The theories of relativity published by Einstein have changed physics in many ways. At first, many people didn't accept the theory, and simply said it wasn't true, much like at the time, people didn't believe Galileo or Copernicus. Experiments have shown that relativity is true, at least in the ways that we can test. It still may be possible (and likely) that relativity is only an approximation of a larger picture, just as Newtonian physics is an approximation of relativity at slow speeds. Relativity theory has led us to other discoveries, and technologies that are enhancing our lives. It has also led to inventions that are not so great, like the atomic bomb.
Relativity has done more than just give us a new way of looking at the universe. It ended the notion that humankind can know everything there is to know. It made scientists have to think more in the abstract, no longer were the laws of the universe explained by intuitive principles. This new way of thinking has "trickled down" into other areas of human endeavors such as art and psychology. It has given science a more philosophical slant, whereas before the concrete observations were not in the realm of the strange. Relativity theory alone did not bring about these changes, and you might say it was inevitable. Had Einstein not discovered relativity, someone else would have.
Most of the predictions of the theories of relativity had to wait many years to be observed. Time dilation was demonstrated after the invention of the jet engine. The first nuclear reaction helped confirm the equivalence of mass and energy. The fact that light is bent by gravity was confirmed in 1919 on an expedition led by Sir Arthur Eddington to observe a solar eclipse. Some took longer to confirm, such as the existence of black holes, the phenomena of frame dragging, and gravitational red shifting.
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