All compact astronomical objects, such as white dwarfs, neutron stars and black holes, have enormous magnetic fields -- as high as 1017 G -- associated with them. The Earth's magnetic field, in contrast, is less than 1 G. However, theorists have also predicted that hypothetical objects called superconductive cosmic strings could have even higher magnetic fields near them of 1047 to 1048 G.

Cosmic strings are believed to be extremely thin 1D topological defects in the fabric of spacetime that stretch across the universe, perhaps making up structures like galaxies as they loop around themselves. They are invoked in grand unified particle physics models and are thought to have been produced just after the Big Bang.

However, the new maximum value for magnetic fields of 1042 G, which has been calculated by Anatoly Shabad of the Lebedev Physics Institute in Moscow and Vladimir Usov at the Weizmann Institute of Science in Rehovot, is lower than that associated with cosmic strings. If correct, it would rule out the existence of extremely strong magnetic fields in the vicinity of these objects.

The value obtained is 109 times lower than the previous upper limit of 1051 G, which had the drawback that it assumed that "Dirac monopoles" exist in Nature. Predicted by some theories that seek to unify the electroweak and strong interactions, these particles have never yet been observed experimentally.

Shabad and Usov obtained their result by considering what the maximum possible value of the magnetic field could be in pure quantum electrodynamics (QED), which describes the fundamental forces between particles as being due to the exchange of "field quanta". Until now, scientists believed that a magnetic field could take on arbitrarily high values in QED.

The duo employed the so-called "Bethe-Salpeter" equation, which is good for studying relativistically bound states formed from charged particles interacting with each other. The physicists solved the equation in the case of a positronium atom, which contains an electron and a positron.

In their calculation, Shabad and Usov place a positronium in a strong magnetic field and find that, at relativistic energies of the electron and positron inside the positronium, the field enhances the attraction between the particles. This attraction becomes stronger and stronger until the electron and positron "fall" onto one another at a maximum field of 1042 G. The authors call this the "collapse" of the positronium.

At this value of field, the energy gap separating the electron and positron shrinks so that the positronium becomes indistinguishable from the vacuum. According to the researchers, this means that fields higher than 1042 are not possible. "If they were," explains Shabad, "the vacuum would explode by producing collapsed positronia." One crucial mechanism in the calculation is that a magnetic field larger than the "maximum value" would be needed to separate the electron from the positron.