THREE LIMITS TO THE PHYSICAL WORLD Pierre Darriulat Quy Nhon, December, 2011
Three limits to the physical world ħ=c=G=1 ξ=l/m η=√(lm) m=η/√ξ l=η√ξ ρ=(ξη)–2 Heisenberg limit lm >1 → η~1 Schwarzschild limit l=2m~m → ξ~1 Planck scale ξ=η=1 Einstein limit ρFRW~10–121~ρΛ ρΛ =Λ/8πG ξη ~1061 ρΛ~mΛ4 → mΛ~mν P.S. Wesson, Mod. Phys. Lett. A19 (2004) 1995; Heisenberg limit Schwarzschild limit Einstein limit Planck scale Universe Proton ρWD ρNS ρA Cyg X Cyg A Sun ξ→ η↑ ρΛ mΛ Proton ξ~1039 Universe η~1061 Sun ξ~106, η~1041 Cyg X η~1039 Cyg A η~1049 ρA~mpme3α3 ~10–93 ρWD~mpme3 ~10–87 ρNS~mp4 ~10–78
The physical world in a Vietnamese hat PLANCK HEISENBERG SCHWARZSCHILD EINSTEIN NEUTRINO UNIVERSE Scale: Λ 1/2~10 60 ħ = c = G = 1