Breadcrumbs Section. Click here to navigate to respective pages.

Chapter

Chapter

# THE THEORY OF SPECIAL RELATIVITY

DOI link for THE THEORY OF SPECIAL RELATIVITY

THE THEORY OF SPECIAL RELATIVITY book

# THE THEORY OF SPECIAL RELATIVITY

DOI link for THE THEORY OF SPECIAL RELATIVITY

THE THEORY OF SPECIAL RELATIVITY book

## ABSTRACT

The previous considerations concerning the conﬁguration of rigid bodies have been founded, irrespective of the assumption as to the validity of the Euclidean geometry, upon the hypothesis that all directions in space, or all conﬁgurations of Cartesian systems of co-ordinates, are physically equivalent. We may express this as the ‘principle of relativity with respect to direction’, and it has been shown how equations (laws of nature) may be found, in accord with this principle, by the aid of the calculus of tensors. We now inquire whether there is a relativity with respect to the state of motion of the space of reference; in other words, whether there are spaces of reference in motion relatively to each other which are physically equivalent. From the standpoint of mechanics it appears that equivalent spaces of reference do exist. For experiments upon the earth tell us nothing of the fact that we are moving about the sun with a velocity of approximately 30 kilometres a second. On the other hand, this physical equivalence does not seem to hold for spaces of

reference in arbitrary motion; for mechanical eﬀects do not seem to be subject to the same laws in a jolting railway train as in one moving with uniform velocity; the rotation of the earth must be considered in writing down the equations of motion relatively to the earth. It appears, therefore, as if there were Cartesian systems of co-ordinates, the so-called inertial systems, with reference to which the laws of mechanics (more generally the laws of physics) are expressed in the simplest form. We may surmise the validity of the following proposition: if K is an inertial system, then every other system K′ which moves uniformly and without rotation relatively to K, is also an inertial system; the laws of nature are in concordance for all inertial systems. This statement we shall call the ‘principle of special relativity’. We shall draw certain conclusions from this principle of ‘relativity of translation’ just as we have already done for relativity of direction.