Planck Constant
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:

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.

The main dynamic parameter of H-atom is the orbital moment of momentum 37 of the electron


where 39 is the electron mass, 40 is the radius of the Bohr first orbit (Bohr radius), 41 is the speed of the electron on the Bohr first orbit.

If we multiply the orbital momentum by 2pi, 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.

On the other hand, one of the dynamic parameters of human being is the threshold of audibility equal to the sound pressure 151 at the frequency nearly 152 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 155 is the average relative mass of air molecules, 156 is the density of air under normal conditions, 157 is the unified atomic mass unit.

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 αmin 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 159 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.

Fine-Structure Constant
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 160), the ratio α of the threshold oscillatory speed, 161, 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 163, 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 164 (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.

The above considered examples show that the "fine-structure constant" of the microworld, 166, 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?"