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 PresentationTRANSCRIPT
Einstein’s Happiest Thought
Micro-world Macro-World Lecture 7
Equivalence between gravity & acceleration
aMan in a closed box on Earth
Man in a closed box on anaccelerating rocket in deep
outer space.
Since mG=mI, if a=-g, theconditions are equivalent
gmGg mIa
The happiest thoughtI cannot tell the difference between being on earth or
in a deep-space rocket accelerating with a=-g
ImaginationThis cannot be due to
coincidence. There must be some basic truth
involved.
Einstein didn’t accept mG=mI as a coincidence
These two environments must be exactly
equivalent.
Einstein Equivalence Principlein his words
we [...] 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 line
sraight line
If the rocket is accelerating, the light beam bends
½at2
Since the accelerating rocket and gravity are
equivalent, gravity must cause light to bend
½gt2
smcLt
sm
88 102
1036
for our room L≈6m:
msgtsm 1528
212
21 10210210 2
very, very tiny effect
L
on Earth’s 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 Eddington1882-1944
earths
mkgm
sun
sunsun g
m
kgN
RGMg 27273
107
102107.62
2
2
28
3011
2
gsun ≈ 27xgearth
02 0005.04
sun
sun
RcGM
Eddington’s 1919 Expeditions
Africa
1919 eclipseMeasurement: =0.000550±0.000030
in agreement with Einstein’s prediction
1919 Eclipse
New York Times:
Gravitational lensing
“Dark Matter” astronomy
Mass induces curvature in space-time
The curvature is what we feel as gravity
Seoul Rio
120
170
Seoul Rio
Cartesian 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 geometry
The shortest distancebetween two points onthe Earth’s surface correspond to “GreatCircles”: the intersectionsof planes passing throughthe center of the Earthwith the Earth’s surface.
In this figure, the shortest distances are indicated bythe blue lines.
