Einstein’s Happiest Thought
Micro-world Macro-World Lecture 7
Equivalence between gravity &
acceleration
a
Man in a closed box on Earth
mG g g
Since mG=mI, if a=-g, the
conditions are equivalent
mIa
Man in a closed box on an
accelerating rocket in deep
outer space.
The happiest thought
I cannot tell the difference
between being on earth or
in a deep-space rocket
accelerating with a=-g
Imagination
This 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 Principle
in 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?
If the rocket is
accelerating, the
light beam bends
½at2
L
Since the accelerating
rocket and gravity are
equivalent, gravity must
cause light to bend
on Earth’s surface
½gt2
for our room L≈6m:
t
1
2
L
6m
8


2

10
s
8 m
c 3 10 s


2
gt 2  12 10 sm2  2 108 s  2 1015 m
very, very tiny effect
Does gravity cause light to bend?
Very tiny effect: need very strong
gravity and a long lever arm. Look
at the bending of light from a star by
the Sun. (Only possible at an eclipse.)

Sir Arthur Eddington
1882-1944
4GM sun
 0.00050
2
c Rsun
gsun ≈ 27xgearth
g sun


11
30
m
GM sun 6.7 10 N kg 2 2 10 kg


 273 sm2  27g earth
2
2
8
Rsun
7 10 m

2

Eddington’s 1919 Expeditions
1919 Eclipse
Africa
1919 eclipse
Measurement:  =0.000550±0.000030
in agreement with Einstein’s prediction
New York Times:
Gravitational lensing
“Dark Matter” astronomy
Mass induces curvature in space-time
The curvature is what we feel as
gravity
120
Cartesian vs non-Cartesian coords
170
The Earth is round
170 ??
This is how KAL goes
Geodesics
The shortest distance between 2 points is
Along a “geodesic.” It is a straight line
In Cartesian systems
Great Circles
spherical geometry
The shortest distance
between two points on
the Earth’s surface
correspond to “Great
Circles”: the intersections
of planes passing through
the center of the Earth
with the Earth’s surface.
In this figure, the shortest
distances are indicated by
the blue lines.