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48
Relativity: The Special and General Theory
Since it has often been contended by opponents of the theory of relativity that the special theory of
relativity is overthrown by the general theory of relativity, it is perhaps advisable to make the facts
of the case clearer by means of an appropriate comparison. Before the development of
electrodynamics the laws of electrostatics were looked upon as the laws of electricity. At the
present time we know that electric fields can be derived correctly from electrostatic considerations
only for the case, which is never strictly realised, in which the electrical masses are quite at rest
relatively to each other, and to the co?ordinate system. Should we be justified in saying that for this
reason electrostatics is overthrown by the field?equations of Maxwell in electrodynamics ? Not in
the least. Electrostatics is contained in electrodynamics as a limiting case ; the laws of the latter
lead directly to those of the former for the case in which the fields are invariable with regard to time.
No fairer destiny could be allotted to any physical theory, than that it should of itself point out the
way to the introduction of a more comprehensive theory, in which it lives on as a limiting case.
In the example of the transmission of light just dealt with, we have seen that the general theory of
relativity enables us to derive theoretically the influence of a gravitational field on the course of
natural processes, the Iaws of which are already known when a gravitational field is absent. But the
most attractive problem, to the solution of which the general theory of relativity supplies the key,
concerns the investigation of the laws satisfied by the gravitational field itself. Let us consider this
for a moment.
We are acquainted with space?time domains which behave (approximately) in a " Galileian "
fashion under suitable choice of reference?body, i.e. domains in which gravitational fields are
absent. If we now refer such a domain to a reference?body K¹ possessing any kind of motion, then
relative to K¹ there exists a gravitational field which is variable with respect to space and time.²
)
The
character of this field will of course depend on the motion chosen for K¹. According to the general
theory of relativity, the general law of the gravitational field must be satisfied for all gravitational
fields obtainable in this way. Even though by no means all gravitationial fields can be produced in
this way, yet we may entertain the hope that the general law of gravitation will be derivable from
such gravitational fields of a special kind. This hope has been realised in the most beautiful
manner. But between the clear vision of this goal and its actual realisation it was necessary to
surmount a serious difficulty, and as this lies deep at the root of things, I dare not withhold it from
the reader. We require to extend our ideas of the space?time continuum still farther.
Next: Behaviour of Clocks and Measuring?Rods on a Rotating Body of Reference
Footnotes
1
)
By means of the star photographs of two expeditions equipped by a Joint Committee of the
Royal and Royal Astronomical Societies, the existence of the deflection of light demanded by
theory was first confirmed during the solar eclipse of 29th May, 1919. (Cf. Appendix III.)
2
)
This follows from a generalisation of the discussion in Section 20
Relativity: The Special and General Theory