  The quantum decay of a relativistic scalar field from a metastable state
("false vacuum decay") is a fundamental idea in quantum field theory and
cosmology. This occurs via local formation of bubbles of true vacuum with their
subsequent rapid expansion. It can be considered as a relativistic analog of a
first-order phase transition in condensed matter. Here we expand upon our
recent proposal [EPL 110, 56001 (2015)] for an experimental test of false
vacuum decay using an ultra-cold spinor Bose gas. A false vacuum for the
relative phase of two spin components, serving as the unstable scalar field, is
generated by means of a modulated linear coupling of the spin components. We
analyze the system theoretically using the functional integral approach and
show that various microscopic degrees of freedom in the system, albeit leading
to dissipation in the relative phase sector, will not hamper the observation of
the false vacuum decay in the laboratory. This is well supported by numerical
simulations demonstrating the spontaneous formation of true vacuum bubbles on
millisecond time-scales in two-component $^{7}$Li or $^{41}$K bosonic
condensates in one-dimensional traps of $\sim100\,\mu \mathrm{m}$ size.
