Emergence of local interaction and quantum uncertainty from Mobius invariance C.S. Lam McGill & UBC, Canada (with Y.-P. Yao, U Michigan) CONTENTS Introduction Cachazo-He-Yuan (CHY) scattering formula Emergence from the evaluation of scalar amplitudes An amusing analogy Conclusion UV divergence strong-weak duality quantum gravity early universe (Penrose) emerging spacetime Locality Problems Black hole entropy Holographic principle Quantum mechanics (EPR) Chinese magic (spinor-helicity formalism) gluon scattering amplitude Parke-Taylor Formula (1986) KLT/BCJ relations Bern, Carrasco, JohanssonKawai, Lewellen, Tye Gravity amplitude ~ (gluon amplitude)(gluon amplitude) If Locality Not Fundamental SCATTERING THEORY how to introduce dynamics? z z Cachazo, He, Yuan (2013) 8 Dynamics Mobius symmetry in the complex plane Tree scattering (arXiv: , , ) z z scattering equations Translation Scaling Inversion Mobius Transformations.. CHY cyclic invariant CHY scalar Gauge boson gravity Trace color factors understood Checked consistency at poles, soft and collinear limits Expects cyclically invariant planar diagrams Double-colored Independent of p,q,r and what p,q,r should I choose ?? but that destroys manifest cyclic symmetry gets much worse ! path diagram (153624) n=4 (first method) emergence of LOCAL INTERACTION (to within deBroglie wavelength) QUANTUM UNCERTAINTY Problems of this approach ( n-3)! degree polynomials n=4 (method 2) n= Path Diagram and Feynman Diagram Mobius covariance of heavily used in establishing the connection (145236) 61, 23, 45612, 123, 234, . (145326) 61, 23, 45, 612, 6123, , 456 ( ) 12, 123, 45, 456, 4567, 89, , 45678 path diagram Analogy with Epigenetics methylation kinematicsdynamics equation propagator QFTCHY dynamics symmetry LorentzMobius Dynamics supplied by Mobius invariance in the underlying complex plane Local interaction (to within deBroglie wavelength) emerging Quantum uncertainty emerging Local non-abelian gauge invariance emerging Local diffeomorphism emerging formulation of Mobius invariance beyond tree diagrams ??