Page:CarmichealPostulates.djvu/12

 conflict with no known experimental facts. Therefore, following that instinct which has always wisely guided the physicist, we make the simplest hypothesis which is in agreement with and explanatory of the totality of experimental facts at present known. If at any time experiments are set forth which do not agree with the theory developed on the basis of the above postulates, then will be the time to consider the question of introducing a more complicated postulate in place of our postulate L above.

§ 5. Consistency and Independence of the Postulates. — Throughout the paper it will be assumed that the postulates as stated are consistent; that is to say, no attempt will be made to prove their consistency. The fact that no contradictory conclusions have been drawn from the postulates will be accepted as (partial) evidence that they are mutually consistent. Moreover, from their very nature and from the differing range of applicability of the several postulates it is difficult to conceive how any one of them can possibly contradict conclusions which may be drawn from the others.

There is another question also which it is our purpose to pass over without discussion, namely, the question of the logical independence of the postulates. Is any postulate or a part of any postulate a logical consequence of the remaining postulates? This question is important from the point of view of formal logic, but in the present case its value to physical science is probably small.

§ 6. Other Postulates Needed. — From the postulates stated above it is possible to draw only those conclusions of the theory of relativity which are of a general nature. If, for instance, it is desired to study the nature of mass or the relation of mass and energy in this theory, it is necessary to have some assumption concerning mass in the first case and concerning both mass and energy in the second case. Thus we might assume the conservation laws of mass, energy, electricity, and momentum and deduce the joint consequences of these assumptions and those given above. It is our purpose to return to this matter in a future paper. For the present we are concerned only with the postulates above stated and their consequences.

II. Relative Measurements of Time and Space in Two Systems of Reference. Transformations.
§ 7. Relations Between the Time Units. — Let us consider three systems of reference $$S, S_1$$ and $$S_2$$ related to each other in the following manner: The lines of relative motion of S and $$S_1$$, of S and $$S_2$$, of $$S_1$$ and $$S_2$$ are all