Special Relativity was immediately testable. In fact, one of the tests for its predictions turns out to be the Michelson?Morley experiment, which was first performed in 1887 before Special Relativity was even a gleam in Einstein's eye. The M-M experiment was refined repeatedly during the period that Special Relativity was first discussed (1905-06) to focus on testing one of SR's basic predictions, so a test of at least one of special relativity's predictions existed by publication date.
? ? ? ? ? General relativity was immediately testable by measuring the Perhelion precession of Mercury. It was also possible to test it by observing solar bending of starlight any time there was a total solar eclipse. Yeah, you couldn't do that on the day of first publication because there wasn't a solar eclipse that day, but the researchers knew there would be total solar eclipses in the future and could set up to test the theory as soon as one happened. But, suppose they had had to wait until the next eclipse after that, or something? Do you really want to advance the claim that a theory isn't scientifically testable if a human event such as a war keeps the observers from getting to the location where it could be tested? Or if cloudy weather blocked observing? That nearly happened.
? ? ? ? Normally, the rule that it isn't science if it doesn't make testable predictions doesn't mean that something becomes unscientific if there are budget cuts or other such events that aren't themselves part of the scientific method.
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