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

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

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

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.