Vectors and Axial Vectors and What it all Means
To understand the two experiments in question, you just have to know a few new physics concepts: the difference between vectors and axial vectors and how they behave differently under reflection. A vector describes quantities like position or momentum that have a both magnitude and a direction. When a vector is mirror image reflected in space all its coordinates simply take negative values. When two vectors are used to form a cross product resulting in a third vector, the third vector is a special type of vector called an axial vector. The components of an axial vector won't change sign under reflection. Because the normal vectors that went into the cross product both change sign when they are are reflected, the two sign changes result in an additional product of -1 times -1 which equals +1, see picture 1 . Consequently, the components of the axial vector do not change sign under mirror image reflection.
What Wu et al. and Garwin et al. saw was that the electrons emitted from each of their experiments had a preferred direction of travel with respect to the spin of the Cobalt 60 nucleus in Wu's case, and with respect to the spin of the incident muon in Garwin's case. Once that preferred direction was measured, the rest was history. If the experiment were reflected in a mirror, the direction of the spin of the nucleus or muon would not change, but the momentum of the electron, (and hence its preferred direction of travel), would change making the mirror image imperfect. This is shown in the figure adapted from Cottingham shown below in picture 2. The thick orange arrows labeled as cobalt 60 indicate the direction of the spin of the Cobalt nucleus.
Coming back again to how small the world of physics is, this morning as I was searching for my papers on Yang and Lee's study of parity violation in beta decays and Wu's subsequent experiment, I came across an earlier paper by Fischbach, who's recent paper on seasonal variations in beta decay led me to my recent foray into all things beta decay and neutrino, (now that my friends is a run-on sentence!). In 1981, Fischbach, Freeman, and Cheng authored a paper that studied the quantum mechanical Hamiltonians of both normal and anti-matter hydrogen-like atoms suspended in a gravitational field. They were looking for aspects of quantum gravity that could be tested experimentally.
So, why did this come up in my search for beta decay papers? Fischbach and Freeman were actually being hosted by Yang at Stony Brook University when they wrote the paper. In other interesting news, Freeman had gone on to work for Hughes Aircraft, either a sister or descendant company of Hughes Research, where Robert Forward was working in the 60's when he wrote his papers on linearized general relativity and communicated with Bryce DeWitt regarding his superconductor as gravitomagnetism detector work.
1. Post-Newtonian gravity
2. Fischbach on hydrogenic gravity
Fischbach E., Freeman B. & Cheng W.K. (1981). General-relativistic effects in hydrogenic systems, Physical Review D, 23 (10) 2157-2180. DOI: 10.1103/PhysRevD.23.2157
3. Forward on linearized gravity and other thigns
4. Test of space tethers as proposed by Forward
5. Lee and Yang
Lee T. & Yang C. (1956). Question of Parity Conservation in Weak Interactions, Physical Review, 104 (1) 254-258. DOI: 10.1103/PhysRev.104.254
6. Wu's experiment
Wu C.S. (1957). Experimental Test of Parity Conservation in Beta Decay, Physical Review, 105 (4) 1413-1415. DOI: 10.1103/PhysRev.105.1413
7. Garwin et al.'s experiment
Garwin R., Lederman L. & Weinrich M. (1957). Observations of the Failure of Conservation of Parity and Charge Conjugation in Meson Decays: the Magnetic Moment of the Free Muon, Physical Review, 105 (4) 1415-1417. DOI: 10.1103/PhysRev.105.1415
8. An Introduction to Nuclear Physics
Cottingham W.N. & Greenwood D.A. An Introduction to Nuclear Physics, DOI: 10.1017/CBO9781139164405