I just saw Lawrence Krauss speak about his new book,

*The Greatest Story Every Told — So Far*, with Alan Alda at the New York Public Library. And during the event Krauss reiterated a point I want to drive home here because I think it's really important.

It has to do with how we understand scientific theories and their relationship with one another. Many people have the mistaken impression that each new scientific idea disproves all the previous ideas of a particular area. For example, before Einstein we had Newtonian physics where we had Newton's laws of motion. However, Einstein's Special and General Theory of Relativity superseded Newton's laws of motion, giving us a more accurate mathematical description of the way large objects behave.

But Einstein didn't

*disprove*Newtonian physics, as if to say, Newton's equations fail to give us

*any*predictive power. Newton's equations got us to the moon after all. Einstein's equations just show us where Newton's equations break down. That is, Newton's equations are a

*close approximation*to the more accurate equations Einstein gave us, and they're accurate in a certain regime, but they break down dramatically at really fast speeds, like near the speed of light.

And where Special Relativity breaks down, General Relativity takes over. Special Relativity doesn't take into account accelerating reference frames, nor does it take into account gravity. But General Relativity didn't

*falsify*Special Relativity. Special Relativity is still accurate in it's regime — that is to say, in it's

*domain of applicability*. It's a description of reality at a certain level, within a certain range of circumstances. In other words, we need to think of scientific explanations as containers within other containers. Each theory or explanation is accurate within its container but not accurate outside of it. But that doesn't necessarily mean that the internal containers are false or disproven because a wider ranging theory eclipsed it.

This doesn't mean that every area or field in science has a hierarchy from the lowest levels of physics to the highest levels of the social sciences. Each field of science may have multiple independent nested hierarchies like the one above with Newtonian and Einsteinian physics.

I think what confuses a lot of people is the fact that Newtonian physics led us to believe time was universal, that there was a cosmic clock that ticked at the same rate for all of us, and that there were things like absolute rest and motion. Einstein showed all that to be wrong. This was of course a major paradigm shift in our understanding of the world, just as dramatic perhaps as evolution was. But I think many people falsely conclude from this that Newton's equations were wrong in the sense that they're 100% wrong and offer no predictive power anywhere. Yes, Newtonian physics gives us the wrong way to see reality, but his equations do work in a certain regime.

Consider this. At low speeds Newton's equations give us the same answers as Einstein's. The space shuttle has a maximum speed of 17,500 mph relative to the earth. But that's only .00002% the speed of light. It's not until you get to 3% the speed of light that you get measurable differences to the hundredth of a meter. That's 20 million miles an hour. So at everyday speeds and even at space shuttle speeds, Newton's equations are just fine. And at speeds up to half of the speed of light they are a decent approximation. But once you go above half of the speed of light they begin to have dramatic discrepancies. See below.

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