MASON ASTR 302 - An Introduction to General Relativity

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An Introduction to General RelativitySo Far, We Have…Frames of ReferenceAssumptions from the PastAn Example: A Rotating DrumGedankenexperiment (Thought Experiment) in a CarGravity vs. AccelerationAn Exercise – Changing Your PerspectiveA ConclusionEinstein in an ElevatorWhat’s next?!Mattress ExampleBowling Balls on a MattressThink of ants trying to go straight on a surfaceGravity = Geometrical DistortionsA Geometrical ApproachMass Tells Space-Time How to CurveCurvature in this room!Quantifying curvatureA Contemporary ViewMore than Meets the EyeAnother Scientific RevolutionIs There a Real (i.e. measurable) Distinction between General Relativity and the Newtonian Viewpoint?The Scientific Method at WorkThe “Classic” Tests of General RelativityPrecession of Mercury’s OrbitMercury PrecessionDeflection of StarlightDeflection of StarlightDeflection of Starlight During an EclipseEddington’s Eclipse Expedition in 1919As GR predicts, starlight is deflectedImprovements over TimeGravitational Time Dilation and Gravitational RedshiftLunar Laser RangingLunar Laser Ranging, continuediClicker QuestionOther Consequences of GRLIGOIs GR the last word on gravity?ReferencesAn Introduction toGeneral Relativity2So Far, We Have…• Galileo’s Concepts– Decided that constant velocity is the “natural” state of things• Newton’s Concepts– Devised a natural philosophy in which acceleration is the result of forces – Unified terrestrial and celestial mechanics & brought order to the Universe• Einstein’s Special Relativity– Decided that all inertial reference frames are equivalent3Frames of ReferenceThis is all fine, but moving with respect to what??Why the Earth, of course!4Assumptions from the Past• The Earth is at the center of the universe...• The Earth is at the center of the solar system...• The world is flat...• The geometry of the Universe is flat...• The surface of the Earth is the “natural” reference frame...• Time and space are independent and absolute conceptsThese assumptions have had a dramatic impact on our view of Nature5An Example: A Rotating Drum• An accelerating frame of reference can give the feel of gravity• General Relativity considers “gravity” as an artifact of doing physics in a particular reference frame!6Gedankenexperiment (Thought Experiment) in a Car• Windows are painted black• Move the car to outer space• Now imagine placing a few objects on the dashboard of this blacked-out car, still in outer space. • If the car accelerates forward, what happens to these objects on the dashboard? (Why?)• If you didn’t know the car was accelerating, what would you infer about a “force” acting on the objects?• How would that force depend on the masses of the objects?7Gravity vs. Acceleration• Can you tell the difference between forward acceleration and gravity from a massive object being brought up behind the car?8Can you tell the difference between gravity and acceleration?A YesBNo9Constant Velocity ElevatorAccelerating Elevator10An Exercise – Changing Your PerspectiveClose your eyes and imagine you’re being accelerated upwards by the room around usThe “natural” (i.e. inertial) coordinate systems are falling past you at 9.8 m/s2!You are being accelerated upwards at 9.8 m/s2by the normal force of the seat you’re in.11A ConclusionDoing Newtonian mechanics in a particular frame of reference can force you to invoke “fictitious-forces”, i.e., artifacts from doing physics in particular coordinate system. Since these fictitious-forces are invoked to explain what is actually an acceleration of the entire reference frame, they arenecessarily proportional to mass. Do you understand why?Examples:• “Centrifugal force” in rotating systems• Gravity!12Einstein in an ElevatorView “elevator animation” film clip from Nova/PBS websitehttp://www.pbs.org/wgbh/nova/einstein/rela-i.html13What’s next?!• If we blame gravity on our doing physics in a particular reference frame, is all of gravitational physics wiped out?–No!• There is still an interaction there, just more subtle than Newton thought.....– Newton couldn’t explain what gravity was– Thought of it as instantaneous action at a distance14Mattress Example• Imagine 2 bowling balls on a mattress, ignore for the moment the “gravitational” interaction between them• As they roll around on the mattress, they make dimples in its surface• If they get close to each other, they sense these dimples and are “attracted” to each other15Bowling Balls on a Mattress1617Think of ants trying to go straight on a surfaceIn each case, the ants do their best to pick out thestraightest path they can. Unless space is flat, theydon’t stay on parallel lines forever, and eitherconverge or diverge.18• The representation of gravity as a curvature of space similar to a flexible rubber sheet was first expressed in– A Einstein's Special Theory of Relativity.– B Einstein's General Theory of Relativity.– C Newton's Laws of Motion.– D Newton's Law of Universal Gravitation.– E Heisenberg's Uncertainty Principle.19Gravity = Geometrical DistortionsView “space animation” film clip from Nova/PBShttp://www.pbs.org/wgbh/nova/einstein/rela-i.html20A Geometrical Approach• Mass tells space-time how to curve• Space tells mass how to move• This naturally explains the Universality of Free Fall Acceleration – All objects move along the same geometrical distortions– Gravity is a property of the geometry of spacetime21Mass Tells Space-Time How to Curve• The illustrations you’ve seen are what would occur if the world were 2-dimensional. This allows us to show the curvature in the 3rddimension. In reality, gravity causes 3 spatial and 1 time dimensions to “curve”, which is tough to visualize!Space Tells Mass How to Move• Objects travel along straight lines in a curved spacetime. • They don’t “accelerate” due to gravity22Curvature in this room!• Space (spacetime for that matter) seems flat to us• Curvature is small– “Strength” of relativity in a room such as this one is given by 2GM/(Rc2), roughly 1.4×10-9– Near sun, this is about 10-6– Actual radius of curvature on earth is about one light-year23Quantifying curvature• Let’s take a projectile traveling straight up– initial speed v (up) means “hang” time is Δt=2v/g– height acquired is h = ½g(Δt/2)2= ½v2/g– in this time, we “travel” cΔt = 2vc/gmeters


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