Ay21_Lec02_GRcosm

Ay21_Lec02_GRcosm - Ay 21 - Lecture 2 An Overview: A...

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Ay 21 - Lecture 2 Global Geometry and Dynamics of the Universe Part I An Overview: • A refresher of the special and general theories of relativity • Homogeneity and isotropy • Metric, Robertson-Walker • Cosmological redshift • Comoving and proper coordinates • The Friedmann Equation • Cosmological parameters Special Relativity (1905) • Reconciles classical electrodynamics and coordinate and velocity transformations • Novel effects: c is the maximum velocity – Lorentz contraction – Time dilation – Equivalence of mass and energy – Explains the anomalous precession of Mercury’s orbit • A fundamental change in viewing the physical space and time, now unified in spacetime • Postulates equivalence among all unaccelerated frames of reference (inertial observers)
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General Relativity (1915) • Introduces curvature of space, predicting a number of new effects: – Light deflection by masses – Gravitational redshift etc. etc. • An even more fundamental change in viewing the physical space and time, and matter/energy • Postulates equivalence among all frames of reference (including accelerated ones) Presence of mass/energy determines the geometry of space Geometry of space determines the motion of mass/energy Einstein already predicted the gravitational deflection of light in 1911. Here is his letter to G. E. Hale in 1913, asking him about the possibility of observing the light deflection around the Sun. Confirmation of the GR Eddington’s 1919 eclipse observations “confirmed” Einstein’s relativistic prediction of ! = 1.78 arcsec Later observations have provided more accurate evidence of light deflection due to the influence of GR
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The Equivalence Principle The equivalence principle results in two effects: • Light should be blue/redshifted in a gravitational field • Light paths in a gravitational field should be curved Mach’s Principle : The gravitational interaction of mass in the universe causes all inertial forces. In an empty universe, there would be no inertia. Einstein argued that gravity can be regarded as an inertial force : “A frame linearly accelerating relative to an inertial frame in special relativity is locally identical to a frame at rest in a gravitational field”. He explored this idea in a famous thought experiment with elevators and rockets. Space
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This note was uploaded on 04/18/2008 for the course AY 21 taught by Professor Djorgovski during the Winter '08 term at Caltech.

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Ay21_Lec02_GRcosm - Ay 21 - Lecture 2 An Overview: A...

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