Welcome to GT5 Wormholes Time machines and Energy conditions Chairperson Dr. Mark Hadley MG11 Berlin

GT5 Schedule

Would Einstein have come to this session?

GT5 + Einstein = χ Causality cannot be violated

Bell’s Inequalities 1963 Aspect’s Experiments GT Einstein = God goes not play dice √

Dr Mark Hadley Time machines and quantum theory

Explaining Quantum Theory Bell’s Inequalities Aspect’s EPR Experiments  We cannot explain quantum theory with any local hidden variables theory.  We cannot model particles as 3-D solutions [of GR] that evolve in time.

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

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← but, {X↑ Y→} does not exist in theory or experiment.

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

Spin measurement {X↑  Y→} = ∅  √ X↑X↑ X↓X↓ Y←Y← Y→Y→ State preparation x-measurementy-measurement Sets of 3 manifolds Incompatible boundary conditions

Quantum Logic Quantum theory is characterised by an orthomodular lattice of propositions – a non- Boolean logic. so is GR with a acausal space times. The only known way to represent experimental probabilities on such a lattice is using subspaces of a Hilbert space.

Testing the orientability of space

Testing the orientability of time ?

Testing the orientability of time

Acausal manifolds Mathematical and physical descriptions of a space time are not the same Space-time +The observer +The experiments +The results....are all interlinked Quantum theory gives a consistent description of such an interlinking.

GR may be the unifying theory after all

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

Other results from non time- orientable manifolds Electric, but not magnetic chare from source-free Einstein-Maxwell equations Diemer and Hadley Class. Quantum Grav. (1999) Explains spin half Hadley Class. Quantum Grav. (2000)

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

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