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" If the law of gravitation be regarded as universal, the point may be stated as follows. The laws of motion require to be stated by reference to what have been called kinetic axes: these are in reality axes having no absolute acceleration and no absolute rotation. It is asserted, for example, when the third law is combined with the notion of mass, that, if m, m' be the masses of two particles between which there is a force, the component accelerations of the two particles due to this force are in the ratio m2 : m1. But this will only be true if the accelerations are measured relative to axes which themselves have no acceleration. We cannot here introduce the centre of mass, for, according to the principle that dynamical facts must be, or be derived from, observable data, the masses, and therefore the centre of mass, must be obtained from the acceleration, and not vice versâ. Hence any dynamical motion, if it is to obey the laws of motion, must be referred to axes which are not subject to any forces. But, if the law of gravitation be accepted, no material axes will satisfy this condition. Hence we shall have to take spatial axes, and motions relative to these are of course absolute motions. 465. In order to avoid this conclusion, C. Neumann* assumes as an essential part of the laws of motion the existence, somewhere, of an absolutely rigid “Body Alpha”, by reference to which all motions are to be estimated. This suggestion misses the essence of the discussion, which is (or should be) as to the logical meaning of dynamical propositions, not as to the way in which they are discovered. It seems sufficiently evident that, if it is necessary to invent a fixed body, purely hypothetical and serving no purpose except to be fixed, the reason is that what is really relevant is a fixed place, and that the body occupying it is irrelevant. It is true that Neumann does not incur the vicious circle which would be involved in saying that the Body Alpha is fixed, while all motions are relative to it; he asserts that it is rigid, but rightly avoids any statement as to its rest or motion, which, in his theory, would be wholly unmeaning. Nevertheless, it seems evident that the question whether one body is at rest or in motion must have as good a meaning as the same question concerning any other body; and this seems sufficient to condemn Neumann’s suggested escape from absolute motion. "

― Bertrand Russell , The Principles of Mathematics

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Bertrand Russell quote : If the law of gravitation be regarded as universal, the point may be stated as follows. The laws of motion require to be stated by reference to what have been called kinetic axes: these are in reality axes having no absolute acceleration and no absolute rotation. It is asserted, for example, when the third law is combined with the notion of mass, that, if m, m' be the masses of two particles between which there is a force, the component accelerations of the two particles due to this force are in the ratio m2 : m1. But this will only be true if the accelerations are measured relative to axes which themselves have no acceleration. We cannot here introduce the centre of mass, for, according to the principle that dynamical facts must be, or be derived from, observable data, the masses, and therefore the centre of mass, must be obtained from the acceleration, and not vice versâ. Hence any dynamical motion, if it is to obey the laws of motion, must be referred to axes which are not subject to any forces. But, if the law of gravitation be accepted, no material axes will satisfy this condition. Hence we shall have to take spatial axes, and motions relative to these are of course absolute motions. 465. In order to avoid this conclusion, C. Neumann* assumes as an essential part of the laws of motion the existence, somewhere, of an absolutely rigid “Body Alpha”, by reference to which all motions are to be estimated. This suggestion misses the essence of the discussion, which is (or should be) as to the logical meaning of dynamical propositions, not as to the way in which they are discovered. It seems sufficiently evident that, if it is necessary to invent a fixed body, purely hypothetical and serving no purpose except to be fixed, the reason is that what is really relevant is a fixed place, and that the body occupying it is irrelevant. It is true that Neumann does not incur the vicious circle which would be involved in saying that the Body Alpha is fixed, while all motions are relative to it; he asserts that it is rigid, but rightly avoids any statement as to its rest or motion, which, in his theory, would be wholly unmeaning. Nevertheless, it seems evident that the question whether one body is at rest or in motion must have as good a meaning as the same question concerning any other body; and this seems sufficient to condemn Neumann’s suggested escape from absolute motion.
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