Relativity theory, philosophical significance of
Authors: Redhead Michael 
Published: September 2018

There are two parts to Albert Einstein’s relativity theory, the special theory published in 1905 and the general theory published in its final mathematical form in 1915. The special theory is a direct development of the Galilean relativity principle in classical Newtonian mechanics. This principle affirms that Newton’s laws of motion hold not just when the motion is described relative to a reference frame at rest in absolute space, but also relative to any reference frame in uniform translational motion relative to absolute space. The class of frames relative to which Newton’s law of motion are valid are referred to as inertial frames. It follows that no mechanical experiment can tell us which frame is at absolute rest, only the relative motion of inertial frames is observable. The Galilean relativity principle does not hold for accelerated motion, and also it does not hold for electromagnetic phenomena, in particular the propagation of light waves as governed by Maxwell’s equations. Einstein’s special theory of relativity reformulated the mathematical transformations for space and time coordinates between inertial reference frames, replacing the Galilean transformations by the so-called Lorentz transformations (they had previously been discovered in an essentially different way by H.A. Lorentz in 1904) in such a way that electromagnetism satisfied the relativity principle. But the classical laws of mechanics no longer did so. Einstein next reformulated the laws of mechanics so as to make them conform to his new relativity principle. With Galilean relativity, spatial intervals, the simultaneity of events and temporal durations, did not depend on the inertial frame, although, of course, velocities were frame-dependent. In Einstein’s relativity the first three now become frame-dependent, or ‘relativized’ as we may express it, while for the fourth, namely velocity, there exists a unique velocity, that of the propagation of light in vacuo, whose magnitude c is invariant, that is, the same for all inertial frames. It can be argued that c also represents the maximum speed with which any causal process can be propagated. Moreover in Einstein’s new mechanics inertial mass m becomes a relative notion and is associated via the equation m=E/c2 with any form of energy E. Reciprocally inertial mass can be understood as equivalent to a corresponding energy mc2.

In the general theory Einstein ostensibly sought to extend the relativity principle to accelerated motions of the reference frame by employing an equivalence principle which claimed that it was impossible to distinguish observationally between the presence of a gravitational field and the acceleration of a reference frame. Einstein here elevated into a fundamental principle the known but apparently accidental numerical equality of the inertial and the gravitational mass of a body (which accounts for the fact that bodies move with the same acceleration in a gravitational field, independent of their inertial mass). By extending the discussion to gravitational fields which could be locally, but not globally, transformed away by a change of reference frame, Einstein was led to a new theory of gravitation, modifying Newton’s theory of gravitation, which could explain a number of observed phenomena for which the Newtonian theory was inadequate. This involved a law (Einstein’s field equations) relating the distribution of matter in spacetime to geometrical features of spacetime associated with its curvature, considered as a four-dimensional manifold. The path of an (uncharged spinless) particle moving freely in the curved spacetime was a geodesic (the generalized analogue in a curved manifold of a straight line in a flat manifold).

Einstein’s theories have important repercussions for philosophical views on the nature of space and time, and their relation to issues of causality and cosmology, which are still the subject of debate.