Typed Letter Signed on Special and General Relativity
EXTRAORDINARY EINSTEIN LETTER IN ENGLISH EXPLAINING SIMULTANEITY, ONE OF THE CENTRAL TENETS OF RELATIVITY THEORY.
Einstein’s “1905 paper [on special relativity] is widely regarded as having destroyed the classical conceptions of absolute time and space, along with absolute simultaneity and absolute length, which had reigned in physics from the times of Galileo and Newton to the dawn of the twentieth century... The Special Theory teaches us that simultaneity is not, as we supposed, an absolute concept, but is always relative to some inertial frame of reference. If we change the inertial frame of reference, we change the events to be reckoned simultaneous.” -Craig and Smith, Einstein, Relativity and Absolute Simultaneity
The concept of simultaneity lies at the core of relativity theory. The very first sub-section of Einstein’s legendary 1905 paper on Special Relativity is introduced by the title “Definition of Simultaneity” and “in the second paragraph of his 1905 relativity paper Einstein proved that simultaneity, as defined in the first paragraph, is a relative concept. This means, as Einstein explained, that ‘we must not ascribe absolute meaning to the concept of simultaneity; instead, two events that are simultaneous when observed from some particular coordinate system can no longer be considered simultaneous when observed from a system that is moving relative to that system.’ In these words Einstein for the first time offered an explicit definition of what he means when he speaks of a relative concept. As we see, it is a concept whose validity depends on the coordinate system chosen or, in brief, it is a frame-dependent concept. Simultaneity is no longer a binary relation depending also on the coordinate-frame involved. Furthermore, Einstein’s proof of the relativity of simultaneity in this paragraph is the first ever published rigorous proof of the relativity of a physical concept. The relativity of simultaneity became also the first major subject of dispute between proponents and opponents of the theory of relativity” (Max Jammer, Concepts of Simultaneity: From Antiquity to Einstein and Beyond).
When Einstein expanded his relativity theory into his General Theory of 1916, the notion of simultaneity became less well-defined and more problematic, and therefore much-debated. Einstein, in the present letter, is answering a question from Dr. Waldron Gardiner (a physician apparently without any particular expertise in relativity theory) about the concept of simultaneity in space (the domain of general relativity). Dated July 10, 1952, the letter reads in full:
Dear Sir:
"Your difficulty stems from the fact that you do not distinguish between general and special theory of relativity, the latter being a limit case, where you neglect gravitation. In the latter case there are special coordinate systems (inertial systems) and with respect to such system the concept of simultaneity has a sharp meaning and can be defined empirically by light signals.
In general relativity the space and time coordinates have no direct physical meaning so that also the concept of simultaneity of spatially distant events has no physical meaning. Physical meaning can be attributed to this concept only in certain special cases which are characterized by certain symmetry qualities. Such case is not realized in nature. But in those idealizations which we use to represent expanding space there are coordinate systems representing space-time in the mathematically simplest form. With respect to such coordinate systems simultaneity has meaning but the definition of simultaneity as defined in special relativity theory is out of place here.
Very sincerely yours,
[Signed]A. Einstein
[Printed]Albert Einstein
In short, Einstein is explaining to Dr. Gardiner that since “space and time coordinates have no direct physical meaning” in cosmological terms, i.e. there are no frames of reference that cover all of space, his understanding of simultaneity in general relativity is flawed and based on the model of special relativity, “a limit case”, achieved only through a reductive and localized application of general relativity.
Einstein concludes the letter with the provocative comment that in idealized systems representing expanding space, simultaneity has meaning and in fact this “meaning” of simultaneity in general relativity has become a fertile area of exploration over the years (see Jammer, ibid).
Note: A carbon of Dr. Gardiner’s original letter to Einstein is included.
Princeton: July 10, 1952. One 8.5 x 11 inch page of Einstein’s Institute for Advanced Study letterhead. Signed “A. Einstein” in ink. Date corrected from July 9th to July 10th. Usual (but very light) folds, small spot of soiling at top left corner; a tiny bit of toning to extreme edges. Housed in custom presentation folder.
LETTERS BY EINSTEIN DISCUSSING MAJOR ELEMENTS OF RELATIVITY (PARTICULARLY IN ENGLISH) ARE EXCEEDINGLY RARE.
Price: $90,000 .