Dr Mark Hadley

Parity Violation:

The Biggest Scientific Blunder of the 20th Century?

Mark Hadley

Is Nature Symmetrical?We thought so until 1956 !!

A Major change in our view of space and time

1. Round Earth

2. Heliocentric view of Universe

3. Special Relativity (time is not absolute)

4. General relativity (spacetime is curved)

5. Big bang – Universe finite in space and time

6. Expanding Universe (time asymmetry)

Mark Hadley

Plan• Parity violation – the conventional view

• My interest

• Review of Parity conservation– Mechanics– Electromagnetism– Weak Interactions

• An alternative view– Parity is Conserved !!

Mark Hadley

Space Inversion

:

x x

y yP

z z

t t

t t

x -x

v = x -v

a = x -a

ω = r× v ω

Inversion = reflection + 180° rotation

Axial or Pseudo vector

Mark Hadley

Effect of Parity - momentum

Before After

The Parity Operator gives the transformation due an inversion of the spatial coordinates

Mark Hadley

Effect of Parity - spin

Before After

Mark Hadley

Physical Review October 1956 p254-258

Tsung Dao Lee Chen Ning Yang

Parity violation in the weak interactions

Start with a symmetrical

state

60Co

Look for an asymmetric

outcomee-

60Ni + e- +υe

I(θ)dθ = k (1 + αcosθ )sinθdθ

θ

Mark Hadley

Experimentalists

Wu   Ambler   Hayward  Hoppes  Hudson

National Bureau of Standards USA 1956

actual result

I(θ)dθ = k (1 –v/c cosθ )sinθdθ

Mark Hadley

Nobel prize winners 1957

Tsung Dao Lee Chen Ning Yang

Parity violation in the weak interactions

Mark Hadley

But not quite so simple…….

Is the initial state symmetrical?

“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:

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

Parity is violated - FACT

All the books say so. The Nobel Prize Committee say so.

Doh !

Mark Hadley

Explanations using GR

• Boundary Conditions

• Common source

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

Parity in Newtonian Mechanics

F = ma

E = ½m v2

F = m(-a)

-F = m (-a)

-F = (-m)(-a)

F = (-m)(-a)

(± )E = ½(± m) v2

Before AfterParity conserved

Mark Hadley

P operator is chosen:

1) For simplicity

2) To conserve parity

3) Supported by:

Special Relativity: (t-component of the energy momentum 4-vector)

General Relativity:

Parity in Newtonian Mechanics

jkkjjkk dSggc

m216

1

2mcE

Magnetic field pointing oute-

e-

e-

e-e- e-

Parity in electromagnetism

Start with a symmetrical state……

Mark Hadley

Parity in Electromagnetism

F = q(E + v x B)

Note:

-F = q(-E + -v x (-B))

-F = q(-E + -v x B)

-F = -q(E + -v x B)

-F = -q(E + -v x (-B))

Before AfterParity conserved

ˆq dSE.n

Parity on magnetic poles

dSQm nB. ˆ dSQm )ˆ( nB.

Magnetic field pointing oute-

e-

e-e- e-

Parity in electromagnetism

Magnetic field pointing ine-

e-

e-

e-

e-

Mark Hadley

Duality Transforamtion• The roles of E and B can be

reversed by a duality transformation:

cossin

sincos

BEB'

BEE'

Parity in Electromagnetism

0

0

0

0

x y z

x z y

y z x

z y x

E E E

E B B

E B B

E B B

F

In this order

4

0c

dF J

d*F

P operator is chosen:

1) To conserve parity

2) For simplicity

3) Supported by the covariant formulation:

Mark Hadley

Effect of ParityThe Parity Operator gives the transformation due 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

“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 !

What is the mirror image of a Cobalt atom?

60Coe-

(not to scale)

e-

60Co

e+

Anti 60Co

Mark Hadley

Parity• Reverses

– Momentum– Lepton number etc.– Charge

• Unchanged– Spin

Is conserved

Mark Hadley

Conclusions

• Space Inversion is a symmetry of Nature

• Parity is conserved

• The conventional P operator is not conserved.

Mark Hadley

Just a change of convention?

• The conventional P operator may be combined with another transformation of degenerate multiplets. (eg particle anti-particle, neutrino flavours)

• Impacts on unifying theories.

“Not merely a matter of convention: on other particles P could have the usual effect.”

Weinberg

Mark Hadley

Parity violation

How could they get it so wrong?

Mark Hadley

How could they get it so wrong?• The Parity operation was defined before the

experiments were done.– Particles were defined as eigenstates of Parity. – Simplicity of the operator took precendence over

conservation - even though QFT required particles and antiparticles to be combined in the same equations.

• There was no higher theory to appeal to.

Watch this space!

Mark Hadley

Parity isConserved

Mark Hadley

,p , p

,k ,k Parity

Lorentz Boost

Eigenvectors of P, H,J3 with eigenvalues 0,M,σ

Mark Hadley

CP violation

• Boundary conditions– Matter dominated Universe

• T asymmetry (CPT theorem)– Expanding Universe

• Parity = CP for some particles only!

• More complicated effects of P on other degeneracies.