Dark matter revolution

The ideas related to dark matter that appeared already for year and half ago as I developed a model for topological quantum computation got a strong boost when I learned about the work of Nottale suggesting that the properties of astrophysical objects could be understood by assuming that dark matter corresponds to a phase in which hbar has a gigantic value, which can be fixed by applying Equivalence Principle. This lead to a revolution propagating through entire TGD (four books making about 5000 pages) and I have been carrying out the painful updating during this year and can now proudly declare that the first two books, TGD and p-Adic TGD are done! A good measure for the power of a new idea is the convergence of ideas and extinction of alternative options measured as a shortening of the text it induces. In many cases the reduction factor has been 1/2 or even more, which I regard really impressive. Also a lot of associative noise which is the unavoidable dark side of creative thinking has been cleaned out.

1. Interpretation of long ranged color and electro-weak gauge fields in terms of dark matter hierarchy

One of the basic predictions of TGD is the existence of long ranged classical color and electro-weak gauge fields. The interpretation of long ranged weak fields has been a longstanding challenge for TGD and I was more than a decade on a wrong track in this respect. The final solution of the problem came with realization that TGD unavoidably predicts infinite hierarchy of physics which are dark or more precisely, completely or partially dark, with respect to each other.

The observed elementary particles represent only a tip of an iceberg in TGD Universe although they contribute a sizable fraction to the energy density of the universe and determine to a high degree the properties of that portion of universe about which we have sensory perceptions. The dark physics corresponds typically to particle spectrum characterized by very light mass scales (say weak length scale of order atomic size or cell size). The fingerprints of dark matter are however visible already in nuclear physics and condensed matter physics and a rather detailed picture about the situation exists already now.

The contribution of these physics to mass density is not expected to be large: p-adic fractality suggests that the density of matter at a space-time sheets characterized by given p-adic prime scales as 1/L_p³, p≈2^k, k integer, preferably prime or power of prime. For instance, in cell length scale this would roughly mean density of few units of weak isospin per cell volume.

More generally, the hierarchies of physics are labelled by values of p-adic primes of particles, algebraic extensions of p-adic number fields, collection of conformal weights associated with a particle spectrum of a particular physics, and values of Planck constant labelled by generalized Beraha numbers B_q= 4cos²(π/q), q rational larger than 3. In particular, dark matter hierarchies with the values of hbar coming as hbar(n)= λ(m)^-nhbar(1), λ(m)=v₀/m≈ 2^-11/m are predicted. hbar(1) has discrete spectrum labelled by B_n, n integer, and varying in the range [1,2]×hbar, where hbar corresponds to the limit n goes to infinity.

One can say that TGD Universe is like a Mandelbrot fractal for which x--> 1/x transformation is performed. For Mandelbroot fractal the increase of resolution reveals completely new worlds endlessly, in TGD Universe the reverse operation does the same ad infinitum.

These physics couple only via the common bosons, such as graviton. The decay of particles of large hbar physics to those of smaller hbar physics is possible through de-coherence in which the Compton lengths and sizes of space-time sheets are reduced by 1/λ so that the particles do not anymore overlap in quantum sense and quantum coherence is lost. Even the de-coherence of ordinary laser beams could correspond to this process.

2. Number theoretical characterization of particles

Number theoretical vision leads to a vision in which elementary particles correspond to infinite primes, integers, or even rationals which in turn can be mapped to finite rationals. To infinite primes, integers, and rationals it is possible to associate a finite rational q=m/n by a homomorphism. q defines an effective q-adic topology of space-time sheet consistent with p-adic topologies defined by the primes dividing m and n (1/p-adic topology is homeomorphic to p-adic topology). The largest prime dividing m determines the mass scale of the space-time sheet in p-adic thermodynamics. m and n are exchanged by super-symmetry and the primes dividing m (n) correspond to space-time sheets with positive (negative) time orientation. Two space-time sheets characterized by rationals having common prime factors can be connected by a #_B contact (join along boundaries contact) and can interact by exchange of particles characterized by divisors of m or n.

This picture would dictate the selection rules for the interactions between particles belonging to the hierarchy of physics predicted by TGD. Particles would be characterized by a collection of p-adic primes defining as their product the integer characterizing the particle. Two particles would interact only if the integers characterizing them have common prime factors. Graviton should correspond to a product of primes common to all particles. Particles are completely dark relative to each other if they interact only via graviton exchange.