GENERAL THEORY OF TIME - Motion,Position And Observation


Jitendra Kumar Barthakur
26 Jan 2005


Motion is a derivative of space and time in classical mechanics. Infinite divisibility of time is involved in calculus; and infinity is included in the system that evolves calculus for dynamics. In the application of Newton's formulas, t is duration. In relativity, space and time are concepts, and inter-connected by light. The circularity of logic in relativity creates multiplicity of space and ruins the subject-object continuum of logic and mathematics.

Space is physicality in Indian philosophy and time first concept. "Position" is the real input for understanding motion. The evolution of the axiomatic deduction of motion takes the route of conscious time. Contrary to this, motion in the epistemology of relativity is but abstraction in "imagination time" and "idealistic space".

The understanding of motion and position frees physics and cosmology from carrying out fruitless experiment based on relativity.

Motion is a derivative in classical mechanics

There is a compulsion in the classical mechanics to view motion as the function of time that is divisible infinitely, and the rate of motion as the differential of space with respect to time. This simplectic system of change circumvents the paradox of "small and big" of Zeno of Elea (born around 490 or 485 B.C.) and the direction of Aristotle (384-322 B.C.) that infinity should not be included in any system. Sir Isaac Newton of England (1643-1727), and his "Treatise of Fluxions", started this type of thinking in "theory of limits" that backed up the process of differentiation. More significant development of calculus probably had Gottfried Wilhelm Leibniz of Germany (1646-1716), and his "dynamics", as the originator. The "community" of mathematicians who succeeded Newton and Leibniz overlook that t or time of Newton was always a discrete variable having a definite and absolute value and it did not call for an infinity in the value of space to let time be less than a chosen unit in "imagination" or, conversely, infinity in the value of time to let space be less than a chosen unit in "imagination". There were documented hesitations of Newton in approving use of his own works; and those were ascribed to his passion for seeking perfect elegance in mathematics. For Newton, the principles of differentiation was a mathematical asset, it had proved to be so for finding solutions for, and in, "infinite series" by the "community". Similarly, the principle of the special theory of relativity, or relativity, is a mathematical asset today - it will certainly be so, it is foreseen, for the further development of the "general theory of time".

Amongst the later developers of classical mechanics one may perhaps pick up the mechanics of Sir William Rowan Hamilton of Ireland (1805-1865) from the cataloguer"s list. Hamilton had utilised the property that light takes the shortest possible path, as against "path of the least resistance" of Leibniz of those "calculus" days. There is always a proposition "A" for realising motion as change in position by time. In this understanding, time and space are foundational and motion is their derivative. Alternately, in "not-A", the change of position is the effect of motion. In this latter alternative, space and energy are foundational and time is the concept that makes a sense of it.


In the scenario that was dominated by A described above, Hamilton had suggested the unique solution of deriving time from the "twosome" of space and motion and called out the concept of "abstract space" and named it "phase-space" for his "conjugate momenta". Taking a leaf out of Plato"s fantasy of light behind the observer inside a cave, the view of Hamilton can be reconstructed thus: Let the shadows of a ball suspended in air be projected in the wall in front. The tilt or wavering of the source of light will move the shadow of the ball that will allow an observer to say that space and time are interdependent under a common purview of light taking the shortest linear path and take on the assumption that motion is derived from space and time, as in A. Thus, Hamilton can be said to be the first to conceive the basic principle of relativity, and he had made a proposition of it for the first time. It was quite possible that he was also duly influenced by the philosopher Immanuel Kant (1724-1804) of Germany, the father of European Idealism that takes space as concept. Thence, one may reach relativity of Professor Albert Einstein (1879-1955) of Germany, which was developed from the wave properties of light in 1905, again correlated to, in cataloguing, Jules Henri Poincare (1859-1941) [the first cousin of the President Raymond Poincare of the French Republic in the days of Great War I], who had published in 1906 an independent paper containing several principles of the special theory of relativity based on the dynamics of electrons.

Relativity is irrelevant to understanding dynamism

If there are two observers and the observers move in different directions and speeds, or they have different relative velocities, then one needs a reference velocity to comprehend motion, which is taken to be the velocity of light in relativity. For relativity, the velocity of light is fixed and never surpassed so that it remains the sole correlate to any and all the local velocities. Is that true?

The first requirement of the velocity of light being fixed entails that the shortest duration of time, which is measurable and required to compute the velocity of light, must also be fixed and unvaried. What is that duration? There has to be a perfect clock to measure it, which is non-existent. Yet there can be a theoretical clock that measures time without variation. Where that clock would be placed? A "fixed" satellite relates to earth"s movement, which is not perfect because earth is not perfect - earth is not perfectly round, wobbles along the axis, and bobs along the equator plane - its all heavenly activities slot in instant or periodic turns and twists. The only one position where that perfect clock can be placed is in the mind of the observer where the perfect clock exists anyway. It is imagination that is called upon for creating a perfect clock and finding a place to set it. Should not that be called "imagination time"? It will be called so. What does that clock measure? To say that the velocity of light is fixed and there is at least a theoretical clock that measures time in a "prefixed" manner, and it can be placed in the "mind" of the observer, the medium that the light travels through has to be uniform to avoid the rules of refraction, diffraction, aberration, and so on, that are inherent to light passing through different media. Where is that medium? Such a medium cannot exist microscopically or macroscopically - it has to be, again, a theoretical medium as was ether in the olden days. That is a product of "idealistic space".

It cannot be established, even theoretically, that the velocity of light is fixed. The science, particularly its discipline of physics that should abide by the logic of observation, should not talk about it even if the disciplines like astronomy may use velocity of light for approximations. The macroscopic use of velocity of light in astronomy is a risk; and the results of astronomical observations are but indications.

The next requirement is that the velocity of light cannot be surpassed. One need not bother to examine this proposition even theoretically. It is not tenable even in a tentative way. Thoughts travel, it is axiomatic, faster than light - because otherwise how the velocity of light is conceived in mind? It has been established that the parts of brain that house stored perceptions and their correlates are functionally different - or a real "distance" between the parts of brain is what thoughts traverse to emerge to do work, like conceiving the velocity of light. In other words, the brain is an entity with real dimensions, so, the thought emerging as the end correlate of mind"s inner workings in different parts of brain should bear a wave-pattern and wavelength, or equivalent to a wave-length, that is shorter than the wavelength of light. Perhaps similar faster than light passage takes place even within a computer storage system that uses a known form of energy, electricity, which perhaps act as a navigator or carrier of other forms of energy - yet to be understood but inherent - in the system of storage and correlation of electrons with their own parts and sub-parts within the storage system. Real experiments of physics have already established that the particles and sub-particles, often the transient ones, move faster than light. Perhaps these particles, sub-particles and may be, sub-sub-particles are all pervasive; and that outdates and rejects relativity straightaway - experimentally.

As has been said before, no theoretical stipulation is necessary to say that the velocity of light is surpassed by the particles and sub-particles of matter - experiments have alreadyit is a product of Riemannian established that fact. It is not established that nothing moves faster than light.

There are three more theoretical objections to take on the concept of relativity - to show that it is not established. First is that relativity includes infinity in the system. There is a well documented literature that claims that relativity is beyond the confines of Euclidean space - it is a product of Riemannian space, named after George Friedrich Vernhard Riemann of Germany (1826-1866). Riemannian geometry is a form of hyperbolic geometry that was first conceived by Carl Friedrich Gauss (1777 - 1855) who, however, did not endorse its "establishment" by two other mathematicians. Hyperbolic geometry is based on the rejection of two Euclidean axioms: (1) A line can be extended indefinitely on both ends and (2) through a point, which is not on a given straight line, only one straight line can be drawn in the plane containing the point and the given straight line, that will not meet the other straight line, or be parallel to it. It is hoped that soon the rejection of these two axioms will be proved invalid. Till that happens, one may use the calculations that are available estimating that the Euclidean geometry, which allows the axioms, extends to 1022 kilometers in all directions. This is a very large expanse within which the relativity has no role to play, or the astronomers who would be positioned in the center of a celestial sphere may never find a black hole or big bang within a perimeter of a sphere that has a radius of 1022 kilometers. And a telescope, radio-scope or spectro-scope is yet to be built to "see" beyond 1022 kilometers; and when these are built to "see" beyond that limit, or "sees" beyond that limit, obviously, the Euclidean space will also have an extended estimate of perimeter.

Secondly, in a space-time continuum of four dimensions, the three dimensions of length, breadth and thickness are required to understand distance; the fourth dimension is time. In this configuration, when distance is measured in term of velocity of light and time is also measured with the velocity of light, clearly, two pre-determined relationships of "distance-light" and "time-light" prevail. That causes the space-time continuum to lose two degrees of freedom, or, in other words, space-time continuum accepts domination by light in two distinct ways leaving only two re-constituted dimensions to remain independent and mathematically valid. It does not take much probing to understand that one of the two degenerated dimensions is "imagination time", mentioned before, which is the "form" of time that allows stipulations of various kind - including big bang and black hole. The other degenerated dimension is "idealistic space", also conceived in European Idealism, which posit speculations like "multiplicity of space", as was done by Hamilton. The advent of the multiplicity of space eventually destroys the subject-object base of logic and mathematics on account of which Professor E. J. Brouwer had proposed intuitionism in mathematics and personally developed the mathematics of arrangement to take over the scenario of relativity through topology. However, Chandra telescope of America cannot be placed anywhere except in "this universe" and the observations made by it cannot but use "conscious time". So, Chandra cannot "see" relativity-based events like black hole or big bang. These exist in imagination time and idealistic space. It has become essential to understand that anew and soon.

Relativity is a mathematical instrument; it is not an observational aid.

The third objection is tense-based. Relativity is valid only for the future and not for past or present. The base of this objection is also founded on the properties of light. The opposite of light is darkness - the absence of light. Or, light has no negative identity. Light is always progressive. It cannot go backward. Light cannot stay still, or it cannot be understood at present. Therefore, the light-time and light-space relationships are always positive, it bears no negative value or zero value. Consequently, the meaning of relativity is always remains in the future - there is no meaning of relativity in the past or at present. All the products of relativity, or mathematical singularity, lies in future - like the "event-horizon" of a black hole is always in the future not only for this reason but also because "zero entropy" requires infinite number of operations, or the operations leading to zero entropy continue for infinite time - the operations cannot end.

Not - A

Motion is the change of position of a body. To observe motion, an elapse of time is required. One may replace "body" with "body or thought"; but dynamics may not deal with that complication. The rate at which the change takes place is essentially, it can be said, a problem of "finite" calculus for which the calculus of Newton provides the base. There are two axioms that were prescribed by the ancients but ignored in the modern literature on dynamics. One is, for dynamics, space is physicality and the other is that time is the first of all concepts. These two axioms are not required for the process of imagination or speculation, as in Hamilton"s "phase-space" or relativity of Einstein - both being the residents of the hyperbolic space.

Also, a new understanding of the theory of number helps. The older theory of number was not compromised by the "multiplicity of space" of relativity to the extent that all "relativistic spaces" supposedly agreed to have a common theory of number. A new "finite foundation for mathematics of change" suggests, in short, that the numbers may be considered to have come one "after" another, or a concept of time - more precisely the concept of conscious time - "precedes" the concept of number. In this understanding, zero is "before" one and open; and numbers differ from each other with a sufficiently small unit for a specified field of enquiry and thus get rid of the problem of irrationality in the number system. [The concept had been discussed elsewhere and partly in this web site.]

The general theory of time is essentially a product of Indian philosophy that takes on not-A through theology; and well, to project epistemological compatibility.

The problem of twosome is projected in Rigvedo (RV) ["i" as in it, "e" as in get, "o" as in got] in the hymns that were subsequently named Vishnu Sukto ["u" as in put] or the hymn of "spread" that includes "space" in a constricted meaning. Vishnu Sukto is RV: 1: 22: 1-21. [The colons in this reference separate part, chapter etc.] RV: 1: 22: 1 invites the elegance, soamosyo pitoye ["oa" as in coat], of the general problem of twosome, osvinou, before knowledge, pratoryuja ["a" as in pizza], of any effortful understanding, viboadhoyo. RV: 1: 22: 2 makes out the case of dynamism for which the twosome is "position", surotha rotheetoma ["ee" as in see], and "motion", deva divisprisha. RV: 1: 22: 13 places, very interestingly, the desirability, podom, at the conclusion of such analysis, osyo somudhom, the small divisions, pangsure, of matter, energy and motion exists, vichokrome, in three forms, tredha, which was interpreted by the commentator Mohorshi Dayanondo Soroswoti as tangible laws of nature, microscopic divisions of matter, energy and motion and the intangible cause of motion. RV: 1: 22: 20 advises the wise, suroyoh, the desirability, podom, of taking vastness or limitlessness of space, Vishnu, for observation everywhere, chokshuratotom, with light or lightlike energy, divi. RV: 1: 22: 21 advises the thinkers, viprasoh viponvovoh, to be aware, jagribasoh, of that understanding of space, yot somindhote, [which is based on light and observation].

[Between RV: 1: 22: 2 and RV: 1: 22: 20 there is a wealth of prescriptions, like RV: 1:22:13 that was somewhat discussed. These relate to what ought to be investigated prior to arriving at the surmise of RV: 1: 22: 20. A deeper study of grammar and word formation is warranted.]

The physicality of space of RV, essentially without elasticity in any part of it, provides the ideal answer to having a stable base for understanding the twosome of position and motion reduced to the one of position, which is tangible. It is explained in another shruti that the motion and lack of motion are essentially the same, and one. Motion is the end of inertia and inertia is the end of motion. Motion has to continue to stay as motion. If any position on the path of motion is observed, then that position separates motion into two. What remains is position, the cause of motion being intangible and motion terminable. Sun is too bright, so its progress in the sky is best observed by the shadow it castes that eyes can see between the winks. Shadow moves and its position can be seen with grains placed on the ground in a row. Moon moves amidst stars and its progress is watched between winks of eyes. The position of eye explains position of what moves. Let the position of eye between two winks be instant. Instants come one after another. One may count n instants while eyes see how far the moon has gone along its path in the sky. The "time of instants" is the first requirement of observation: Eye or light is the media to conceive time. There is no other stipulation regarding light. [Observation defines the "time of observation", or conscious time, as explained in the general theory of time.] Light could be replaced by sound, like in the jingling of bells fastened to a chariot while eyes were closed, or touch, like the feeling an irregularity on a rolling wheel with hand placed on it or the touching and counting of the spokes as they passed with the rolling of wheel while one rode the chariot with both eyes and ears closed.

The finite calculus can take on now - light is unnecessary. (See extract from "TIME")


Not-not-A or A is then essentially not-position. Motion with no relation to position is imagination, speculation, memory, count and so on; or abstraction in general. The time forms that are related to the abstractions of motion are also abstractions: They are imagination time, speculation time, memory time, counting time and so on; or paratime in general.

What are in A today, are relevant for dynamics. Finite calculus of not-A is but a modification of calculus of A. The relativity and the hordes of the accessories relativity has developed in mathematics can now be modified for use in not-not-A.


The debate on motion and position sees a ray reaching the cave of Plato from without. The acceptance of axioms in general, and the neglected axiom of space being physicality and time the first concept in particular, opens a new era for physics: Frees physics and cosmology from finding explanation and physical evidence of results of relativity, like black hole and big bang, through actual observation of the universe.

Physics need not tread on the shoes of the astronomers any way.

Epistemologically, one may rename "A" as "B", "not-A" as "C" or "motion and conscious time" and "not-not-A" as "not-C" or "abstraction and para-time".

Not-not-A is not the exclusive third of A.


  1. Barthakur, Jitendra Kumar; Time; Kumud Books, C-8806 Vasant Kunj, New Delhi - 110070, India; 1999
  2. Barthakur, Jitendra Kumar; General Theory of Time; Kumud Books, C-8806 Vasant Kunj, New Delhi - 110070, India; 2004


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