**1. Introduction**

Until a few decades ago capturing molecular dynamics was in the realm of Gedanken- or thought experiments [1, 2]. Chemists know about the reactants and the final products of chemical reactions, but how the molecules and atoms rearrange themselves to produce the reaction products had always remained in the realm of imagination. This is due to the technical difficulties in making these measurements. In solids, chemical reactions occur at the speed of sound (1000 m/s) and atomic bond lengths are on the order of 1 Å, which means that the time resolution required is on the order of femtoseconds [3, 4].

Recent advances in laser technology have made it possible to produce laser pulses that are femtoseconds and even attoseconds in duration [5]. This has enabled rapid

developments in the field of ultrafast science. Typically, a short laser pulse initiates a photo-induced reaction dynamic in a molecular sample, which is then probed by a probe pulse. Probe pulses can be short X-ray pulses [6] in X-ray free electron lasers (XFELs) [7] or compressed electron pulses [8] in tabletop experiments [3, 9]. Additionaly, laser pulses can be used in table-top spectroscopy experiments, which temporally probe molecules and atoms but not with the same spatial resolution as X-rays [10, 11]. XFELs are multibillion dollar facilities that are very costly to operate and entail very complex engineering [12]. However, electron beams are generated in table-top experiments. The electrons are usually accelerated via a DC electric field for a short distance in order to avoid rapid expansion due to Coulomb forces between them [13], or they are accelerated via a DC field, then compressed via an RF field [14, 15]. There are also designs where acceleration and compression take place through the same RF field [16]. Furthermore, utilizing relativistic electron sources can also improve brightness and time resolution since they greatly reduce pulse broadening effects [17–19]. In all cases a short probe pulse is produced. Probe pulses capture molecular dynamics and produce a diffraction pattern. By varying the time delay between pump and probe pulses, the molecular dynamics at different time points can be captured and a'molecular movie' can be generated. As a result, the time resolution is mainly limited by the technological ability to produce ever-shorter laser and electron pulses [20], both for triggering a photo-induced dynamic rapidly and for imaging it. In other approaches, the probe pulse is dissected to increase time resolution. In the case of electrons, streak cameras [21] that spatially separate a long electron beam into smaller pieces have been developed, enabling higher time resolutions [22]. Another proposed method, known as optical gating [23], uses ultrashort laser pulses to dissect the electron beam and achieve a higher time resolution than was originally possible based on the length and speed of the beam.

For the sake of making this chapter as self-encompassing as possible, we will start with a review of special relativity (SR) and the concepts of time dilation and length contraction. This shall make for a smoother understanding of the core ideas of the proposed novel experiment.
