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. I have considered 3 models for the Donut battery.

There are semiclassical models for which protons are thought to move along the magnetic body to the other electrode. There are two options depending on whether tunneling occurs or not. The claimed stored energy is 400 Wh/kg and the total charge is 10⁵ C. If the mass of the battery is .1 kg the stored energy per Pollack proton is 1.44 eV.

1. For the tunneling option, the energy corresponds to the energy naturally associated with the Pollack effect, .33 eV (see this), and is rather small. This does not explain the claimed energy unless there is also chemical or other energy storage.
2. For the option without quantum tunnelling, the energy per proton without chemical storage is proportional to the total voltage as the sum of the total voltages. If the mass of the battery is .1 kg, this would correspond to electrostatic energy of E=1.44 eV per unit charge gained in acceleration along the flux tubes.

   The Pollack effect occurs for the second electrode of the battery, let us call it E1. The battery consists of N layers having 4 sub-layers (electrodes E1 and E2 and the analog of the electrolyte between them acting as a catalyst plus fourth sub-layer).

   The volume contributing to the stored energy corresponds to the mass of the E1 electrode and would be roughly 1/4:th of the total mass. The stored energy per E1 type electrode would be E= E/N eV where N is the number of layers. For N=3 layers acting like capacitors in series with voltage .46 V, each layer would give energy .46 eV per unit charge, which happens to be the value of the metabolic energy currency.

   Therefore Pollack effect for protons could explain both the claimed energy density and the total charge.

There is also a purely quantum model, which was partially inspired by the observation that the Pollack effect for hydrogen atoms explains the reduction of pendulum frequency in Allais effect (see this). For this model Pollack effect occurs for hydrogen atoms instead of protons and for very large values of h_eff the stored energy per hydrogen atom is the ionization energy E_H=13.7 eV of hydrogen atom. Although proton based model looks more realistic, this model deserves to be mentioned.

1. For the actual battery, one expects a weight of order .1 kg so that the stored energy per proton would be by a factor .1 smaller, about 1.44 eV, 1/10 smaller than E_H. The idea that dark hydrogen atoms having a large value of h_eff, could store the energy nearly equal to the hydrogen ionization energy, is however attractive.

   The difference between the total electronic binding energies between -C=O + H and -COH is .79 eV meaning that C=O+H has higher energy. If H is made dark then its binding energy is reduced dramatically and approaches hydrogen binding energy 13.7 eV for large h_eff. The storing of electrostatic energy to this dark energy is analogous to the storage of chemical energy. Whether this kind of storage is possible is of course far from obvious.

2. The energy per hydrogen atom/proton would be R&sim ; E_H/10. This energy cannot be explained as a change of the hydrogen binding energy in transition h→ h_eff or any choice of h_eff=nh, n>1. It seems that there is now way to save the identification of this variant of Pollack battery as Donut battery. The very optimistic view would be that this option makes possible a battery with 10 times higher energy density.
3. We would no longer be talking about the protons flowing to the other electrode but only about hydrogen atoms transferred to the flux tubes where they are polarized so that the protons are near the target electrode and the electrons near the source electrode. When the load is added, the dark hydrogen atoms would fall back to the source electrode E1. This would be the quantum counterpart for the protons flowing along the current wire, the presence of which makes this quantum transition possible.

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 for the classical variant of the model 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. For a moment I believed that the dielectric property of the target electrode E2 could be relevant  for energy storage. As a side product, it turned out that TGD could offer an elegant first principle description of dielectrics 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.
   See the article Are Pollack batteries possible? and the chapter with the same title.

   For a summary of earlier postings see Latest progress in TGD.

   For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.