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Symmetry means that something is unchanged after some sort of operation. In the case of geometrical symmetry it is the configuration that remains the same after rotating 180o as shown in Figure 01ea. Whereas in theoretical physics symmetry the invariance is about the form of the equations before and after the transformation. Symmetry in mathematical expressions constrains the form from an infinite number of choices, it also allows extraction of information without deluging in detailed computation. A good example is the conservation laws emerging from the global symmetry of the equations. Some people see beauty in such formulation. | ||
Figure 01ea Symmetry |
Figure 01eb Conservation |
Figure 01fa Parity |
Figure 01fb Parity Violation |
However, it was demonstrated conclusively in 1957 by an experiment that parity conservation is violated in weak interaction (Figure 01fb). |
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Figure 01fc Parity, Even and Odd [view large image] |
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Figure 01fd Time Reversal, Symmetry and Violation |
Figure 01fd shows the time reversal invariance in physical law and quantum process with T represents the operation. It also portrays a sequence of time irreversible implosion. |
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Figure 01fe CPT for Electron |
There were many tests of CPT invariance over the years. The latest one in 2015 achieved an accuracy of several parts per trillion in its chance of being wrong. The test compares the cyclotron frequencies of antiproton p- and protron p+ (in the form of H- atom for technical reason) by running them alternatively in the machine. As the formula shown in Figure 01ff, for a constant magnetic field B the cyclotron frequency is proportional to the charge to mass ratio q/m. After correcting the effect of the electrons in the H- atom, the cyclotron frequency | |
Figure 01ff Test for CPT Invariance with Cyclotron |
ratio is calculated to have the value : [(q/m)p-/(q/m)H-]cal = 1.001089218754(2) if CPT invariance holds. Results from 6500 measurements yield : [(q/m)p-/(q/m)H-]exp - [(q/m)p-/(q/m)H-]cal = 1(69)x10-12. |