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Breaking the rules of space-time? The possibility and challenge of CPT symmetry violation!
Charge (C), parity (P), and time-reversal (T) symmetries play a key role in the fundamental laws of physics. The combination of these quanta forms CPT symmetry, which is believed to be the only precise symmetry observed in nature at a fundamental level. According to the CPT theorem, all Lorentz-invariant local quantum field theories must possess this symmetry. In other words, if there is an antimatter, mirror, and time-reversed universe, the laws of physics should be exactly the same as our own. Such a claim is thought-provoking: Under the concept of the multiverse, is there an antimatter universe that we cannot actually observe?
History
The CPT theorem first appeared in 1951, when Julian Schwinger attempted to prove the connection between spin and statistics. In 1954, Gerd Lüders and Wolfgang Pauli gave a more explicit proof, and the theorem is sometimes called the Lüders–Pauli theorem. Later, John Stewart Bell also proved this theorem independently.
These proofs are based on the principles of Lorentz invariance and locality in quantum field interactions.
With the research in the late 1950s, researchers discovered that the violation of P symmetry in weak interactions gradually surfaced. At the same time, reliable violations of C symmetry also occur. Although CP symmetry was once thought to be preserved, research in the 1960s revealed that this belief was wrong, and T symmetry was also found to be violated based on CPT invariance.
Derivation of CPT Theorem
The process of deriving the CPT theorem involves the understanding of Lorentz lifting, which can be viewed as an operation of rotating the time axis to the Z axis. If the rotation parameter is a real number, then a 180 degree rotation will reverse the time and Z directions. Such changes are a reflection of space for any dimension of space.
Using the Feynman-Stuckelberg theory, we can think of antiparticles as their counterparts running in reverse time.
This interpretation requires a slight analytic continuation and is only well defined if the following assumptions hold: the theory is Lorentz invariant, the vacuum is Lorentz invariant, and the energy is bounded downward. When these conditions hold, quantum theory can be extended to Euclidean theory. Due to the commutation relation between the Hamiltonian operator and the Lorentz generator, Lorentz invariance is guaranteed to be equivalent to rotational invariance, so any state can be rotated 180 degrees. This fact can be used to prove the spin-statistics theorem.
Consequences and Implications
The significance of CPT symmetry is that the "mirror" of our universe will be exactly the same in terms of physical laws, that is, the position information of all objects will be arranged through reflection at any point, all momentum will be reversed, and all matter will be replaced by antimatter.
The CPT transformation turns our universe into its "mirror image" and vice versa.
Therefore, CPT symmetry is considered to be a fundamental feature of the laws of physics. In order to preserve this symmetry, the breaking of the symmetry of any two components (such as CP) must correspond to the breaking of a third component (such as T). And mathematically, these are the same. The violation of T symmetry is often called CP violation. It is worth mentioning that the CPT theorem can be generalized to consider nail groups under certain conditions. In 2002, Oscar Greenberg showed that under reasonable assumptions, CPT violation implies a violation of Lorentz symmetry.
Phenomena related to CPT violation are predicted by some superstring theory models and some models of quantum field theories beyond point particles. Some scientists believe that compact dimensions such as the size of the universe may also lead to CPT violations, while non-unit theories, such as black holes, which violate unitarity, may also violate CPT. It is worth noting that fields with infinite spin may violate CPT symmetry. So far, most experiments on Lorentz violation have not yielded positive results, and in 2011 Kosteltsky and Russell conducted a detailed statistical analysis of this result.
With further exploration of CPT symmetry and its violation, we may be able to reveal deeper mysteries of the universe. But in this process, how will science challenge traditional ideas and positions?
