How quantum arithmetics affects basic TGD and TGD inspired view about life and consciousness?The vision about real and padic physics as completions of rational physics or physics associated with extensions of rational numbers is central element of number theoretical universality. The physics in the extensions of rationals are assigned with the interaction of real and padic worlds.
How does the replacement of rationals with quantum rationals modify quantum TGD and the TGD inspired vision about quantum biology and consciousness? What happens to padic mass calculations and quantum TGD? The basic assumption behind the padic mass calculations and all applications is that one can assign to a given partonic 2surface (or even lightlike 3surface) a preferred padic prime (or possibly several primes). The replacement of rationals with quantum rationals in padic mass calculations implies effects, which are extremely small since the difference between rationals and quantum rationals is extremely small due to the fact that the primes assignable to elementary particles are so large (M_{127}=2^{127}1 for electron). The predictions of padic mass calculations remains almost as such in excellent accuracy. The bonus is the uniqueness of the canonical identification making the theory unique. The problem of the original padic mass calculations is that the number of common rationals (plus possible algebraics in some extension of rationals) is same for all primes p. What is the additional criterion selecting the preferred prime assigned to the elementary particle? Could the preferred prime correspond to the maximization of number theoretic negentropy for a quantum state involved and therefore for the partonic 2surface by quantum classical correspondence? The solution ansatz for the modified Dirac equation indeed allows this assignment (see this): could this provide the first principle selecting the preferred padic prime? Here the replacement of rationals with quantum rationals improves the situation dramatically.
What happens to TGD inspired theory of consciousness and quantum biology? The vision about rationals as common to reals and padics is central for TGD inspired theory of consciousness and the applications of TGD in biology.
For details and background see the new chapter Quantum Arithmetics and the Relationship between Real and pAdic Physics.
