Revisiting the Concept of Force in Classical Mechanics

In classical mechanics, force is the physical entity mediating interactions between physical objects. Such objects consist of point masses, or appear as continuous bodies formed by a continuum of point masses. Force is defined as the sole entity capable of altering a point mass’s state of motion (velocity) and is mathematically represented as a bound vector. However, this description of the physical world no longer holds at the atomic or subatomic level, where matter is discretized into quanta and interactions occur through the exchange of quanta of linear momentum and energy. While this dichotomy is currently accepted as the status quo, efforts to harmonize these frameworks into a more coherent formulation remain highly desirable. This paper investigates the extent to which interactions in classical mechanics can be reinterpreted as an exchange of linear momentum quanta. This investigation leads to a coherent reformulation of Newton’s laws, in which forces are treated as flow rates of these quanta. Therefore, classical mechanics admits a discretized description of the physical world even at the macroscopic level.