Two Objections Against p-adic Thermodynamics & Their Resolution

Abstract

There are two basic objections against p-adic thermodynamics. The mass calculations require the presence of states with negative conformal weights giving rise to tachyons. Furthermore, by conformal invariance, L₀ should annihilate physical states so that all states should have vanishing mass squared! In this article a resolution of these objections is discussed. The solution is based on the very definition of thermodynamics and on number theoretic vision predicting quark states with discretized tachyonic mass, which are counterparts for virtual states in QFTs. Physical states for the entire Universe would be indeed massless but for subsystems such as elementary particles the thermal expectation of the mass squared is non-vanishing. This conforms with the formula of blackhole entropy stating that it is proportional to the mass square of the blackhole and vanishes for a vanishing mass: this would indeed correspond to a pure state.