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.
Albert Einstein · Place
Berlin
123 Einstein records associated with Berlin.
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.
Berlin Academy Appointment
Moves to Berlin for a senior research appointment and membership of the Prussian Academy of Sciences.
Covariance Problem in Gravitation
Publishes work refining the mathematical and covariance problems of his developing gravitational theory.
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.
Einstein-Grossmann Covariance Analysis
Continues with Grossmann to examine covariance properties of their gravitational equations, exposing problems that eventually drive Einstein back toward general covariance.
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.
Formal Foundations of General Relativity
Publishes a detailed formal treatment of the developing gravitational theory, presenting its mathematical structure before he restores fully general covariance.
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.
Manifesto to Europeans
Co-signs a pacifist appeal opposing wartime nationalism among European intellectuals.
Nordstrom Gravitation Recast with Fokker
With Adriaan Fokker, reformulates Nordstrom's competing gravitation theory using tensor methods, clarifying how relativistic gravity could be expressed geometrically.
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.
Einstein-de Haas Effect
Publishes experimental work with Wander de Haas linking magnetism to angular momentum.
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.
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.
Revised Solar Light-Bending Value
Using the completed theory, obtains the full gravitational deflection predicted for starlight grazing the Sun, approximately twice his earlier 1911 estimate.
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.
Restricted Covariance Equations
Presents revised gravitational field equations to the Prussian Academy during his final push toward general relativity.
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.
Second November Field Equations
Presents improved gravitational equations to the Prussian Academy and moves substantially closer to the generally covariant form completed later that month.
Unimodular Gravitation Equations
Presents another formulation of gravitation using a restricted coordinate condition with unit determinant.
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.
Mercury Perihelion
Explains Mercury's anomalous perihelion advance using the emerging general theory of relativity.
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.
Final Generally Covariant Field Equations
Presents the final generally covariant gravitational field equations to the Prussian Academy, completing the mathematical core of general relativity.
General Relativity Field Equations
Presents the final generally covariant gravitational field equations to the Prussian Academy.
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.
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.
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.
Energy Conservation in General Relativity
Develops the treatment of energy and momentum in the gravitational field, addressing how conservation laws operate within the generally covariant theory.
Foundation of General Relativity
Publishes a systematic presentation of the general theory of relativity and its field equations.
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.
German Physical Society Presidency
Serves as president of the German Physical Society during the consolidation of general relativity.
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.
Hamilton Principle for General Relativity
Formulates general relativity using Hamilton's variational principle, providing a compact mathematical route to the gravitational field equations and their conservation properties.
Kottler Equivalence Hypothesis Response
Responds to Friedrich Kottler's criticism of the equivalence hypothesis, defending the conceptual basis on which his route from special to general relativity depended.
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.
Quantum Theory of Radiation
Develops a quantum theory of radiation introducing transition probabilities later represented by Einstein coefficients.
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.
Schwarzschild Solution Presented to Academy
Communicates Karl Schwarzschild's exact solution of the new field equations to the Prussian Academy, demonstrating that general relativity admits important exact solutions.
Gravitational Waves
Predicts gravitational waves as propagating disturbances in spacetime within general relativity.
Relativity: The Special and General Theory
Publishes his popular introduction to special and general relativity.
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.
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.
Kaiser Wilhelm Institute Directorship
Becomes founding director of the Kaiser Wilhelm Institute for Physics.
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.
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.
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.
Relativistic Cosmology
Applies general relativity to the universe and introduces the cosmological constant in a static cosmological model.
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.
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.
Stimulated Emission
Formulates stimulated emission in his quantum theory of radiation, a principle later fundamental to lasers.
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.
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.
Mach Principle Formulation
Publishes a foundational discussion of general relativity in which he explicitly names Mach's principle and distinguishes it from the equivalence and relativity principles.
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.
Quadrupole Formula for Gravitational Waves
Refines gravitational-wave theory and derives the quadrupole form for radiated energy.
Quadrupole Radiation Formula
Derives the quadrupole formula for gravitational radiation, relating emitted wave power to changing mass distributions in accelerating systems.
International Scientific Fame
Becomes internationally famous after eclipse observations are widely reported as confirming general relativity.
Anti-Relativity Campaign
Publicly confronts organized attacks on relativity amid growing political and antisemitic hostility.
General Relativity Foundation Supplement
Publishes a proposed addition to the foundations of general relativity, continuing his effort to strengthen the conceptual and mathematical basis of gravitational field theory.
Nobel Prize in Physics
Awarded the 1921 Nobel Prize in Physics for theoretical physics, especially the law of the photoelectric effect.
Geometry and Experience Lecture
Explains how geometry acquires physical meaning through measurement and discusses the relationship between mathematical geometry and the spacetime structure of general relativity.
Early Unified Field Program
Begins sustained attempts to combine gravitation and electromagnetism within a single field framework.
Photoelectric Law Highlighted in Nobel Citation
The Nobel citation singled out Einstein's quantitative law of the photoelectric effect, giving formal recognition to a result rooted in his 1905 light-quantum hypothesis.
Nobel Award Announced for Photoelectric Law
The Royal Swedish Academy of Sciences announced Einstein as the recipient of the reserved 1921 Nobel Prize in Physics, emphasizing his discovery of the law of the photoelectric effect.
Affine Field Theory
Explores an affine field theory as a possible extension of general relativity, seeking a unified geometric description of gravitation and electromagnetism.
Compton Scattering Strengthens Light-Quantum Momentum Picture
The emerging evidence from Compton scattering gave strong experimental support to the energy-and-momentum properties of radiation quanta that Einstein had advocated for years.
General Relativity Academy Paper
Publishes a further Prussian Academy paper on general relativity, revisiting technical aspects of the theory after its rapid international acceptance.
Photon Momentum Evidence Reinforces Einstein Radiation Theory
Experimental scattering results increasingly supported the view that individual radiation quanta carry directed momentum, a requirement already embedded in Einstein's 1917 radiation theory.
Pour le Merite for Sciences and Arts
Is admitted to the Pour le Mérite for Sciences and Arts.
Bose Counting Recasts Planck Radiation Law
Einstein recognized that Bose's counting method obtained Planck's spectrum by treating light quanta statistically without relying on the classical independent-particle counting used for ordinary gases.
Bose Light-Quantum Manuscript Reaches Einstein
Satyendra Nath Bose sent Einstein a manuscript deriving Planck's radiation law by a new statistical counting method applied directly to indistinguishable light quanta.
Bose Paper Translation
Translates Satyendra Nath Bose's paper on Planck's law into German and arranges its publication.
Bose-Einstein Condensation Prediction
Predicts that ideal bosonic particles can accumulate in the lowest quantum state at low temperature.
Bose-Einstein Statistics
Extends Bose's statistical method from photons to particles of an ideal gas.
Einstein Recommends Bose Radiation Paper for Publication
Einstein submitted Bose's translated paper for publication and endorsed its new derivation of the black-body radiation law from quantum statistics.
Einstein Translates Bose Photon Statistics Paper
Einstein translated Bose's manuscript on the quantum statistics of radiation into German after recognizing the importance of its treatment of light quanta.
Photon Indistinguishability Gains Statistical Role
Bose's method, promoted by Einstein, treated light quanta as statistically indistinguishable objects, an idea that became fundamental to quantum statistics.
American Academy Foreign Honorary Membership
Accepts election as a Foreign Honorary Member of the American Academy of Arts and Sciences.
BKS Statistical Conservation Challenged by Photon Picture
Einstein continued to favour exact energy and momentum conservation in individual radiation processes rather than the merely statistical conservation proposed by the Bohr-Kramers-Slater approach.
Einstein Extends Radiation Duality Analogy to Matter
Einstein drew an analogy between the wave-particle duality he had identified for radiation and the emerging wave description of material particles, reinforcing the broader quantum duality concept.
Hebrew University Administrative Council
Joins the administrative council of the Hebrew University of Jerusalem.
Quantum Mechanics Critique Begins
Engages critically with the emerging matrix and wave formulations of quantum mechanics.
Second Quantum Gas Paper
Publishes further work on the quantum theory of the ideal monatomic gas.
Unified Gravitation and Electromagnetism Paper
Publishes a unified field theory of gravitation and electricity, beginning a long programme to extend relativity into a single classical field framework.
Canal-Ray Radiation Coherence Test Proposed
Einstein proposed experiments on light emitted by moving canal-ray atoms to test how quantum emission events could coexist with the coherence properties expected from wave optics.
Einstein-Szilard Refrigerator Work
Works with Leo Szilard on safer refrigerator designs without moving mechanical parts.
Kaluza Five-Dimensional Theory Reconsidered
Reconsiders Theodor Kaluza's five-dimensional approach after developments by Oskar Klein, seeing new possibilities for unifying gravitation and electromagnetism geometrically.
Rupp Experiments Initially Reported as Supporting Coherence
Emil Rupp reported experimental results that appeared to support Einstein's proposed coherence tests, although the measurements were later recognized as unreliable and fraudulent.
Rupp Radiation Experiments
Collaborates with Emil Rupp on proposed tests of whether atomic radiation behaves as waves or quanta.
Schrodinger Wave Mechanics Discussion
Studies and discusses Schrödinger's wave mechanics while questioning its physical interpretation.
Wire-Grid Interference Test Suggested for Emitted Light
Einstein devised a wire-grid arrangement intended to probe the coherence length and wave character of radiation emitted in individual atomic processes.
General Relativity and Law of Motion
With Jakob Grommer, investigates whether the motion of particles can be derived from the gravitational field equations rather than imposed as a separate law.
Motion from Field Equations
Investigates with Jakob Grommer whether particle motion can follow directly from gravitational field equations.
Kaluza Theory Academy Papers
Presents Academy papers on Kaluza's connection between gravitation and electricity, deriving important aspects of the five-dimensional unified-field framework.
Distant Parallelism Geometry
Introduces a geometry that preserves distant parallelism, adopting teleparallel structures as a new mathematical basis for attempts to unify gravity and electromagnetism.
Einstein-Szilard Refrigerator Patent
Patent work with Leo Szilard advances an absorption refrigerator using electromagnetic pumping concepts.
Teleparallel Unified Field Programme
Develops the teleparallel unified-field programme, replacing ordinary Riemannian geometry with tetrad-based structures intended to encompass gravitation and electromagnetism together.
Teleparallel Unified Field Theory
Develops a unified-field approach using distant parallelism, also called teleparallel geometry.
Tetrad Fields Introduced for Unified Gravitation
Einstein adopted tetrad fields and distant parallelism as a new geometric language in an attempt to place gravitation and electromagnetism inside one unified classical field theory.
Helen Dukas Becomes Assistant
Employs Helen Dukas as his secretary and assistant, beginning a long professional association.
Unified Field Theory and Hamilton Principle
Publishes a unified field formulation based on distant parallelism and Hamilton's principle, continuing his search for equations joining gravitational and electromagnetic fields.
Unified Field Theory Publication
Publishes a widely publicized unified-field theory based on teleparallel geometry.
Max Planck Medal
Receives the inaugural Max Planck Medal for outstanding achievement in theoretical physics.
Space and Ether Harnack House Lecture
Lectures at Harnack House on the problem of space and ether, revisiting how relativity changes the physical interpretation of spacetime and field structure.
Exact Static Unified-Field Solutions
Publishes work with Walther Mayer giving exact static solutions of unified-field equations, testing whether the programme can represent physically meaningful configurations.
Riemann Metric and Distant Parallelism
Further develops spaces combining a Riemann metric with distant parallelism, refining the geometric machinery behind his teleparallel unified-field theory.
Unified Field Equation Compatibility
Examines the compatibility of equations in the unified-field programme, addressing mathematical consistency before the theory can be regarded as physically viable.
Expanding Universe Paper
Adopts an expanding cosmological model and abandons the need for his earlier static-universe construction.
Expanding-Universe Cosmology Paper
Publishes a non-static cosmological model within general relativity, accepting cosmic expansion and dispensing with the static balance that motivated his cosmological constant.
Unified Gravitation and Electricity Theory
Publishes another unified theory of gravitation and electricity, continuing to test alternative geometrical structures beyond the standard equations of general relativity.