Galilean and Newtonian Mechanics: A Historical Analysis
Galilean Mechanics: Challenging Aristotle’s Authority
Historians of science often credit Galileo Galilei as the first to study mechanics free of presuppositions, moving beyond Aristotelian frameworks.
Aristotle approached the problem of motion (or change) qualitatively. He developed a dual ontology, where the supralunar and terrestrial regions, composed of different elements, were governed by distinct physical laws. The supralunar region was thought to consist of the fifth element, ether, characterized by immutability. In contrast, the terrestrial region was believed to contain a universal substrate, or raw material, capable of adopting the various forms of matter we observe. These forms could change from mere potential to actuality through the interaction of four basic qualities: cold, warm, dry, and wet. Unlike the supralunar region, the terrestrial realm was subject to continuous changes, transformations—motion—where the forms (potential) constituting matter were actualized.
For Aristotle, the term “movement” signified change or transformation. He distinguished two types of motion:
- Violent motion: This type of motion forces a body to leave its natural place or move in a direction other than the vertical, deviating from its path toward its natural place. It requires a motor (external cause) in permanent contact with the moving object. Once contact is lost, the object ceases to move.
- Natural motion: This refers to the tendency of all bodies to occupy their natural place and is identified with falling bodies. Galileo refuted this explanation through his demonstration at the Tower of Pisa, ultimately establishing the law of falling bodies.
Galileo’s alternative was to use Archimedes’ hydrostatic principle as a model for combining dynamic movement factors. His conclusion was that homogeneous bodies fall at the same speed because differences in gravity, proportional to volume, are offset by resistance, also proportional to volume. Thus, in the Discorsi, Galileo laid the foundations of the new mechanics:
He questioned the Aristotelian explanation of free fall and presented the law of falling bodies, the first law of classical physics. However, understanding why bodies fall would have to wait for Newton. This law provides compelling reasons to consider Galileo the father of classical science:
For the first time, motion is seen as the result of a force inherent in the moving object. This motion no longer requires an external cause to maintain it; it is self-sustaining and can continue indefinitely in Galileo’s geometrized space. This marked a step toward the principle of inertia, though it was not fully realized yet. The speed of a falling object, starting from rest, is not uniform but continuously accelerates, following a specific mathematical law. Importantly, speed increases with time, not distance.
Newtonian Mechanics: A Giant Leap Forward
As Bernard Cohen states in The Newtonian Revolution (1980), Newton revolutionized mechanics by radically restructuring the principles and concepts of motion, introducing the concepts of mass, acceleration, and force. He also developed a new system of the world where universal gravitation was the driving force and inertia was an essential property of matter.
Newton’s scientific development occurred within the context of Cambridge Neoplatonism, in opposition to the Cartesian philosophy prevalent in continental Europe at the time.
Newton’s objective was similar to Galileo’s, but he achieved a more complete realization. He constructed a deductive axiomatic system, akin to Euclidean geometry, enabling him to mathematically deduce the entire operation of nature from a few fundamental concepts and laws. The Principia begins with definitions of physical quantities (force, inertial force, impressed force, centripetal force) and then states the three laws of motion and principles of mechanics. These laws introduce a new concept absent in Galileo’s laws of motion: force. Galilean kinematics was now complemented by dynamics.
- Law of Inertia: Every body perseveres in its state of rest or uniform motion in a straight line unless compelled to change that state by the action of some impressed force.
- Law of Force: This law establishes the relationship between the force applied to a body and the change in its motion.
- Law of Action-Reaction: This law affirms the impossibility of a single force existing without a corresponding reaction force.
Newton introduced two distinct types of forces and enabled their quantification: the innate force of inertia and the impressed force that modifies a body’s state.
The Law of Universal Gravitation is a powerful law that explains diverse phenomena, such as falling objects, the motion of the Moon and planets, and the tides. It states: Any two bodies attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.