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:
Dark Matter astronomy
Mass induces curvature in space-time
The curvature is what we feel as gravity
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.