CPT symmetry

This dipole s broken 3-space symmetry in EM energy flow, provides a relaxation to a more fundamental EM energy flow symmetry in 4-space where P and T symmetries are broken but CPT symmetry is maintained. 

On the most fundamental level, we have shown how this experimental scheme might be used for a fundamental test of CPT symmetry violation [8]. While still somewhat hypothetical, at present, this would constitute the most sensitive currently proposed test on CPT symmetry. The sensitivity expressed as a baryon mass difference Am between particles and antiparticles (with mass m) would be of the order of Am/m = 10"30 [8]. The best currently proposed other experiment is on antihydrogen spectroscopy at CERN (not yet carried out) with Am/m = 10 18, and the best existing result for the proton-antiproton pair is Am/m < 10 9 [9]. 

Time reversal invariance describes the fact that in reactions between elementary particles, it does not make any difference if the direction of the time coordinate is reversed. Since all reactions are invariant to simultaneous application of mirror inversion, charge conjugation, and time reversal, the combination of all three is called CPT symmetry and is considered to be a very fundamental symmetry of nature. 

There has been an unusual amount of debate concerning the development of 0(3) electrodynamics, over a period of 7 years. When the 2 (3) field was first proposed [48], it was not realized that it was part of an 0(3) electrodynamics homomorphic with Barrett s SU(2) invariant electrodynamics [50] and therefore had a solid basis in gauge theory. The first debate published [70,79] was between Barron and Evans. The former proposed that B,3> violates C and CPT symmetry. This incorrect assertion was adequately answered by Evans at the time, but it is now clear that if B<3) violated C and CPT, so would classical gauge theory, a reduction to absurdity. For example, Barrett s SU(2) invariant theory [50] would violate C... 

There are both theoretical and experimental reasons to search for CPT violations. The strong theoretical incentive is that, even though the CPT invariance is required to formulate a quantum field theory consistent with special relativity, it turns out to be difficult to construct a gravitational relativistic quantum field theory of the GUT type with the CPT symmetry maintained. In other words it is difficult to incorporate the CPT invariance in the GUT-type extensions of the Standard Model. 

An experiment aiming at the production of cold antihydrogen is presently being conducted at CERN. Hence it will be feasible to test CPT symmetry by the direct comparison of the spectroscopic properties of the simplest atom and its antiatom. 

What can be tested As mentioned before, CPT invariance guarantees the equality of masses, charges and lifetimes of particles and antiparticles. This means that the experimental investigations of masses, charges, etc. of particle - antiparticle pairs are tests of CPT symmetry. Such experiments are not easy to do with the charged particles themselves (because of their interactions with stray fields). Comparison of neutral atom - antiatom pairs is much more convenient. In particular, the fine structure, hyperfine structure and Lamb shifts of atoms and antiatoms should be identical - and can be tested in laboratory. 

In the absence of a direct measurement on antiprotons and protons one can use various indirect arguments to study the compliance of antiparticles with the WEP. In this context it is important to note that if the antiproton or the positron violate the WEP, this would not imply a violation of energy conservation [14] or of CPT symmetry [15]. 

The apparent violation of global CPT symmetry has no other explanation but that an equal amount of antimatter exists elsewhere so as to ensure an overall balance. Since the time axis needs to be reversed in whatever region the antimatter exists, time symmetry will be restored as well. It should be obvious that reversal of the time axis could be the result of continuous symmetry breaking along a manifold, curved in such a way as to produce an involution. This proposition is discussed in chapter 7. 

Why study antihydrogen Because hydrogen, in its antimatter form, provides the opportunity to test two bedrock principles of physics CPT symmetry and the equivalence principle. Once again, the hydrogen atom begs the attention of physicists, who will look to it for enlightenment. 

CPT symmetry is deeply embedded in fundamental physics. One can prove that quantum field theory and special relativity (as we currently understand these theories) respect CPT symmetry. If CPT were to be proven invalid, contemporary physics would be scrambled. 

The antihydrogen atom puts both the CPT symmetry principle and the equivalence principle to the most exacting test now conceived. Before considering how this can be done, it is appropriate to consider briefly how the antiproton and the positron can be brought together to form antihydrogen. Dan Kleppner said in 1992 at a workshop in Munich, in the past six years the creation of antihydrogen has advanced from the totally visionary to the merely very difficult. Since 1992, the merely very difficult remains very difficult. 

Whereas energy appears to be distributed almost continuously, compared to matter, the distribution of matter presents the more tractable problem. When delving into the nature of matter, in its most elementary state, it is encountered in two antagonistic forms with equal probability. These two forms, called matter and anti-matter are best considered as the complementary forms of elementary stuff in two symmetry-related modes of existence. Symmetry-related units of matter and antimatter have the same mass but opposite electric charges and behave in opposite sense with respect to time. This relationship obeys the dictates of what is probably the most fundamental symmetry in Nature, known as CPT (charge conjugation-parity-time inversion) symmetry. Wherever it has been investigated, all natural phenomena have been found to obey CPT symmetry without exception. 

The alternative of increased space-like curvature results in relentless compression that compacts all matter into infinitesimal space with parity inversion at ZjN = 0. Our contention is that these alternatives are inseparable in curved space-time where inversion of total CPT symmetry occms on compression. 

Analysis of the periodicity of atomic matter therefore guides us to a projective model of a closed imiverse in the double cover of four-dimensional projective space-time. Transport across the interface, or along the involution, results in the inversion of CPT symmetry. 

To avoid the problem of CPT symmetry standard cosmology makes the empirical assumption that the universe contains no anti-matter and that all cosmological models need to explain this observation. This is clearly an unsubstantiated assumption because spectroscopic observation, on which astronomy relies, cannot distinguish between material and anti-material galaxies. 

Inflation also distorts the mass budget of the universe so badly that less than 1% of the total mass appears visible, but this is the total mass that neatly balances the large-number coincidences of the anthropic principle. The excess must therefore be non-baryonic matter, for which there is no evidence. At the same time, the equal mass of antibaryons, implied by CPT symmetry, is declared non-existent. Antileptons are simply ignored. 

There are no separate matter and antimatter domains as chiral forms transform smoothly into each other, preserving an element of CPT symmetry in the interface. 

My assessment is that Oldershaw has identified a major symmetry of the cosmos, but like most symmetries in Nature, it is not perfect. Extrapolation to infinities and singularities is therefore not valid. A major deficiency is the failure to recognize CPT symmetry and the role of antimatter which, in our view, implies a closed universe. 

Figure 3.9 provides an overview of chiral molecules in their four different enantiomeric forms being made of matter and antimatter. As we have discussed in [29], spectroscopic investigations of these four isomeric molecules are well suited, in principle, for a very exact test of the underlying CPT symmetry of the combination of C, P, and T. Such experiments are certainly imaginable [23] with sources of antimatter being in principle available today however, they are not to be expected in the near future. 

Fig. 3.9 Diagram of enantiomeric molecules (L and R) made of matter and antimatter (L and R ) with the notation Left and Right, used by physicists for the enantiomers instead of D/L or R/S. With CPT symmetry, the pair L and R (L and R) have the same energy. Thus,...

The demonstration [1] that both Lorentz transformation and quantum spin are the direct result of quaternion rotation implies that aU relativistic and quantum structures must have the same symmetry. This is the basis of cosmic self-similarity. The observation that the golden mean features in many known self-similarities confirms that r represents a fundamental characteristic of space-time curvature. The existence of antimatter and the implied CPT symmetry of space-time favors... 

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