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CU-Boulder ASTR 1120 - SUMMARY OF KEY CONCEPTS

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ASTR 1120 Section 1 (3 credit hours): Spring 2006SUMMARY OF KEY CONCEPTS: WEEK #5Lecture #9 – textbook Chapter S2 `Space and Time’We began discussing the Theory of Relativity, which was developed in two parts. The SpecialTheory of Relativity describes how space and time, which we normally perceive to be completelydifferent concepts, are actually closely linked. The Special theory does not include gravity. TheGeneral Theory of Relativity goes much further, and explains how mass curves spacetime.Special relativity is based on two concepts:1) The laws of physics are the same in all inertial frames (an inertial frame is one in whichthe experimenter is not subject to any external forces, such as gravity). In particular, thismeans that there is no preferred frame as far as velocity is concerned – observers movingat different velocities relative to each other are in equally valid positions.2) The speed of light is the same constant when measured in any inertial frame, regardlessof how that frame is moving relative to the source of the light. This is very weird, but it’san experimental fact!We showed that these concepts imply some strange behavior – moving clocks appear to runslow (we actually derived this one) and moving objects appear to be length contracted. Theeffects are only significant once we are moving close to the speed of light, hence we don’t noticethem in everyday life.We outlined the twin paradox – suppose one twin flies in a super-advanced spaceship to adistant star at close to the speed of light and then returns to Earth. Because of time dilation, thetwin on the spaceship can reach the distant star even if it’s (say) 100 light years away (since theclock on the spaceship runs `slow’, a journey that takes at least 100 years as seen from Earthrequires less time as seen by the astronaut). But, when the twin returns to Earth, there’s a bigmismatch in the amount of time that has elapsed on Earth as compared to on the spaceship, andthe twin on Earth is probably long dead.Lecture #10 – textbook Chapter S3 `Spacetime and Gravity’The central physical idea (there’s also a lot of mathematics) behind the General Theory ofRelativity is the equivalence principle – the effects of gravity and acceleration are exactlyequivalent (indistinguishable) locally (locally here means that we restrict ourselves toexperiments that could be done in a small box – on much larger scales we can measure effectssuch as tides which are characteristic of gravity not acceleration).The equivalence principle is in some ways obvious (in an elevator accelerating upward youcertainly feel heavier, just as if gravity had become stronger), but it’s also profound sincegravity and acceleration appear to be completely different concepts! One of the most immediateconsequences is that gravity deflects light, by an amount that turns out to be exactly twice whatNewtonian theory predicts.This light bending was detected shortly after the publication of the General Theory of Relativity,and has subsequently been measured very accurately. It agrees with the prediction very well.More recently, examples of gravitational lensing have been observed, which are anothermanifestation of the same


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