Notes on Relativity and Cosmology - Physics Department, UCSB
Notes on Relativity and Cosmology - Physics Department, UCSB Notes on Relativity and Cosmology - Physics Department, UCSB
24 CONTENTS Course Calendar The following is a tentative calendar for PHY 312, Spring 2001. Week 1: (1/14) Background material on pre-relativistic physics (coordinate systems, reference frames, the Newtonian assumptions about time and space, inertial frames, begin Newton’s laws). Week 2: (1/21) Newtonian mechanics: inertial frames and Newton’s laws. Electricity, magnetism and waves. The constancy of the speed of light. The ether and the Michelson-Morely experiment. Week 3: (1/28) The postulates of relativity. What do the postulates of relativity imply? Spacetime diagrams, simultaneity, light cones, and time dilation. Week 4: (2/4) More work with spacetime diagrams: length contraction and more subtle problems – the train ‘paradox,’ the interval, proper time and proper distance, a bit on Minkwoskian geometry, the twin ‘paradox.’ Week 5: (2/11) More on Minkowskian geometry. Begin acceleration. The headlight effect. Week 6: (2/18) Acceleration in special relativity. Week 7: (2/25) Dynamics (forces, energy, momentum, and E = mc 2 ). Week 8: (3/4) Gravity, light, time, and the local equivalence principle. Exam 1. Week 9: (3/11) SPRING BREAK Week 10: (3/18) Nonlocal calculations in GR. Time dilation and GPS. Week 11: (3/25) Curved spaces and curved spacetime. Week 12: (4/1) The Metric: the mathematical description of a curved surface. Week 13: (4/8) The Einstein equations and the Schwarzschild solution. The classic tests of GR: Mercury’s orbit, the bending of light, and radar time delays. Begin black holes. Week 14: (4/15) More on Black Holes: inside, outside, etc. Week 15: (4/22) Second exam. A little cosmology. Week 16: (4/29) More cosmology. If time permits, we may discuss compact universes, closed timelike curves, the periodic Milne Universe. Kaluza-Klein, higher dimensions, other extensions of Einstein’s theories. Brief Project Presentations: 5pm Tuesday, May 6.
Chapter 1 Space, Time, and Newtonian Physics Read Einstein, Ch. 1 -6 The fundamental principle of relativity is the constancy of a quantity called c, which is the speed of light in a vacuum 1 : c = 2.998 × 10 8 m/s, or roughly 3 × 10 8 m/s. This is fast enough to go around the earth along the equator 7 times each second. This speed is the same as measured by “everybody.” We’ll talk much more about just who “everybody” is. But, yes, this principle does mean that, if your friend is flying by at 99% of the speed of light, then when you turn on a flashlight both of the following are true: • The beam advances away from you at 3 × 10 8 m/s. • Your friend finds that the light beam catches up to her, at 3 × 10 8 m/s. Now, this certainly sounds a bit strange. However, saying that something “sounds a bit strange” will not be enough for us in PHY312. We’ll want to investigate this more deeply and find out exactly where this runs into conflict with our established beliefs. To do this, we’ll have to spend a little bit of time (just a week or so) talking about ‘Newtonian’ physics; that is, the way people understood physics before Einstein came along. I know that Newtonian physics is old hat to some of you, but some people here have never studied any physics. In addition, we will emphasize different features than you focussed on if you saw this before in 1 Light traveling through air, water, etc. does not travel at speed c, nor is the speed of light through air, water, etc. constant in the same way that c is. 25
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24 CONTENTS<br />
Course Calendar<br />
The following is a tentative calendar for PHY 312, Spring 2001.<br />
Week 1: (1/14) Background material <strong>on</strong> pre-relativistic physics (coordinate systems,<br />
reference frames, the Newt<strong>on</strong>ian assumpti<strong>on</strong>s about time <strong>and</strong> space, inertial<br />
frames, begin Newt<strong>on</strong>’s laws).<br />
Week 2: (1/21) Newt<strong>on</strong>ian mechanics: inertial frames <strong>and</strong> Newt<strong>on</strong>’s laws. Electricity,<br />
magnetism <strong>and</strong> waves. The c<strong>on</strong>stancy of the speed of light. The ether<br />
<strong>and</strong> the Michels<strong>on</strong>-Morely experiment.<br />
Week 3: (1/28) The postulates of relativity. What do the postulates of relativity<br />
imply? Spacetime diagrams, simultaneity, light c<strong>on</strong>es, <strong>and</strong> time dilati<strong>on</strong>.<br />
Week 4: (2/4) More work with spacetime diagrams: length c<strong>on</strong>tracti<strong>on</strong> <strong>and</strong><br />
more subtle problems – the train ‘paradox,’ the interval, proper time <strong>and</strong> proper<br />
distance, a bit <strong>on</strong> Minkwoskian geometry, the twin ‘paradox.’<br />
Week 5: (2/11) More <strong>on</strong> Minkowskian geometry. Begin accelerati<strong>on</strong>. The headlight<br />
effect.<br />
Week 6: (2/18) Accelerati<strong>on</strong> in special relativity.<br />
Week 7: (2/25) Dynamics (forces, energy, momentum, <strong>and</strong> E = mc 2 ).<br />
Week 8: (3/4) Gravity, light, time, <strong>and</strong> the local equivalence principle. Exam<br />
1.<br />
Week 9: (3/11) SPRING BREAK<br />
Week 10: (3/18) N<strong>on</strong>local calculati<strong>on</strong>s in GR. Time dilati<strong>on</strong> <strong>and</strong> GPS.<br />
Week 11: (3/25) Curved spaces <strong>and</strong> curved spacetime.<br />
Week 12: (4/1) The Metric: the mathematical descripti<strong>on</strong> of a curved surface.<br />
Week 13: (4/8) The Einstein equati<strong>on</strong>s <strong>and</strong> the Schwarzschild soluti<strong>on</strong>. The<br />
classic tests of GR: Mercury’s orbit, the bending of light, <strong>and</strong> radar time delays.<br />
Begin black holes.<br />
Week 14: (4/15) More <strong>on</strong> Black Holes: inside, outside, etc.<br />
Week 15: (4/22) Sec<strong>on</strong>d exam. A little cosmology.<br />
Week 16: (4/29) More cosmology. If time permits, we may discuss compact<br />
universes, closed timelike curves, the periodic Milne Universe. Kaluza-Klein,<br />
higher dimensi<strong>on</strong>s, other extensi<strong>on</strong>s of Einstein’s theories.<br />
Brief Project Presentati<strong>on</strong>s: 5pm Tuesday, May 6.
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