Einstein’s Famed Defense of Relativity, In Which He Uses Mathematical and Theoretical Arguments to Explain and Defend the 20th Century’s Most Important Scientific Theory

Einstein adds equation notations in his hand and states, “The general theory of relativity rises and falls with this interpretation”; written just days before he learns he is awarded the Nobel Prize

In 1905, while a young patent clerk and physicist in Bern, Switzerland, Albert Einstein obtained his doctorate and published a paper that explained his newly developed Special Theory of Relativity. This unlocked many mysteries of the universe, and introduced the world to "E=mc2," equating mass and the speed of light with energy.  It established that time and space are not fixed, and in fact change to maintain a constant speed of light regardless of the relative motions of sources and observers. It showed space as a four dimensional universe, with time added as the fourth dimension.  Just 10 years later, in 1915, Einstein published his General Theory of Relativity, in which gravitational effects are explained by the warping of space-time.  In this theory, Einstein incorporated gravity as a geometric property of space-time. This expanded upon Special Relativity to describe the overall structure of the universe and the impulses of a gravitational universe.  The two theories built on each other and were intimately related.

The geometry of Einstein's space-time, as spelled out in Relativity, or the metric by which Einstein determined the properties of space and time, is best illustrated by Einstein's mentor, Hermann Minkowski, via the formula ds2=dt2-dx2-dy2-dz2.  This is the basis of relativity, an equation which Einstein used and, along with E=mc2, is among the most important related to his theories.  In this equation, the x, y, and z represent spatial positions, while "t" represents time.  Ds2 therefore is a fundamental representation of their relationships in Einstein's space-time, as applied to General and Special relativity.  It would allow you to measure objects in space and do so in infinitesimal intervals.  In short, this equation is what space-time looks like.

At its essence, General Relativity is a theory of gravity, and a very common class of theoretical problems is something called a central-symmetric static solution.  When a large object exists in space-time, its energy and momentum exert an influence or gravity on the space around it, as a bowling ball on a trampoline would do.  It literally bends space-time, producing a curvature.  In this way, our Sun curves space and exerts an influence on Earth and the other planets which orbit around it.  Also, a black hole would behave in this way, and Einstein's work on relativity has been measured using this type of central-symmetric example.

In all this, as with his life in general, Einstein relied on objective results.  Something could not exist without a means of measuring it.  If a "resting clock," as he often put it, were present at the location of measurement, could it be measured, or was another extraneous, hypothetical element required.  If the latter, it would not do.  For Einstein, a measurable result was required. Only in this way could General and Special Relativity stand the test of time. Just as Special Relativity on a geometric plane had to be measurable, so did the more complex fields in General Relativity have to be measurable.  And these effects of curvature of space are tiny and applied at the most basic level, not only to the plane as a whole but with General Relativity to every element.

On December 10, 1921, Einstein was awarded the Nobel Prize for his work, and he would accept that prize one year later.  But not everyone accepted relativity.  A few prominent detractors sought to reconcile what they saw as inconsistencies and "correct" Einstein's work.  Among the most prominent was French physicist Paul Painleve, who was also a politician and 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.  Painleve 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 and frequently cited reply, in which he uses mathematical and theoretical arguments to defend Relativity and to compare Special and General Relativity.

This famous letter contains in it the basis of Einsteinian thought, representing his mathematical and theoretical defense of the most important scientific principle of the 20th century (and among the most important of all time).

Typed Letter Signed, Berlin, December 7, 1921, three days before he learned he would receive the Nobel Prize, to French Physicist Paul Painleve in Paris.

“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 co-ordinates x, y, z, t are measurable directly by means of resting clocks relative to the co-ordinate 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.”

A search of public records shows nothing having sold that is comparable.

This famous letter contains in it the basis of Einsteinian thought, representing his mathematical and theoretical defense of the most important scientific principle of the 20th century (and among the most important of all time). It also shows his core philosophy that phenomena must be objective and measurable to be believed, which has impacted on not merely his scientific but philosophical and religious thought as well. This is among the most important letters Einstein wrote to have reached the market. It has for decades been in the collection of a private institution before being offered here for sale.