La magie des mathématiques naturellement!
Today is November 25th 2015. I have decided to celebrate here the 100th anniversary of the publication of the last of the four papers Einstein wrote the same month about the general theory of relativity. In this paper he overcame the remaining central tension in the relation between mathematical formalism and physical interpretation. This fits nicely with the theme of this blog thus let's go a little further quoting the interesting book "The road to relativity" by Hanoch Gutfreund and Jürgen Renn:
The tension expressed itself either in a physically meaningless coordinate restriction (in the case of the theory of November 4th [a coordinate restriction followed from the {energy-momentum} conservation principle requirement]) or in a speculative hypothesis about the structure of matter (in the case of the theory presented ... on November 11th {a gravitational field equation based on the Ricci tensor was derived from the assumption that the only fields occurring as sources of gravitation are electromagnetic ones})... All that was required to achieve this final version was to change the way in which the sources of the gravitational field were inserted on the right-hand side of the gravitational field equation. If the trace of the energy-momentum tensor... is appropriately added to the source term on the right-hand side of the field equation then all the additional conditions become superfluous. In particular, the conservation principle is also satisfied as an automatic consequence of the modified field equation...
In his latter writings Einstein frequently emphasized that the new solution of the problem of gravitation is a natural consequence of the mathematical theory centered on the Riemann tensor... So he himself described the breakthrough of late 1915 not as the result of a convergence of physical and mathematical strategies but an exclusive success of the latter. Even in his first November paper, Einstein was fascinated by the power of mathematical formalism to lead to the correct theory: "Nobody who really grasped [the general theory of relativity] can escape from its charm, because it signifies a real triumph of the general differential calculus as founded by GAUSS, RIEMANN, CHRISTOFFEL, RICCI AND LEVI-CIVITA"
Here is the original quotation in German of the last sentence from the wonderful website The collected papers of Albert Einstein
Dem Zauber dieser Theorie wird sich kaum jemand entziehen können, der sie wirklich erfasst hat; sie bedeutet einen wahren Triumph der durch GAUSS, RIEMANN, CHRISTOFFEL, RICCI AND LEVI-CIVITA begründeten Methode des allgemeinen Differentialkalküls.
Zur allgemainen Relativitätstheorie, Albert EinsteinSubmitted 4 November 1915, Published 11 November 1915
