Time-symmetry violation

After the discovery of the combined charge and space symmetry violation, or CP violation, in the decay of neutral mesons [2], the search for the EDMs of elementary particles has become one of the fundamental problems in physics. A permanent EDM is induced by the super-weak interactions that violate both space inversion symmetry and time reversal invariance [11], Considerable experimental efforts have been invested in probing for atomic EDMs (da) induced by EDMs of the proton, neutron, and electron, and by the P,T-odd interactions between them. The best available limit for the electron EDM, de, was obtained from atomic T1 experiments [12], which established an upper limit of de < 1.6 x 10 27e-cm. The benchmark upper limit on a nuclear EDM is obtained from the atomic EDM experiment on Iyt,Hg [13] as d ig < 2.1 x 10 2 e-cm, from which the best restriction on the proton EDM, dp < 5.4 x 10 24e-cm, was also obtained by Dmitriev and Senkov [14]. The previous upper limit on the proton EDM was estimated from the molecular T1F experiments by Hinds and co-workers [15]. 

Figure 1. Parity (P) and time (T) reversal symmetry violation.

As mentioned earlier, heavy polar diatomic molecules, such as BaF, YbF, T1F, and PbO, are the prime experimental probes for the search of the violation of space inversion symmetry (P) and time reversal invariance (T). The experimental detection of these effects has important consequences [37, 38] for the theory of fundamental interactions or for physics beyond the standard model [39, 40]. For instance, a series of experiments on T1F [41] have already been reported, which provide the tightest limit available on the tensor coupling constant Cj, proton electric dipole moment (EDM) dp, and so on. Experiments on the YbF and BaF molecules are also of fundamental significance for the study of symmetry violation in nature, as these experiments have the potential to detect effects due to the electron EDM de. Accurate theoretical calculations are also absolutely necessary to interpret these ongoing (and perhaps forthcoming) experimental outcomes. For example, knowledge of the effective electric field E (characterized by Wd) on the unpaired electron is required to link the experimentally determined P,T-odd frequency shift with the electron s EDM de in the ground (X2X /2) state of YbF and BaF. 

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. 

Physical applications An early application of relativistic molecular theory was to heavy atom collisions, and the production of supercritical fields involving highly stripped ions [234-237]. Studies have been made of parity- and time-reversal symmetry violation in diatomic molecules [74,238,239], and of parity violation in small chiral molecules [240-242]. 

In a separate contribution [11], we have analysed within the present framework an assessment of the various arrows of time and the possible symmetry violations instigated by gravitation including the fundamental problem of molecular chirality [12]. Other related developments involve Penrose s concept of objective reduction (OR), i.e. gravity s role in quantum state reduction and decoherence as a fundamental concept that relates micro-macro domains including theories of human consciousness [13], see also Ref. [3] for more details. Note also efforts to derive quantum mechanics from general relativity [14]. 

In keeping with the current interest in tests of conservation laws, we collect together a Table of experimental limits on all weak and electromagnetic decays, mass differences, and moments, and on a few reactions, whose observation would violate conservation laws. The Table is given only in the full Review of Particle Physics not in the Particle Physics Booklet. For the benefit of Booklet readers, we include the best limits from the Table in the following text. Limits in this text are for CL=90% unless otherwise specified. The Table is in two parts Discrete Space-Time Symmetries, i.e., C, P, T, CP, and CPT and Number Conservation Laws, i.e., lepton, baryon, hadronic flavor, and charge conservation. The references for these data can be found in the the Particle Listings in the Review. A discussion of these tests follows. 

Cho, D., Sangster, K., and Hinds, EA., Tenfold improvement of limits on T violation in thallium fluoride, Phys. Rev. Lett., 63, 2559, 1989 Cho, D., Sangster, K., and Hinds, E.A., Search for time-reversal-symmetry violation in thallium fluoride using a jet source, Phys. Rev. A, 44, 2783,1991. 

Cold, trapped radioactive atoms open up new experimental opportunities in nuclear physics. Trapped radioactive atoms can be used in experiments on the fundamental symmetries, including experiments on nuclear / -decay, atomic parity nonconservation, and the search for parity-violating and time-reversal-violating electric dipole moments. The first successful experiments on the trapping of radioactive atoms were performed with the isotope Na (Lu et al. 1994). It is expected that further activity in this direction will be concentrated on efforts to undertake meaningful measurements with trapped radioactive species. 

On the other hand, the permanent EDM of an elementary particle vanishes when the discrete symmetries of space inversion (P) and time reversal (T) are both violated. This naturally makes the EDM small in fundamental particles of ordinary matter. For instance, in the standard model (SM) of elementary particle physics, the expected value of the electron EDM de is less than 10 38 e.cm [7] (which is effectively zero), where e is the charge of the electron. Some popular extensions of the SM, on the other hand, predict the value of the electron EDM in the range 10 26-10-28 e.cm. (see Ref. 8 for further details). The search for a nonzero electron EDM is therefore a search for physics beyond the SM and particularly it is a search for T violation. This is, at present, an important and active held of research because the prospects of discovering new physics seems possible. 

I would like to draw attention here to some work on chiral molecules, which allows very fundamental tests of symmetries in physics and chemistry. The experiment outlined in Scheme 2 [4] allows us to generate, by laser control, states of well-defined parity in molecules, which are ordinarily left handed (L) or right handed (R) chiral in their ground states. By watching the time evolution of parity, one can test for parity violation and I have discussed in detail [4-6] how parity violating potentials AEpv might be measured, even if as... 

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... 

In 1964 Cronin and Fitch [14, 15] showed experimentally by studying the decay of kaons that the combined operation CP is not an exact symmetry of Nature. This discovery is even more perplexing when viewed in the context of time evolution. If the (so far unchallenged) CPT theorem is to hold, then violations of joint CP symmetry imply violations of T symmetry (with T reversing the motion of particles). The laws of physics are therefore not the same when the time changes direction. 

Even if allowed by the CPT theorem, the non-conservation of CP symmetry was hard to accept - not least because it was not consistent with the Standard Model. In 1972, Kobayashi and Maskawa predicted that CP violation would be consistent with the Standard Model provided that three generations of quarks exist (and only two were known at the time). The subsequent discoveries of the r lepton by Pearls (1975) and of the top and bottom quarks at the Fermilab confirmed the existence of a third family, this resulted in the incorporation of the CP violation into the Standard Model. 

Time dependences of the phases Aa and AE are shown in Figure 7.16. Despite the erratic nature of these phases, it is seen that the states of different symmetry evolve in parallel. The shapes Ea and Eb show almost no difference in the realization. Moreover, at T Tc/8, the difference of phases in the E and A states is to a good accuracy the same as at T = 0. In other words, coupling to a stochastic reservoir violates coherence only slightly, and the tunneling splitting may be observed at temperatures up... 

In 1977, Sharpless proposed the intermediacy of a four-membered metal-lacycle in the oxidation of cyclododecene by Cr02Cl2.60 This was an attempt to explain a minor but primary product, in which an oxygen and a chlorine were added in a syn fashion to one face of the /3-bond. Later, this type of intermediate was incorporated into a new mechanism for osmylation,61 in which an initial [2 + 2] cycloaddition led to an osmaoxetane which in a second step underwent ring expansion to form the observed metal diolate product. At the time, the [2 + 2] process was viewed as a violation of orbital symmetry rules, and it was not until the extensive work in the 1970s and 1980s on cycloadditions to metal carbenes that a theoretical basis for such a process allowed its broader acceptance. 

The variable-sign result Eq. (81) produces results that fail to satisfy such time-reversal symmetry, as shown by Andrews et al. [50], The requirement for temporal symmetry remains unequivocal, despite the violation of time-reversal invariance by the system itself (its engagement of molecular interaction with the bath leading to state decay), specifically because of the inclusion of damping. The two conventions agree in ostensibly the most crucial signing, that which relates to potentially resonant denominator terms they differ in antiresonant terms. Nonetheless, in certain processes they can lead to results with experimentally very significant differences. 

At that time, in the 1950s, there was a problem whereby the calculations from quantum electrodynamics for the Lamb shift, 2 Si/2 — 2P /2 in the states of hydrogen, were not in exact agreement with the measurements. Thus it occurred to me that a small violation of parity symmetry in the electromagnetic interaction might be responsible for this discrepancy. 

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