The Experimental Confirmation Of General Relativity
Table of Contents
FROM a systematic theoretical point of view, we may imagine the process of evolution of an empirical science to be a continuous process of induction.
Theories are evolved, and are expressed as statements of many individual observations in the form of empirical laws, from which the general laws can be ascertained by comparison.
In this way, the development of a science bears is like the compilation of a classified catalogue. It is a purely empirical enterprise.
But this point of view does not embrace the whole of the actual process for it slurs over the important part played by intuition and deductive thought in the development of an exact science.
As soon as a science has emerged from its initial stages, theoretical advances are no longer achieved merely by a process of arrangement.
Guided by empirical data, the investigator rather develops a system of thought which is built up logically from a few fundamental assumptions, as axioms.
We call such a system of thought a theory.
The theory finds the justification for its existence in the fact that it correlates many single observations. It is just here that the “truth” of the theory lies.
Corresponding to the same complex of empirical data, there may be several theories, which differ from one another considerably.
But as regards the deductions from the theories which are capable of being tested, the agreement between the theories may be so complete, that it becomes difficult to find such deductions in which the two theories differ from each other.
For example, there is agreement between:
- the Darwinian theory of evolution by selection in the struggle for existence and the theory of development based on the hypothesis of the hereditary transmission of acquired characters.
- the deductions from two theories in Newtonian mechanics on the one hand, and the general theory of relativity on the other.
Newton’s theory and my theory have a profound difference in the fundamental assumptions. Yet there is agreement between them.
Up to the present, we have been able to find only a few deductions from General Relativity which are capable of investigation, and to which pre-relativity Physics does not also lead.
I shall discuss the deductions and the empirical evidence for them.
A. The Perihelion Of Mercury
According to Newton’s law of gravitation, a planet revolving around the sun would travel in an ellipse.
In such a system, the sun is the common centre of gravity and lies in one of the foci of the orbital ellipse. This makes the sun-planet distance in a revolution grows from a minimum to a maximum, and then decreases again to a minimum.
If instead of Newton’s law, we insert a somewhat different law of attraction into the calculation.
- In this law, the motion would still take place in such a manner that the distance sun-planet exhibits periodic variations.
- But in this case, the angle described by the line joining sun and planet during such a period (from perihelion — closest proximity to the sun — to perihelion) would differ from 360°.
The line of the orbit would not then be a closed one, but in the course of time it would fill up an annular part of the orbital plane, namely between the circle of least and the circle of greatest distance of the planet from the sun.
According to General relativity, a small variation from the Newton-Kepler motion of a planet in its orbit should take place.
In such a way, that the angle described by the radius sun-planet between one perihelion and the next should exceed that corresponding to one complete revolution by an amount given by:
24 π 3 a 2 +__________________ T 2 c 2 ( 1 − e 2 )
Einstein Note: One complete revolution corresponds to the angle 2π in the absolute angular measure customary in physics. The above expression gives the amount by which the radius sun-planet exceeds this angle during the interval between one perihelion and the next.)
- “a” is the major semi-axis of the ellipse
- “e” its eccentricity
- “c” the velocity of light
- “T” the period of revolution of the planet
According to General relativity, the major axis of the ellipse rotates round the sun in the same direction as the orbital motion of the planet.
General relativity requires that this rotation should be 43 seconds of arc per century for Mercury.
But for the other planets, its magnitude would be so small that it would be undetectable especially since Venus has an orbit that is almost an exact circle. This makes it more difficult to precisely locate the perihelion.*
Superphysics Note
Astronomers have found that Newton’s theory does not suffice to calculate the exact observed motion of Mercury.
After taking account of all the disturbing influences exerted on Mercury by the remaining planets, it was found (Leverrier — 1859 — and Newcomb — 1895) that an unexplained perihelial movement of the orbit of Mercury remained over, the amount of which does not differ sensibly from the above-mentioned + 43 seconds of arc per century.
The uncertainty of the empirical result amounts to a few seconds only.