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Monday, December 12, 2011

Zeno’s Motion Paradoxes and Modern Physics


The special relativity theory began with the initiative of Lorentz who suggested a general hypothesis, something crude, startling and bold. From Morley and Michelson’s experiments he concluded that any moving body must have undergone a contraction in the direction of its motion, and with a velocity v, a contraction in the ratio of 1: (1-v2/c2)1/2. He assumed that molecular forces, like the electric and magnetic forces, were also transmitted through the ether. The translation would affect the action between two molecules or atoms in a manner resembling the attraction or repulsion between charged particles. Since the intensity of molecular actions ultimately conditions the form and dimensions of a solid body, there is a possibility to be a change of dimensions as well.


Combined with the hypothesis of time dilatation that Einstein subsequently put forward, Minkowski proved that, by unifying space and time called spacetime, the world configuration was 4-dimensional rather than the ordinary 3-dimensional. He demonstrated that the Lorentzian hypothesis was much more intelligible when explained under this new conception of space and time. For him, the length contraction was not to be looked upon as a consequence of resistance in the ether or anything of that kind but merely as a gift from the above, - as a companion circumstance to motion 3.

The problem of motion is not only the subject of modern physicists but had already become a brainteaser for the ancient people. For the ancients, the motion was different from the appearance they saw in daily life but rather the inner principle of change in nature. For over two millennia nobody offered better clues about more profound nature of motion than Zeno of Elea (ca. 490 - 430 BC) even over more modern scientist such as Newton and many others. Among his famous 60 paradoxes, only one of the most profound puzzles of mystery survives to our time, i.e., the flying arrow paradox, a) thanks to Aristotle who preserved them in his book of Physics.

Zeno raised the question about the continuation of space and time that even today's quantum physicists are struggling. Zeno saw that time consisted of a series of indivisible instants which make it impossible for something to move during a period at such an indivisible instant. He argued that an arrow would remain stationary if it occupied the same space at every indivisible instant. For Zeno, being at rest means that from one instant to another different instant, the body in question and all its parts occupy the same place 1. Zeno hypothesized that for a motion to occur, an object must change the position which it occupies; thus, it should be shortening. 

However, still, Zeno missed the explanation on how the mechanism of shortening worked. We are not ashamed of helping Zeno by taking an example of a looper caterpillar’s motion. The method of this animal locomotion is incredible because of a walking style on two widely spaced groups of legs. At the front, just behind the head, are three pairs of small, segmented legs ending in tiny claws that help to grab onto plant material. Then, towards the end of the muscular and quite powerful body, a few more pairs of non-articulated fleshy lobes act as the hind legs. This set-up is perfect for creating the looping motion when the caterpillar is moving about on the plant. It stretches the front legs out to where it wants to go, grabs onto the plant material, then drags the hind legs up, while the body forms an impressive loop, like the U letter upside down or the Greek letter omega (Ω). As such, the contraction and straightening of the looper body make it advance. 

With such comparison, under our new interpretation of quantum theory, we can now illustrate the motion of an arrow flying ahead across its trajectory (Figure-1). Let l1 be the length of the arrow flying following its path starting from an instant t1 to another instant t4.

Now, viewed at the quantum level in which the same arrow is the appearance of a series of different arrows consecutively created and annihilated (depicted respectively as the solid and dash-arrow). However, in such a moving body, the length of the arrow shortens to become l2 in the subsequent creation the length of answers the fundamental question which nobody dares to pose as why the Lorentz contraction occurs. 

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 do not 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, also, scrutinize the second part of Zeno argument which holds the indivisibility of instants during which motion is impossible to occur. Such argument was correct if such a series of instants continued 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 underlying quantum 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 previous 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.

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 questions. The mathematical models of motion, space and time are merely intellectual constructions built for the convenience of simple calculations, not for the broader purpose of representing the structure of reality. The underlying reality that the paradox addresses is, thus, evaded.
b) The Lorentzian hypothesis is entirely 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.
d)  It is 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.
e) 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 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).
f)      This problematic, contradictory situation that C belongs to both A and B was not learned 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.
g)     Microscopically prevailing over its quantum kinds of stuff.
h)   A newly interpreted quantum theory with the constant 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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Thursday, December 8, 2011

Eternalism vs Presentism


The relativity theory unifies space and time into a single 4-dimensional continuum called the spacetime.  Albeit their unity, however, the theory inexplicably assumes that the nature of dimensions at every point in the continuum differentiates into those of the space and time.

Such concept of spacetime sometimes is referred to as the block time, block universe or eternalism. We have considered time as having similar ontology to that of space, that future events are already there, and that there is no objective flow of time. The spacetime is viewed as an unchanging 4-dimensional block as opposed to the view of the world as a 3-dimensional space perpetually modulated by the passage of time 1.


This concept of the block universe adopted by mainstream physics makes the physics now in trouble. This concept is wrong both physically and philosophically. A continuum should have inherently similar dimensions at its every point, except there is a discontinuity or boundary a) along which the block's dimensions are transformed into spatial (Figure-1).


In our daily life, one observes the difference between the past, the present, and the future. One perceives that as time passes, the moment that was once the present becomes part of the past, and part of the future, in turn, becomes the new present. As such, we experience or at least perceive the passage of time, with a present moment moving forward into the future and leaving the past behind 2. Philosophically, such a view of time is called presentism.

As we explain in the previous articles, our concept about the spacetime continuum is in line with this presentism, except that everything exists ephemerally. As such, when the part of the [nebulous] future transformed into the new present, the moment that was once the present is annihilated into part of the [void] b) past. In this view, only the present is real, as opposed to eternalist idea that all points in time are equally real.


This act of perpetual creation and annihilation gives us the perception of time passage. This modified presentism accentuates the actuality of the present and its obvious difference from the potentiality of the future and the nullity of the past. Matters which exist only in the present are exerted by the gravity and held together as a single whole on the plane c) of the present.



In order that the cause and effect principle prevails in their "chaotic" block universe, the physicists are forced to set up a light-cones system in which the individual light-cone may have a different orientation (Figure-2). However, such a concept may lead us to a chaotic closed timelike curve three that questions the integrity of such physical edifice.

The physicists are unaware that in such a symmetric block universe, which is timeless and eternal, no matter can exist, neither movement nor changes can occur. Sooner or later the mainstream physicists should abandon their concept of the block universe which has led us to many misinterpretations such as determinism, time travel, many-worlds interpretation and so forth.

In the presentist universe, the block is spontaneously broken d) in two halves, creating a 3-dimensional interface in between the two as it is transforming the dimension along the interface into spatial. Space and the present time are, in fact, two different aspects of the same thing which is the smallest unit of time. The eternity is, thus, broken bearing perpetually the present moment which splits the past barely from the future.

Notes:

a). Such as an interface or a surface in the case of liquid-like or a fissure in the case of a solid-like continuum.
b). Void of matter but not of energy.
c). or a wavy surface or interface in order to be in line with the general relativity theory.
d). It may happen because of the segregation of a pair of energy's opposing elements: the positive and negative energy.

Reference:

2.  Ibid.
3.  Penrose, R.: "The Road to Reality," Vintage Books, London, 2005, p. 409.


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