In any Big Bang cosmology , the frequency \omega of light detected from a distant source is continuously and linearly changing ( usually redshifting ) with elapsed observer ’ s time \delta t , because of the expanding Universe .
For small \delta t , however , the resulting \delta \omega shift lies beneath the Heisenberg frequency uncertainty .
And since there 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 \omega been ‘ frozen ’ for a minimum threshold interval before any redshift could take place , i.e .
the light propagated as a smooth but periodic sequence of wave packets or pulses , and \omega 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 observable , being e.g . \Delta t \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 ) \Delta t would represent direct verification of the redshift phenomenon .
The basic formula for \Delta t is \Delta t \sim 1 / \sqrt { | \alpha| \omega _ { 0 } H _ { 0 } } where H _ { 0 } is the Hubble constant , \omega _ { 0 } is the mode frequency at detection , and \alpha = 1 for the cosmic microwave background ( CMB ) and \approx 0.1 for non-CMB extragalactic sources .
Thus , for the CMB one expects significant Fourier power , that as given by the black body spectrum and no less , on the ten minute timescale .
It is a clinching test .