Einsteins Zurich Notebook John D Norton Department of

Einstein’s Zurich Notebook John D. Norton Department of History and Philosophy of Science University of Pittsburgh 1

Eight Years 1907 1908 Einstein begins investigation of relativistic theories of gravity. Principle of equivalence. 1909 1910 1911 1912 Novel theory of static gravitational fields. Speed of light c is the gravitational potential. !! !! Einstein moves from Prague to Zurich and collaborates with Marcel Grossmann. Gravity is connected with the curvature of spacetime. First sketch of the general theory of relativity. Field equations are not generally covariant. Completed theory. Mercury explained. 1913 1914 November 1915 2

Written from both covers… 3

Starting from the front… 4

Starting from the front… Planck energy distribution ρ for black body radiation. Heat capacity ∂ρ/∂T Means square energy density fluctuation κT 2 ∂ρ/∂T = Particle term + Wave term 5

Starting from the rear… “Relativitätstheorie” 6

Starting from the rear… Introductory Minkowskian fourdimensional electrodynamics. Then more similar pages, some pages computing quantities in statistical physics, then… 7

Line element of spacetime written for the first time. Special case of static gravitational field. Gravitational field equation of the 1912 theory. 8

“Γ tensor of G Apparently Div Γ = 0 Is this invariant? ” 9

Newton’s equations of motion for a mass constrained to a surface f=0 Variational calculation 10

Moving body in Newtonian mechanics constrained to a surface …. . . traces a geodesic of the spatial geometry. “woraus die Behauptung” “from which the assertion [follows]” 11

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Flip back to the front… 13

“Gravitation” 14

Physical approach 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. Physical naturalness. Extreme case: thought experiments direct theory choice. versus Formal approach Exploit formal (usually mathematical) properties of emerging theory. Covariance principles. Group structure. Theory construction via mathematical theorems. Geometrical methods assure automatic covariance. Formal naturalness. Extreme case: choose mathematically simplest law. 15

The physical approach to energy-momentum conservation… Equations of motion for a speck of dust (geodesic) Expressions for energymomentum density and four -force density for a cloud of dust. Combine: energy-momentum conservation for dust Rate of accumulation energymomentum Force density 16

…and the formal approach to energy-momentum conservation. Is the conservation law of the form Check: form It should be 0 or a four-vector. It vanishes! Stimmt! 17

The formal approach to the gravitational field equations 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. ” 18

“zu umständlich” “too involved” 19

“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 “ 20

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” 21

“Grossmann” [Ricci tensor] “Presumptive gravitation tensor” Tensor under unimodular transformations. Reduces to Newtonian form under coordinate condition 22