The Analog-In, Digital-Out Universe - FQXi

The Analog-In, Digital-Out Universe© Edwin Eugene KlingmanrSo we need math, but where does math come from? The φ -field will support particles fromwhich structures 3 that generate integers are built, and, per Kronecker, man can producethe rest of math—so we needn’t go outside the universe for math 4 but can use math to solver2the Master equation, yielding Gr r r= / r hence G ⋅ G ⇒ | Gr |2 = 1 . In 1953 Eugenio Calabiessentially asked if our Master equation was valid:"Could there be gravity … even if space is a vacuum totally devoid of matter?"He reasoned: "…being non-linear, gravity can interact with itself and in the process createmass”, and he conjectured, "curvature makes gravity without matter possible". The Calabi-Yau manifold confirms 5 our Master equation—based only on gravity —but his conjecturewas based on special geometry in which "time is frozen". Meaning what? Newton'sr r r−1requation is time independent, but if we scale r → λr, then G(λ ) = λ G() and ourMaster field equation is seen to be scale invariant (appendix C):r r r r− −1r → λr ⇒ λ 1 ∇ ⋅ G = λ G ⋅ G(2)Nottale has shown 6 that the laws of scale can actually take the place of the laws of motion:that is, scale invariance implies motion invariance ( t ↔ λ ). This can be visualized as:If scale invariant is motion invariant, time has no obvious meaning. But action orthogonalto a radial field vector can produce a vortex or cyclical phenomenon in a region of space,introducing duration or cycle time. So time appears when the G r -field symmetry breaks andlocal oscillations, i.e. natural clocks, occur. The time dependent phase occurs as symmetrybreaking; thus formal time dependence 4,8 of the solution | Gr | 2 = 1 yields [appendix D]:⎛ Δm⎞⎜⎟ ( Δx)⎝ Δt⎠2+ 2mvr= 0This equation and two possible physical interpretations (shown) make sense only if bothterms have a constant value, call it h , leading to the quantum principle:r r r r∇ ⋅ G = G ⋅ G Classical Field equation - continuum physics (4)⇓Δ m( Δx)2 = h Quantum Principle - physics of observables (5)ΔtThis generalization of Heisenberg's uncertainty principle also implies mvr = h / 2 , Bohr'sorbital condition. Nottale says "it’s remarkable that the Heisenberg relations are universal2