4 9 8 D O C U M E N T 5 0 3 N E W T O N S M E C H A N I C S energy.[9] The theory also showed that Newton’s law of motion can only be consid- ered as a limiting law valid only for small velocities and substituted for it a new law of motion, in which the velocity of light in a vacuum appears as the limiting velocity. The last step in the development of the program of the field theory was the gen- eral theory of relativity. Quantitatively it made little modification in Newton’s theory, but qualitatively a deep-seated one. Inertia, gravitation, and the metrical be- havior of bodies and clocks were reduced to the single quality of a field, and this field in turn was made dependent on the bodies (generalization of Newton’s law of gravitation, or of the corresponding field law, as formulated by Poisson). Space and time were so divested, not of their reality, but of their causal absoluteness (absoluteness—influencing, that is, not influenced), which Newton was compelled to attribute to them in order to be able to give expression to the laws then known.[10] The generalized law of inertia takes over the role of Newton’s law of motion. From this short characterization it will be clear how the elements of Newton’s theory passed over into the general theory of relativity, the three defects above mentioned being at the same time overcome. It appears that within the framework of the gen- eral theory of relativity the law of motion can be deduced from the law of the field, which corresponds to Newton’s law of force.[11] Only when this aim has been fully attained can we speak of a pure theory of fields. Newton’s mechanics prepared the way for the theory of fields in a yet more for- mal sense. The application of Newton’s mechanics to continuously distributed masses led necessarily to the discovery and application of partial differential equa- tions, which in turn supplied the language in which alone the laws of the theory of fields could be expressed.[12] In this formal connection also Newton’s conception of the differential law forms the first decisive step to the subsequent development. The whole development of our ideas concerning natural phenomena, which has been described above, may be conceived as an organic development of Newton’s thought. But while the construction of the theory of fields was still actively in prog- ress the facts of heat radiation, spectra, radio-activity, and so on, revealed a limit to the employment of the whole system of thought, which, in spite of gigantic suc- cesses in detail, seems to us today completely insurmountable.[13] Many physicists maintain, not without weighty arguments, that in face of these facts not only the differential law but the law of causality itself—hitherto the ultimate basic postulate of all natural science—fails. The very possibility of a spatio-temporal construction which can be clearly brought into consonance with physical experience is denied. That a mechanical system should permanently admit only discrete values of energy or discrete [p. 276]
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