Consider a particle P described by a repetitive chain of historically ordered space-time events . Let these events be characterized by their position and time of occurrence . We represent this trajectory of P with the expression
So if there are no forces acting on P, then there are also no changes in P’s momentum, and vice versa
The forgoing statement is just a special case of the second law of motion. Yet Newton included this null relationship as part of his first law of motion. It may seem redundant, but the first law is more than simply a special case of the second law because it also establishes exactly what we mean by a straight line segment or a straight rod. The first law is also known as the law of inertia, it has been translated1Isaac Newton, Mathematical Principles of Natural Philosophy, page 416. Translated by I. Bernard Cohen and Anne Whitman. University of California Press, 1999. into modern English as
For EthnoPhysics this first law is uniquely important because by our premise we prefer to avoid mysteriously received knowledge about length and lines. So this aspect of Newton’s first law is formally restated in the following explicit definition: If P has the same momentum for all events in its trajectory, then describes uniform linear motion and we say that P is moving in a straight line. This sort of force-free motion is obtained if the frame of reference is inertial and P is isolated It is only well-defined for particles that are at least as big as atoms.