Physics/Essays/Anonymous/Weak natural scale

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In physics, Weak Natural scale is the fundamental scale of matter, named after

It defines the Weak Natural coupling constant:



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Usually, the Weak Natural scale now considered for definition of the weak interaction force and has not appropriate attention that should be fo the scale of matter. However, the real strength of forces is determined by the scale only, but not the metter type: charge or mass.

Fundamental units of vacuum

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Dielectric constant [1]:

F m−1

Magnetic constant:

H m−1

Electrodynamic velocity of light:

m s−1

Electrodynamic vacuum impedance:


Dielectric-like gravitational constant:

kg s2 m−3

Magnetic-like gravitational constant:

m kg−1

Gravidynamic velocity of light:

m s−1

Gravidynamic vacuum impedance:

m2 kg−1 s−1

Considering that all Natural, Stoney and Planck units are derivatives from the vacuum units, therefore the last are more fundamental that units of any scale.

Weak interaction Natural scale units

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The weak scale of Natural units is based on the electron neutrino mass. As is known, neutrinos are generated during the annihilation process, which is going through intermediate positronium atom. The effective mass of the positronoum atom is:

where are electron and positron mass respectively. The energy scale for the positronium atom is:

where is the length scale for positronium, and is the upper value for the neutrino mass, and is the weak interaction force constant (or weak fine structure constant).

Table 5: Base weak Natural scale units
Name Dimension Expressions SI equivalent with uncertainties [1]
Neutrino mass Mass (M) kg
Neutrino wavelength Length (L) m
Weak interaction force constant Dimensionless
Weak gravity force constant Dimensionless
Weak Natural "dynamic mass" Dynamic mass (L2T −1) m2 s−1
Weak Natural "dynamic mass" force constant Dimensionless
Weak Natural time Time (T) s

Weak Planck scale units

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The primordial level of matter has two standard scales: Planck (defines the Planck mass) and Stoney (defines the Stoney mass). However, it has the third primordial scale that could be named as the weak interaction scale, which has the following force constant:

that is the same as in the weak natural scale.

The weak primordial mass will be:


where is the Planck mass.

The weak primordial wavelength is:


The weak primordial time is:


Work function and Universe scale

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The standard definition of the work function in the strength field is:

So, the complex weak displacement work in the weak natural force will be:


is the weak natural force, and is the weak Planck wavelength.

Considering the Universe bubble as the minimal energy scale:

where is the Universe wavelength, and equating the above energies, we derive the following fundamental relationship:

from which the Universe length parameter could be derived:


which value is consistent with the 15 billion years.

Weak Planck scale and Solar planatery system

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Planet resonator characteristics

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Geometrical parameters of any planetary object determine the following resonance frequency:


here is used the Earth as an example. This resonance frequency could be connected with the "minimal mass":


where is the reduced Planck constant, and is the speed of light.

Considering that gravitational resonator has its oscillations on the surface, therefore it is interesting to determine the minimal surface radius connected with the "minimal mass":


The relationship between minimal radius and the Weak Planck length is:


where is the Weak Planck length. Thus, considering the Solar Planetary System, all objects as gravitational resonators, we will have the small surface area about the Weak Planck scale, where the minimal resonator energy quant replaced.

The full sets of the planetary data are presented in the Table 2.

Table 2: Solar planatery system
Object Radius, m Mass, kg Minimal Mass, kg Minimal Radius, m

See also

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  • 1. Latest (2006) values of the constants [1]