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When we talk about Einstein overthrowing Newton, there's a degree to which the language we use is wrong. After all, as a mechanical engineering student, I had six or seven semesters of Newtonian mechanics and one semester of Einsteinian mechanics. Newton must have been really, really wrong, for his theories to still be taught in that depth a century after he was relegated to the dustbin.
If you drop an apple to the ground, it falls according to Einstein's equations, not Newton's (to the best of our understanding at the moment). But if you try to measure the position of the apple as a function of time, that measurement will look as if it follows Newton's equation just as much as it follows Einstein's equations. That's because the difference between Einstein's result and Newton's result is infinitesimal in the speed regime of the apple's fall, at such a small fraction of the speed of light.
So to a certain extent the choice of using Einstein's equations or Newton's equations in this regime is arbitrary. We could, every time we wanted to calculate the speed of that apple, use general relativity. The result might be closer to the physical reality. Then again, we know that Einstein is 'wrong' too by the same definition that says that Newton is wrong. We believe there are regimes in which Einstein's equations don't accurately model reality, and that there are other equations we don't yet have that do a better job of modeling the movement of bodies in these regimes, the so-called equations of the Grand Unified Theory.
And yet in spite of that, in spite of us knowing for sure that both sets of equations are inaccurate models of the universe, either Einstein's or Newton's equations can be used to calculate the motion of the ball with accuracy sufficient for any practical purpose. What's more, we can simplify those equations yet further- leave out forces like air resistance that both theories know are part of the math, for example- and still get useful results much of the time.
Saying that science is never settled, that scientists are constantly disproving past theories, misses this point. The value of science is not its elegance. The value of good science is its descriptive power, which endures even after good theories fall.
If you drop an apple to the ground, it falls according to Einstein's equations, not Newton's (to the best of our understanding at the moment). But if you try to measure the position of the apple as a function of time, that measurement will look as if it follows Newton's equation just as much as it follows Einstein's equations. That's because the difference between Einstein's result and Newton's result is infinitesimal in the speed regime of the apple's fall, at such a small fraction of the speed of light.
So to a certain extent the choice of using Einstein's equations or Newton's equations in this regime is arbitrary. We could, every time we wanted to calculate the speed of that apple, use general relativity. The result might be closer to the physical reality. Then again, we know that Einstein is 'wrong' too by the same definition that says that Newton is wrong. We believe there are regimes in which Einstein's equations don't accurately model reality, and that there are other equations we don't yet have that do a better job of modeling the movement of bodies in these regimes, the so-called equations of the Grand Unified Theory.
And yet in spite of that, in spite of us knowing for sure that both sets of equations are inaccurate models of the universe, either Einstein's or Newton's equations can be used to calculate the motion of the ball with accuracy sufficient for any practical purpose. What's more, we can simplify those equations yet further- leave out forces like air resistance that both theories know are part of the math, for example- and still get useful results much of the time.
Saying that science is never settled, that scientists are constantly disproving past theories, misses this point. The value of science is not its elegance. The value of good science is its descriptive power, which endures even after good theories fall.