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
