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

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.