits. Such abstractions do not invalidate the basic laws as long as they lead to quantitative approximations for the observational physicality, and they are surely welcome for that purpose.


A force must cause a planet curve its path around the sun. Newton introduced the abstraction of "point mass", or that, for the "nearly spherical" objects like the sun and planet, the mass is located at the centre of the hypothetical spheres. According to the third law of Kepler, the square of the period during which the planet orbits the sun is proportional to the cube of its distance from sun - or, a given period of revolution is proportional to the (3/2)th power of distance from sun. Therefore, in the second law of Newton, the force acting towards sun on the point mass of a planet in orbit around the sun will be inversely proportional to the square of its distance from the point mass of the sun. Newton called this force acting towards sun, or the attraction by the sun, the force of gravitation. Newton generalised the idea to say that two massive circular bodies attracted each other with a force that is proportional directly to the products of their masses and inversely to the square of the separation of their centres; and this he called the "universal law of gravitation", and the constant of the proportion the "universal constant of gravitation", which is now depicted by the symbol "G" in all scientific literature. [G has the physical dimensions of (separation)3 / (mass)(time)2. If everything else is removed from the cosmos and two perfectly spherical bodies with the mass of one gram each is placed with their centres kept one centimetre apart in it, then G is 6.67 x 11-8dynes cm2/gm2. It is obvious that G is a very small force indeed and would cause the two bodies under con-sideration go round each other rather than clash.]

The universal law of gravitation can be derived from Kepler's laws if the idea and the definition of the momentum and the force of Newton's laws are introduced to them; naturally so, because Newton had used the experiment-based empirical third law of Kepler to define gravitation. The commonality between the experiments and observations of Kepler and the laws of mechanics of Newton is significant.

Galileo had suggested that the fall of an object accelerated in proportion to the square of the distance from the centre of a spherical earth. Newton had shown that this property applied to all falling objects on earth, also to moon that orbits the earth. The orbit of the moon equals 60 Earth radii and its period of revolution around earth is 27.3 days. Assuming that G carried the same value both for moon and earth, these led to the approximation that Moon's inward acceleration is 0.0027 metre per second per second, or (1/60)2 times the acceleration of the falling body on the surface of earth, which is approximately about 9.8 metres per second per second on the average and depicted by the symbol "g" in science literature. The value of g varies on mountaintop, ocean bottom and place-to-place depending upon what the ground underneath contains. Usually the variations are so small that they are unimportant for several purposes. Yet they are important for certain fields of inquiry and that had led to a special unit of measurement equalling 1/100 of one metre per second per second, gal. The use of instrumental calibrations in standard gravimeters is milligal or (one/million)th part of a gal. Even the modern electronic instruments are calibrated to keep a relationship with milligal.

The importance of g in its extreme smallness implies the possibility of local variations in G in different parts of the cosmos - because g represents the earth-case of G and there is really nothing like total emptiness in the space. The derivation of g on the surface of earth, on a point on the perimeter of the idealised earth-sphere, equals G times the mass of the earth ( for this Newton assumed that earth's average density was 5.5 times that of pure water) divided by the square of the idealised radius of earth. The abstraction of G is earth bound. It is also light bound, considering that it is an abstraction that is derived from the astronomical observations under the conditions prevailing in the solar system; and applied to the distant objects under the presumption of its invariability. G is one of the least studied of the physical constants, except for the very recent times when satellites are employed to do some work on gravitation; and its value has not been calculated more accurately than one part in million till this day.

It is known now that the moon does not move in an idealised elliptical orbit. Moon's movements are affected by the tide on the earth, attraction by the sun and other planets. Earth is not an idealised sphere; it has a bulge in the middle along the equator, it is somewhat pear-shaped, it flattens and caves on the poles and basically rugged under the ocean and over the land, its density is not uniform, and so on. And it does orbit the sun in an idealised manner in an idealised path. It bobs along the equator, wobbles along the axis, and sways from side to side on the orbital path. And the orbit is somewhere a screw, somewhere wavy, and good or sporty at other stretches. When it comes to other planets, the local variations become weirder. The orbits of the planets around the sun are a crazy collection of roadways - especially for Uranus, Neptune and Plato. Seen from another place in the cosmos, the solar system must resemble drunkards going round a lamppost. There is a case that G is not as uniformly same as it is made out to be.

Newton had doubted himself if the bodies could attract each other without a time-gap. This aspect surfaces in the science literature from time to time. It is the basis on which gravitational wave may be conceived in the Euclidean space.

Gravitation is not geometry

Geometry is an abstraction, a language, and a map. For Kepler, the orbits of the planets around the sun were elliptical; and that based on the actual observation of the planets and fitting the data to abstract elliptical orbits of the planets around the sun. The fittings were good. It is possible to derive the properties of an ellipse with a pure language of logic - like that it has two epicentres - and these properties could be associated with the theoretical ellipse of the orbit of a planet and verified again with observations. The observations agreed with what was projected of the elliptical properties. Ellipse is a part of conics - a system that is derived from the possible shapes of the surfaces cut out of a right cone in different ways. Newton used this inter-relation and proposed that the "eccentricity" e of the orbit of objects moving around fixed centres like the sun due to attractive force that obeys the "inverse square rule of distance" is a bound ellipse if e is greater than 1, which is so when the initial velocity is not very high, parabolic if e equals 1, which is so when the initial velocity is intermediate, and hyperbolic if e is smaller than 1, which is so when the initial velocity is very high. These properties agreed with the actual observations and so they are deemed established. Observation - abstraction - observation - abstraction - language - observation - abstraction again, can now be projected to future. Neptune was discovered in 1846 following this type of logic in almost the same position and turned out to be of almost of the same mass that were calculated by the astronomers. Such is the power of geometry. In Euclidean space, the geometry follows all rules of logic and relates to all tenses; but it is not the "thing in itself" - it is not the body that moves, force that creates the velocity of things or the cause of the "existence" of position, motion and observation. Geometry is explanation, reasoning; it is potent with ideas to come, but it is not, repeating a differently used phrase of Immanuel Kant of Germany (1724-1804), the "thing in itself".

Therefore, the applicability of the propositions that (1) gravitation is the product of the "curvature" of the Riemannian space, (2) Riemannian space is related to the distribution of matter and (3) the "image" of gravitation, as it prevails in the Riemannian space, can really affect an actual observation made with real electro-magnetic waves, require scrutiny. Such assertions literally lead to saying that the Riemannian geometry creates gravitation; and that adage is not tenable. Riemannian geometry has the foundation in the rejection of certain Euclidean axioms, possibly on insufficient ground, and its associates are para-time, and not conscious time of observation, and idealised-space of European Idealism, not real space. This had been explained in some more details in this web site. [Essay on - "Motion, Position and Observation".]

There is an experimentally found principle of equivalence of gravitation: The accelerations of bodies depend only on their masses and not on their chemical or nuclear constitution. The force between two bodies is proportional to the product of their masses and the inverse square of their separation. Attempts to show that gravitational force could couple with other forces like heat and electro-magnetism have not produced convincing outcome.

A new set of explanations has emerged: Since gravitation is the result of geometry, it has no dependence on the matter. So, the determination of G commands no priority. It is not very clear why this set of reasoning carried the best minds of the world on and on. One point could be because Newton defined mass as the constant of proportion between momentum and velocity in his first law and the same mass, product of mass of two attracting bodies, appears again to define G as the constant of proportion of the product of masses divided by the square of separation in the second law. That could lead to a way of thinking that motion defines mass, mass defines G, so, motion defines G. Almost irrefutable argument cuts in to say that the local motion affects G. The inhabitants of a cabin falling freely under gravity would experience weightlessness; and the floor of the cabin would come up to meet the inhabitants in case the cabin is pulled upwards in a theoretical "no gravity" district of the cosmos and give out an experience of gravity.

The first instance of weightlessness inside the falling body is trivial - without gravity a body would not fall, and gravity does not affect the cohesiveness of the body; therefore the inhabitants of the cabin stay disassembled while G makes the cabin fall. In the second example of a cabin being pulled in a theoretical zero-gravity area of cosmos, it is the force that simulates the semblance of gravity and the floor provides equal reaction to that force. G is the constant that makes a rule that an attractive force that obeys the inverse square law is directly proportional to the product of the masses of two attracting bodies and inversely to the square of their separations. The constant G makes that rule sustain itself, and work for other similarly placed force and bodies. G is an associate of force and force's inverse square law of separations. [It is possible to place a cabin on the earth and make its inhabitants feel weightlessness with a skilful use of force.]

G is associated with the forces that constitute celestial motions in the cosmos as are observed from the earth with electro-magnetic waves. Quantitatively, G is extremely small; its existence is meaningful only when the mass is large enough. G may not have the same value in all parts of the cosmos or in the parts of cosmos, or for objects not yet seen or cannot be seen with electro-magnetic waves; but the thin airs of the "idealistic space" and the associated "para-time" of the Riemannian geometry can produce only an "image" of G as a product of the curved space. One may ignore this image, and in fact, the whole of the Riemannian geometry, while observing things in the physicality of space, and experimenting - as in physics. What the Riemannian geometry offers comes after the observation: One may brood over the result of observation with it, speculate and devise finer points in arguments, just like Newton used conics to speculate the eccentricity of the planetary orbits around the sun.

Effects Of Freeze decay

It has been suggested in one of the references of this website, and also in a separate essay that can be accessed easily and freely, that at a critical point of temperature lower than 0 K when the force that keeps the particles and the sub-particles together inside the confine of an atom becomes less than the gravitational force, the particles and the sub-particles dissipate into space as free elements. The popular black hole literature dramatically describes one of such situations as the pre-condition to forming black hole in the Riemannian space - zero entropy at 0 K. The general theory of time requires force of gravity to alter, as required in the black hole literature, in quanta, because change comes in quanta and the parts of conscious time of observation are indivisible instants. Also the particles and sub-particles are units of matter and the scientists have worked out their dimensions.

The dissipated particles and sub-particles carry both mass and energy with them. It has been suggested that the idea of black matter and black energy, which emerge because there is more matter and more energy in the universe than speculated, can be explained with this theory of the dissipating matter and energy at the critical temperature below 0 K.

One may get a glimpse of what happens next from the popular big bang literature that speculates that the matter that is shattered outwards after the big bang in the Riemannian space, first cools and then collects themselves to form proto types of stars and becomes hotter to start thermo-nuclear reaction of converting hydrogen into helium when they are hot enough and sufficiently condensed. There is no contradiction that the process of collection of matter and the subsequent thermo-nuclear reactions may take place in Euclidean space. In fact, big bang literature provides swap from Riemannian space to Euclidean space without giving a "notice" for the switch. So, there is a peer-reviewed possibility that the dissipated particles and the sub-particles that could not be held and kept back by the atomic structure, because the atomic structure had lost its capacity to do so because of the extreme cold condition, can collect themselves at an appropriate stage and form stars again. Incidentally, "cold condition" is not the only reason why there are free particles and sub-particles, atoms and molecules in the space. There are other reasons too that has been described in various ways in the big bang and black hole literature.

The story could be thus: The matter and energy dissipate in quanta and possibly a burst of energy accompany dissipation; the phenomenon being very similar to how novae are created from cold-condition. The burst of energy would send the matter further away and allow the process of reformation of free-atoms soon enough as the temperature rises above the critical point at a relatively more distant part of cosmos mainly due to the motion created by the dissipating burst of energy. The free atoms and ions then rotate around one another, form clusters and move, possibly in overlapping rings, around live stars and galaxies. This leads to the thinking that every star or galaxy ought to have an envelope of matter and energy in a primitive stage of existence. An envelope like that would create a process of refraction for the passing light rays and bend them [freeing G from doing such a job all by itself as required by the pre-conditions of the Riemannian space. One may also reassemble the orbital data of Mercury and look for an alternative explanation for the observed rate of advance of Mercury's perihelion.]

There is a possibility that the star-free zones of the cosmos have differentials in the density of matter and energy. Considering that the matter would collect closer, and also cluster, a van der Waal type of weak mutual attraction may result all over and in varying intensity; and that may eventually manifest as gravitation in totality. Considering the estimates of large mass of black matter and large store of black energy, G might have this unseen source as the reason for its constancy. The value of G should not be the same in all parts of cosmos for this reason. When the matter has formed observable objects like stars and the planets, the value of G may stay close to a universal sameness between two observable objects. After all, the sum of the masses of the observable objects cannot be determined by watching stars and galaxies. There are difficulties in making a firm statement regarding the sameness of the "behavioural" G all over the cosmos. It is the product of G with mass that is the meaningful astronomical property of a star or galaxy; the mass of a star or galaxy cannot be determined uniquely. Can G be?


Matter and energy dissipate below a critical point of temperature in quanta, in rhythm. They reform in quanta into simple atoms, certainly in rhythm. Clusters of free-atoms and ions send out their feelers of existence, gravitation, in quanta and possibly in waves. Then they join together to form stars, cluster-wise, in quanta and in rhythm. Nuclear reactions are individualised to atoms and they occur continuously in rhythm. The star that is formed gives out heat in quanta, light in quanta, quanta of gravitation as it rotates along the bulge in the middle, flattening of the tops, wavering along the axis, shaking of the middle, sending out of bursts of gases into space and other activities that produces a rhythmic change in the gravitational attractive force originating from the star, the g of the star to which G is related. The consequence is easier to see. On earth every living or non-living existence follow a rhythm of existence.

The rhythm has accompaniment. Parts, combinations and the whole of the physical world are rhythmic. It is like a song, varied as a song varies in tone, pitch, allegretto, moderato, and everything else of music and musicology.

It is proposed that this unexplored region of physics, universal rhythm, possibly holds key to understanding the nature more completely. The gravitational waves can be conceived in Euclidean space. For these, a Riemannian formulation of the cosmos is unnecessary

However, foundationally, the purpose of existence remains unexplained. Space exists. Matter exists. Force exists. Motion exists.


The purpose of existence may be a common rule, Rule 2. Logically, there is a Rule 1 that should not be comprehensible in ordinary manner other than that it is there. Rule 1 to Rule 2 is a down flow of irreversible logic that allows more rules to originate and flow downwards and hold systems at logical states and stages. One may assign names to all these.

"These are all names".


  1. Barthakur, Dr.(Mrs) I. K. and Barthakur, Akash; The Law of Mobility that is Followed by All Life Forms and All Natural Forces; Indian Science Congress Association; Delhi; India; January,1997.
  2. Barthakur, Jitendra Kumar; Time; Kumud Books, C-8806 Vasant Kunj, New Delhi - 110070, India; 1999
  3. Barthakur, Jitendra Kumar; General Theory of Time; Kumud Books, C-8806 Vasant Kunj, New Delhi - 110070, India; 2004


Click on a title below

Motion, Position And Observation

Limit Of Low Temperature, Freeze Decay

Gravitation And Universal Rhythm

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Link: Content of the book

Link: Content of the book