janna_levin's picture
Professor of Physics and Astronomy, Barnard College of Columbia University; Author, Black Hole Survival Guide; Director of Sciences, Pioneer Works
The Principle of Least Action

Complexity makes life interesting. A universe of just Hydrogen is quite bland, but the helpful production of Carbon in stellar cores allows for all kinds of chemical connections.  A universe of just two dimensions is pretty limited, but live in at least three and enjoy the greater range of motion and possible spatial permutations. Sitting on a bench in my friend’s garden in California, there’s a lot to look at. The visual information filling my field of view is incredibly complicated. The dry winter leaves trace vortices in the air’s motion. Plants respire and we breathe and the neural connections fire and it’s all complex and interesting. The physicist’s job is to see through the overwhelming intricacy and find the rallying, organizing principle.  

Everything in this garden, from the insects under the rocks to the blue dome overhead to the distant stars washed out by the sunlight can be traced to a remarkably lean origin in a big bang. Not to overstate the case. There’s much we don’t understand about the first trillionth of a trillionth of a trillionth of a trillionth of a second after the inception of our universe. But we can detail the initial 3 minutes with decent confidence and impressive precision 

Our ability to comprehend the early universe that took 13.8 billion years to make my friend’s yard is the direct consequence of the well-known successes of unification. Beginning with Maxwell’s stunning fusion of electricity and magnetism into one electromagnetic force, physicists have reduced the list of fundamental laws to two. All the matter forces—weak, electromagnetic, and strong—can be unified in principle (though there are some hitches). Gravity stands apart and defiant so that we have not yet realized the greatest ambition of theoretical physics: the theory of everything, the one physical law that unifies all forces, that pushes and prods the universe to our current complexity. But that’s not the point. 

The point is that a fundamental law is expressible as one mathematical sentence. We move from that single sentence to the glorious Rube Goldberg machine of our cosmos by exploiting my favorite principle, that of least action. To find the curves in spacetime due to matter and energy, you must find the shortest path in the space of possibilities. To find the orbit of a comet around a black hole, you must find the shortest path in the curved, black-hole spacetime 

More simply, the principle of least action can be stated as a principle of least resistance. If you drop a ball in mid air, it falls along the shortest path to the ground, the path of least resistance under the force of gravityIf the ball does anything but fall along the shortest path, if it spirals around in widening loops and goes back up in the air, you would know that there are other forces at work—a hidden string or gusts of air. And those additional forces would drive the ball along the path of least resistance in their mathematical description. The principle of least action is an old one. It allows physicists to share the most profound concepts in human history in a single line. Take that one mathematical sentence and calculate the shortest paths allowed in the space of possibilities and you will find the story of the origin of the universe and the evolution of our cosmological ecosystem.