Zeno’s Motion Paradoxes and Modern Physics

The problem of motion becomes a big quandary and a deep contemplation for the ancient people. For them, nature is an inner principle of change which needs further explanation of  motion’s underlying reality.

For over 2 millennia nobody offered better clues about motion’s deeper nature than Zeno of Elea (ca. 490 – 430 BC) even over Aristotle, Galileo, Newton and many others. Zeno claimed that he had issued around 60 paradoxes, but only four of them survive to our time preserved in Aristotle’s Physics. Aristotle refuted some of them leaving us with one of the deepest puzzle of space and time mystery i.e. the flying arrow paradox a).

What Zeno basically raised was about the continuation of space and time that even today’s physics are struggling with. Zeno saw that time consisted of a series of indivisible instants which make it impossible for something to move during a period of time at such an indivisible instant. He argued that an arrow in flight should be stationary at an instant and that if it was stationary at that instant then it should be stationary at any and every instant.

Zeno hypothesized, as conveyed by Aristotle, that objects occupying the same space as they do at rest must be at rest. For motion to occur, an object must change the position which it occupies. If the arrow is stationary at that instant, and if time is entirely composed of instants, then motion is impossible. For Zeno, being at rest means that from one instant to another entirely different instant, the body in question and all its parts occupy the same place 1.

This Zeno assertion may lead us to conclude that in order a body to move, it and all its parts must occupy less space than when it is stationary, in other words the body must have    undergone a contraction (Figure-1). This boldly answers the fundamental question which nobody dares to pose as why the Lorentz contraction occurs.

As we all know, Lorentz suggested a general hypothesis which was startling, crude and bold that any moving body must have undergone a contraction in the direction of its motion (by the fraction of (1-v2/c2)1/2),  which becomes the basis of the relativity theory  b).

Minkowski commented on this hypothesis as extremely fantastical, for the contraction was not to be looked upon as a consequence of of resistance in the ether or anything of that kind, but simply as a gift from the above, – as a companion circumstance to motion 3.

It is, therefore, imperative to see this phenomenon in the other way round. We used to see the motion of the body as the cause and its contraction is the effect. We don’t see as what Zeno did, that as far as the length of the body remains the same (no contraction) at any and every instant then the motion is impossible.

We may, therefore, conclude that the contraction is the prerequisite for the motion to happen. The shorter the body has undergone a contraction the faster the motion of the body would be c).

We should, in addition, scrutinize the second part of Zeno argument which holds the indivisibility of instants during which motion is impossible to occur. Such argument was true if such  a series of instants was continue with no gaps in between two consecutive instants, which is not the case d). We have elaborated in the previous articles that the perpetual creation and annihilation, the quantum underlying mechanism, resulting in a motion-pictures-like which is a series of time gaps separating the ephemeral spaces (Figure-2).

We should, therefore, make up our mind that the arrow e) existing in any instant is entirely different from that of immediately annihilated in the succeeding instant. As such, the newly created arrow can always take a different position from that in the preceding instant.

It is unbelievable that a man who lived in such olden time may have such a deep insight puzzling the reality of motion that can only be answered by the relativity theory and quantum mechanics f) which, alas, nobody is aware of.

The 2500 years old Zeno flying-arrow paradox is in its every respect, thus, comprehensively solved.

Notes:

a)   Most scholars regarded that motion had fully explained and calculus could explain the dichotomy paradox. Some philosophers, however, say that Zeno’s paradoxes and their variations are still relevant to metaphysical problems. The mathematical models of motion, space and time are merely intellectual constructions built for the convenience of simple  calculations, not for the deeper purpose of representing the structure of reality. The underlying reality that the paradox addresses is, thus, evaded.

b)   The Lorentzian hypothesis is completely equivalent to the conception of Minkowski spacetime which makes the hypothesis much more intelligible.

c)   The relativity theory asserts that a rigid body is shorter when in motion than when in rest. In this theory the speed of light c plays the part of a limiting velocity, which can neither be reached nor exceeded by any real body.

This is exactly how we have to interpret the underlying reality that Zeno addressed in his dichotomy, one of Zeno’s four famous paradoxes, which was expressed in ordinary [non-relativist] velocities, thus, easily refuted by anybody.

d)  Against Zeno’s theory of the continuation of time, Aristotle argued that if time is continuous and the points of time are represented as points of space, then the point’s position must be represented by both the past and future. For him the point of division lies in one segment or the other, but not in both. If a white object were changing to black in a period of time divided into two intervals – A, during which it is white, and B, during which it is black – then there must be some instant C when it is both black and white 2).

This perplexing contradictory situation that C belongs to both A and B was not learnt as it is repeated in modern time by the similar proposition of Schrodinger’s cat paradox where the cat was potentially found both dead and alive at the same time.

e)   Microscopically prevailing over its quantum stuffs.

f)  Newly interpreted quantum theory with the perpetual creation and annihilation of matter, to and fro energy, as its fundamental mechanics.

References:

  1. Mazur, J.: “The Motion Paradox”, Dutton, New York, 2007, p. 41.
  2. ibid, p. 40.
  3. Einstein et al.: “The Principle of Relativity”, Dover Publications, Inc., New York, 1952, p. 81
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