TCP theorem

Elementary particle physics has explored the notion that there is a ‘Lagrangian for the universe’, a key that will unlock all the doors of reality. Over the decades, various symmetries of the currently understood Lagrangian have come and gone. An important development was the overthrow of parity, that is, the observation that the laws of physics are not totally left-right symmetrical.

As more and more details of the Lagrangian of the Standard Model were acquired, one dominant theme emerged. There were various symmetry operations, such as spatial inversion P, charge conjugation C, and time reversal T, that individually might be broken. However, a theorem in quantum field theory asserts that the combination CPT is a true symmetry of the universal Lagrangian Lv, that is, (CPT)LV (CPT)-1 = Lv. Equivalently, [CPT, Lv] = 0. From this it follows that if any two of these operations together do not commute with Lv then the third does not commute either.


Kaons are a quartet of unstable elementary particles, some of which have unusual properties involving time. The four species of Kaon are denoted K +, K-, K0, and K°. In the standard model, Kaons are described as bound states with the quantum numbers of a quark and an antiquark.

The K+ and K~ are antiparticles of each other and have equal and opposite electrical charge and the same rest mass. Their lifetime is of the order 1.2 x 10-8 seconds, which is regarded as extremely slow compared to the fastest decay lifetimes observed in particle physics (typically 10-24seconds). The decay of these Kaons has no unusual properties.

The really interesting Kaons are the K0 and the K°. These are antiparticles of each other, having electrical charge zero. There are three unusual temporal properties of these Kaons that can be understood if the and are considered superpositions of two very different components denoted KS (short) and KL (long). The KL has a much longer lifetime than the KS, living about one thousand times longer. This has the following consequences.

When a beam consisting of particles was created in some apparatus and carefully monitored in flight, it was observed that the beam would turn into a beam of particles and then back into a beam of particles, and so on. This known as oscillation.

When a beam of K0 particles is directed onto a target, the short-lived component KS can decay before the beam reaches the target, leaving a pure beam of KL. But those objects can be considered a superposition of and K°. When they hit the target, these two components react differently with the matter in it, resulting in an emergent beam that now contains some KS component. This is the phenomenon known as regeneration.

Finally, it was observed that some decays of the KL component violated CP symmetry: before decay, the KL is an eigenstate of CP with eigenvalue -1 but some decays with eigenvalue +1 were observed. The spectacular inference from this is that Kaon physics does not respect T symmetry.

The complete implications of these results are still to be understood and time reversal remains an active area of theoretical and empirical research.

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