,
',
'' respectively, is zero or
The latter expression is equivalent to the former statement, as soon as a sufficient number and sufficiently great and extensive masses are taken into consideration...." This formulation cannot satisfy us. For, in addition to a certain requisite accuracy, the character of a "contact" law is lacking, so that its promotion to the rank of a fundamental law (in place of the law of inertia) is quite out of the question.
The inner ground of these difficulties is without doubt to be found in an insufficient connection between fundamental principles and observation. As a matter of actual fact, we only observe the motions of bodies relatively to one another, and these are never absolutely rectilinear nor uniform. Pure inertial motion is thus a conception deduced by abstraction from a mental experiment—a mere fiction.
However necessary and fruitful a mental experiment may often be, there is the ever-present danger that an abstraction which has been carried unduly far loses sight of the physical contents of its underlying notions. And so it is in this case. If there is no meaning for our understanding in talking of the "motion of a body" in space, as long as there is only this one body present, is there any meaning in granting the body attributes such as inertial mass, which arise only from our observation of several bodies, moving relatively to one another? If not, then we cannot attach to the conception "inertial mass of a body," an absolute significance, that is, a meaning which is independent of all other physical conditions, as has hitherto been done. Such doubts received fresh strength when the special theory of relativity endowed every form of energy with inertia (vide [Note 17]).
The results of the special theory of relativity entirely unhinged our view of the inertia of matter, for they robbed the theorem concerning the equality of inertial and gravitational mass of its strict validity. A body was now to have an inertial mass varying with its contained internal energy, without its gravitational mass being altered. But the mass of a body had always been ascertained from its weight, without any inconsistencies manifesting themselves (vide [Note 18]).