General Relativity Dr Mark Hadley Parity Violation. The biggest - PowerPoint PPT Presentation

Explaining CP violation using General Relativity Dr Mark Hadley

Parity Violation…. The biggest scientific blunder of the 20 th century

Plan… • Motivation • Parity and Parity violation … a fresh look • CP violation … a brief look • General Relativity ……. and the Kerr Metric • The connection … and a prediction Mark Hadley

Motivation…. General Quantum Relativity Theory • Quantum gravity • String theory • A gravitational theory of quantum mechanics 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 Mark Hadley

Doh ! Mark Hadley

Parity is violated - FACT The Nobel Prize All the books say so. Committee say so. Mark Hadley

Doh !! Doh!! Mark Hadley

Where have they gone wrong? • Exactly what has been observed? • Exactly what has been violated? • What, exactly, is the definition of Parity? Mark Hadley

Space Inversion Inversion = reflection + 180 ° rotation  x -x      x x  t t      y y       v = x -v P :      z z  a = x -a             t t  ω = r × v ω Axial or Pseudo vector Mark Hadley

Psuedo vectors don’t exist? • Angular momentum is a bi-vector: • Base vectors: 𝒆𝒚 ∧ 𝒆𝒛, 𝒆𝒛 ∧ 𝒆𝒜 𝒃𝒐𝒆 𝒆𝒜 ∧ 𝒆𝒚 • Isomorphic to dx,dy,dz • But different transformation properties. • 𝐐 𝑈𝑃𝑈 = 𝐐 𝑀𝑗𝑜 + 𝜆𝐐 𝑏𝑜𝑕 is nonsense 𝜄 • 𝑀 = 𝐻 𝜈𝜉 𝐻 𝜈𝜉 + 32𝜌 2 𝜗 𝜈𝜉𝛽𝛾 𝐻 𝜈𝜉 𝐻 𝛽𝛾 is also nonsense Mark Hadley

Parity in Newtonian Mechanics Parity Before After conserved  F = m a F = m(- a )  -F = m ( -a )  -F = (-m)( -a )  F = (-m)( -a ) (± )E = ½( ± m) v 2 E = ½m v 2 Mark Hadley

Parity in Newtonian Mechanics P operator is chosen : 1) For simplicity 2) To conserve parity E  2 3) Supported by: mc Special Relativity: ( t -component of the energy momentum 4-vector) 1      m g g dS General Relativity:  k jk j kk j 2 16 c Mark Hadley

Parity in e - electromagnetism Start with a symmetrical state…… e - e - e - e - e - Magnetic field pointing out

Parity in Electromagnetism Parity Before After conserved  F = q( E + v x B ) -F = q(- E + - v x (- B ))  -F = q(- E + - v x B )  Note:   E.n -F = -q( E + - v x B ) ˆ q dS  -F = -q( E + - v x (- B )) Mark Hadley

Parity in Electromagnetism P operator is chosen : 1) To conserve parity In this order 2) For simplicity 3) Supported by the covariant formulation:   0 E E E x y z     𝑒𝐪 E 0 B B     𝑒𝜐 = 𝑟 𝐆. 𝐰 x z y F    E B 0 B  y z x      E B B 0   z y x

Start with a Look for an symmetrical asymmetric state outcome e - θ 60 Ni + e - + υ e 60 Co I( θ )d θ = k (1 + α cos θ )sin θ d θ

actual result I( θ )d θ = k (1 – v/c cos θ )sin θ d θ

“We see from this analysis that the logical path from the observed asymmetry to the inferred nonconservation of parity in β decay is considerably more complex than the popular presentations would indicate.” L. E. Ballentine: The assumption that the Cobalt nucleous is symmetrical is not only non-trivial - it may well be wrong ! Mark Hadley

Effect of Parity The Parity Operator gives the transformation due to an inversion of the spatial coordinates. We do not have a free choice of P operator. What are the transformations in beta decay? Mark Hadley

What is the mirror image of a Cobalt atom? e - e + 60 Co 60 Co e - Anti 60 Co (not to scale) Mark Hadley

Claim: The real parity operation is what we call CP Particles are intrinsically anti-symmetric. Parity is conserved in the weak interactions… …….…. almost Mark Hadley

CP violation is the real mystery Can it be defined away? Could it be an external influence? Mark Hadley

Mark Hadley

General Relativity Our ONLY theory of Space and time   x x G ( ) 8 T ( ) Curvature of Energy, Momentum Space and Time and Stress Tensor • Accepted and understood • Non-linear equations • Local equations - Does not prescribe the topology • Describes a curved spacetime • Allows closed timelike curves CTCs Mark Hadley

The metric 𝑒𝑡 2 = −𝑑 2 𝑒𝑢 2 + 𝑒𝑦 2 + 𝑒𝑧 2 + 𝑒𝑨 2 𝑒𝑡 2 = −𝑑 2 𝑒𝑢 2 + 𝑒𝑠 2 + 𝑠 2 𝑒𝜄 2 + sin 2 𝜄 𝑒𝜚 2 Schwarzschild metric 𝑒𝑡 2 = − 1 − 𝑠 𝑠 𝑑 2 𝑒𝑢 2 + 1 − r s −1 dr 2 + 𝑠 2 𝑒𝜄 2 + sin 2 𝜄 𝑒𝜚 2 𝑡 r General case: 𝑒𝑡 2 = 𝑕 𝜈𝜉 𝑒𝑦 𝜈 𝑒𝑦 𝜉 Mark Hadley

The Kerr metric 𝑒𝑢 2 + 𝜍 2 𝑒𝑡 2 = − 𝑑 2 − 2𝐻𝑁𝑠 Δ 2 𝑒𝑠 2 𝜍 2 +𝜍 2 𝑒𝜄 2 𝑁 2 𝑑 2 + 2𝐻𝐾 2 𝑠 𝐾 2 +(𝑠 2 + 𝑑 4 𝜍 2 𝑁 sin 2 𝜄) sin 2 𝜄𝑒𝜚 2 + 4𝐻𝑠𝐾 𝑑 2 𝜍 2 sin 2 𝜄𝑒𝑢𝑒𝜚 Where: 𝐾 2 𝐾 2 𝜍 2 = 𝑠 2 + 𝑁 2 𝑑 2 cos 2 𝜄 and Δ 2 = 𝑠 2 − 2𝐻𝑁 𝑑 2 𝑠 + 𝑁 2 𝑑 2 Mark Hadley

𝑕 𝑢𝜚 ≈ 4𝐻𝐾/𝑑 2 𝑠 sin 2 𝜄 • One component of a second rank tensor • Measures the asymmetry. • 𝑢 and 𝜚 are symmetry directions (they define killing vector fields) • … but also define an invariant scalar field. Mark Hadley

Relative magnitudes Earth Sun Galaxy 6.3 10 6 1.5 10 11 2.5 10 20 r m 7 10 3 2 10 41 10 66 kg m 2 s -1 J 3 10 3 10 20 m 2 s -1 rad -1 g t Φ 3 10 -15 10 -14 10 -9 h tx dimensionless Mark Hadley

Hypothesis • Particles are intrinsically antisymmetric. • They interact with the asymmetric gravitational potential to produce an apparent CP violation effect Mark Hadley

Predictions: • CP violation is local, not universal. • It varies according to the 𝑕 𝑢𝜚 term of the metric. • There is a sin 2 𝜄 variation in the magnitude with respect to the galactic plane. • Earth based experiments may give anisotropic results for CP violation. Mark Hadley

The Quest • Choose a CP violating reaction • Collect associated directional parameters • Correct for the Earth’s rotation • Plot on a galactic co-ordinate system Mark Hadley

Results so far……. Plots of asymmetry vs B0 momentum direction David Goude. University of Warwick 2012 Mark Hadley

Can you do better? Mark Hadley