The introduction of neutrons brings in an additional bit. Therefore one could use only dark protons, if one could bring in this additional bit in some way. An obvious candidate would be the direction of a monopole magnetic flux assignable to the letter of the codon as a closed flux tube with respect to reference direction defined by the DNA sequence. If the letters of codon are closed linked flux tubes containing dark protons forming dark DNA as a chain, this kind of option might work. Consider first the topology of the monopole flux tubes.
- Magnetic monopole flux tubes correspond to closed 3-surfaces in the TGD framework. They are closed because the boundary conditions do not allow boundaries with a monopole charge nor boundaries at all. In dimension 3, these flux tubes can become knotted and closed flux tubes can get linked.
- If one has a braiding of N flux tubes, one can connect the ends of the N flux tubes. There are many manners to connect the ends, and one obtains at most N linked closed flux tubes, which are knots. The simplest option is that the ends of each braid strand are connected so that one has N linked flux tubes. This corresponds to the "upper" ends as a trivial permutation of the "lower" ends.
- Any permutation in the permutation group SN is possible. A given permutation can be expressed as a product of permutations such that each permutation leaves invariant a subset. Permutations are therefore characterized by a partition of N objects to subsets such that the given set consist of Ni objects with ∑ Ni=N and that these sets do not decompose to smaller subsets. The allowed permutations for Ni objects correspond to elements of the cyclic group ZNi. These cyclic permutations give rise to a single closed tube when the ends of the braid ends and permuted braid ends are connected. The number of closed flux tubes is therefore the number of summands in ∑ Ni=N. These permutations are obtained by reconnections from the permutation corresponding to N closed loops so that there are two levels: the level of braiding and the level of reconnections behind the stages not visible in the properties of the braiding.
- Chemical bonds are classified into ionic bonds, valence bonds involving delocalization of electrons, and hydrogen bonds involving delocalization of protons. Chemical bonds are not well-understood in the framework of standard chemistry. TGD suggests that they involve space-time topology: monopole flux tube pairs would be associated with the bonds and the splitting of the bond would correspond to a reconnection splitting the pair to two U-shaped flux tubes. Flux tubes and connecting molecules as nodes are proposed to form a network.
- I have not considered in detail how the U-shaped flux tubes are associated with the nodes. Bonding=linking metaphor encourages a crazy question. The members of the flux tube pairs, which are proposed to connect molecules, which serve as nodes of a network . These flux tubes must close and could be linked with shorter closed flux tubes assignable to molecules.
- Could this linking bind the molecules and atoms to a single topological structure. If so, both chemistry and topological quantum computation (TQC) in the TGD framework would involve linking, braiding, and reconnections as new topological elements. Biomatter at molecular level would consist of chains of closed flux tubes which can be also stretched and give rise to braids.
Note that 2 U-shaped flux tubes can reconnect and this transition can lead to a pair of flux tubes or to a linked pair of U-shaped flux tubes so that 3 different states are possible.
- I have proposed that the pairing of molecules by a pair of monopole flux tubes serves as a correlate for entanglement. If dark protons are associated with closed flux tubes, they must entangle. Could also the linking of the U-shaped flux tubes give rise to entanglement? Stable linking correlates the positions of the flux tubes but this need not mean entanglement since wave function can be a product of wave functions in cm coordinates and relative coordinates.
- Could the presence of valence-/hydrogen bonds involve a closed flux tube at which the electron (pair)/proton is delocalized and that this flux tube is linked with another such flux tube. This picture is consistent with the proposed role of quantum gravitation in metabolism (see this) and generation of the predecessor of the nervous system (see this) based on ver,y long variants of hydrogen bonds characterized by gravitational Planck constant. In this view, living matter would be an extremely highly organized structure whereas in the standard chemistry organism would be a soup of biomolecules.
- What comes to mind as an example, is the secondary structure of proteins (see this) involving α- helices, β-strands and β-sheets. Tertiary structure refers to 3-D structure created by a single protein molecule. It can have several domains. There are also quaternary structures formed by several polypeptide chains. Proteins consist of relatively few substructures known as domains, motives and folds. Could these structures involve braided and linked flux tube structures with dynamical reconnections?
- One can imagine that dark protons are associated with closed flux tubes acting as hydrogen bonds, such that 3 closed flux tubes as letters are linked to form a dark codon. The dark codons could in turn be linked to form genes as sequences of codons. The direction of the magnetic flux can be opposite or parallel to that of the chain so that each closed flux tube represents a bit of topological information. The chains of links would define sequences of bits and even qubits. Could this define the predecessor of the genetic code for which letter represents a single bit?
- If one has only dark protons, one obtains only 32 dark codons. An additional bit is required to get 64 codons. Could the direction of the closed flux tube in the chain provide the missing bit?
This need not be the case at the level of dark codons. In (see this) it was found that the earlier 1-1 correspondence between dark codons and ordinary genetic codons is unnecessarily strict and a modification of the earlier picture of the relation between dark and chemical genetic code and of the function of dark genetic code was considered.
- Dark DNA (DDNA) strand is dynamical and has the ordinary DNA strand associated with it and dark gene state can be in resonant interaction with ordinary gene only when it corresponds to the ordinary gene. This applies also to DRNA, DtRNA and DAA (AA is for amino acids).
This would allow DDNA, DRNA, DtRNA and DAA to perform all kinds of information processing such as TQC by applying dark-dark resonance in quantum communications. The control of fundamental biomolecules by their dark counterparts by energy resonance would be only one particular function.
- Most importantly, flux tubes magnetization direction could define qubit. If the additional qubit corresponds to nucleon isospin, it is not clear whether this is the case. One can also allow superpositions of the dark genes representing 6-qubit units. A generalization of quantum computation so that it would use 6-qubits units instead of a single qubit as a unit, is highly suggestive.
- Genetic code code could be also interpreted as an error code in which dark proteins correspond to logical 6-qubits and the DNA codons coding for the protein correspond to the physical qubits associated with the logical qubit.
- The teleportation mechanism discussed in (see this) could make possible remote replication and remote transcription of DNA by sending the information about the ordinary DNA strand to the corresponding dark DNA strand by energy resonance. After that, the information would be teleported to a DNA strand in a ferromagnetic ground state at the receiver. After this, ordinary replication or transcription, which would also use the resonance mechanism, would take place.
For a summary of earlier postings see Latest progress in TGD.