by Tasneem Zehra Husain
It sounds a bit ridiculous when you admit your jealousy of inanimate objects. If you confess that you covet the skill with which these lifeless forms navigate their circumstances, you're bound to get some strange looks. So, you keep it to yourself – for the most part. But honestly, there are times when – if you know about the least action principle – it takes all your strength to keep from declaring that you would trade places with a subatomic particle, or a ray of light, or a rubber ball, in a heartbeat. Chances are, if you know about the principle of least action, you know enough science to realize that electrons and photons and rubber balls are not active decision makers, but that doesn't keep you from envying their ability to always follow the optimal route from one point to another. In fact, it almost makes the whole thing worse. These objects are not sentient beings; it's not as if they'd suffer if they took a circuitous route! But somehow, they manage to get it right every time, whereas you – well, you often manage to take what seems like the most complicated possible life path from Point A to Point B.
So what exactly is this mysterious knowledge that subatomic particles seem to possess, and how does one go about acquiring it? We begin by recognizing that these particles aren't furiously calculating their every move, maximizing the effect thereof; they are merely obeying the laws of nature – familiar laws, like those transcribed by Newton. The least action principle offers an approach that enables us to calculate the motion of a classical object, without recourse to conventional mechanics. But this principle should not be thought of as just an alternative to Newton's laws; it is much more powerful and far deeper than that. The chief strength of the least action principle is its flexibility. It is applicable not just within the province of classical mechanics, but can be extended to the realms of optics, electronics, electrodynamics, the theory of relativity and – perhaps most shockingly – even quantum mechanics. In fact, (as is evident in Feynman's path integral formulation) the least action principle is the most logically smooth way to connect classical and quantum physics! Suffice it to say that many well known laws are encapsulated in the elegant statement that “a physical system evolves from a fixed beginning to a fixed end in such a manner that its action is minimized.”
Having drummed up the anticipation, l should at least attempt to explain what the principle is, and give you a glimpse of how it works.
