### Metabolic energy, ATP, and negentropic entanglement

The ideas about the detailed relationship between metabolism and negentropic entanglement are still in a state of turmoil. Let us sum up those concepts and ideas which look reasonably reliable.

- Negentropic entanglement is the first basic notion. There is a strong tendency to consider the presence of a magnetic flux tube connecting two objects and carrying negentropically entangled quantum state as a fundamental structure giving rise to a directed attention. Negentropic entanglement would be basic element of conscious cognition, and one can assign to it various attributes like experience of understanding. The mildest assumption is that negentropic entanglement is associated with the flux tube. A stronger assumption is that it is between states assignable to the ends of the flux tube identifiable as observer and target of attention.

An analogy with Orch OR is suggestive. The period of negentropic entanglement - period of directed attention - would correspond to Orch Or and its end to state function reduction.

- The identification of the increments zero point kinetic energies as universal metabolic energy quanta is one of the oldest hypothesis of TGD inspired theory of consciousness. Zero point kinetic energy is associated with the zero point motion of particle at space-time sheet. The finite size of the space-time sheet gives rise to this energy for which non-relativistic parametrization is E
_{0}= k× 3hbar^{2}π^{2}/2mL^{2}(k). L(k)=2^{(-k+151)/2}L(151), L(151) ≈ 10 nm is the p-adic length scale of the space-time sheet, and k is a numerical factor not far from unity. Particle in 3-D box gives k=1.

As particle is transferred to a larger space-time sheet the zero point kinetic energy is reduced, and the difference is liberated as usable metabolic energy. For proton the size scale of this space-time sheet could be atomic size scale k=137. For electron it could electron Cooper pair k=149 (prime) corresponding to a lipid layer of cell membrane could be in question. Entire hierarchy of metabolic energy quanta is predicted and the energy scale depends on the particle mass and p-adic length scale and geometric factors characterizing the shape of space-time sheet only.

One can ask whether the high energy phosphate bond in the phosphate of ATP molecule contains this kind of smaller space-time sheet and in the transition ATP → ADP, electron or proton drops from this kind of space-time sheet. The following considerations show that this hypothesis is not necessary, and that one can also modify the identification of the fundamental metabolic energy quantum as zero point kinetic energy without losing anything. Therefore the details of the scenario are far from being fully nailed down.

- Magnetic flux tubes are carriers of charged particle and the hypothesis is that cyclotron Bose-Einstein condensates for fermionic Cooper pairs and bosonic ions are relevant for consciousness. In particular, cyclotron transitions in which bosons in these condensates are excited would be important for the generation of conscious experiences. The hierarchy of Planck constants and the fact that cyclotron energy is proportional to hbar allows to have arbitrarily high cyclotron energies in given magnetic field. This is essential in the model for the effects of ELF em fields on living matter (see this).

- Becker's findings about the relevance of DC currents for healing of wounds lead to an idea about how electromagnetic radiation interacts with the charged particles at magnetic flux tubes (see this). What would happen is that charged particles experience the electric and magnetic fields of the radiation field described in terms of massless extremals. Electric field would generate acceleration in the direct of the flux tube and could excite Becker currents which would give rise to biological effects - healing of wound in the simplest case. The proposal has been that this process gives rise to what could be seen as a loading of metabolic batteries.

The combination of this view with the notion of cyclotron BE condensate leads to a slightly more complex picture. Radiation field can excite single boson states both in transversal and longitudinal degrees of freedom. Transversal ones correspond to cyclotron states with energies E

_{c,n}= (n+1/2)E_{c}, E_{c}= hbar qB/m and the energies of excitations are of form nE_{c}. Longitudinal degrees of freedom correspond to a particle in 1-D box -possibly in presence of longitudinal electric field: a simple model for the states was derived in the model for Becker's DC currents.

In the absence of longitudinal electric field the energy spectrum is E

_{n}=n^{2}E_{0}, E_{0}=hbar^{2}π^{2}/2mL^{2}, L the length of the flux tube. Longitudinal excitations correspond to energies (n_{f}-n_{i})^{2}E_{0}and would classically correspond to the acceleration in the electric field component parallel to the flux tube giving rise to Becker currents. For both excitations negentropically entangled states result very naturally as superpositions of single particle excitations and possibly also multi-particle excitations. Both incoming photons and liberation of metabolic energy quantum as photon can induce the excitation.

One could reinterpret the idea about universal metabolic energy quanta by interpreting it as increment of longitudinal energies at flux tube. For the excitation n=1→ 2 the energy would be 3hbar

^{2}π^{2}/2mL^{2}which is same as zero point kinetic energy for a particle in 3-D box of side L. Quantitative prediction is therefore same as that of the original model. One can of course consider also the original option that the transfer of particles from the flux tube to a larger space-time sheet indeed liberates metabolic energy.

- Could one assign negentropic entanglement with high energy phosphate bond?If so, the period of negentropic entanglement (having Orch OR as a counterpart) would correspond to the presence of ATP and the end of this period to ATP→ ADP. I have considered this possibility earlier. The problem is that it is difficult to understand how negentropic entanglement could be assigned simultaneously both to ATP and to the magnetic flux tube whose length and thickness are proportional to hbar and therefore varies. One should treat ATP and flux tube as single basic structure and this does not sound convincing since the scales of flux tubes are expected to be much longer than the size scale of ATP molecule. Therefore the safest assumption would be that ATP is just what it is believed to be: provider of metabolic energy only. One can leave also open the question whether high energy phosphate bond can be interpreted in terms of zero point kinetic energy or not.

- Could the non-local excitations of cyclotron Bose-Einstein condensates by large hbar photon give rise to the negentropically entangled states? Excitation of cyclotron BE condensate requires energy so that metabolic energy is required. ATP could provide this energy. Cyclotron energy quantum is given by E
_{c}= hbar qB/m , q and m are charged and mass of the boson. As already found, the energy of boson is sum of two contributions: energy E_{n}∝ n^{2}associated with free longitudinal motion and magnetic energy E_{c,n}∝ n+1/2. Longitudinal excitations could be assigned to the generation of Becker currents. This proposal would integrate metabolism, negentropy generation, and quantum like behavior of ELF em fields in living matter to single picture.

- Could it be that ATP - instead of being a carrier of negentropic entanglement as suggested earlier - only provides the metabolic energy quantum transformed to cyclotron energy quantum or longitudinal energy quantum when negentropic entanglement is generated by exciting the cyclotron BE condensate? Or could ATP carry both metabolic energy and negentropic entanglement and both of them are transferred to the magnetic flux tube

in ATP → ADP process?

- Cyclotron energies are quite too small for this to make sense for the ordinary value of Planck constant. The nominal value of the metabolic energy quantum is E
_{0}=0.5 eV which by E_{0}= h_{0}f_{0}corresponds to frequency f_{0}= 5 × 10^{13}Hz in near infrared. The value of electron's cyclotron frequency in the endogenous magnetic field B_{end}=.2× 10^{-4}Tesla postulated to explain the effects of ELF em fields on vertebrate brain is f_{c,e}≈ 6× 10^{5}Hz. If metabolic energy quantum is to excite cyclotron state (n→ n+1), one must have E_{c}=E_{0}.

Even for electron E

_{c}is much below E_{0}small for B=B_{end}and hbar=hbar_{0}. One can however scale both B from B_{end}and hbar from hbar_{0}. Requiring E_{c}(hbar,B)= E_{0}and using E_{c}= hf gives f_{c,e}/f_{0}=r_{1}r, r_{1}= B/B_{end}and r=hbar/hbar_{0}, where hbar_{0}denotes the standard value of Planck constant. This gives r_{1}r≈ (5/6)× 10^{8}.

- There are many manners to achieve the desired upwards scaling of cyclotron energies. Magnetic flux quantization gives further constraints. One could require that magnetic flux is quantized, and that for hbar=hbar
_{0}the flux quantum has radius of order L(151) (1 nm, cell membrane thickness) corresponding to the thickness of a flux tube assignable to single DNA nucleotide.

The radius of flux quantum corresponds to the magnetic length r

_{B}= (hbar/qB)^{1/2}. In the scaling B_{end}→ 1 Tesla (r_{1}= 2.5× 10^{4}), magnetic length scales as r_{B}≈ 2.5 μm → 11 nm. From the condition r_{1}r= (5/6)× 10^{8}one has for the scaling of Planck constant r ∼ 3.3× 10^{3}. The scaling of the flux tubes length of L(151) would give flux tube length of order 3× 10 μ m, which corresponds to cell size so that a flux tube connecting DNA and cell membrane could be in question. Note that the scaling of hbar does not affect zero point kinetic energy in the longitudinal direction since L scales as hbar.

- For flux tube length L(151) and for hbar=hbar
_{0}the energy of the lowest longitudinal excitation is same order of magnitude as metabolic energy quantum so that the excitation of longitudinal states could be in key role in the generation of Becker's currents. There is evidence about non-local excitations of electrons in photosynthesis (see also the blog posting), which suggests that the longitudinal energy excitations for Cooper pairs could indeed play the role of fundamental metabolic energy quantum transferred to the the energy of high energy phosphate bond of ATP. This interpretation leaves open the structure of high energy phosphate bond and there is no absolute need to assign zero point kinetic energy with it.

Longitudinal energies are negligible, one must require flux tube length to be considerably longer than L(151) for the ordinary value of hbar. Longitudinal energies are significant only for electron for given flux tube length. Indeed, Becker currents are known to be carried by electrons.

- If one allows ionic Bose Einstein condensates the value of Planck constant must be scaled up by the mass ratio m
_{I}/m_{e}, where m_{I}and m_{e}are the masses of ion and electron. For proton this would give scaling ratio r=2^{11}and one would end up with the hierarchy of Planck constants coming as powers of 2^{11}suggests years ago. What is remarkable that in cyclotron degrees of freedom also protons and ions can play a signification role: the quantal effects of ELF em fields on vertebrate brain suggest that this is the case.

- Cyclotron energies are quite too small for this to make sense for the ordinary value of Planck constant. The nominal value of the metabolic energy quantum is E
- What happens if one has just electrons rather than Cooper pairs? In both transversal and longitudinal degrees of freedom one would have the analog of Fermi sphere with electron states filled up to some maximum values integers characterizing cyclotron energy and longitudinal momentum. Transitions induce also now negentropic entanglement. For cyclotron states the energy increment would be E
_{c}so that basic metabolic energy quantum can induce the transitions. In longitudinal degrees of freedom the minimal energy increment would be (2N+1)E_{0}, where N characterizes the populated state with maximal longitudinal momentum. This energy should be equal to the metabolic energy quantum. This can be arranged but is not so natural. Experimental work is sooner or later bound to reveal whether electrons or their Cooper pairs are in question.

The option developed above is perhaps the most elegant found hitherto: it would raise the BE condensates of electronic and ionic Cooper pairs in a special position, it would lead to explicit proposal for what negentropic entanglement is, and it would requires no modification of the ideas related to ATP, even the standard view about ATP can be kept. It suggests that electronic cyclotron BE condensates are essential also for the understanding of photosynthesis. The absorption of dark photon would generate a non-local excitation of BE condensate of electron Cooper pairs- also a negentropically entangled state. The energy gain in this process could be interpreted as a fundamental metabolic energy quantum, and the subsequent steps in photosynthesis would only take care of the storage of the energy to ATP. Also the metabolic energy liberated in ATP→ ADP could be realized universally as IR dark photon absorbed by cyclotron BE condensate at magnetic flux tube so that dark photon beams would become the key actors of metabolism and negentropy generation. Note that a maximal negentropy gain is obtained if the number of Cooper pairs in the condensate is power of prime. Relatively small primes in the scale defined by the p-adic length scales assignable to elementary particles would be in question.