The structure of spacetime. Eli Hawkins Walter D. van Suijlekom

Transcription

1 The structure of spacetime Eli Hawkins Walter D. van Suijlekom

2 Einstein's happiest thought After Einstein formulated Special Relativity, there were two problems: Relativity of accelerated motion The monstrous [Newtonian] notion of absolute space (Mach, 1893) leading to the principle of locality Both problems are combined in what Einstein called the happiest thought in my life. He states that for an observer falling freely from the roof of a house there exists no gravitational field.

3 Equivalence principle we [...] assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system. (Einstein 1907)

4 Einstein and Grossmann Although Einstein formulated the equivalence principle in 1907, he needed another 8 years to arrive at the proper mathematical formulation of General Relativity. After working on quantum theory for a few years, he picked up the general relativity track in In August 1912, he tells his friend and mathematician Marcel Grossmann: Grossmann, you must help me or else I'll go crazy! Grossmann realized that the general covariant formalism Einstein was looking for was provided by Riemannian geometry. In their joint papers (1913), Grossmann suggested the possibility for including the Riemann curvature tensor; this was rejected based on Einstein's physical requirements...

5 Hilbert vs. Einstein E. submits 4 papers to Preussische Akademie der Wissenschaften on Thursday 4, 11, 18 and 25 Nov November: several postcards between H. and E. every other day 20 Nov.: H. presents to the Gesellschaft der Wissenschaften in Göttingen and derives the correct equations (generally covariant). Submits paper and gives credit to Einstein 25 Nov.: E. submits 4th paper: proposes without derivation the equations. No mention of Hilbert's name in the paper.

6 Classical tests GRT Perihelion Mercury (GR: 43,0; Obs: 43,1±0,5) Starlight deflection Dyson, Eddington & Davidson, (1920, Mem. R. Astron. Soc., 220, ) Gravitational redshift (0,9970±0,0076) Pound & Snider (1964, Phys.Rev.Lett., 13, )

7 Binary pulsars A binary system will emit gravitational waves, thereby losing energy. Due to this loss, their orbital period decreases. First observed by Hulse and Taylor using binary pulsar PSR they had discovered in 1974 (Nobelprize in 1993) Orbital decay for PSR

8 LIGO Laser Interferometer Gravitational Wave Observatory LIGO will detect the ripples in space time by using a device called a laser interferometer. Measures: Measures: the time it takes light to travel between suspended mirrors with high precision using controlled laser light. Colliding neutron stars [Caltech & MIT, 2008]

9 LISA Laser Interferometer Space Antenna using laser interferometry over astronomical distances: equilateral triangle with sides about 5 million km long (launch 2018) [NASA & ESA, 2008]

10 Gravity Probe B Gyroscope experiment: electrically supported spheres, spinning in vacuum Measures: rotation of spacetime (frame dragging) curvature of spacetime (geodetic effect) (initial results: accuracy of 1%) [NASA & Stanford, May 2008]

11 Overview Differential geometry: what is it about? In General Relativity the metric is dynamical look at more fundamental things. Forget distances, angles from geometry Riemannian geometry: Geometrical meaning of curvature Geometry of spacetime, generalizing Minkowski Symmetry as a calculation tool Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality. (Minkowski, 1908)

12 General relativity The physical meaning of curvature: tidal forces Energy, momentum, and pressure T Einstein's Equations: Relationship between Einstein's and Newton's theories Causal Structure: Conformal transformations Penrose diagrams Black holes & event horizons

13 Singularities: The Big Bang: the beginning of time Black holes Singularity theorems: Einstein's Equations imply that singularities are inevitable.