1. Emergence of local interaction and quantum uncertainty from Mobius invariance C.S. Lam McGill & UBC, Canada (with Y.-P. Yao, U Michigan)

2. CONTENTS Introduction Cachazo-He-Yuan (CHY) scattering formula Emergence from the evaluation of scalar amplitudes An amusing analogy Conclusion

5. 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)

6. gluon scattering amplitude

7. Parke-Taylor Formula (1986)

8. KLT/BCJ relations Bern, Carrasco, JohanssonKawai, Lewellen, Tye Gravity amplitude ~ (gluon amplitude)(gluon amplitude)

9. If Locality Not Fundamental SCATTERING THEORY how to introduce dynamics?

10. 3 2 4 5 7 z z 1 3 2 4 5 6 Cachazo, He, Yuan (2013) 8 Dynamics Mobius symmetry in the complex plane Tree scattering 8 2 1 5 3 4 6 7

11. (arXiv: 1306.6575, 1307.2199, 1309.0885)

12. 3 2 4 5 7 z z 1 3 8 4 5 6 scattering equations Translation Scaling Inversion

13. Mobius Transformations.. CHY cyclic invariant

14. CHY scalar Gauge boson gravity Trace color factors understood Checked consistency at poles, soft and collinear limits Expects cyclically invariant planar diagrams Double-colored

15. Independent of p,q,r and what p,q,r should I choose ?? but that destroys manifest cyclic symmetry gets much worse !

18. path diagram (153624)

19. n=4 (first method) 1 3 2 4 2 3 4 1

20. emergence of LOCAL INTERACTION (to within deBroglie wavelength) QUANTUM UNCERTAINTY

21. Problems of this approach ( n-3)! degree polynomials

22. n=4 (method 2) 1 3 2 4 2 3 4 1

23. n=5 2 3 5 1 4

25. Path Diagram and Feynman Diagram Mobius covariance of heavily used in establishing the connection (145236) 61, 23, 45612, 123, 234, ….

26. (145326) 61, 23, 45, 612, 6123, 345234, 456

27. (127546 10 893) 12, 123, 45, 456, 4567, 89, 89 101234, 45678

31. path diagram

32. Analogy with Epigenetics methylation kinematicsdynamics

33. equation propagator QFTCHY dynamics symmetry LorentzMobius

35. 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 ??