Observational Tests of the Topology of Planckian Space-time

Observational diagnostics are constructed which reflect the underlying topology of Planckian space-time, and are directly related to phenomena on much larger scales. Specific predictions are made for the masses of elementary particles, coupling constants, quark confinement , black hole states, and the cosmological constant. In particular, a mass of 131.6 GeV is found for the Higgs boson. The main presented result is a discrete spectral signature at inverse integer multiples of the zero point frequency ν0 = 857.3588 MHz (34.96698 cm). That is, each photon of frequency ν0m, for an integer m, is paired with an otherwise identical photon ν0/m, produced by the vacuum, but not vice versa. The reader interested in the latter result only, should proceed to Section 6 after the Introduction. §1. Introduction Recently, it has been proposed that space-time on the Planck scale exhibits a definite non-trivial topology generated by the three-torus T 3 and the handle S 1 × S 2 [1,2]. The interested reader is referred to these papers for an exhaustive description of the resulting theory. Only those elements relevant to the investigations of this work will be discussed in more detail in the subsequent sections. A summary, not aimed at being comprehensive, of the formalism in [1,2] is as follows. A thought experiment leads to the ground state of the Universe as the Lorentz invariant topological manifold Q = 2T 3 ⊕ 3S 1 × S 2 ≡ P ⊕ Θ with a λφ 4 + µ 2 φ 2 self-interaction potential, and an equation of motion 4πi∂ ν φ[(∂ ν q λ)q µ q µ − (∂ ν q µ)q µ q λ ] = q λ q µ 2q µ − q µ q µ 2q λ , (1a) q µ q µ = cst, (1b) for the four component wave function q λ. The manifold Q has 23 = 2 · 7 + 3 · 3 (14 for P 9 for Θ) degrees of freedom, corresponding to the number of elementary particles which depend on the homotopy of space-time, i.e. excluding the photon and graviton. The intrinsic measures of Q, P and Θ are 23 −3 , 14 −3 and 7 −3 , respectively, where the cubic powers reflect the threefold identifications of the three-torus. When the mini black holes evaporate the lattice of three-tori, L(T 3), is described by the equation of motion q µ q µ 2q …