Biosystems as superconductors: part II
This chapter is devoted to further applications of
the theory of high T_{c} superconductors as quantum
critical superconductors involving dark matter
hierarchy and large values of hbar. The theory
is applied to explain the strange findings about
ionic currents through cell membrane, exotic
neutrino superconductivity and the notion of
cognitive neutrino pair are discussed, and the
possibility that superconductivity and
BoseEinstein condensates are involved with
atmospheric phenomena is considered.
1. Strange behavior of cellular water and
quantal ionic currents through cell membrane
The fact that cellular water does not leak out of
cell in a centrifugal force suggests that some
fraction of water inside cell is in different
phase. One explanation is that the nuclei of
water inside cell are in doubly dark phase whereas
electrons are in singly dark phase (having Compton
length of 5 nm and perhaps directly "visible" using
day technology!) as indeed predicted by the model
of high Tc superconductivity. This conceptual
framework could explain various findings
challenging the notions of ionic pumps.
The empirical findings challenging the notions of
ionic pumps and channels, nicely summarized by G.
Pollack in his book, provide a strong support for
the notions of manysheeted spacetime and ionic
superconductivity.
 The selectivity of the cell membrane implies
that channels cannot be simple sieves and there
must be complex information processing involved.
 The needed number of pumps specialized to
particular ions is astronomical and the first
question is where to put all these channels and
pumps. On the other hand, if the cell constructs
the pump or channel specialized to a given molecule
only when needed, how does it know what the pump
looks like if it has never seen the molecule? The
needed metabolic energy to achieve all the pumping
and channelling is huge. Strangely enough, pumping
does not stop when cell metabolism stops.
 One can also wonder why the ionic currents
through cell membrane look quantal and are same
through cell membrane and silicon rubber membrane.
These observations suggest strongly the presence
nondissipative ionic currents and quantum
selforganization. The TGD based explanation would
be in terms of high T_{c} electronic and possibly
even ionic superconductivity associated with cell
membrane made possible by the large hbar phase
for nuclei and electrons in the interior of cell.
It however seems that thermal stability conditions
allow only protonic Cooper pairs in the model of
ionic Cooper pairs based on direct generalization
of the model of high T_{c} electronic super
conductivity. This does not however mean that
quantal ionic currents would be absent. This
empirical input also supports a view about
homeostasis as a manysheeted ionic flow
equilibrium controlled by larger spacetime sheets
with the mediation of massless extremals (MEs)
serving as spacetime correlates for BoseEinstein
condensates of massless bosons (also of scaled
down dark electroweak bosons and gluons).
In the proposed picture one can understand how
extremely low densities of ions and their supra
currents can control much higher ion densities at
the atomic spacetime sheets. The liquid crystal
nature of the biomatter is crucial for the model.
This vision allows also much better understanding
of the effects of ELF em fields on biomatter. Also
the effects of homeopathic remedies and acupuncture
known to crucially involve electromagnetic
frequency signatures of chemicals can be understood
if homeostasis is based on manysheeted ionic flow
equilibrium.
2. Cell membrane spacetime sheet almost vacuum extremal?
It has been clear from the beginning that the nearly vacuum extremals of Kähler action could play key role key role in living systems. The reason is their criticality making them ideal systems for sensory perception. These extremals carry classical em and Z^{0} fields related to each other by a constant factor and this could explain the large parity breaking effects characterizing living matter. The assumption that cell membranes are nearly vacuum extremals and that nuclei can feed their Z^{0} charges to this kind of spacetime sheets (not true for atomic electrons) in living matter leads to a modification of the model for the cell membrane as Josephson junction. Also a model of photoreceptors explaining the frequencies of peak sensitivity as ionic Josephson frequencies and allowing the dual identifications Josephson radiation as biophotons (energies) and EEG radiation (frequencies) emerge since the values of Planck constant can be very large. The value of the Weinberg angle in this phase is fixed to sin^{2}(θ_{W})=.0295, whereas in standard phase the value is given by sin^{2}(θ_{W})=.23. The significance of this quantitative success for TGD and TGD inspired quantum biology cannot be overestimated. It seems that membrane like structures near vacuum extremals analogous to cell membrane could provide a general approach to various anomalous phenomena involving plasma phase and luminous phenomena.
2. Hierarchies of preferred padic length scales and values of Planck constant
TGD inspired quantum biology and number theoretical considerations suggessuggests preferred values for r=hbar/hbar_{0}. For the most general option the values of hbar are products and ratios of two integers n_{a} and n_{b}. Ruler and compass integers defined by the products of distinct Fermat primes and power of two are number theoretically favored values for these integers because the phases exp(i2π/n_{i}), i=a,b, in this case are number theoretically very simple and should have emerged first in the number theoretical evolution via algebraic extensions of padics and of rationals. pAdic length scale hypothesis favors powers of two as values of r. The hypothesis that Mersenne primes M_{k}=2^{k}1, k=89,107,127, and Gaussian Mersennes M_{G,k}=(1+i)^{k}1, k=113,151,157,163,167,239,241.. (the number theoretical miracle is that all the four padic length scales sith k=151,157,163,167 are in the biologically highly interesting range 10 nm2.5 μm) define scaled up copies of electroweak and QCD type physics with ordinary value of hbar and that these physics are induced by dark variants of each other leads to a prediction for the preferred values of r=2^{kd}, k_{d}=k_{i}k_{j}, and the resulting picture finds support from the ensuing models for biological evolution and for EEG.
3. Fractal hierarchy of magnetic flux
sheets and the hierarchy of genomes
The notion of magnetic body is central in the TGD
inspired theory of living matter. Every system
possesses magnetic body and there are strong
reasons to believe that the magnetic body
associated with human body is of order Earth size
and that there could be an entire hierarchy of these bodies
with even much larger sizes. Therefore the question
arises what one can assume about these magnetic bodies. The quantization of
magnetic flux suggests an answer to this question.
 The quantization condition for magnetic flux reads involves in the most general form both the momentum of super conducting particles and magnetic field. If supra currents flowing at the boundaries of the flux tube are absent one obtains standard quantization of the magnetic flux as a multiple of Planck constant, which
requires that the scaling of the Planck constant scales up the flux tube thickness by r^{2} and scaling of B by 1/r. If one assumes that the radii of flux tubes do not depend on the value of r, magnetic flux is compensated by the contribution of the supra current flowing around the flux tube. The supra
currents would be present inside living organism but in the faraway region where flux quanta from organism fuse together, the standard quantization conditions for magnetic flux would be satisfied.
 From the point of view of EEG especially interesting are the flux
sheets which have thickness L(151)=10 nm (the thickness of cell membrane) carrying magnetic field having
strength of endogenous magnetic field. In absence of supra currents
these flux sheets have very large total transversal length proportional to r^{2}. Strongly folded flux sheets of this thickness might be associated with living matter and connect their DNAs to single coherent
structure. One can of course assume the presence of supra currents but outside the organism the
flux sheet should fuse to form very long flux sheets.
 Suppose that the magnetic flux flows in head to
tail direction so that the magnetic flux arrives
to the human body through a layer of cortical
neurons. Assume that the flux sheets traverse
through the uppermost layer of neurons and also
lower layers and that DNA of each neuronal nuclei
define a transversal sections organized along flux
sheet like text lines of a book page. The total
length of DNA in single human cell is about one
meter. It seems that single organism cannot provide the
needed total length of DNA if DNA dominates the
contribution. This if of course not at all
necessarily since supra currents are possible and outside
the organism the flux sheets can fuse together. This implies
however correlations between genomes of different cells and even different
organisms.
These observations inspire the notion of super and hyper genes. As a matter fact,
entire hierarchy of genomes is predicted.
Super genes consist of genes in different cell
nuclei arranged to threads along magnetic flux
sheets like text lines on the page of book whereas
hyper genes traverse through genomes of different
organisms. Super and hyper genes provide an
enormous representative capacity and together with
the dark matter hierarchy allows to resolve the
paradox created by the observation that human
genome does not differ appreciably in size from
that of wheat.
4. BoseEinstein condensates at magnetic
flux quanta in astrophysical length scales
The model for the topological condensation at
magnetic flux quanta of endogenous magnetic field
B_{end}=.2 Gauss is based on the dark matter hierarchy
with levels characterized by the values of Planck constant.
The hypothesis for the preferred values of Planck constans allows
to build quantitative model for the BoseEinstein condensation at magnetic
flux quanta assuming that the value of B_{end} scales like 1/hbar. A justification
for this hypothesis comes form flux quantization conditions and from the similar scaling of Josephson
frequencies.
 There are several levels of dynamics. In
topological condensation the internal dynamics of
ions is unaffected and hbar has the ordinary
value. For instance, the formation of Cooper pairs involves
dynamics at k_{d}=24=151127 level of dark matter hierarchy if one assumes that electrons
and Cooper pairs have size given by the cell membrane thickess L(151).
Also the dynamics of ionic Cooper pairs remains
unaffected in the topological condensation to
magnetic flux quanta obeying k_{d}>24 dynamics.
 Cyclotron energies scale as as hbar
so that for a sufficiently high value of k_{d}
thermal stability of cyclotron states at room
temperature is achieved for a fixed value of B. Same applies to spin flip
transitions in the recent scenario. The model for EEG based on dark matter
hierarchy involves the hypothesis that EEG quanta correspond to Josephson
radiation with energies in the visible and UV range and that they produce
in the decay to ordinary photons either bunches of EEG photons or visible/UV photons.
This identification allows to deduce the value of k_{d} when the frequency of
the dark photon is fixed. The Mersenne hypothesis for the preferred padic length scales
and values of Planck constants leads to very precise predictions.
 Cyclotron energies E= (hbar/2πi)
\times ZeB/Am_{p} are scaled up by a factor
r=2^{kd} from their ordinary values and for 10 Hz cyclotron frequency
are in the range of energies of visible light for k_{d}=46.
5. Atmospheric phenomena and
superconductivity
There is a considerable evidence that various
electromagnetic time scales associated with the
atmospheric phenomena correspond to those
associated with brain functioning. If magnetic
sensory canvas hypothesis holds true, this is just
what is expected. In this section these phenomena
are considered in more detail with the aim being to
build as concrete as possible vision about the
dynamics involving the dark matter BoseEinstein
condensates at superconducting
magnetic flux quanta. A new element is the assumed
presence of cell membrane like structures near vacuum extremals.
If the potentials differences involved are same order of magnitude as in
the case of cell membrane, the luminous phenomena can be understood
in terms of effects caused by Josephson radiation at visible and UV frequencies.
Tornadoes and hurricanes provide the first example
of selforganizing systems for which BoseEinstein
condensates of dark matter at magnetic and Z^{0}
magnetic flux quanta might be of relevance. Auroras
represent a second phenomenon possibly involving
supra currents of Cooper pairs and of exotic ions.
Lightnings, sprites and elves might also involve
higher levels of dark matter hierarchy. pAdic
length scale hypothesis and the hierarchy of Planck
constants provide a strong grasp to these far from
wellunderstood phenomena and allow to build rather
detailed models for them as well as to gain
concrete understanding about how dark matter
hierarchy manifests itself in the electromagnetic
phenomena at the level of atmosphere.
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