Unlike Higgs mechanism, p-adic thermodynamics provides a universal description of massivation involving no other assumptions about dynamics except super-conformal symmetry which guarantees by the existence of p-adic Boltzmann weights.
The number theoretic picture leads to a deeper understanding of a long standing objection against p-adic thermodynamics (see this) as a thermodynamics for the scaling generator L0 of Super Virasoro algebra.
If one requires super-Virasoro symmetry and identifies mass squared with a scaling generator L0, one can argue that only massless states are possible since L0 must annihilate these states! All states of the theory would be massless, not only those of fundamental particles as in conformally invariant theories to which twistor approach applies! This looks extremely beautiful mathematically but seems to be in conflict with reality already at single particle level!
The resolution of the objection is that thermodynamics is indeed in question.
- Thermodynamics replaces the state of entire system with the density matrix for the subsystem and describes approximately the interaction with the environment inducing the entanglement of the particle with it. To be precise, actually a "square root" of p-adic thermodynamics could be in question, with probabilities being replaced with their square roots having also phase factors. The excited states of the entire system indeed are massless (see this).
- The entangling interaction gives rise to a superposition of products of single particle massive states with the states of environment and the entire mass squared would remain vanishing. The massless ground state configuration dominates and the probabilities of the thermal excitations are of order O(1/p) and extremely small. For instance, for the electron one has p= M127=2127-1≈ 1038.
- In the p-adic mass calculations (see this and this), the effective environment for quarks and leptons would in a good approximation consist of a wormhole contact (wormhole contacts for gauge bosons and Higgs and hadrons). The many-quark state many-quark state associated with the wormhole throat (single quark state for quarks and 3-quark-state for leptons (see this).
- In M8 picture (see this and this) tachyonicity is unavoidable since the real part of the mass squared as a root of a polynomial P can be negative. Also tachyonic real but algebraic mass squared values are possible. At the H level, tachyonicity corresponds to the Euclidean signature of the induced metric for a wormhole contact.
Tachyonicity is also necessary: otherwise one does not obtain massless states. The super-symplectic states of quarks would entangle with the tachyonic states of the wormhole contacts by Galois confinement.
- The massless ground state for a particle corresponds to a state constructed from a massive single state of a single particle super-symplectic representation (CP2 mass characterizes the mass scale) obtained by adding tachyons to guarantee masslessness. Galois confinement is satisfied. The tachyonic mass squared is assigned with wormhole contacts with the Euclidean signature of the induced metric, whose throats in turn carry the fermions so that the wormhole contact would form the nearby environment.
The entangled state is in a good approximation a superposition of pairs of massive single-particle states with the wormhole contact(s). The lowest state remains massless and massive single particle states receive a compensating negative mass squared from the wormhole contact. Thermal mass squared corresponds to a single particle mass squared and does not take into account the contribution of wormhole contacts except for the ground state.
- There is a further delicate number theoretic element involved (see this and this). The choice of M4⊂ M8 for the system is not unique. Since M4 momentum is an M4 projection of a massless M8 momentum, it is massless by a suitable choice of M4⊂ M8. This choice must be made for the environment so that both the state of the environment and the single particle ground state are massless. For the excited states, the choice of M4 must remain the same, which forces the massivation of the single particle excitations and p-adic massivation.
See the article Two objections against p-adic thermodynamics and their resolution or the chapter TGD as it is towards the end of 2021.
For a summary of earlier postings see Latest progress in TGD.