We confirmed that the uncertainty relation between time and energy is established in fluctuations in the space and time domains that appear when coherent optical pulses propagate through a disordered static medium. The widths of temporal and spectral correlation functions of these fluctuations satisfy the relation $\ensuremath{\delta}\ensuremath{\tau}\ensuremath{\delta}\ensuremath{\omega}\ensuremath{\sim}1$, that is, $\ensuremath{\delta}\ensuremath{\tau}\ensuremath{\delta}E\ensuremath{\sim}\ensuremath{\hbar}$. The number of fluctuations is discussed on the basis of the uncertainty relation.
We investigate the fluctuations of light transmitted through static disordered media in time and frequency domains. When the pulse duration of the incident light is much shorter than the typical time of flight through the medium, fluctuations appear both in time and frequency domains and the uncertainty relation, δτδω∼1 or
δτδE∼ℏ, holds good in these fluctuations. We discuss the necessary condition to observe this relation. Precise calculations of the correlation functions also reveal that the exact shape and width of the correlation functions depend on the pulse duration and the observation time. Experimental results with picosecond pulses through thick and thin samples show good agreement with the theoretical calculations.