Abstract. A synchrotron source with a random distribution of velocity vectors for radiating charges will assumedly have no systematic phase relation between radiation fields from individual charges and would thereby give rise to an incoherent emission. It is known that synchrotron radiation mechanism does not allow a MASER type coherent emission. Here we show that a partial coherence due to antenna mechanism can be inherently present in any compact synchrotron source. Synchrotron radiation at an observing frequency selectively arises from relativistic electrons having a narrow range of Lorentz factors and moving in a cone of a narrow opening angle with respect to the line of sight to the observer, and thus having similar velocity vectors. As we show, even opposite charges moving within the cone augment each others radiation fields, contrary to what may be normally expected. The coherence volume grows with wavelength λ as ∝ λ³, giving rise to the possibility of coherence occurring at wavelengths larger than a certain value λ _p; in a source. The coherence resolves many long standing astrophysical problems where theoretical predictions were not borne out by the observational data. For example, the spectrum gets enhanced by a factor ∝λ³ in the self-absorbed region. This resolves the observational puzzle of a flat spectrum instead of the theoretical steep slope - known in literature as a ``cosmic conspiracy''. It further explains the brightness temperatures observed in space VLBI up to two orders of magnitude higher than the theoretical incoherent synchrotron limit ∼10^11.5K. A simple model for the variability, based on an injection of large number of particles resulting in coherence, explains the observed range of variability time scales (from less than a day to years) and the inferred extremely high brightness temperatures, up to ∼10^18-19K, millions of time more than the theoretical limit. Coherence also explains the correlation observed in the optical/X-rays and the radio variabilities. In the case of a dense beam of monoenergetic electrons, e.g. in the case of synchrotron accelerators, the synchrotron spectrum may be that of an incoherent source at the peak near the characteristic frequency, but at sufficiently longer wavelengths coherence could be present, without the need of some specific mechanism for coherence.