lecture5_general_relativity

lecture5_general_relativity - Equivalence Principle No...

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Equivalence Principle • No local experiment can distinguish between constant acceleration and effects of gravity.
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Gravity • Newton says objects experience the force of gravity through distant masses pulling on each other. • Einstein says masses follow local space-time coordinates taking the straightest possible path. Mass works to distort space-time leading to large scale curvatures of space- time. Gravity IS the distortion of space-time.
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Parable of the Apple
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Einstein’s equation • General Relativity is actually simple in one sense – it is local. – The presence of matter or energy distorts space and time. – Objects follow the straightest possible path through this distorted Universe
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Einstein’s equation • But its very non-linear – By moving you gain mass relative to others so your own distortion of space-time increases. – This affects other masses which then affect you… etc… • There are actually very few exact solutions for real systems. – Single rotating spherical object – Entire Universe!!!
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Your Universe • Universe on very large scales (>100 Mpc, 300 Million light years) is homogeneous. – Vast majority of matter is moving slowly. • Solutions of Einstein’s equations for uniformly sprinkled stationary matter is sufficient. – Universe has no center and no edge
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Global Curvature • So what if the universe is filled with masses?
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Global Curvature
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Shape of the Universe • For the Universe as a whole, Einstein's equations predict the shape and curvature of space-time depending on the amount of mass within the Universe. The solutions fall into three basic forms:
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“Flat” space (3d flat)
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Closed Universe?
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Open Universe
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What is the shape of the Universe? • Depends on its density. • More than a critical amount, it closes. • Less than that amount its open. • Exactly the right amount is “flat” • Critical Density is 10 -26 kg/m 3 (about 8 atoms per cubic meter) • You are 1000 kg/m 3 • Energy counts too (E=mc 2 ) and can actually be negative.
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geometry of the universe is determined by total density of
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lecture5_general_relativity - Equivalence Principle No...

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