The recent view of Pollack battery allows to understand the claims of Donut Lab at quantitative level!

The model for the Pollack battery developed through many twists and turns and several breakthroughs in the understanding of the physical interpretation of TGD were required (see this). The recent view of the charging of the Pollack battery would be as follows.

So, let us take the claims of Donut Lab (see this) seriously and look for what follows.

1. The number N_p of Pollack protons can be estimated from the transferred charge of Q=10⁵ Coulombs as N_p=Q/e. The claimed value for the stored energy E= 400 Wh. That would be equivalent to a proton energy E_p=E/N_p= 13.8 eV. For a Pollack battery this energy would be the energy gained by the Pollack electron when accelerated at the monopole flux tube in a voltage =13.8 V without dissipation. In a normal battery, the energy is dissipated quite thoroughly in Ohmic conduction.

   The energy transferred by the Pollack effect would be smaller by a factor of 1/8 if the voltage is assumed to be 1.5 Volts. 8 of these four-layer units would be needed.

2. Then comes an important observation without which I would never have arrived at the recent model. The claimed 13.8 eV per Pollack electron corresponds to the binding energy 13.7 eV of a hydrogen atom! Is this a mere coincidence?
3. This induces the idea is that the Pollack protons on the target electrode induce a phase transition which increases the relative dielectric constant ε_r from, say, 1 to 80, its value for water. These phase transitions are very common in condensed matter physics.
4. The electrostatic energy of the electric field of an insulator is proportional to ε_r². However, this energy is completely insignificant.
5. For the atoms of an insulator, the standard description predicts a reduction in the scale of the energy levels. The charge is screened and effectively reduces to e/ε_r. The energy levels E_n of a hydrogen atom are proportional to the product of the two charges, and scale as E_n→ E_n/ε_r². The upper limit ε_r= 100 of ε_r gives a reduction factor of 10^-4. The atomic states are energetically close to ionization.

   That is, in the phase transition that Pollack protons would induce, energy would be released that is very close to the hydrogen atom binding energy of 13.7 eV per Pollack proton! This is exactly what follows by taking the claims of Donut Lab seriously. The phase transition generating a dielectric would store the electrostatic energy during the charging.

6. What would happen in a phase transition that increases the dielectric constant ε_r? The necessary energy would come from the electrostatic energy of the field used for charging. Each Pollack proton would produce a hydrogen atom whose binding energy would be reduced by a factor of 1/ε_r². For example, the conversion of OH^- ions to H₂O in a background with ε_r = 1/80 formed in the transition, comes to mind.
7. There was also the problem of whether the accelerated Pollack protons give too much momentum to the target electrode. Would that explain the reported swelling, which was in the order of 4 per cent? It turned out that a simple estimate gives a completely negligible force, which is as much as ten orders of magnitude smaller than the estimate of the swelling force given by Google LLM, which is of order 10⁵ N.

   The situations simply cannot be compared. In a standard battery, the currents are ohmic and produce swelling and also heating through dissipation. For a Pollack battery, electrons travel in flux tubes and would transfer impulse and energy directly to the target electrode.

I have not previously taken the standard description of insulators quite seriously in this way although it works. It turned out that TGD offers an elegant first principle description of insulators using spacetime surfaces.

1. While building a model for the Allais effect (see this), I realized that the universal solutions of field equations that I found 47 years ago come to the rescue. They correspond to "warped" embedding of Minkowski space as a surface of H=M⁴× CP₂, come to rescue.

   They do not involve gravitational or gauge fields, but they are warped, which means that they are tilted to the direction of M⁴× S¹ ⊂ H. The angular coordinate of S¹ is given by Φ = ω t implying that the time component g_tt of the induced metric decreases from 1 to 1-R²ω². The speed of light reduces to c_#= (1-R²ω²)^1/2 <c.

2. The warped space-time surfaces are quantum critical against the change of c_#. A vibrating thin metal plate serves as a good analogy. The metal plate corresponds now to the M² ⊂ M⁴. Warping generalizes to Hamilton-Jacobi structure (see this) so that the notion applies also to non-vacuum extremals. The quantum criticality would be a geometric correlate for that of quantum phase transitions.

   This has several applications:

   1. c_#/c corresponds in a natural way to the velocity parameter β₀ of the gravitational Planck constant GMm/β₀, whose identification has been a long standing mystery. This can be applied to the Allais effect (see this), which General Relativity cannot explain.
   2. The speed of light also decreases for insulators. Refractive index is given by n= c_#/c. Dielectric constant is given by ε_r= 1/n² = (c_#/c)². The transition c→ c_# would occur when the system becomes an insulator. Could the atoms of the insulator be on a different space-time sheet, characterized by c_#<c? Water would be the most important example of this.