# Einstein’s Happiest Thought

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Einstein’s Happiest Thought. Micro-world Macro-World Lecture 7. Equivalence between gravity & acceleration. a. Man in a closed box on Earth. m I a. m G g. g. Since m G =m I , if a=-g , the conditions are equivalent. Man in a closed box on an accelerating rocket in deep outer space. - PowerPoint PPT Presentation

### Text of Einstein’s Happiest Thought

• Einsteins Happiest ThoughtMicro-world Macro-World Lecture 7

• Equivalence between gravity & accelerationaMan in a closed box on EarthMan in a closed box on anaccelerating rocket in deep outer space.Since mG=mI, if a=-g, theconditions are equivalentgmGgmIa

• The happiest thoughtI cannot tell the difference between being on earth orin a deep-space rocket accelerating with a=-g

• ImaginationThis cannot be due to coincidence. There must be some basic truth involved.

• Einstein didnt accept mG=mI as a coincidenceThese two environments must be exactly equivalent.

• Einstein Equivalence Principlein his wordswe [...] assume the complete physical equivalence of a gravitational field and a corresponding acceleration o the reference system [Einstein, 1907]

• So what?What would happen if I were to shine a light beam through a window on the rocket?sraight linesraight line

• If the rocket is accelerating, the light beam bendsat2

• Since the accelerating rocket and gravity are equivalent, gravity must cause light to bendgt2for our room L6m:very, very tiny effect Lon Earths surface

• Does gravity cause light to bend?Very tiny effect: need very stronggravity and a long lever arm. Lookat the bending of light from a star bythe Sun. (Only possible at an eclipse.)Sir Arthur Eddington1882-1944gsun 27xgearth

• Eddingtons 1919 Expeditions

• Africa1919 eclipseMeasurement: q =0.0005500.000030in agreement with Einsteins prediction1919 Eclipse

• New York Times:

• Gravitational lensing

• Dark Matter astronomy

• Mass induces curvature in space-time

• The curvature is what we feel as gravity

• Seoul Rio120

• 170Seoul RioCartesian vs non-Cartesian coords

• The Earth is round

170??This is how KAL goes

• GeodesicsThe shortest distance between 2 points isAlong a geodesic. It is a straight line In Cartesian systems

• Great Circlesspherical geometryThe shortest distancebetween two points onthe Earths surface correspond to GreatCircles: the intersectionsof planes passing throughthe center of the Earthwith the Earths surface.

• In this figure, the shortest distances are indicated bythe blue lines.

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