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The mysterious influence of CPT on the rules of the universe: Is our universe really unique?
In physics, CPT symmetry, namely charge conjugation (C), quark symmetry (P) and time reversal (T), is the fundamental symmetry underlying all natural laws. This symmetry is considered to be the only absolute symmetry at the fundamental level. According to the CPT theorem, CPT symmetry holds for all physical phenomena, which means that any local quantum field theory that is Lorentz invariant and has a Hermitian Hamiltonian must have CPT symmetry.
Historical Background"CPT symmetry is a profound and beautiful law of nature that reveals the structure of the universe and the boundaries at which it operates."
The CPT theorem first appeared in 1951, in the work of Julian Schwinger, who implied this concept of symmetry. This was followed by a more explicit proof by Hertha Lüders and Wolfgang Pauli in 1954, and is sometimes referred to as the Lüders–Pauli theorem. At the same time, John Stewart Bell independently proved the theorem.
These proofs are based on the Lorentz invariance and locality principles. This was followed in 1958 by Les Yost, who gave a more general proof in the framework of postulated quantum field theory. As the research deepened, scientists discovered that the phenomena involved in weak interactions showed violations of P symmetry, and cases of C symmetry violations were also common. Initially, CP symmetry was thought to be unviolated, however this was also found to be incorrect in the 1960s, meaning that T symmetry was also violated according to CPT invariance.
Derivation of CPT Theorem
Considering the Lorentz lift in a fixed direction z, this can be interpreted as a rotation of the time axis into the z axis with an imaginary rotation parameter. If this parameter is true, a rotation of 180° will reverse the direction of time and z. In any dimension, reversing an axis is a reflection of space. This process can be explained using the Feynman–Stueckelberg antiparticle theory as the corresponding particle moving in reverse time. This explanation requires a slight analytical continuation, which is explicit under the following assumptions: the theory is Lorentz invariant; the vacuum is Lorentz invariant; the energy lower bound is bounded.
When the above conditions are met, quantum theory can be extended to a Euclidean theory by converting all operators into imaginary time. The commutation relation between the Hamiltonian and the Lorentz generators ensures that Lorentz invariance implies rotational invariance, so that any state can be rotated 180 degrees. According to CPT reflection, fermions will change sign after two CPT reflections, while bosons will not. This property can be used to prove the spin-statistics theorem.
Consequences and Implications
The meaning of CPT symmetry is that if there is a "mirror" of our universe, the positions of all objects are reflected through an arbitrary point (corresponding to symmetry inversion), all momentum is reversed (corresponding to time reversal), and all matter If antimatter were substituted (corresponding to a reversal of charge), such a universe would evolve according to the same physical laws. The CPT transformation transforms our universe into its "mirror image" and vice versa. Therefore, CPT symmetry is recognized as a fundamental property of the laws of physics.
To maintain this symmetry, any violation of a symmetry in two of its components (such as CP) must have a corresponding violation in a third component (such as T); in fact, mathematically speaking, these It's the same thing. Therefore, the violation of T symmetry is often called CP violation. The CPT theorem can be generalized to consider the case of pin groups. In 2002, Oscar Greenberg showed that, under reasonable assumptions, CPT violation implies a violation of Lorentz symmetry.
Some string theory models, as well as some models beyond point-particle quantum field theories, might expect CPT violations. Certain proposed violations of Lorentz invariance, such as compact dimensions with cosmological scales, could also lead to CPT violations. Furthermore, non-unit theories, such as the proposal that black holes violate unitarity, may also violate CPT as a technical point, fields with infinite spin may violate CPT symmetry. To date, the vast majority of experimental detections of Lorentz violations have come back negative. In 2011, Kostelecky and Russell conducted a detailed statistical analysis of these results.
We may be able to gain new insights into the way the universe works from CPT symmetry, but what is its deeper meaning? Does this mean that our universe is just one of an infinite number of possible multiverses?
