Complex sentence: It remains the key to measurement for much of modern science and technology; but at the end of the 19th Century observers discovered phenomena in both the large (macro) and the small (micro) worlds which classical physics could not explain.
Split into simpler sentences: It remains the key to the measurement for much of modern science and technology. But starting at the end of the 19th century observers discovered phenomena in both the large (macro) and the small (micro) worlds that classical physics could not explain.