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 puzzle of mystery survive 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.
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.
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 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 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.
e)
Microscopically prevailing over its quantum kinds of stuff.
f)
A newly interpreted quantum theory with the constant creation and
annihilation of matter, to and fro energy, as its fundamental mechanics.
References:
- Mazur,
J.: "The Motion Paradox," Dutton, New York, 2007, p. 41.
- Ibid,
p. 40
- Einstein
et al.: "The Principle of Relativity," Dover Publications, Inc.,
New York, 1952, p. 81
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