Objections against the notion of Pollack battery

The basic counter-arguments against the notion of Pollack battery relate to dynamics.

1. The number of dark protons matters. According to the findings of Pollack, every fourth proton in the water in the EZ region is transferred to the magnetic body. This is quite a large number. This provides an order of magnitude estimate of the maximum amount of charge transferred via quantum tunnelling followed by the reverse Pollack effect. If the electrodes are wrinkled, as would happen for the ase of SiNT, the area of the electrodes increases and so does the maximal number of dark protons.
2. The time scale for the lifetime of (H₃ O₂)^- phase is attosecond in water. The large fraction of dark protons would give reason for optimism. In the case of DNA, RNA, and cell membrane the region with negative charge is stable and formation of dark nuclei from dark protons should imply the stability against the reverse Pollack effect.
3. At what speed does the transfer to the opposite electrode by quantum tunnelling occur? The tunneling probability could be estimated based on the existing formula for quantum tunnelling by simply replacing Planck constant h with h_eff. The tunnelling rate is an exponent exp(-X) of a term X proportional to 1/ℏ.

   The intuitive expectation is that for ordinary Planck constant X is very large in the scales considered so that tunnelling probability is essentially zero. However, the replacement ℏ → ℏ_gr,E= GM_em_p/β₀ ∼ 10¹³ for a proton could make X∝ 1/ℏ_gr small enough. An additional parameter possibly needed as a multiplicative factor is the amplitude for OH → O^- + dark proton decay. The optimistic first guess is that this parameter is of order 1.

Consider now an estimate for the tunnelling amplitude A, whose modulus squared gives the tunnelling probability.

1. Apart from the numerical factor of order one, the amplitude A can be written as an exponent and represents the value of a wave function at point L at E₂. In the classically forbidden region 00^yk(x)dx is analogous to a plane wave exp(iky) with imaginary momentum. By using the relationship k(x)= p(x)/ℏ and p(x)= (2m(E-V(x)) between wave vector and momentum, one obtains

   A= exp(-X)

   X= (1/h_eff) ∫₀^L p(x)dx .

   p(x)=(2m(E-V(x))^1/2.

   In the recent case, V(x) is Coulomb energy V(x)= eE₀x for the proton and m is proton mass. In the Earth’s gravitational field one has h_eff =ℏ_gr,E = GM_Em_p/β₀= r_s(E)m_p/2β₀, r_s(E)∼ 1 cm. The velocity parameter β₀= v₀/c≤ 1 has a spectrum of values but there are arguments supporting β₀∼ 1 as the most plausible value for the Earth. For the Sun the value β₀∼ 2^-11 is favored.

2. The boundary condition is that the proton, kicked by Pollack effect from the electrode E₁, arrives at rest to the electrode E₂. This gives

E= V(L) = eE₀L = eV₀

where E₀ is a constant electric field of the battery and V₀ the voltage between E₁ and E₂. This gives

p(x)= (2m_p(V(L)-V(x))^1/2 = (2m_pV₀)^1/2 (1-x/L)^1/2

The integral appearing in the definition of X can be calculated analytically and one obtains

X= [(4×2^1/2/3] (eV₀/m_p)^1/2× L/r_s(E) .

3. An order of magnitude estimate is obtained by assuming eV₀=1 eV implying eV₀/m_p∼ 10^-9, L=10 cm. For β₀=1, this gives

X∼ 6× 10^-4 .

The value happens to be quite near to the value of β₀∼ 2^-11 for the Sun. The value of X is so small that exp(-X) ∼ 1 is true in a good approximation.

The conclusion is that, unless the additional coefficient possibly present is very small, the tunnelling probability can be large enough.

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.