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An attempt is done to calculate the value of the elementary electron charge from its relation to the Planck constant and the speed of light. This relation is obtained, in the first step, from the Pauli analysis of the strength of the electric field associated with an elementary emission process of energy. In the next step, the uncertainty principle is applied to both the emission time and energy. The theoretical result for e is roughly close to the experimental value of the electron charge.

As soon as the atomic theory of matter occured to be a right idea, there arose a tendency to describe the physical properties of matter with the aid of a possibly low number of the elementary notions concerning the atoms and their structure. A further step in this direction has been provided by the quantum theory. In effect numerous properties of the atomic world could be represented in terms of the so-called fundamental constants of physics which are evidently few in their number. Perhaps the most widely used constants became e, m, h and c, which are respectively the electron charge and electron mass, the elementary action called the Planck constant and the speed of light.

Simultaneously a mutual reference between the constants mentioned above seemed to be not so much evident. The aim of the present paper is to demonstrate that, in fact, a reference between e, h and c can be supplied in effect of i) an elementary analysis of the forces entering the emission process of the electron energy, ii) an application of the uncertainty principle for energy and time which couples the parameters considered in i).

The energy-time aspect of the uncertainty principle has been presented originally by Heisenberg [

where

which on many occasions can be replaced by an approximate equation

The formula (2a) allowed us to approach several problems of the elementary quantum theory, for example the spectrum of the Bohr hydrogen atom [

where

One of the notions useful to this purpose is a minimal distance between two particles having the same mass m. This is

Equation (3) has been derived also on the basis of the formula (2a); see [

Pauli’s idea was to consider the strength of the electric field

In effect the intensity square of the electric field

In order to derive (4a) two formulae for the momentum change

where

where

or

On the other hand the change

so

Therefore a final formula gives

According to Pauli the square root of

However, for simplicity, let us assume that this excess is small and the change of the field intensity in the emission is

In result the force acting on the electron particle becomes

We assume that the force given in (11) is acting along an elementary (minimal) space interval

As a final step we substitute the energy change (12) to the uncertainty formula (2a). This gives an approximate equation

which can be simplified to the relation

or

coupling the constants h, c, and e. A substitution of

and

into (15) gives

The well-known value of the measured e is

The difference between (18) and (18a) is about 50 percent of (18). In some earlier papers (see [

is proposed which is larger than

An approximate character of the formalism applied in the present paper is evident.

The electron charge e has been calculated from the Planck constant h and the speed of light c. This has been done on the basis of i) the Pauli expression for the emission strength of the electric field, ii) the uncertainty principle for energy and time. The emitted energy is obtained as a product of the force of the electric field and the elementary distance

In case the factor of 1/2 introduced by Pauli as a multiplier of

This number is different by less than 40 percent of its value from the experimental e represented in (18a).

The particle mass does not interfere in the equations of the paper. This implies that the absolute value of e can be the same for electrons and protons.