A Gravitational Explanation for Quantum Theory & non-time-orientable manifolds

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

2. Einstein’s dream • 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 explanation

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

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

5. 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. Topology change • A Simple Model in 1+1D t

7. 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. Definition of electric charge: If V3 is not orientable then use divergence theorem. If the spacetime is not time orientable then V3 is not co-orientable * Operator is not globally defined. Is not globally defined even when F is well defined.

9. The Faraday Tensor F

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

11. Mobius Strip

12. Einstein Rosen Bridgeis not time-orientable Einstein Rosen bridge: Phys Rev 48, 73 (1935)

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

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

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

18. 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) • Demo

19. 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. 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. Prepare a beam of electrons Evolving 3-manifolds… Y X Stern Gerlach

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

23. {M: X↑ and Y→} • 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

24. 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. 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. Spin measurement Incompatible boundary conditions Sets of 3 manifolds State preparation x-measurement y-measurement X↑ Y→ X↓ Y← X↑∩ Y→ = ∅

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

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

29. 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. See: • The Logic of Quantum Mechanics Derived From Classical General RelativityFoundations of Physics Letters Vol. 10, No.1, (1997) 43-60. • Topology change and context dependenceInternational 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. GR may be the unifying theory after all