Mirror Matter and Positronium In part II we have seen that astronomical observations have revealed tantalizing evidence that mirror matter really exists in the Universe. Despite our inability to see it, we can (tentatively) infer its existence by its gravitational effects. Actually, this is not the only place to search for mirror matter. If it exists its effects will be felt on the Earth as well as in the Heavens. Such terrestrial effects are of crucial importance since they allow the idea to be put under ‘the microscope’, thereby providing a means of potentially rigorously proving that mirror particles really exist. Mirror matter on Earth and in the Heavens There are two broadly different ways in which mirror matter can show itself. One is its implications for some of the largest objects known: planets, stars and galaxies. Mirror matter is important on these very large scales because it is influenced by gravity. What about the influence of mirror matter on microscopic particle processes? I have already explained that mirror matter and ordinary matter do not interact with each other by any of the known forces, except via gravity. Is it possible for new types of interactions to connect ordinary and mirror matter? Certainly such interactions would have to be very small if they exist, but the question is they exist? The answer is yes – but in only two ways. In this and subsequent chapters I will describe these new types of interactions and explain how their effects may be observed. In fact, there is evidence that the observable effects have already been observed! I have discussed earlier that the interactions of sub-atomic particles seem to obey various symmetries such as rotational symmetry, translational symmetry and more abstract symmetries called Lorentz and gauge symmetry. The gauge symmetries govern the three nongravitational forces: electromagnetism, strong and weak nuclear forces, while gravity can be related to the curvature of space-time. This distinction between the gravitational and non-gravitational forces is the reason why we expect both ordinary and mirror particles to experience the same gravitational force. Ordinary and mirror particles live in the same space-time so they are both affected by the curvature of space-time. For example, the motion of an ordinary planet orbiting around a star does not depend on whether the star is made of ordinary matter or mirror matter because the curvature of space-time is simply due to the star’s mass. However, the three nongravitational forces are related to symmetries on an ‘internal’ space which is nothing to do with space-time. Nobody has ever seen this internal space, so it is not known how big it is or how many symmetries it contains. For this reason it is possible for ordinary and mirror particles to have independent but otherwise identical gauge symmetries. The effect of this is that the non-gravitational forces can act separately on ordinary and mirror particles. Given these symmetries, the only way in which ordinary and mirror matter can interact with each other besides gravity is through ‘transition forces’ mixing ordinary with mirror particles. This type of interaction can only occur for neutral particles, since the conservation of ordinary electric charge forbids, for example, an electron from becoming a mirror electron. Ordinary and mirror particles have independent gauge symmetries which means that mirror particles have no ordinary electric charge. (However they do have mirror electric charge). The only known fundamental neutral particles are photons and neutrinos. One might also add the neutron, but actually the neutron (and proton) are not believed to be really elementary. Indeed, as I already mentioned in chapter 2, neutrons and protons are believed to be composed of quarks. The only thing that we really need to know about all this is that there aren’t any neutral quarks, so there can’t be any quark-mirror quark transition forces. Thus, it seems that symmetry arguments do not forbid transition forces between photons and mirror photons and also between neutrinos and mirror neutrinos. One thing that we have learned from the study of particle interactions is that if something is not forbidden then it usually occurs, and so it is worth taking such effects seriously. To summarize, there are only two ways for the (known) ordinary and mirror particles to interact with each other besides gravity. That is, by a photon-mirror photon transition force (also called ‘mixing’ force), and by neutrino-mirror neutrino mixing. The effect of neutrino-mirror neutrino mixing and the substantial evidence for it will be described later on. Our purpose now is to describe the effects of photon-mirror photon mixing. Photon-Mirror Photon mixing What effect does photon-mirror photon transitions have? As I discussed in Chapter 2, microscopic interactions can be discussed in terms of interaction diagrams. The photon-mirror photon transition force is represented by the interaction diagram shown in Figure 5.1. Figure 5.1: The photon-mirror photon transition force is simply represented by a ‘cross’ interaction in which a (virtual) photon ( ) turns into a (virtual) mirror photon ( ). The parameter characterises the strength of the transition force, in much the same way in which the electric charge ( ) characterises the strength of electromagnetism.Recall that the photon is the force particle for electromagnetism. The electromagnetic force arises fromthe interactions of the charged elementary particles, electrons and protons with each other through the exchange of an ordinary (virtual) photon. In the case of electrons this was illustrated in Figure 2.2. In the absence of any photon-mirror photon mixing, an ordinary electron cannot interact with a mirror electron because ordinary photons do not interact with mirror electrons (and mirror photons do not interact with ordinary electrons). However, if there is a photonmirror photon transition force, then now an ordinary electron can actually interact with a mirror electron. What happens is that the ordinary electron can emit a photon which then undergoes a transition to a mirror photon which then interacts with the mirror electron. This effect is illustrated in the interaction diagram given in Figure 5.2. The net effect of the transition force is to make mirror electrons interact slightly with ordinary electrons. That is, mirror electrons behave as if they have a tiny ordinary electric charge. The size of the effect depends on the strength of the photon-mirror photon transition force – which is characterised by the parameter . If I use the symbol for the ordinary charge of an electron, then the mirror electrons effectively have an ordinary electric charge of (and ). [A similar effect also happens for mirror protons too]. This is really very important if it exists. It means that ordinary and mirror matter can repel (or attract) each other. In chapters 1,2 the merits of trying to pick up a rock made of mirror matter was discussed. It was suggested that a mirror rock would fall through our hand and the Earth as well, because it was assumed that the only force acting between ordinary and mirror matter was gravity. In the introductory discussion I neglected the possibility that an ordinary photon-mirror photon transition force could exist. If this force does exist then a rock made of mirror matter may not fall through our hand when we pick it up. The point is that the force of gravity is not very strong and even a small electromagnetic coupling can be enough to oppose the feeble gravitational force. An important question to answer is to find out what the strength of this new force is. That is, how big is ? Clearly, if the force connecting ordinary and mirror matter was big enough then its effects would have already shown up in laboratory experiments. An obvious place to start is by looking at experiments searching for exotic particles with tiny ordinary electric charges. There have been such experiments, and the most sensitive laboratory limit on these ‘milli charged particles’ implies that . However, this is not the most sensitive way to search for the mirror world effect. Sometimes things are more subtle. The question that needs to be asked in this type of situation is the following. Out of all the experiments that have been done in the history of the world, which experiment would be most sensitive to photonmirror photon mixing? The answer it turns out is the effects on a system called ‘orthopositronium’ – a weird type of atom composed of matter and anti-matter.
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