Hubble redshift and the Heisenberg frequency uncertainty: on a coherence (or pulse) time signature in extragalactic light

Abstract

In any Big Bang cosmology, the frequency $ω$ of light detected from a distant source is continuously and linearly changing (usually redshifting) with elapsed observer's time $δt$, because of the expanding Universe. For small $δt$, however, the resulting $δω$ shift lies beneath the Heisenberg frequency uncertainty. And since there {\it is} a way of telling whether such short term shifts really exist, if the answer is affirmative we will have a means of monitoring radiation to an accuracy level that surpasses fundamental limitations. More elaborately, had $ω$ been `frozen' for a minimum threshold interval before any redshift could take place, i.e. the light propagated as a smooth but {\it periodic} sequence of wave packets or pulses, and $ω$ decreased only from one pulse to the next, one would then be denied the above forbiddingly precise information about frequency behavior. Yet because this threshold period is {\it observable}, being $Δt \approx 1/\sqrt{ω_0 H_0} \sim$ 5 -- 15 minute for the cosmic microwave background (CMB), we can indeed perform a check for consistency between the Hubble Law and the Uncertainty Principle. If, as most would assume to be the case, the former either takes effect without violating the latter or not take effect at all, the presence of this characteristic time signature (periodicity) $Δt$ would represent direct verification of the redshift phenomenon.