Can one deduce the value of the effective Planck constant for a bio-system from empirical data?

The TGD inspired view of consciousness involves the proposal that the effective Planck constant h_eff, identified as a dimension of an extension of rationals, serves as a measure for algebraic complexity and in this way serves as a universal IQ. The reason would be that the higher the complexity of the system, the higher its capacity to represent. Marko Manninen posed in the Galilei meeting an interesting question related to this hypothesis.

Assuming that you have a concrete biological or computational system, how do you actually compute n (dimension of extension) in a non-arbitrary way?

Consider first the notion of h_eff. One must start from the system and try to deduce the value for that system. Assuming that one has a formula for h_eff in terms of the parameters of the system, one can calculate it. Gravitational and electric Planck constants assignable to classical gravitational and electric long range fields are in a special role. It is not clear whether there are other kinds of effective Planck constants or whether h_eff always is a parameter characterizing a 2-particle system (this is proposed to reflect the presence of Yangian symmetries, which are multilocal).

There are two especially important cases: h_gr and h_em assignable to classical gravitational and electric fields.

1. There is an explicit formula for computing both gravitational and electric Planck constants for a pair M,m or Q,q. The products Mm and Qq appear in the formulas. It is not clear whether all values of h_eff are expressible as products of two charges or two masses. In most applications this assumption can be made.

   The proposal is that when the value of coupling strength appearing in perturbative expansion at QFT limit is so large that perturbative series fails to converge, a phase transition increasing the value of H to h_eff guaranteeing the convergence occurs since coupling strength is scale down by h/h_eff.

   One can compute h_gr and h_em when the velocity parameter v₀/c\leq 1 is given. The outcome conforms with the fact that increase of M and Q means increase of the "IQ".

2. For Earth, Sun, etc gravitational Compton length is Λ_gr= ℏ_gr/m= 2GM/β₀, where β₀ is velocity parameter. For the Earth β₀=1 implies that Λ_gr equals to 1/2 of Schwartschild radius r_S= 2GM. There is no dependence on the small mass m. This reflects the Equivalence Principle. The same is true for dark cyclotron energies. This has strong consequences for biology.

   For Earth Λ_gr equals .5 cm, the size of a snowflake, which is a mysterious structure from the point of view of standard physics, since it can be seen as a zoomed version of water molecule crystal in atomic scale. In Mars it would be by a factor 1/10 smaller. There is also the corresponding universal frequency, which for Earth is in the 10 GHz range and could be an important biological frequency. These predictions are very strong and could be killer predictions.

3. h_em is proportional to a product Qq of charges must be so large that Qqα/β₀ is larger than 1 so that perturbation series making sense at the QFT limit of TGD and involving Qqα fails to converge. β₀=v₀/c is a velocity parameter and for Earth its value equals to 1 for ℏ_gr in the case of the Earth. For q=1, Q must be large enough.

   DNA charge density is constant and Q is proportional to 3N, N the number of codons. Q is therefore proportional to the length of the DNA unit considered. Genes increase in length with evolution and also DNA itself. For DNA strand pairs Q² is very large! For cells Q is proportional to the surface area S of the cell membrane. For large neurons, in particular pyramidal neurons and the trigeminal nerve it is very large and would correspond to the highest neuronal IQ. Neurons can also fuse to larger systems and this occurs temporarily in nerve pulse transmission at synaptic contacts and this increases the value of h_em.

4. What about atomic nuclei? When nuclear charge exceeds n=137 h_em becomes larger than h even for v₀/c=1. In the 1970s it was observed that at energies exceeding Coulomb wall particles that I interpreted as electropions were created (see this).

See the article The recent view of TGD inspired theory of consciousness and quantum biology or 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.