Parity

Extraordinary claims require extraordinary evidence.

Carl Sagan

Mirror Symmetry

Parity in physics refers to the relationship between a function and its spatially inverted counterpart (spatial inversion consists of mirror imaging followed by rotation of 180 degrees about the axis orthogonal to the mirror plane). For example, velocity has parity of (−1) since it changes sign under spatial inversion. Angular velocity (vorticity) has parity of (+1) because it is the cross product of the gradient operator and velocity, both of which change sign under spatial inversion (the cross product is defined in a right-handed sense regardless of spatial inversion). 'Parity conservation' means that a physical phenomenon and its mirror image are equally abundant in nature. 'Parity violation' means that a physical phenomenon and its mirror image are not equally represented in nature. This is commonly the result of historical accidents (e.g. all DNA is right-handed but there appears to be no chemical reason for this. It is an example of “symmetry breaking”). “Maximal parity violation” means that the mirror image of some physical phenomenon never occurs (or cannot occur) in nature. This could also be the result of historical accident but may also be interpreted as an asymmetry of physical laws.

In physics we are more concerned with the possibility or impossibility of mirror phenomena, rather than with historical accidents. So the question “What is the mirror image of an electron?” is more fundamental to physics than the question “Do electrons and their mirror images occur with equal frequency in nature?”

Historically, parity conservation was a fundamental assumption of physics. Any physical bias toward right- or left-handed processes would be completely arbitrary and therefore unjustifiable. However, Lee and Yang⁽¹⁾ proposed that weak interactions may violate parity conservation, and experiments by Wu⁽²⁾ demonstrated that beta decay exhibits left-right asymmetry. Electrons emitted in decay of Co⁶⁰ are preferentially emitted in the direction of nuclear spin. In the mirror, these particles appear to be emitted opposite to the direction of nuclear spin (spin and velocity have opposite parity). This means that some elementary particles, including electrons and protons, have a distinct handedness and are therefore not parity eigenfunctions. This asymmetry has been mistakenly interpreted as implying maximal parity violation (mirror asymmetry), although Lee and Yang mention that their theory could be consistent with parity conservation if protons and electrons are not identical to their mirror images.

If Wu’s experiment could be constructed using antimatter, all indications are that such an experiment would behave exactly like a mirror image of the original. The simplest interpretation of this result is that matter and anti-matter are mirror pairs, consistent with mirror symmetry (but not parity conservation, since electrons and positrons do not occur in equal abundance). Instead, physicists have interpreted this mirror symmetry of matter and anti-matter in weak interactions as maximally violating parity (mirror asymmetry) but conserving the operator PC (where the “charge conjugation” operator C represents exchange of matter and anti-matter). If the question is “Does spatial inversion exchange matter and anti-matter?” then the experimental answer is “Yes”, but conventional theory says “No”.

Mirror asymmetry can only be claimed if what is seen in a mirror has no valid physical interpretation. Yet in the case of beta decay, there is an obvious interpretation: the mirror process has exchanged matter and anti-matter. Therefore it is more reasonable to suppose that the theoretical parity operator is incorrect.

Citations:

(1) Lee TD and Yang CN 1956 Question of Parity Conservation in Weak Interactions, Phys. Rev. 104, 254

(2) Wu CS, et al. 1957 Experimental test of parity conservation in beta decay, Phys. Rev. 105, 1413

Created: 27 February 2006; Last updated: 06 April 2024