Berlin Notebook Gravitational Lens Calculation
During work recorded in a 1912 notebook, Einstein calculated how a foreground mass could bend light from a background source and produce the geometry of a gravitational lens.
Historical biography archive · Updated 2026-11-03
Albert Einstein Biography and Timeline
Follow Albert Einstein through 56 dated historical records for Germany.
Albert Einstein, historical timeline
A chronological timeline drawn from matching World History Database records.
56Distinct records
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1912–1918Years on this page
1912
Double-Image Lens Geometry Derived
Einstein's notebook analysis showed that gravitational deflection could allow light from one distant source to reach an observer along two paths, producing two apparent images.
Lens Magnification Formula First Calculated
Einstein worked out a magnification relation for the gravitational-lens configuration, anticipating formulae he would publish when he returned to the subject decades later.
1914
Covariance Restrictions Defended
Einstein defended the restricted covariance of his provisional gravitational equations, believing at the time that broader coordinate freedom would prevent a unique physical description.
Formal Entwurf Theory Presented in Berlin
Einstein gave a systematic mathematical presentation of the Entwurf gravitational theory after moving to Berlin, clarifying its field equations, coordinate restrictions and physical assumptions.
Gravitational Conservation Laws Reconsidered
Einstein investigated how energy and momentum conservation should be formulated when the gravitational field itself participates in the dynamics of spacetime.
Rotating Coordinates Test the Entwurf Theory
Einstein examined rotating coordinate systems as a demanding consistency test for the Entwurf equations, exposing difficulties that contributed to his later rejection of the provisional theory.
1915
November 4 Covariant Gravity Equations
Einstein presented new gravitational field equations to the Prussian Academy that restored much broader covariance and marked the first of his decisive November 1915 communications.
November 11 Vacuum Field Equations
Einstein refined his field equations under a trace condition and showed how the revised framework could approach fully covariant gravitation in regions outside matter.
Mercury Anomaly Reproduced without Adjustable Parameters
The relativistic Mercury calculation matched the anomalous perihelion advance using the gravitational theory itself rather than introducing an additional planet or an adjustable correction to Newtonian gravity.
November 18 Mercury Advance Calculation
Einstein used the emerging general theory to account for Mercury's unexplained perihelion advance, obtaining the observed residual shift that earlier gravitational models had failed to reproduce.
November 25 Matter-Coupled Field Equations
Einstein presented the final generally covariant field equations including their coupling to matter, completing the mathematical core of general relativity.
Revised Solar Deflection Reaches Full Relativistic Value
With the completed geometric treatment of gravity, Einstein obtained a solar light-deflection prediction approximately twice the value produced by his earlier equivalence-principle calculation.
Zangger Letter Revisits Gravitational Lensing
Einstein mentioned the possibility of gravitational lensing in a letter to Heinrich Zangger, revisiting the double-image effect he had calculated in his 1912 notebook.
Return to General Covariance
Einstein abandoned key restrictions of the Entwurf approach and returned to generally covariant tensor equations, beginning the final rapid reconstruction of his gravitational theory.
1916
Absorption Probability Coefficient Defined
Einstein represented the probability of an atom absorbing incident radiation and moving to a higher energy state with a coefficient proportional to the surrounding radiation density.
Atomic Transition Probabilities Introduced
Einstein formulated radiation processes in terms of probabilities for transitions between atomic energy states, creating a statistical framework for absorption and emission.
Detailed Balance Applied to Matter and Radiation
Einstein required upward and downward atomic transitions to balance in thermal equilibrium, using that condition to connect transition probabilities with the equilibrium radiation spectrum.
General Relativity Review Article Published
Einstein published a comprehensive exposition of general relativity that assembled the geometric framework, field equations and physical consequences into a systematic theory.
Geodesic Motion Described in Curved Spacetime
Einstein's mature theory described freely falling bodies as following the straightest possible world-lines through curved spacetime rather than being pulled by a Newtonian gravitational force.
Gravitational Energy Flux Treated with Pseudotensor
Einstein developed a gravitational energy-momentum construction to discuss how changing gravitational fields can transport energy despite the special conservation difficulties of general relativity.
Gravitational Waves Propagate at Light Speed
Einstein's wave analysis showed that physical gravitational disturbances in the relativistic theory propagate through empty space at the speed of light.
Nonlinearity of Gravitational Field Established
Einstein's field equations made gravity nonlinear, so the gravitational field contributes to the dynamics instead of behaving as a simple superposition of independent Newtonian forces.
Planck Spectrum Recovered from Transition Statistics
Einstein showed that his statistical rules for absorption, spontaneous emission and induced emission can reproduce Planck's black-body radiation law under thermal equilibrium.
Radiative Transitions Linked to Discrete Energy Differences
Einstein treated the frequency of absorbed or emitted radiation as fixed by the discrete energy difference between the participating atomic states.
Spontaneous Emission Probability Defined
Einstein introduced a coefficient describing the probability that an excited atom will emit radiation spontaneously and fall to a lower energy state.
Stimulated Emission Probability Coefficient Defined
Einstein introduced a second radiation-dependent transition probability in which incident radiation stimulates an excited atom to emit additional radiation.
Stress-Energy Identified as Source of Curvature
General relativity connected spacetime curvature with the energy, momentum and stresses of matter, making the physical contents of the universe sources of the gravitational geometry.
Weak-Field Gravitational Waves Derived
Einstein linearised the gravitational field equations in the weak-field limit and identified wave-like disturbances capable of propagating through spacetime.
1917
Cosmological Term Added to Field Equations
To support a static cosmological solution, Einstein modified the gravitational field equations with an additional cosmological term that could counterbalance large-scale attraction.
Machian Motivation Shapes Einstein Cosmology
Einstein designed his early relativistic cosmology partly around the hope that inertia would be determined by the overall distribution of matter, reflecting his interpretation of Mach's ideas.
Static Closed Universe Model Proposed
Einstein applied general relativity to the universe as a whole and proposed a spatially closed, homogeneous model intended to remain static on cosmic scales.
Atomic Recoil Required by Photon Momentum
By assigning momentum to individual radiation quanta, Einstein concluded that atoms must recoil when they emit or absorb directed packets of light.
Light Quantum Momentum Set by Energy and Light Speed
Einstein's radiation theory assigned each emitted or absorbed light quantum a momentum equal to its energy divided by the speed of light.
Radiation Equilibrium Connects Quantum Events and Thermodynamics
Einstein united discrete atomic transitions with thermodynamic equilibrium, demonstrating that quantum absorption and emission rules could generate the observed black-body spectrum.
Random Emission Directions Linked to Molecular Motion
Einstein showed that randomly directed quantum emission events contribute to molecular momentum fluctuations and must be balanced statistically in thermal equilibrium.
Spontaneous Emission Formalized in Quantum Radiation Theory
Einstein's published quantum theory of radiation formalized spontaneous emission as an intrinsically statistical process occurring without an externally applied radiation field.
Stimulated Emission Predicted from Thermal Equilibrium
Einstein's equilibrium analysis required an induced emission process in which incident radiation increases the probability that an excited atom emits matching radiation.
1918
Gravitational Wave Energy Calculation Corrected
Einstein revisited his gravitational-wave analysis and corrected the treatment of radiated energy, removing misleading wave modes from the earlier calculation.
Mass Quadrupole Identified as Leading Radiation Source
Einstein showed that the leading gravitational radiation from an isolated slow-moving system is governed by changes in its mass quadrupole moment rather than by a simple mass dipole.
Records, sources and methodology
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