The factor two

Examples are given of physical problems where factor two played an important role. First, we consider the irregularities of the Moon trajectory that Newton correctly, attributed to the differences in the attraction by the Sun of Earth and Moon because of the small differences in their location. Newton’s estimate of those (small) irregularities was off the measures by a factor close to two, which was restored mater by Clairaut and seen as a major success for Newton’s dynamical theory. Another factor two appears in the Sun’s estimate of the deviation of light. The deviation computed by using special relativity is half the one measured. As Einstein showed, the factor is restored by considering general relativity which considers the changes in the metric due to gravity. Lastly, we consider a more recent problem, the one of the apparent doubling of electric charges in a superconductor as measured by the quantum of flux, which is half the one predicted by London, namely ℏc /2 e instead of ℏc / e . This doubling is classically explained by assuming that, in superconductors current carrying fermions are in pairs so that the unit charge becomes 2 e instead of e . We argue instead that if one takes into account that the fermions carry a spin 1/2 the quantization element of magnetic flux is divided by two as implied by looking at the second class of homotopy of the group of transformation SU (2) × U (1) of the ground state, as it follows from Toulouse theory of defects in ordered media.