Planck Constant
and
Threshold of Audibility
Nature demonstrates the perfect harmony within any and between
different its levels, in particular, atomic and molecular. The natural thought
arises in this connection:
Whether does it exist a
correlation between the basic parameters of the
hydrogen atom and human being
created of hydrogen atoms in 9.5%? Let us consider some dynamic
parameters of the same dimensionality characterizing both aforementioned objects
belonging to very different levels of the Universe.
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The main dynamic parameter of H-atom
is the orbital moment of momentum
of the
electron
,
where
is the electron
mass, 
is the
radius of the Bohr first orbit (Bohr radius),
is the speed of
the electron on the Bohr first orbit.
If we multiply the orbital momentum by
, we obtain the
orbital action of the electron h called the Planck
constant:
,
Hence, the numerical value and dimensionality of the
orbital action h are
◄►
◄►
that corresponds to the
CODATA
Internationally recommended value.
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On the other hand, one of the dynamic parameters of
human being is the threshold of audibility equal
to the sound pressure
at the frequency
nearly 
in the
air under the normal conditions, i.e., normal temperature and pressure (300 K, 1 atm).
The following expression relates the sound pressure P with the
acoustic action hs:
,
where m is the average mass of air molecules and ρ
is the density of air. Then, the minimal acoustic action on the
threshold of audibility of man, corresponding to the minimal sound
pressure Pmin , is
◄►
◄►
where
is the average
relative mass of air molecules,
is the density
of air under normal conditions,
is the unified
atomic mass unit.
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As we see, the action hs,min, related to the
acoustic process, practically coincides with Planck's action h
having relation to electromagnetic processes.
It is very interesting also to note that on the level of the threshold of
audibility, the minimal threshold amplitude of acoustic oscillations
amin at the frequency 1781.25 Hz is equal to the value
of the electron radius re obtained theoretically in the
framework of
dynamic model
of elementary particles:
where
is the speed of
sound in air under normal conditions.
Thus, the coincidence of magnitudes of the orbital action of
the electron in H-atom and minimal acoustic action on the
threshold of audibility of man is the obvious fact. It enables to
conclude that the strict correlation of basic parameters of the hydrogen atom
and human being actually takes place. We can confirm this conclusion with other
examples. Below is one of them.
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Fine-Structure Constant
and
Threshold of Pain
Let us turn to the so-called "fine-structure
constant" (alpha), which is very nearly equal to 1/137.
In the language of modern physics, it is the "coupling constant" or measure of
the strength of the electromagnetic force that governs how
electrically charged elementary particles (e.g., electron, muon) and
light (photons) interact.
Returning again to man, we find that on the upper acoustic threshold of
pain (at the sound pressure
), the ratio α of
the threshold oscillatory speed,
, to the
sonic speed υs (the base wave speed) in air is
◄►
◄►
The sound level at Pmax is close to the peak
level at ear of 0.303 caliber rifle (sound pressure
,
sound level 160 dB).
At the electromagnetic field level, the "threshold" speed of
oscillations is called the Bohr first speed υ0. And
the ratio υ0 to the speed of light 
(which is
the
basis wave speed of exchange of
matter-space-time at the subatomic level) is
◄►
◄►
Hence, the Bohr speed υ0, in some sense, is
also the threshold speed, as the limit speed of the electron at the first orbit
of the hydrogen atom.
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The above considered examples show that the "fine-structure
constant" of the microworld,
, reflects the
scale correlation of threshold states of conjugate oscillatory-wave processes at different levels
of the Universe, not only electromagnetic.
More correctly and strictly speaking, the fine-structure constant reflects the scale
correlation of
basis and superstructure of
wave fields-spaces of objects in the Universe, having the contradictory
spherical-cylindrical character. With
that, the physical field-space of the Universe represents by itself an infinite
series of spaces embedded in each other (recalling a set of nesting dolls, or an
infinite functional series). This series of spaces expresses the fundamental
concept of natural philosophy concerning the infinite divisibility of matter. As concerns the speeds υs
and c, these are the base wave speeds of two distinct spaces of the field of
matter-space-time, in which the corresponding wave motion takes place.
And the wave motion is the collective motion of a great variety of microparticles belonging to given space. All this is revealed in
details in the book "Atomic
Structure of Matter-Space" (2001).
Very like that we arrived at the right answer to the
questions on
"Why is the fine structure constant, which measures the strength of
electromagnetism, about 1/137.036?" and "Where did this dimensionless
constant of nature come from?"
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