  In non-relativistic quantum mechanics, path integrals are normally derived
from the Schroedinger equation. This assumes the two formalisms are equivalent.
Since time plays a very different role in the Schroedinger equation and in path
integrals, this may not be the case.
  We here derive path integrals directly by imposing two requirements: correct
behavior in the classical limit and the most complete practicable symmetry
between time and space.
  With these requirements, the path integral formalism predicts quantum
fluctuations over the time dimension analogous to the quantum fluctuations seen
over the three space dimensions. For constant potentials there is no effect.
But the coupling between rapidly varying electromagnetic fields and the quantum
fluctuations in time should be detectable.
  We consider a variation on the Stern-Gerlach experiment in which a particle
with a non-zero electric dipole moment is sent through a rapidly varying
electric field, oriented parallel to the particle's trajectory. The
Schroedinger equation predicts changes to the precession frequency of the wave
function about the trajectory but no physical splitting of the beam. With the
approach here, path integrals predict the changes to the precession frequency
and in addition that the beam will be split in velocity and time.
