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 · Year
1912
Albert Einstein records dated 1912, drawn directly from the World History Database source collection.
Curved Spacetime Approach Takes Shape
Einstein's Zurich work moved toward describing gravity through non-Euclidean spacetime geometry, connecting gravitational phenomena with the mathematical curvature of the metric.
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.
Grossmann Tensor Collaboration
Collaborates closely with Marcel Grossmann, who guides him toward Ricci and Levi-Civita tensor calculus as the mathematical language for gravitation.
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.
Metric Tensor Becomes Gravitational Variable
Einstein increasingly identified the spacetime metric as the quantity that should represent gravitation, replacing the idea of gravity as an ordinary force field on fixed space and time.
Ricci Calculus Adopted for Gravity
With Marcel Grossmann's mathematical guidance, Einstein began using Ricci and Levi-Civita tensor calculus as the formal machinery needed to describe a relativistic gravitational field.
Rotating Disk Reveals Non-Euclidean Geometry
Einstein used the thought experiment of a rotating disk to show that ordinary Euclidean geometry need not describe measurements made in accelerated systems, strengthening the geometric approach to gravity.
Scalar Gravity Model Tested in Zurich
Before settling on tensor field equations, Einstein explored restricted scalar descriptions of gravitation and tested whether they could preserve relativity while reproducing known gravitational effects.
Static Gravitational Field Theory
Develops field equations for a restricted static gravitational problem while searching for a theory that can extend relativity beyond inertial reference frames.
Tensor Calculus Collaboration
Works with Marcel Grossmann to master tensor calculus for a relativistic theory of gravitation.
Turn to Non-Euclidean Geometry
Realises that gravitation may require non-Euclidean geometry, redirecting the search for a relativistic gravity theory toward curved spacetime mathematics.
Variable Light Speed in Gravity
Explores a formulation in which the coordinate speed of light varies with gravitational potential, an intermediate step toward a geometric theory of gravity.
Zurich Notebook
Uses the Zurich Notebook to explore candidate gravitational field equations and differential geometry.
Zurich Notebook Tensor Calculations
Fills the Zurich Notebook with tensor calculations while testing candidate gravitational field equations and learning the differential geometry needed for a covariant theory.
ETH Zurich Professorship
Begins work as professor of theoretical physics at ETH Zurich.