There may never be another Einstein or another Newton, but we can all learn to utilize their equations under the right physical circumstances. We can become excellent at physics the same way they did: by solving problems quantitatively, and using the appropriate mathematical relationships to make predictions about physical phenomena. (Credit: Orrin Turner (L), Godfrey Kneller (R))

Ask Ethan: Can we turn Einstein’s equations into Newton’s law?

Einstein’s General Relativity has reigned supreme as our theory of gravity for over a century. Could we reduce it back down to Newton’s law?

Although Einstein is a legendary figure in science for a large number of reasons — E = mc², the photoelectric effect, and the notion that the speed of light is a constant for everyone — his most enduring discovery is also the least understood: his theory of gravitation, General Relativity. Before Einstein, we thought of gravitation in Newtonian terms: that everything in the universe that has a mass instantaneously attracts every other mass, dependent on the value of their masses, the gravitational constant, and the square of the distance between them. But Einstein’s conception was entirely different, based on the idea that space and time were unified into a fabric, spacetime, and that the curvature of spacetime told not only matter but also energy how to move within it.

Despite these conceptual differences, in nearly all practical cases, Einstein’s equations and Newton’s law of universal gravitation yield identical predictions. Does that imply that Einstein’s equations can somehow be collapsed, or reduced, down to Newton’s laws? It’s what James Raymond wants to know, asking:

“It seems like an amazing coincidence that Einstein’s equations give almost exactly the same result as Newton’s law of gravity. Popular lectures on gravity never seem to address this. I suspect it is not a coincidence. Is it possible to make a tiny change in Einstein’s equations to make them collapse to Newton’s law?”

It’s a great question, and one with a very nuanced answer. Yet, we can modify Einstein’s equations to recover Newton’s law. But no, it’s not a “tiny” change; it requires ignoring the most Einsteinian aspect of the theory of all: the principle of relativity itself. Here’s what it all means.

Newton’s law of universal gravitation (left) and Coulomb’s law for electrostatics (right) have almost identical forms, but the fundamental difference of one type vs. two types of charge open up a world of new possibilities for electromagnetism. In both instances, however, only one force-carrying particle, the graviton or the photon, respectively, is required. (Credits: Dennis Nilsson/RJB1, Wikimedia Commons)

Newton’s law of universal gravitation is perhaps the best place to start: because it’s so apparently simple and straightforward. It simply says, as…