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Explore Einstein's Zurich Notebook, where he begins his investigation of relativistic theories of gravity and develops the theory of general relativity. This notebook covers Einstein's collaboration with Marcel Grossmann, the explanation of Mercury's orbit, and the derivation of the gravitational field equations.
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Einstein’s Zurich Notebook John D. Norton Department of History and Philosophy of Science University of Pittsburgh
Eight Years ! ! ! ! Einstein begins investigation of relativistic theories of gravity. Principle of equivalence. 1907 1908 1909 1910 1911 1912 Einstein moves from Prague to Zurich and collaborates with Marcel Grossmann. 1913 1914 November 1915 First sketch of the general theory of relativity. Field equations are not generally covariant. Gravity is connected with the curvature of spacetime. Novel theory of static gravitational fields. Speed of light c is the gravitational potential. Completed theory. Mercury explained.
Starting from the front… Planck energy distribution ρ for black body radiation. Heat capacity ∂ρ/∂T Means square energy density fluctuation κT2 ∂ρ/∂T = Particle term + Wave term
Starting from the rear… “Relativitätstheorie”
Starting from the rear… Introductory Minkowskian four-dimensional electrodynamics. Then more similar pages, some pages computing quantities in statistical physics, then…
Line element of spacetime written for the first time. Special case of static gravitational field. Gravitational field equation of the 1912 theory.
“Γ tensor of G Apparently Div Γ = 0 Is this invariant?”
Newton’s equations of motion for a mass constrained to a surface f = 0 Variational calculation
Moving body in Newtonian mechanics constrained to a surface … ... traces a geodesic of the spatial geometry. “woraus die Behauptung” “from which the assertion [follows]”
Based on physical principles with evident empirical support. Principle of relativity. Conservation of energy. Special weight to secure cases of clear physical meaning. Newtonian limit. Static gravitational fields in GR. Exploit formal (usually mathematical) properties of emerging theory. Covariance principles. Group structure. Theory construction via mathematical theorems. Geometrical methods assure automatic covariance. Physical naturalness. Extreme case: thought experiments direct theory choice. Formal naturalness. Extreme case: choose mathematically simplest law. Physical versus Formal approach approach
Equations of motion for a speck of dust (geodesic) Expressions for energy-momentum density and four-force density for a cloud of dust. Combine: energy-momentum conservation for dust Rate of accumulation energy-momentum Force density The physical approach to energy-momentum conservation…
Check: form It should be 0 or a four-vector. It vanishes! Stimmt! …and the formal approach to energy-momentum conservation. Is the conservation law of the form
Einstein writes the Riemann curvature tensor for the first time… with Grossmann’s help. First contraction formed. To recover Newtonian limit, three terms “should have vanished.” The formal approach to the gravitational field equations
“zu umständlich” “too involved”
“Nochmalige Berechnung des Ebentensors” “Once again, calculation of the surface tensor [Ricci tensor]” Newtonian term “bleibt stehen” “remains” Harmonic coordinate condition. “Result is certain. Holds for coordinates that satisfy the equation “
Failure of the formal approach Einstein finds multiple problems with the gravitational field equations based on the Riemann curvature tensor. “Static special case” Stress tensor of gravitational field of the 1912 static theory. “Special case apparently incorrect”
“Grossmann” [Ricci tensor] “Presumptive gravitation tensor” Tensor under unimodular transformations. Reduces to Newtonian form under coordinate condition
Restrict coordinate systems to those in which this quantity transforms as a tensor. Then this Newtonian like quantity is a tensor.
“Entwurf” gravitational field equations Derived from a purely physical approach. Energy-momentum conservation.
64=8x8 65=5x13 64=65
