Albert Einstein

1
Albert Einstein
By Leiwen Wu

• The Special and General Theory of Relativity and
  his Thought Experiments

2
A Little About Albert Einstein

• Born 14 March 1879 in Ulm, Württemberg, Germany
• Died 18 April 1955 in Princeton, New Jersey, USA
• Einstein contributed more than any other
  scientist to the modern vision of physical
  reality. His special and general theories of
  relativity are still regarded as the most
  satisfactory model of the large-scale universe
  that we have.

3
Brief Overview of the Genius

• 1879 Einstein born Ulm, Germany.
• 1885 - 1925 Michelson and Morley began a series
  of puzzling experiments which made the Newtonian
  Universe impossible.
• 1900 Max Planck shocked the physics community
  with the concept of quantization
• 1905 The miracle year in physics Einstein
  published papers on Brownian motion as well as
  the seminal papers on his theory of relativity.
  He developed the Special Theory of Relativity in
  which he described how space and time are
  relative or related to each other.
• 1915 Einstein extended his discussion of
  relativity to include gravity and thereby
  explained the problem of Mercury. He developed
  the general theory of relativity which dealt with
  gravity and acceleration and a 4 dimensional
  space in which everything is related to each
  other.
• 1919 Eddington confirms Einstein's prediction
  concerning deflection of starlight.
• 1915 - 1925 Einstein was a co-leader in the
  birth and development of quantum mechanics
• 1925 - 1935 Einstein and Bohr engaged in a
  fascinating series of "debates" over the
  interpretations of physics especially the notion
  of determinism (God does not play dice)
• 1930 - 1955 Einstein searches for a unified
  theory of the universe
• 1933 - Hubble and Humanson discover the
  recessional nature of galaxies - Einstein's
  theories of the universe take shape.
• 1955 Einstein dies, Princeton, N.J.

4
Einsteins Personal Life

• Einstein marries Mileva in 1903
• Mileva divorced Einstein in 1914
• Einstein married his cousin Elsa in 1919

5
Newton, Einstein, and Gravity
6
Newtons Laws of Motion
I. A body continues at rest or in uniform motion
in a straight line unless acted on by some
net force.  
III. To every action, there is an equal and
opposite reaction.
7
Newtons Law of Gravitation
where G is the gravitational constant,
M is the mass of the larger body, m is
the mass of the smaller body, r is the
separation between them. 
8
Gravity and Orbital Motion
The gravitational attraction between the Earth
and the Moon causes the Moon to orbit around the
Earth rather than moving in a straight line.
9
Newton's Laws Gravity and Motion

• If a rocket is fired up from Earth, gravity will
  slow it down so that it either
• falls back to Earth
• enters a closed orbit around the Earth
• escapes from Earth

Cannon ball applet http//zebu.uoregon.edu/js/as
t122/lectures/lec03.html
10
Newton and Kepler
Newton showed that objects moving along closed
orbits under the influence of gravity follow
elliptical paths.  Recall Keplers First Law
11
Newton and Kepler
Newton also showed that objects in these orbits
conserve angular momentum. Recall Keplers
Second Law
12
Newton and Kepler
An object orbiting in a circle around mass M has
speed
The orbital period of this object is the
circumference of its orbit divided by its speed
so
Recall Kepler's Third Law
13
Quantum Theory of Light

• Before Einstein, people thought that space, the
  empty space in our universe, composed of things
  called ether.
• Einstein thought that light came in tiny packets,
  or particles called photons.
• It was the most shocking idea about our universe
• We live in a quantum universe built out of tiny,
  discrete chunks of energy and matter.
• Einstein would later try to combine the theory of
  relativity and quantum mechanics in his unified
  theory which would explain our whole universe.
  Unfortunately, he died before he was able to
  complete it.

14
What is relativity?
15
The making of the special Theory of Relativity

• The Special theory of Relativity disproves
  Newtons long held idea that space and time are
  absolute
• It creates a whole new way of thinking about our
  universe
• It creates a four dimensional universe where
  everything is related
• Special relativity is much simpler mathematically
  than general relativity, but harder to visualize
  and imagine.

Einstein was 26 when he devised the special
theory of relativity
16
The Special theory of Relativity Explained

• The special theory of relativity states that time
  and space(distance) is relative or depends on
  each other
• Everything is related to each other and is not
  absolute.
• Newton thought that time is the same every where.
• Special relativity disproves

1 year old
Imagine two twin brothers.
One in a space ship and one on the launch pad
Now the spaceship travels at 99.9 of light for
100 years earth time
100 years old
Time to both are very different.
17
Postulates of the Special Theory of Relativity
1. Observers cannot detect absolute uniform
motion, only motion relative to other
objects
or The laws of physics are the same for
all observers. 2. The speed of light is the
same for all observers, independent of their
motion relative to the source of the light.
18
If c were not absolute, youd see car A reach the
collision point before car B! You would see a
different event!
19
Consequences of an absolute speed of light for
all observers time dilation
20
The Equivalence Principle
21
(No Transcript)
22
Einsteins View of Gravitation
In his General Theory of Relativity, Einstein
explained the force of attraction between massive
objects in this way   Mass tells space-time
how to curve, and the curvature of space-time
tells masses how to accelerate.
23
Orbits in Curved Space-Time
24
Gravity à la Einstein
Einsteins general theory of relativity predicted
that light paths should be affected by massive
objects.
25
Gravity à la Einstein
Einsteins predictions were confirmed when the
positions of stars near the sun were observed to
be shifted during a 1919 solar eclipse.
26
The Making of the General Theory of Relativity

• Einstein was 36 when he developed the theory of
  relativity.
• Einstein came up with this when he imagined a man
  falling of the roof.

27
The General Theory of Relativity Explained

• Einstein Discovered in his General Theory of
  Relativity that gravity and acceleration are the
  same phenomenon.

Imagine an elevator and a person standing in it.
What would happen to the person if the elevator
free-falls?
The person would be floating in the elevator
while it is free-falling.
Now Imagine that person in a space ship far away
from any gravitational force. He would be
floating in the ship.
If the ship the person is in accelerates at the
right amount of speed, the person would feel the
same as if gravity was pulling on him.
28
General Relativity Conclusion

• Einstein concluded that 4 dimensional

29
Principle of Equivalence Einstein 1907
Box stationary in gravity field
Box accelerates in empty space
Box falling freely
Box moves through space at constant velocity
30
Equivalence Principle

• Special relativity all uniformly moving frames
  are equivalent, i.e., no acceleration
• Equivalence principle
• Gravitational field acceleration
• freely falling frames in GR
• uniformly moving frames in SR.

31
Aberration of Light
Moral direction of light beam is relative
32
Gravitational deflection of Light
Now assume boxes are accelerating
Light path is curved
33
Light ray curved in accelerating frame
Principle of Equivalence (acceleration gravity)
Gravity attracts light!
34
Paradox How can gravity attract light if light
has no mass?
35
MASS-ENERGY EQUIVALENCE

• Gravity extracts energy from escaping matter
• Gravity extracts energy from escaping light
• Gravitational redshift, time dilation
• Other points of view same result
• accelerating frames of reference - apply special
  relativity
• spacetime is curved

36
Emc
2

• This equation is the most important single result
  of relativity theory
• Its the idea that mass and energy are
  equivalent.
• Energy mass times the speed of light squared
• Em, the c squared is just to express how much
  energy can be made from one unit of mass.

37
Curved Spacetime

• Remember Gravity warps time

BUT in spacetime, time and space are not
separable
fast
gt Both space and time are curved (warped)
This is a bit hard to vizualize (spacetime
already 4D)
slow
38
Tides

• Problem
• Gravity decreases with distance gt stretch

r2
r1
moon
39
Tides

• Tides gravity changes from place to place

not freely falling
?
?
?
?
freely falling
not freely falling
40
CURVATURE OF SPACETIME

• How to tell difference between accelerating frame
  and gravity?
• tidal forces curvature
• Eliminates Newtons action at a distance
• Freely moving bodies follow shortest path
• not necessarily a straight line

41
GENERAL RELATIVITY EINSTEIN 1915

• Matter energy determine curvature of spacetime
• Curvature of spacetime determines motion of
  matter energy

42
Light Rays and Gravity II

• In SR light rays travel on straight lines
• gt in freely falling frame, light travels on
  straight lines
• BUT to stationary observer light travels on
  curved paths
• gt Maybe gravity has something to do with
• curvature of space ?

43
GR Einstein, 1915

• Einstein mass/energy squeeze/stretch spacetime
  away from being flat
• Moving objects follow curvature (e.g.,
  satellites, photons)
• The equivalence principle guarantees
  spacetime is locally flat
• The more mass/energy there is in a given volume,
  the more spacetime is distorted in and around
  that volume.

44
GR Einstein, 1915

• Einsteins field equations correct action at a
  distance problem
• Gravity information propagates at the speed of
  light
• gt gravitational waves

r?
45
Curvature in 2D

• Imagine being an ant living in 2D
• You would understand
• left, right, forward, backward,
• but NOT up/down
• How do you know your world is curved?

46
Curvature in 2D

• In a curved space, Euclidean geometry does not
  apply
• - circumference ? 2? R
• - triangles ? 180
• - parallel lines dont stay parallel

2?R
R
??180?
47
Curvature in 2D
48
Curvature in 2D
49
Geodesics

• To do geometry, we need a way to measure
  distances
• gt use ant (lets call the ant metric), count
  steps it has to take on its way from P1 to P2
  (in spacetime, the ant-walk is a bit funny
  looking, but never mind that)
• Geodesic shortest line between P1 and P2
• (the fewest possible ant steps)

ant
P1
P2
50
Geodesics

• To the ant, the geodesic is a straight line,
• i.e., the ant never has to turn
• In SR and in freely falling frames, objects move
  in straight lines (uniform motion)
• In GR, freely falling objects (freely
  falling under the influence of gravity only, no
  rocket engines and such objects apples,
  photons, etc.)
• move on geodesics in spacetime.

51
Experimental Evidence for GR

• If mass is small / at large distances, curvature
  is weak
• gt Newtons laws are good approximation
• But Detailed observations confirm GR
• 1) Orbital deviations for Mercury (perihelion
  precession)

Newton
52
Experimental Evidence for GR

• 2) Deflection of light

53
Experimental Evidence for GR
54
Black Holes

• What happens as the star shrinks / its mass
  increases? How much can spacetime be distorted by
  a very massive object?
• Remember in a Newtonian black hole, the escape
  speed simply exceeds the speed of light
• gt Can gravity warp spacetime to the point where
  even light cannot escape its grip?
• That, then, would be a black hole.

55
Black Holes
56
Black Holes

• Time flows more slowly near a massive object,
• space is stretched out (circumference lt 2?R)
• Critical the ratio of circumference/mass of the
  object.
• If this ratio is small, GR effects are large
  (i.e., more mass within same region or same mass
  within smaller region)

1) massive
2) small
???
???
57
The Schwarzschild Radius

• GR predicts If mass is contained in a
  circumference smaller than a certain size
• space time within and around that mass
  concentration qualitatively changes. A far away
  observer would locate this critical surface at a
  radius
• Gravitational time dilation becomes infinite as
  one approaches the critical surface.

gravitational constant
critical circumference
speed of light
mass
Schwarzschild radius
58
Black Holes

• To a stationary oberserver far away, time flow at
  the critical surface (at RS) is slowed down
  infinitely.
• Light emitted close to the critical surface is
  severely red-shifted (the frequency is lower) and
  at the critical surface, the redshift is infinite.

From inside this region no information can escape
red-shifted
red-shifted into oblivion
59
Black Holes

• Inside the critical surface, spacetime is so
  warped that objects cannot move outward at all,
  not even light.
• gt Events inside the critical surface can never
  affect the region outside the critical surface,
  since no information about them can escape
  gravity.
• gt We call this surface the event horizon
• because it shields the outside completely from
  any events on the inside.

60
Black Holes

• Critical distinction to the Newtonian black hole
• Nothing ever leaves the horizon of a GR black
  hole.
• Lots of questions
• What happens to matter falling in?
• What happens at the center?
• Can we observe black holes anyway?
• And much, much more

Newton
Einstein
61
Conclusion Unified Theory

• The unified theory is Einsteins attempt to
  combine quantum mechanics and his two Theories of
  Relativity
• Einstein wanted this to be the most perfect idea
  of the universe
• Einstein never finished and died.
• Einstein moved to Princeton, NJ to escape the
  Nazis
• Einstein was Jewish, but did not practice the
  religion until the end. He believed that the
  universe was so complex that only God could have
  created it.