Mathematical physics: Glitches in time

A mathematical technique has now been developed that reveals the underlying dynamics of time-dependent data collected with extreme temporal uncertainty, without using additional, costly instrumentation. See Letter p.471 When reconstructing climate histories from ice cores or ultrafast dynamics from X-ray free-electron laser (XFEL) experiments, the uncertain time stamps can muddle the sequence of events, making it difficult to recover accurate dynamical information. These authors introduce a data analysis technique, based on nonlinear Laplacian spectral analysis, that circumvents this problem and is capable of extracting dynamical information from noisy data despite the timing uncertainties. They demonstrate reconstruction of few-femtosecond dynamics using XFEL data with 300-femtosecond timing uncertainty. In principle, this approach could be useful in all measurements plagued by time uncertainty, so might find applications from geoscience to gravitational physics.