einstein’s happiest thought micro-world macro-world lecture 7
Post on 20-Dec-2015
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Einstein’s Happiest Thought
Micro-world Macro-World Lecture 7
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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
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The happiest thoughtI cannot tell the difference between being on earth or
in a deep-space rocket accelerating with a=-g
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ImaginationThis cannot be due to
coincidence. There must be some basic truth
involved.
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Einstein didn’t accept mG=mI as a coincidence
These two environments
must be exactly equivalent.
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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]
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So what?What would happen if I were to shine a
light beam through a window on the
rocket?sraight line
sraight line
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If the rocket is accelerating, the light beam bends
½at2
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Since the accelerating rocket and gravity are
equivalent, gravity must cause light to bend
½gt2
sm
c
Lt
sm
88
102103
6
for our room L≈6m:
msgtsm 1528
212
21 10210210 2
very, very tiny effect
L
on Earth’s surface
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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
R
GMg 27273
107
102107.62
2
2
28
3011
2
gsun ≈ 27xgearth
02
0005.04
sun
sun
Rc
GM
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Eddington’s 1919 Expeditions
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Africa
1919 eclipseMeasurement: =0.000550±0.000030
in agreement with Einstein’s prediction
1919 Eclipse
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New York Times:
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Gravitational lensing
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“Dark Matter” astronomy
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Mass induces curvature in space-time
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The curvature is what we feel as gravity
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Seoul Rio
120
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170
Seoul Rio
Cartesian vs non-Cartesian coords
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The Earth is round
170??
This is how KAL goes
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GeodesicsThe shortest distance between 2 points isAlong a “geodesic.” It is a straight line In Cartesian systems
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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.
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In this figure, the shortest distances are indicated bythe blue lines.
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