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Albert Einstein

By Leiwen Wu

- The Special and General Theory of Relativity and

his Thought Experiments

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.

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.

Einsteins Personal Life

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

Newton, Einstein, and Gravity

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.

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.

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.

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

Newton and Kepler

Newton showed that objects moving along closed

orbits under the influence of gravity follow

elliptical paths. Recall Keplers First Law

Newton and Kepler

Newton also showed that objects in these orbits

conserve angular momentum. Recall Keplers

Second Law

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

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.

What is relativity?

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

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.

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.

If c were not absolute, youd see car A reach the

collision point before car B! You would see a

different event!

Consequences of an absolute speed of light for

all observers time dilation

The Equivalence Principle

(No Transcript)

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.

Orbits in Curved Space-Time

Gravity à la Einstein

Einsteins general theory of relativity predicted

that light paths should be affected by massive

objects.

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.

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.

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.

General Relativity Conclusion

- Einstein concluded that 4 dimensional

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

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.

Aberration of Light

Moral direction of light beam is relative

Gravitational deflection of Light

Now assume boxes are accelerating

Light path is curved

Light ray curved in accelerating frame

Principle of Equivalence (acceleration gravity)

Gravity attracts light!

Paradox How can gravity attract light if light

has no mass?

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

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.

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

Tides

- Problem
- Gravity decreases with distance gt stretch

r2

r1

moon

Tides

- Tides gravity changes from place to place

not freely falling

?

?

?

?

freely falling

not freely falling

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

GENERAL RELATIVITY EINSTEIN 1915

- Matter energy determine curvature of spacetime
- Curvature of spacetime determines motion of

matter energy

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 ?

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.

GR Einstein, 1915

- Einsteins field equations correct action at a

distance problem - Gravity information propagates at the speed of

light - gt gravitational waves

r?

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?

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?

Curvature in 2D

Curvature in 2D

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

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.

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

Experimental Evidence for GR

- 2) Deflection of light

Experimental Evidence for GR

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.

Black Holes

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

???

???

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

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

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.

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

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.

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