”The General Theory of Relativity rises and falls with this interpretation of ds....”
AN EXTRAORDINARY LETTER IN WHICH EINSTEIN DEFENDS THE GENERAL THEORY OF RELATIVITY.
Although by 1921 Einstein had achieved great fame and world renown, there were still influential members of the scientific community who did not accept many aspects of relativity and sought to reconcile what they saw as inconsistencies in the theory and "correct" Einstein's work. Among the most prominent detractors was French physicist Paul Painlevé, who was also a politician who served twice as Prime Minister of France. He argued that the existence of two possible fields for the same distribution of mass demonstrated the ambiguity or incompleteness of General Relativity, and sought to remedy this with a function "r," a theoretical construct that would bridge the gap. This function "r" would not be measurable in the same ways as Einstein's variables. Painlevé presented his paper to the French Academy of Sciences on October 24, 1921 and invited Einstein to come debate him.
This is Einstein’s original reply to Panlevé’s challenge, and Einstein uses mathematical and theoretical arguments to defend relativity and to compare special and general relativity.
The letter is dated December 7, 1921, just three days before Einstein learned that he would be awarded the Nobel Prize in physics. Translated from the original German, it reads:
Your friendly greetings have reached me, as regards two invitations to Paris for the time around New Years. I thank you heartily, all the more so for the joy that I felt when I found out that as a renowned scholar and politician, you are, at the same time, an enthusiastic proponent of pacifist ideas. Unfortunately, I am not now in a position to accept these invitations , but I would like to use the opportunity to briefly answer the criticism regarding the General Theory of Relativity, which you raised at the academic meeting on the 24th of October.
If, in the central-symmetric static solution, any function of r is joined in place of ds2, you do not get a new solution because the quantum r itself has no physical meaning whatsoever, but only the quantum ds itself, or better, the system of all ds in their four-dimensional multiplicity has. It must always be kept in mind that the co-ordinates as such have no meaning physically, i.e. they [equations based on the variable “r”] do not represent any measurable results. Only results gained by eliminating the co-ordinates [Einstein’s equation] can claim objective significance. Furthermore, the metrical interpretation of the quantum ds is not "pure imagination" but the very essence of the whole theory.
The matter is as follows: According to the Special Theory of Relativity, the coordinates x, y, z, t are measurable directly by means of resting clocks relative to the coordinate system. Consequently, the invariable ds, defined by the equation ds2 = dt2-dx2- dy2-dz2, also has the significance of a measurable result. The General Theory of Relativity is based completely on the assumption that every infinitesimal element of the multiplicity of space and time is physically in proportion to the four-dimensional multiplicity of the Special Theory of Relativity, i.e. there are infinitesimal co-ordinate systems (inertial systems) which can help define the ds physically just as according to the Special Theory of Relativity. The General Theory of Relativity rises and falls with this interpretation of ds. The interpretation is just as important to it [the theory of relativity] as the requirement for infinitesimal geometry of surfaces, that an infinitesimal surface element behaves like a portion of a plane in metric relationship. If you take this argument into consideration, you will probably come to the conclusion, that your criticism has not been justified.
[signed] A. Einstein
Berlin: December 7. 1921. Two pages, signed “A. Einstein”. Two pages; usual folds, some foxing.
LETTERS WHERE EINSTEIN DISCUSSES RELATIVITY THEORY IN SUCH DETAIL ARE EXCEEDINGLY SCARCE. A REMARKABLE LETTER, ONE OF THE MOST SIGNIFICANT IN PRIVATE HANDS.