Re: Mirror Symmetry

From: George Levy <>
Date: Wed, 06 Feb 2002 20:59:13 -0800

Hi Saibal

Speculation about mirror matter is interesting. If invisible mirror
planets did exist they would have been detected through their
gravitational interaction with the visible planets. This fact seems to
argue against a galactic model in which ordinary matter and mirror
matter are mixed. If mirror matter does exist it would have to be
separated from ordinary matter on the scale of galaxies.

The nice thing about symmetry is that it emerges when there is no
fundamental reason why something is in one particular way. Then it must
be in all possible ways.

When symmetry is broken because of an *arbitrary* configuration in the
laws of nature, then we can be assured that symmetry will also be broken
according to all other possible configurations.

Another form of symmetry of interest is negative mass matter/energy.

Consider a scenario involving negative matter. Two particles m1 and m2
in close proximity where m1 is ordinary matter and m2 is negative

In simple Newtonian terms:

F = m1 m2 / sq(r) (gravitational attraction)
Since m1 is positive and m2 is negative F between the two particles is
negative (repulsive force)

Since F= ma
F = m1a1 = m2a2
Therefore a1 = F/m1 is negative (m1 runs away from m2)
and a2 = F/m2 is positive (m2 is attracted to m1!!!)

As a result, m1 accelerates away from m2 and m2 follows m1 in hot
pursuit. The kinetic energy of m1 increases without limit. The kinetic
energy of m2 decreases without limit, and the total kinetic energy of
the system (1/2)m1v1**2 + (1/2)m2v2**2 remains at zero.
Using the same equations as above you can prove that a particle of
negative matter repels both ordinary matter and negative matter. A
particle of ordinary matter attracts both ordinary matter and negative
matter. Hence:

m1 -> <- m1
<- m1 <- m2
<- m2 m2 ->
If the universe consisted of such particles, the velocity of the
particles would continuously increase. Ordinary particle matter may form
clumps because of gravity and would become hotter and hotter without
limit. The negative matter would not form clumps but would zip-by faster
and faster. Eventually the temperature would get so high that elementary
particles of ordinary matter would be generated from collisions between
particle of ordinary matter, and particles of negative matter would be
generated from collitions between particles of negative matter. The
large scale space-time curvature would remain absolutely flat.

Assuming that the only interaction between ordinary and negative matter
is gravitational, then the negative matter world would remain invisible
but would be responsible for a continuous increase in the energy and
mass of the ordinary matter universe.


> Saibal Mitra wrote:
> 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!
> Saibal
> References:
> [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
> ( )
> [2] Can the mirror world explain the ortho-positronium lifetime
> puzzle?
> R. Foot, S. N. Gninenko
> Phys.Lett. B480 (2000) 171-175
> ( )
> [3] Have mirror planets been observed?
> R. Foot
> Phys.Lett. B471 (1999) 191-194
> ( )
> [4] Have mirror stars been observed?
> R. Foot
> Phys.Lett. B452 (1999) 83-86
> ( )
> [5] The mirror world interpretation of the 1908 Tunguska event and
> other
> more recent events
> R. Foot
> Acta Phys.Polon. B32 (2001) 3133
> ( )
> [6] A mirror world explanation for the Pioneer spacecraft anomalies?
> R. Foot, R. R. Volkas
> Phys.Lett. B517 (2001) 13-17
> ( )
> [7] Mirror World versus large extra dimensions
> Z.K. Silagadze
> Mod.Phys.Lett. A14 (1999) 2321-2328
> ( )
> [8] A quest for weak objects and for invisible stars
> S.I.Blinnikov
> [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 Wed Feb 06 2002 - 21:02:35 PST

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