  In this paper we present an analysis of information transfer time based on
holomorphism, causality and the classical principle of stationary phase. We
also make a preliminary study of the effect of noise on information transfer
time, and find that noise tends to increase transfer times. Noise and
information signals are both essentially acausal, such that analytic
continuation (i.e. prediction) is impossible, which also implies that their
frequency spectra cannot be holomorphic. This leads to the paradox of a
non-holomorphic information-bearing light signal, yet whose underlying Maxwell
equations governing the propagation of the EM wave describe a holomorphic
function in spacetime. We find that application of stationary phase and entropy
arguments circumvents this difficulty, with stationary phase only suggesting
the most likely transfer times of an information signal in the presence of
noise. Faster transit times are not excluded, but are highly improbable.
Stationary phase solutions, by definition, do not include signal forerunners,
whose detection in the presence of noise is also unreliable. Hence a finite
information capacity ensues, as expected from Shannon's law, and information
cannot be transferred faster than c. We also find that the method of stationary
phase implies complex transfer times. However, by considering spacetime to be
isomorphic with the complex temporal plane, we find that an imaginary time is
equivalent to a real distance, and can be interpreted as the uncertainty in the
spatial position of the information pulse. Finally, we apply our theory to a
photonic band gap crystal, and find that information transfer speed and
tunneling is always subluminal.
