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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). “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?” If electrons have mirror-image particles which occur in nature, but less often than electrons, we will say that parity is violated but nature is mirror-symmetric. Hence “maximal parity violation” will be called “mirror asymmetry”, and lack of “maximal parity violation” will be called “mirror symmetry”.

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”. The conventional parity operator was originally interpreted to imply that beta decay would be equally likely to yield beta particles parallel and anti-parallel to the nuclear spin. This prediction was incorrect and should have led to a rapid demise of the theory behind it. But instead of adapting the theory to match the observed mirror symmetry of matter and antimatter (the usual scientific method), new particles were invented to explain the mirror image. These so-called “mirror particles” have never been observed, and their lack of existence has since been attributed to yet another unobserved particle: the Higgs boson. This procedure violates the principle of parsimony. Occam's razor should be invoked to remove these additional unseen particles in favor of the simpler theory which explains all the experimental results in terms of known particles.

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 mirror symmetry is conserved and the theoretical parity operator is incorrect. Other claims of maximal parity or PC violation are also based on a flawed theory of spatial inversion.

Errors in the conventional derivation of the parity operator are described in the paper, "The Mirror Symmetry of Matter and Antimatter". The conventional parity operator requires the existence of a mixed-parity vector space, defined relative to velocity, which is otherwise isomorphic to the spatial axes. The conventional parity operator inverts only two of these three relative axes. A proper spatial inversion operator is derived which inverts all three of the relative velocity axes. The new spatial inversion operator exchanges matter and anti-matter, consistent with experimental observations. A new time reversal operator is also derived, which preserves the handedness of the same relative velocity coordinates.


(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: 10. October 2009

Copyright © 2006-2008  Robert A. Close