Mother “Nature” has a mystic economical character. We may begin to understand this by following many examples around us, take a few. A straw put in a glass of water appears bent because light avoids doing extra work to travel through the denser medium with same speed as in the air. Similarly the rain drops spread out as little as possible being not ready to bear any more surface tension than necessary and thus acquire the shape of a perfect sphere while falling through vacuum. But while passing in the air, these adapt to the air density and take a teardrop shape which is perfectly aerodynamic. All this happens spontaneously in real time without any planning.
While walking beside a river or a stream, one may notice that the course of flow of water through the hard and soft soil is unyielding to the plan of straight line and adapts to whatever it meets at each point of its journey. The behavior of stream, in fact, reveals one of the most fundamental laws of nature that shapes our entire Universe and is called the principle of least action. One of the first scientists to formulate this principle was Pierre Louis Maupertuis, who felt that “Nature is thrifty in all its actions.”
In the 17th century, Pierre de Fermat had postulated that “Light travels between two given points along the path of shortest time” known as the principle of least time or Fermat’s Principle which was one of the first formulations of the principle of least action. Leonard Euler gave the least action principle a mathematical formulation later that year. However, there is also an evidence that Gottfried Leibniz had first formulated the least action principle in 1707. The modern formulation of the least action principle was given by the Euler–Lagrange equation in the 1750s.
All diverse phenomena which we can observe from galaxies to subatomic particles are following the path of least resistance.
The principle of least action (PLA) is one of the most general laws of theoretical physics and simultaneously one of the most philosophically conflicting laws being always surrounded by a fog of mysticism. A system moving from a point “A” to a final point “B”, does not know the optimal trajectory in advance, but the flow explores the path from all sets of possibilities. The paths which are particularly efficient in abolishing the energy gradients in the universe become naturally selected. These lead to a faster increase in entropy equivalent to a more rapid decrease in the free energy. The second law of thermodynamics states that the entropy (the measure of disorder) of any closed system increases with time. Chaos increases because the system evolves towards the state of the lowest energy—the state of thermodynamic equilibrium or rest.
This teleological behavior of a physical system aiming at achieving a certain goal, the state of rest, has profound philosophical ramifications. If rest is the teleological goal of evolution of every system in physics, perhaps we can generalize this notion and define a broader concept of rest as the state of achieving a goal. Simply put, every system gravitates and evolves towards the state of rest.
However, until today, we have not empirically understood why a physical system chooses a path which involves minimal action. The empirical paradigms of science do not coordinate with the simplicity, perfection and parsimony of nature. The simple and constant rules of the combination of possibilities constitute the reason why our universe seems to us so uniform, ordered and harmonious. Therefore, only a few numbers of laws, most wisely established, have sufficed to explain all movements, be it even the vegetative growth of plants or the movement of animals as well.
The PLA does not follow from other physical laws and so far it has only been accepted as a mathematical tool equivalent to the differential equations of motion. There are three opinions regarding the philosophical reasoning of the minimum action: the perfection of God (theological view), the economy of nature (teleological view), and the economy of the human mind (instrumental view). Historically, the PLA arose from the optical-mechanical analogy with Fermat’s principle, in which the light moves along the path that takes the minimal amount of time. The PLA is used in electromagnetism, statistical mechanics, special and general relativity.
Thus PLA seems to be midway between the laws of motion with a limited physical necessity and those with a metaphysical necessity. The events or objects can be classified as “actual” and “possible”. The realized manifestations of a phenomenon constitute the “actual” while as the unrealized manifestations constitute the “possible.” Possibilities are not the things that exist at least in our part of world instead, they are things that have being in our world but do not exist. Thus, we are faced with a dilemma that if we accept modal properties we accept other possible worlds. As PLA appeals to a modal notion of “possibilities” the idea that the universe may have multiple histories is now accepted as a scientific fact. Some physicists are working to combine Einstein’s general theory of relativity and Feynman’s theories into a complete, unified theory that will describe everything that happens in the universe although the main obstacles, as always, will be our habits of thinking and that of our common sense.
Dr. Qudsia Gani is Assistant Professor, Department of Physics, Cluster University Srinagar