Research website of Vyacheslav Gorchilin
All articles/Free energy. Theory
Where does the energy
The famous free energy researcher Don Smith believed that the famous Einstein formula E=mc2 describes a way to store energy. This approach clearly represents what we will talk about next.
Let's approach this issue from the standpoint of limiting values. What is the maximum potential energy of a solitary sphere? If you look at the classic formula: \[W_ {c} = \frac {Q^{2}} {2C} \qquad (2.1) \] it turns out that the less \(C\), i.e. capacity, the higher the potential energy. Then what is the minimum capacity? To do this, recall the formula for the capacity of a solitary sphere: \(C = 4 \pi \varepsilon \varepsilon_{0} r \), where: \(r \) — this is the radius of the sphere, and \(\varepsilon, \varepsilon _ {0} \) is the relative and absolute permeability. What is the minimum radius a ball with a charge can have? Yes, that's right, — this is the radius of the electron \(r_ {e} \) [1]. Where do we find its own capacity: \[C_ {e} = 4 \pi \varepsilon \varepsilon _ {0} r_ {e} \qquad (2.2) \] It is clear that the charge of such a ball will be exactly equal to the charge of an electron — \(e \). Relative dielectric constant \(\varepsilon \) we take equal to one (as for vacuum) and get the maximum energy for the minimum capacity — potential energy of the electron charge: \[W_ {ce} = \frac {e ^ {2}} {8 \pi \varepsilon _ {0} r_ {e}} \qquad (2.3) \]

Recall that the electron charge is \(e = 1.6 \cdot 10 ^ {- 19} \) (Kl), and the classical radius of an electron is \(r_ {e} = 2.82 \cdot 10 ^ {- 15} \) (m).

But the resulting formula is exactly half the Einstein mass-energy: \[W_ {ce} = \frac {e ^ {2}} {8 \pi \varepsilon _ {0} r_ {e}} \; = \; \frac {m_ {e} c ^ {2}} {2}, \qquad (2.4) \] where: \(m_ {e} \) — electron mass equal to \(9.1 \cdot 10 ^ {- 31} \) (kg), \(c \) — the speed of light is equal to \(3 \cdot 10 ^ {8} \) (m/s). Thus, we got a bunch: charge-mass-energy and answered the question — where does the energy come from.

The potential energy of the system of electrons will be maximum if the capacity of the capacitor in which they are located tends to zero. Apparently, such a limiting state of the system of electrons is an electron gas or an electron plasma in vacuum.

This is the same answer to the original question — Where does the energy go if the capacity of the system of electrons is increased? Electrons are simply bound by the capacity and cease to be free, and the larger the capacity, the more they are bound.

Where is the second half of the mass-energy?
Apparently, it is contained in the magnetic field inside the electron. It is known that an electron has its own angular momentum, or spin, the properties of which cannot be explained from the point of view of conventional mechanics [4]. But this means that the electric charge in the electron is mobile, albeit not in the classical representation, but if so, then it must also be a magnetic charge. Thus, we get a electron model, suitable for our further calculations and research: outside of it there is an electric charge, and inside there is a magnetic charge. We will further support the second statement by the presence of inductance in the electron.
In this work, we will not delve into the jungle of electrodynamics and quantum physics, but we will consider free charges from the point of view of electrical engineering and radio electronics.
Is an electron an ideal oscillatory circuit?

Since an electron is a kind of elementary capacity, why can't it be the same elementary inductance? Indeed, we find such a justification in work [2], from where we take the formula for the inductance of an electron: \[L_ {e} = \frac {m_ {e}} {n \, e ^ {2}} = {m_e r_e ^ 2 \over e ^ 2} = \frac {\mu_ { 0} r_ {e}} {4 \pi} \qquad (2.5) \] where: \(n \) - specific charge density, \(\mu_ {0} \) — magnetic constant equal to \(1.26 \cdot 10^{-6} \) (H/m). Formula (2.5) is obtained if only one charge is taken as \(n \). By the way, in [3] it is proposed to consider such an inductance an analogue of the mass of a substance.

For a complete picture, it remains for us to make the last assumption that an electron is an ideal oscillatory circuit, with its resonant frequency, characteristic impedance and infinite quality factor. As you know, the energy in an ideal oscillatory circuit can circulate forever or until a radiating antenna is connected to the circuit, for example.
Another interesting conclusion can be this: since an electron is an oscillatory circuit, it means that while it is a particle, all of its potential energy is reactive . It becomes active when the electron becomes a wave, and we can feel the manifestations of this energy in the form of light, heat, etc.
If all our assumptions are correct, then the problem of extracting energy from an electron is reduced to one simple rule: we must create conditions for the electron under which its reactive energy can be converted into active energy. In the next section, we will consider such conditions, and now we will give some parameters of the electron, which are far from always found in the classical literature.
Some parameters of an electron
Let's get one more value, and then we put together all the data about the electron. From formula (2.2) we take the intrinsic capacity of an electron and calculate the potential on its conditional surface: \(\varphi_e = e / C_e = 5.1 \cdot 10^5 \) (V). Hence, a natural question arises: where does this potential go when we charge, for example, a metal ball with negative charges? For an answer, one can draw an analogy with a capacitor of small capacity, but charged with high voltage, which is connected to a discharged capacitor of large capacity; the entire potential is distributed over a large capacity, and on the total one we get only a small increase in voltage.
Knowing that half the potential energy of an electron is in a magnetic charge, we can calculate the current inside it: \(I_e = c \sqrt {m_e / L_e} = c \, e / r_e = 1.7 \cdot 10^4 \) (A). The interesting thing here is that if the potential on the surface of the electron is divided by this current, then we get a resistance of 30 Ohms. But since, according to our model, the electric charge is outside, and the magnetic charge is inside the electron, then in the reactive state they do not intersect, and they begin to interact only upon transition to an active state, for example, to radiation. Then this resistance starts to work as a wave resistance. The model of a spherical dielectric resonator of the H-type is perfectly suited to this approach.
Let us present the reference data on the electron, which we will need in further work:
  • classic radius:   \(r_ {e} = 2.82 \cdot 10 ^ {-15} \) (m);
  • mass:   \(m_ {e} = 9.1 \cdot 10 ^ {-31} \) (kg);
  • charge:   \(e = 1.6 \cdot 10 ^ {-19} \) (C);
  • surface potential:   \(\varphi_e = 5.1 \cdot 10 ^ 5 \) (V);
  • own capacity:   \(C_ {e} = 3.14 \cdot 10 ^ {-25} \) (F);
  • self-inductance:   \(L_ {e} = 2.82 \cdot 10 ^ {-22} \) (H);
  • wave impedance:   \(Z_ {e} = \sqrt {L_{e} / C_ {e}} = 30 \) (Ohm);
  • Thompson resonant frequency:   \(\nu_ {e} = \frac {1} {2 \pi \sqrt {L_ {e} C_{e}}} = 1.69 \cdot 10^{22} \) (Hz);
  • wavelength:   \(\lambda_ {e} = c / \nu_ {e} = 1.77 \cdot 10 ^ {-14} \) (m).
Closing the problem, we can get this length in another way - from the classical radius of an electron, simply by multiplying it by \(2 \pi \): \[\lambda_ {e} = 2 \pi r_e \qquad (2.6) \] Formula (2.6) is a test for all the above reference data. Here we mean the wavelength of the electron from the point of view of radio electronics, since, for example, the Compton wavelength is \(2.43 \cdot 10^{-12} \) m (which differs from the one obtained by us by the value of the fine structure constant [5]), and according to de Broglie, it generally depends on its speed.
It is interesting that if we calculate the internal energy of an electron through the Planck constant \(h \) and the resonance frequency \(\nu_ {e} \) according to Thompson, then it will coincide with Einstein's, with an accuracy that is determined by the fine structure constant \(\alpha\): \[W_e = m_e c ^ 2 = h \, \nu_ {e} \alpha \qquad (2.7) \] From this point of view, it may be interesting to look at the laws of Coulomb and Ampere.
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The materials used
  1. Wikipedia. Classic electron radius.
  2. Mende F.F. Kinetic inductance of charges and its role in classical electrodynamics. [PDF]
  3. I. Misyuchenko. The last secret of God. 5.3. Inductance and capacity of the model elementary charge.
  4. Wikipedia. Spin.
  5. Wikipedia. Fine structure_constant.