2. Actions#

What is an action?1 Following the introduction of fundamental mechanics concepts in his Principia Naturalis, Newton conceived the concept of action—including both forces and moments—as the possible causes of variation in the “true motion” of a mechanical system or, equivalently, the causes of the difference between true motion and a generic relative motion.

Definition 2.1 (“True motion”)

Newton’s concept of true motion is meant as the motion w.r.t. an inertial reference frame. So what is an inertial reference frame? From an operational point of view, dynamometers measure no force and moment associated with uniform motion w.r.t. a inertial reference frame.

A force is a vectorial physical quantity that, from an operational point of view, can be measured with a 3-axis force sensor (which measures its three components in a 3-dimensional space) or with a dynamometer (which measures its intensity), provided it is free to orient itself along the force direction or if the force direction is known and the instrument is aligned with it.

Definition 2.2 (True forces in classical mechanics)

Referring to the four fundamental interactions, the significant interactions in the realm of classical mechanics are only those of gravitational and electromagnetic nature. Electromagnetic interactions can manifest with bodies having a net charge or, more frequently in classical mechanics, between bodies with no net charge. Among the latter cases, in classical mechanics, it is common to observe the macroscopic manifestation of the microscopic electromagnetic interaction between the elementary components of matter in the form of:

  • contact interactions, where it is possible to distinguish:

    • a normal component to the contact surfaces responsible for the impenetrability of bodies,

    • and a tangential component to the surfaces that manifests as friction

  • material response to stresses, such as in the elastic constitutive law for springs

A measured action that is not a result of the fundamental interactions is due to non-inertial motion of the dynamometer - or, very unlikely, to a new interaction you’ve just discover. If you experience this situation, please remember to send me an invitation for the Nobel cerimony.

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The answer to the question “what is an action?” might imply a “true” knowledge—whatever that means—of the object-concept “action.” Here too, as in other cases, the question “what is…?” can be replaced with “what do we mean by…?”, and an “operational answer” can be considered satisfactory, as it reflects the mode of knowledge and formation of understanding in the scientific field: without delving into more abstract philosophical domains, in physics, we are content to define something through its interactions and effects on other systems, its properties, and a reliable process for its measurement.