Hungarian stamp commemorating 100 years of general relativity. Image from philatelicdatabase.com
…: “Gravity, where did it come from?”
when a four-dimensional pseudo-Riemannian manifold and a Landau–Lifshitz stress-energy tensor love each other very much, they produce a geodesic in curved spacetime. And that’s the story of gravity.
Thanks to Dr. Science at Mother Jones magazine for coming up with a compelling theory of gravity. I had never expected to read about a “four-dimensional pseudo-Riemannian manifold” and “Landau–Lifshitz stress-energy tensor” in a piece about presidential campaign :-). Moreover, it’s one of the most hilarious pieces to remember from the celebration of 100 years of General Relativity.
“Einstein arrived at the general theory of relativity after thinking for eight years about gravitation… The final steps leading to his November 25, 1915, paper were made in an intense burst of activity that lasted for less than two months.”
(Abraham Pais, Subtle is the Lord)
Einstein equation entwines the curvature of spacetime (spacetime is the aforementioned “four-dimensional pseudo-Riemannian manifold”) and motion of material objects embodied in that spacetime (the energy and momentum of these objects are described by the aforementioned “Landau–Lifshitz stress-energy tensor”). “Love” is complicated, but so is the mathematics used to formulate and solve the equations of general relativity. The aforementioned geodesics are lines that “curve as little as possible” so they are the shortest distance between two points in a curved geometry. According to general relativity, small, light (‘test’) bodies move along these geodesics.
Complicated? Notoriously so, yet general relativity is considered the most beautiful physical theory ever invented. In addition to its elegance, the theory has been repeatedly tested. And everything works as predicted!
PS. When “a four-dimensional pseudo-Riemannian manifold” and “a Landau–Lifshitz stress-energy tensor” do not love each other that much and things move pretty slow (as compared to the speed of light), Einstein equations reduce to the familiar Newtonian gravity. For every practical intent, apples still fall down in a straight line.
The 1987 British set of stamps, designed to commemorate the 300th anniversary of Isaac Newton’s Philosophiae Naturalis Principia Mathematica. Image from Ian Ridpath