Einstein's Path to General Relativity Mu-In Park Sogang Univ., Korea International Conference on General Relativity: Centennial Overviews and Future Perspectives (21, Dec. 2015, Ewha Womans U., Seoul)

I. Main Works (for Relativity) 1905 (age 26) : Special Relativity (30 June) (age 36) : General Relativity (25 Nov.) 1916 : Gravitational Wave 1917:Cosmology Model (Cosmological Constant) (age 56): Wormhole (ER bridge) 1936 : Gravitational Lensing 1938 : Einstein–Infeld–Hoffmann equations (Post -Newtonian approx.)

Main Works (with Q.M.) 1905 (age 26) : Photon (18 March), Brownian motion (11 May), Special Relativity (30 June) : Specific Heat (age 36) : General Relativity (25 Nov.) 1916 : Gravitational Wave, Laser : Cosmology Model (Cosmological Constant) : Bose-Einstein Statistics 1935 (age 56): EPR, Wormhole (ER bridge) 1936 : Gravitational Lensing 1938 : Einstein–Infeld–Hoffmann equations (Post-Ne wtonian approx.)

II. Einstein's Path to General Relativity “Relativity principle” is implicit in Newtonian mechanics: For all inertial observers, no preferred reference frame. (No logical problem with absolute time and space) But this is troubled when we consider EM wave (light) and its propagating medium (aether) which may be considered as a “preferred frame” and we must be able to determine motion relative to the aether.

From the failure of experiment (Michelson- Morley (1887)) to detect the motion through the aether, Lorentz (1895) invented “Lorentz transformation (LT)” so that the Maxwell Eq. has the “same from” (i.e., the same speed of light) in all reference frames, with reference to the aether. Einstein (30 June 1905) derived the LT from “the relativity principle” and “constancy of speed of light”, without reference to the aether: The relativity principle become “explicit” and all ad hoc hypotheses (including aether) were removed while all the known observed results were derived in a few pages. [Cf. Poincare (23 July 1905)]

After formulating SR, Einstein realized that it is incomplete in two aspects, at least. (1). Newton’s gravity, with action at a distance, is contradict to the SR: Observer dependent (due to relative simultaneity); violates the speed limit c. Cf. EM fields (forces) propagates with light speed c. (2). SR does not work for “accelerating observers”.

1907 (4 Dec): Einstein “argued” that (1) Relativity principle “could” be extended to gravity: “The Equivalence principle”; (a). For free falling observer, SR applies, (b). One can not distinguish (uniform) gravity with a (uniformly) accelerating motion. (2) Predictions: Light reflection (preliminary), gravitational time dilation (or red shift of spectral lines). (3) However, Einstein was “skeptical” about comparison with experience due to small effects; No clear “observational” indication that his direction is correct or not !

1911: (1) More rigorous (the first order approx) than 1907 paper. (2) Confident of experimental tests: Light bending near the sun, 0.83 arcsec; Propose experiment at the eclipses of the Sun. (3) Grav. red shift from the sun: 2x10^(-6); Einstein quoted a similar shift (of the same order of magnitude) (1909) in experience but he was not clear whether this is the confirmation of his result [Confirmed in 1959 !] (4) No clear confident indication still !

Episode There was a solar eclipse at 21 Aug Two teams (Germany, USA) went … to detect the light reflection (19 July). The second world war occurred (28 July). German team was captured in Russia ! USA term failed the detection due to clouds. But, later Einstein’s result turned out to be wrong (just half of the correct value)! Actually, Newton gravity (incorrectly) predicts the same light bending !

But, for generic non-uniform accelerations, which corresponds to generic non-uniform gravity, the space and time would be “non-Euclidean” (e.g. co-rotaing observer on a rotating disk). (1911 ?) He noticed that Minkowski (1907)’s 4- dimensional formulation (time as a fourth coordinate of space-time contiuum) is useful to treat the curved space-time: 4 vector, world line, proper time, Lorentz invariance/covariance, etc…

1912: Einstein returned to ETH (Switzland), where he his classmate M. Grossmann is. He learned about “differential geometry “ and “tensor calculus” with the help of Grossman. At the urging of Levi-Civita, he began expl oring the general covariance (i.e., the use of tensors) for his gravitational theory.general covariancetensors The theory should (1) contain Newtonian gravity limit, (2) produce light bending effect, (3) explain the Mercury’s precession anomaly.

Einstein and Grassman tried all the possible covariant Eq (Riemann tensor, Ricci tensor,…) [Zurich Notebook (1912)]. But they (incorrectly) found that (1) the Newtonian limit can not be obtained and (2) matter’s energy momentum are not conserved. 1913: Einstein abandoned that approach, argui ng that it is inconsistent based on the "hole ar gument".hole ar gument : Einstein tried other field Eqs based on another approach. When that approach wa s proven to be inconsistent, he revisited the a pproach (1912) with general covariance.field Eqs

1915 (Oct.-4. Nov.): He proposed the field Eq., This produce non-Newtonian Mercury precession, but Energy-momentum is not conserved, generally (25 Nov. (published): He presented the final Eq. (in the current notation) Results: (1) Newtonian limit for weak gravity (2) Explains Mercury’s precession anomaly (43 arcsec/century) (3) predicts light bending around the sun (1.7 arcsec),,

Notes The same gravitational red shift (or time dilation) with the 1911’s analysis (only with Equivalence principle, without Einstein Eq) at the leading order: Only the effect of curved time contributes. Produce Newtonian gravity for weak gravity limit. But, it explains the Mercury’s anomaly (for the first time): This is the observational indication that his theory is in the right direction; actually, this was the guide line for the right theory !!

Notes-Continued. The light bending is “twice” of 1911’s analysis: Here, the effect of curved space also contribute which was not considered in Einstein was confidant about his theory, after explaining the Mercury’s anomaly. Cf. SR Cf. Hilbert (16 (submitted)-20 (published) 2015).

Later Works (with Q.M.) 1905 (age 26) : Photon (18 March), Brownian motion (11 May), Special Relativity (30 June) : Specific Heat (age 36) : General Relativity (25 Nov.) 1916 : Gravitational Wave, Laser : Cosmology Model (Cosmological Constant) : Bose-Einstein Statistics 1935 (age 56): EPR, Wormhole (ER bridge) 1936 : Gravitational Lensing 1938 : Einstein–Infeld–Hoffmann equations (Post-Ne wtonian approx.)

Thank you !