1. Dr Mark Hadley A Gravitational Explanation for Quantum Theory & non-time-orientable manifolds

2. Mark Hadley Particles as solutions of the field equations An explanation for Quantum theory A unification of the forces of Nature A realist interpretation An antidote to string theory Einstein’s dream explanation

3. Mark Hadley But… Models must give particle properties Charge, mass etc AND Interactions AND Particle behaviour Quantum Theory

4. Mark Hadley Two problems (at least!) 1.Interactions Topology change requires a non-trivial causal structure – Geroch, R P (1967) 2.Quantum theory is incompatible with local realism

5. Mark Hadley Topology Change and GR A topology change cannot take place in GR without either: Singularities appearing. –A breakdown of GR Closed timelike curves. –Which need negative energy sources for their creation. A failure of time orientability –interesting!!

6. Mark Hadley Topology change A Simple Model in 1+1D t

7. Mark Hadley Consequences of non time- orientable manifolds Charge and the topology of spacetime Diemer and Hadley Class. Quantum Grav. Vol. 16 (1999) 3567- 3577 Spin half and classical general relativity Class. Quantum Grav. Vol. 17 (2000) 4187-4194 The orientability of spacetime Class. Quantum Grav. Vol. 19 (2002) 4565-4571

8. Mark Hadley Definition of electric charge: If the spacetime is not time orientable then V 3 is not co-orientable * Operator is not globally defined. Is not globally defined even when F is well defined. If V 3 is not orientable then use divergence theorem.

9. Mark Hadley The Faraday Tensor F

10. Mark Hadley Examples of non-orientable surfaces Mobius Strip Wormholes Monopoles Einstein Rosen Bridge

11. Mark Hadley Mobius Strip

12. Mark Hadley Einstein Rosen Bridge is not time-orientable Einstein Rosen bridge: Phys Rev 48, 73 (1935)

13. Mark Hadley Spin half Intrinsic spin is about the transformation of an object under rotations. If a particle is a spacetime manifold with non-trivial topology, how does it transform under a rotation?

14. Mark Hadley Rotations of a manifold Defining a rotation on an asymptotically flat manifold with non trivial topology. Physical rotation is defined on a causal spacetime. Model spacetime as a line bundle over a 3-manifold

15. Mark Hadley A rotation defines a path in a 3-manifold A physical rotation defines a world line in a spacetime Defines a time direction !!

16. Mark Hadley A physical rotation of a non-time-orientable spacetime The exempt points form a closed 2 dimensional surface.

17. Mark Hadley The exempt points prevent a 360 degree rotation being an isometry, but a 720 degree isometry can be always be constructed. If time is not orientable then:

18. Mark Hadley An object that transforms in this way would need to be described by a spinor. –Tethered rocks (Hartung) –Waiter with a tray (Feynman) –Cube within a cube (Weinberg) –DemoDemo

19. Mark Hadley Acausal Manifolds and Quantum theory With time reversal as part of the measurement process – due to absorption/topology change. The initial conditions may depend upon the measurement apparatus. →A non-local hidden variable theory. →Resulting in the probability structure of quantum theory.

20. Mark Hadley The essence of quantum theory Propositions in Classical physics satisfy Boolean Logic Propositions in quantum theory do not satisfy the distributive law –They form an orthomodular lattice

21. Mark Hadley Evolving 3-manifolds… Prepare a beam of electrons Stern Gerlach X Y

22. Mark Hadley Spin measurement Venn diagram of all 3-manifolds X↑X↑ X↓X↓ Y←Y←Y→Y→ X↑ Y→ X↓ Y→ X↓ Y← X↑ Y← All manifolds consistent with the state preparation X↑ Y→ X↓ Y→ X↓ Y← X↑ Y←

23. Mark Hadley Cannot be prepared experimentally Cannot be described by quantum theory Is a local hidden variable theory Would violate Bell’s inequalities in an EPR experiment. Is NOT context dependent {M: X↑ and Y→}

24. Mark Hadley Geometric models We cannot model particles as 3-D solutions that evolve in time. Need context dependence Non-locality Non-trivial causal structure as part of a particle: 4-geon

25. Mark Hadley 4-geon Non-trivial causal structure as part of the particle. Particle and its evolution are inseparable. Time reversal is part of a measurement Context dependent –Signals from the “future” experimental set up. –Measurement can set non-redundant boundary conditions

26. Mark Hadley Spin measurement X↑ ∩ Y→ = ∅ X↑X↑ X↓X↓ Y←Y← Y→Y→ State preparation x-measurementy-measurement Sets of 3 manifolds Incompatible boundary conditions

27. Mark Hadley How do calculate probabilities if Boolean Logic does not apply? That is the question the Gerard ‘t Hooft is looking for !

28. Mark Hadley From General Relativity to Quantum Mechanics a) Jauch (1968) Beltrametti and Cassinelli (1981) b) Ballentine(1989) Weinberg(1995) General Relativity Quantum Logic Hilbert Space Schrödinger’s equation Planck’s constant etc. a a b

29. Mark Hadley A gravitational explanation for quantum theory Aims to explain –QM –Particle spectrum –Fundamental interactions Predictions –No graviton (Gravity waves are just classical waves) –Spin-half –Parity is conserved

30. Mark Hadley See: The Logic of Quantum Mechanics Derived From Classical General Relativity Foundations of Physics Letters Vol. 10, No.1, (1997) 43-60. Topology change and context dependence International Journal of Theoretical Physics Vol. 38 (1999) 1481-149 Time machines and Quantum theory MG11 July 2006 Berlin A gravitational explanation of quantum mechanics FFP8 October 2006 Madrid

31. Mark Hadley GR may be the unifying theory after all