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It has been conventional wisdom that the fundamental laws of physics are not invariant under parity. A small minority of physicists, however, have taken a different view. They have argued that a so-called mirror world could exist. Nature would then be symmetric under parity. Their so-called exact parity model predicts the existence of so-called ''mirror matter''. Each particle is postulated to have a mirror partner with similar properties (they behave exactly as the mirror image of their partners). This is thus similar to anti-matter, the main difference is that mirror particles and ordinary particles only have very weak interactions, otherwise they would have been detected already.
Mirror particles could thus act as dark matter. Because mirror matter has similar properties as ordinary matter, you could have mirror stars, galaxies, planets etc. Note that mirror stars would be invisible because they would emit mirror photons, which don't interact with ordinary electrons (to be precise there could be a very weak interaction, see below).
Besides gravity, there are other ways that mirror matter could interact with ordinary matter. E.g. a term like in the Lagrangian, where F (F') is the (mirror) electromagnetic field tensor, gives every charged mirror particle an effective ordinary charge that is epsilon times as small. Epsilon would have to be smaller than about 10^(-6). This bound arises from experiments measuring the lifetime of orthopositronium. Positronium is a bound state consisting of an electron and a positron. Positronium with total spin 1 is called othopositronium. A nonzero value for epsilon would cause the eigenstates of the Hamiltonian to be linear combinations of orthopositronium and mirror orthopositronium. So, if you start at t = 0 with orthopositronium, part of it will have oscillated into mirror orthopositronium at a later time t > 0. Once orthopositronium has oscillated into mirror orthopositronium it has effectively disappeared, because it will subsequently decay into three invisible mirror photons. Experiments measuring the decay rate of orthopositronium should thus measure a faster decay rate than predicted. However, it makes a difference if the experiment is performed in vacuum or in some other kind of medium. In a medium containing, say, gas, the frequent collisions between orthopositronium and the gas molecules will inhibit the oscillation of orthopositronium into mirror orthopositronium. This effect is known as the quantum Zeno effect. A nonzero value for epsilon thus manifest itself in a shorter lifetime of orthopositronium in vacuum, while leaving the lifetime in a medium unaffected.
If epsilon is larger than about 10^(-9), a small amount of mirror matter in our solar system would have observable consequences. Interestingly, there are a number of anomalies that could be caused by mirror matter. The anomalous slowing down of the pioneer spacecraft could be caused by a drag force exerted by mirror gas or mirror dust. Another anomaly that could be caused by mirror matter has been observed on the asteroid 433 Eros. It was observed that this asteroid has far fewer craters smaller than 70 meters than had been expected. This can be explained if there are a lot of small mirror matter spacebodies in our solar system. Unlike ordinary objects, a mirror matter object colliding with a body will only leave a crater provided it is large enough. This is because the mirror matter object will penetrate some distance into the body and thus its kinetic energy will be released more slowly than in the case of an ordinary object. If the mirror matter object is larger than this ''penetration depth'', a crater will be formed. The lack of craters smaller than 70 meters suggests that epsilon is between 10^(-7) and 10^(-9). Note that on larger bodies, such as the Moon, the dominant source of small craters are secondary impacts. On such bodies the size distribution of craters should show the usual behavior. Still the crater rates on the Moon does suggest the presence of mirror matter space bodies in our solar system. A recent sky survey detected far fewer potential earth crossing asteroids than had been expected according to earlier estimates by the late Shoemaker. He arrived at a much higher estimate by studying the cratering record on the Moon. Finally there are a number of observations of anomalous meteoritic events that could be caused by impacting mirror matter objects.
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