Snowmass White Paper: Precision Studies of Spacetime Symmetries and Gravitational Physics

High-energy physics is primarily concerned with uncovering the laws and principles that govern nature at the fundamental level. Research in this field usually relies on probing the boundaries of established physics, an undertaking typically associated with extreme energy and distance scales. It is therefore unsurprising that particle physics has traditionally been dominated by large-scale experimental methods often involving high energies, such as colliders and storage rings, cosmological and astrophysical observations, large-volume detector systems, etc. However, high-sensitivity measurements in smaller experiments, often performed at lower energies, are presently experiencing a surge in importance for particle physics for at least two reasons. First, they exploit synergies to adjacent areas of physics with recent advances in experimental techniques and technology. Together with intensified phenomenological explorations, these advances have led to the realization that challenges associated with weak couplings or the expected suppression factors for new physics can be overcome with such methods while maintaining a large degree of experimental control. Second, many of these measurements broaden the range of particle-physics phenomena and observables relative to the above set of more conventional methodologies. Combining such measurements with the conventional efforts above therefore casts both a wider and tighter net for possible effects originating from physics beyond the Standard Model (BSM). This paper argues that this assessment points at a growing impact of such methods and measurements on high-energy physics, and therefore warrants direct support as particle-physics research. Leveraging the recent rapid progress and bright outlook associated with such studies for high-energy physics, could yield high returns, but requires substantial and sustained efforts by funding agencies.