We report on new investigations of spontaneous symmetry breaking in non-adiabatic phase transitions. This Zurek-Kibble (ZK) process is mimicked in solid state systems by trapping of magnetic flux quanta, fluxons, in a long annular Josephson tunnel junction quenched through the normal-superconducting transition. A trapped fluxon unambiguously is detected as a zero-field step in the DC I-V characteristic. Experimentally we plot the fluxon trapping probability versus the quench rate, varied over 4 decades. An allometric scaling behavior is found. By fitting to the theoretical curve we get sigma sime 0.5 for the ZK critical scaling exponent sigma, which does not agree with an earlier theoretical prediction of sigma = 0.25. A novel theory based on the proximity effect leading to sigma = 0.50 has been proposed. The dependence of the gap voltage on temperature is measured and used for precise monitoring of the fast temperature variation during the quench.