The Twin Paradox example above is fairly esoteric and hypothetical. What about the widespread claims that our GPS satellite systems would fail without relativistic corrections?
These are actually unverified claims repeated by theorists with vested interests in propagating this belief. The US Dept. of Defense, for example, manually updates GPS satellite times daily. These updates factor in many theoretical and practical adjustments, both large and small. When pure theory alone can’t fully account for observations, as is generally the case in real-world scenarios, practical models are created then adjusted with various “correction factors” to better match real-world conditions, and these “correction factors” are then applied. Such empirical correction factors must be adjusted and fine-tuned however may be necessary to achieve the best agreement and modeling of observations, regardless of whether or not any tiny theoretical calculations are part of this picture. The claims that our GPS systems would not function properly without relativistic corrections, often repeated by Special Relativity theorists and enthusiasts, are based on purely theoretical calculations
