Mirror Symmetry

From: Saibal Mitra <smitra.domain.name.hidden>
Date: Sun, 3 Feb 2002 17:13:40 +0100

It has been conventional wisdom that the fundamental laws of physics are not invariant under parity. Now, the computational complexity of a model that lacks mirror symmetry is much larger than a similar mirror symmetric model. It would thus be very strange if Nature is indeed 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 there partners, e.g. mirror neutrino's would be right-handed). This is thus similar to anti-mater, the main difference is that mirror particles and ordinary particles only have very weak interactions, otherwise they would have been detected already (mirror neutrino's would thus appear to be sterile right-handed neutrinos).

Mirror particles could thus act as dark matter. Now, 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

$ \frac{\epsilon}{2} F_{\mu,\nu} F\prime^{\mu,\nu} $

in the Lagrangian, where $ F\prime $ 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^-4 to avoid conflict with experiments performed to detect millicharged particles.

 In the last few years Dr. Foot has proposed that epsilon could be about
10^{-6} (see [2]). That value would nicely explain the ortho-positronium lifetime puzzle. Positronium is a bound state consisting of an electron and a positron. Experiments have yielded conflicting results for the lifetime of this system. A nonzero value for epsilon would cause the eigenstates of the Hamiltonian to be linear combinations of positronium and mirror positronium. So, if you start at t = 0 with positronium, part of it will have oscillated into mirror positronium. If you measure the rate of decay of positronium you have to take this into account. Once positronium has oscillated into mirror positronium it has effectivly disappeared, because it will subsequently decay into three invisible mirror photons. Now, 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 positronium and the gas molecules will inhibit the oscillation of positronium into mirror positronium. This effect is known as the quantum Zeno effect. It was precisely the experiment that was performed in vacuum that had reported the shortest lifetime for ortho-positronium.

 However, a value as large as 10^-6 for epsilon would mean that a mirror meteor hitting the earth would dissipate its energy over a distance of about 10 cm (assuming an impact velocity of about 60 km/s). Large mirror meteors would thus behave in a similar way as ordinary meteors. Of course, no trace of the meteor would be found, but the crater would be just as large (see [5]).

Recently a 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. Maybe there are a lot of invisible mirror meteors out there!



[1] Seven (and a half) reasons to believe in Mirror Matter: From neutrino
puzzles to the inferred Dark matter in the Universe
      R. Foot
      Acta Phys.Polon. B32 (2001) 2253-2270
  ( http://xxx.lanl.gov/abs/astro-ph/0102294 )

[2] Can the mirror world explain the ortho-positronium lifetime puzzle?
      R. Foot, S. N. Gninenko
     Phys.Lett. B480 (2000) 171-175
    ( http://xxx.lanl.gov/abs/hep-ph/0003278 )

[3] Have mirror planets been observed?
     R. Foot
     Phys.Lett. B471 (1999) 191-194
     ( http://xxx.lanl.gov/abs/astro-ph/9908276 )

[4] Have mirror stars been observed?
     R. Foot
     Phys.Lett. B452 (1999) 83-86
     ( http://xxx.lanl.gov/abs/astro-ph/9902065 )

[5] The mirror world interpretation of the 1908 Tunguska event and other
more recent events
     R. Foot
     Acta Phys.Polon. B32 (2001) 3133
    ( http://xxx.lanl.gov/abs/hep-ph/0107132 )

[6] A mirror world explanation for the Pioneer spacecraft anomalies?
      R. Foot, R. R. Volkas
      Phys.Lett. B517 (2001) 13-17
      ( http://xxx.lanl.gov/abs/hep-ph/0108051 )

[7] Mirror World versus large extra dimensions
     Z.K. Silagadze
     Mod.Phys.Lett. A14 (1999) 2321-2328
    ( http://xxx.lanl.gov/abs/hep-ph/9908208 )

[8] A quest for weak objects and for invisible stars

[9] TeV scale gravity, mirror universe, and ... dinosaurs
      Z.K. Silagadze
     Acta Phys.Polon. B32 (2001) 99-128

[10] Mirror objects in the solar system?
        Z.K. Silagadze
Received on Sun Feb 03 2002 - 08:23:50 PST

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