Loading...

PPT – Chapter 26a Cosmology PowerPoint presentation | free to view - id: 1bbc3-MTllN

The Adobe Flash plugin is needed to view this content

Chapter 26a Cosmology Einstein's Theory of

Relativity Special and General Olbers

Paradox Cosmological Assumptions Models 1916

Einsteins static universe and the cosmological

constant 1921-1935 FRW models 1922 Three models

by A Friedmann H. P. Robertson, A. G. Walker---

Three Models---plus Friedmann

Einsteins Theory of Relativity

Albert Einstein (1879-1955) is pictured here in

the Swiss Patent Office where he did much of his

great work.

Special Relativity Space

and Time

- 1905 Postulates of Special Relativity
- 1. The speed of light is the same as measured by

all nonacclerating (Inertial) observers. - 2. No experiment can single out any special

inertial reference frame ( non accelerating).

- Consequences
- Moving Lengths Contract
- Moving clocks run slow
- Moving Mass appears to increase
- EM C2

Lorentz Contraction

Length Contraction

As speed increases, length in the direction of

motion decreases. Lengths in the perpendicular

direction do not change.

The meter stick is measured to be half as long

when traveling at 87 the speed of light

relative to the observer.

time dilation

The Clock is at rest

My clock ticks are 2.3 sec apart .

The Moving Clock

V 0.9c

The clock ticks on the moving clock are 5 sec

apart

Energy-Mass Equivalence

E mc2

- When a uranium nucleus
- splits, the mass of the
- remnants is less than the
- original mass. The difference
- appears as light, heat, and
- kinetic energy.

Energy is mass m E /c2

Mass is energy E mc2

You can create a particle-antiparticle pair when

high-energy photons collide. In this process,

called pair production, the photons disappear,

and their energy is replaced by the mass of the

particle-antiparticle pair.

In the process of annihilation, a colliding

particle-antiparticle pair disappears and high

energy photons appear

General Theory of Relativity1915

It took Einstein 10 years from the publication of

special relativity to the publication of GR

What is Gravity?

Einstein's Picture

Newtons Picture

Isaac Newton (1642-1726)

the gravitational field.

The key idea of General Relativity, called the

Equivalence Principle, is that gravity is

equivalent to an acceleration.

Principle of Equivalence It is impossible to

tell, from within a closed system, whether one is

in a gravitational field, or accelerating

General Relativity and Gravity

In Einsteins General Theory of Relativity,

gravity arises from the curvature of spacetime

continuum.

The curvature of the spacetime continuum is

produced by the presence of mass. Massive

object distorts spacetime continuum more.

Spacetime is stretched near objects with large

mass, like our Earth.

Mass and Curvature

- Einstein no longer thought of gravity as a force

but a curvature of space-time. - Space is "curved" by massive objects causing

objects to fall toward them.

Orbits of Planets

43 arcsec/100years

The extra amount of precession of planet

Mercurys orbit is explained by GTR.

Eddingtons Eclipse Expedition Experience, 1919

Consequences of GR Bending of Light

- Went to Principe Island in the Gulf of Guinea.

After months of drought, it was pouring rain on

the day of the eclipse Clouds parted just in

time, they took photographic plates showing the

location of stars around the limb of the sun - Deflection in agreement with the GR prediction

Einstein urged astronomers to measure the effect

of gravity on starlight, as in this 1913 letter

to the American G.E. Hale. They could not respond

until the First World War ended.

GRAVITATIONAL LENSE

Clocks and Curvature(Gravity)

fast

slow

Harvard 1959 Atomic clock in basement - slower

by about 2.50x10-15

Fast

slow

The stronger a gravitational field, the slower a

clock runs. A clock at the surface of the Earth

runs slower than a clock farther away.

More mass more spacetime curvature

Flat space

Neutron star

Black hole

The sun

More curvature means stronger attraction

Clocks in stronger gravity fields appear to

slow down to an external observer.

Time Slows

Gravitational

Red Shift Light emitted from compact object(

strong gravity) is red shifted The photon is

giving up energy as it escapes from the pull of

the gravitational field

The more massive and/or more compact an object,

the greater the redshift. 0.01 10-8 cm shift

for the Sun. 1 10-8 cm shift for a white

dwarf.

- What is a black hole?
- A curvature so steep light cannot climb out

The gravitational force or warping of space-time

increases at the surface of a collapsing star.

Light rays find it increasingly more difficult

to escape the surface. A black hole is a

collapsed star where light cannot escape.

- The blackhole has such a high density that at its

Surface the escape speed exceeds the speed of

light so nothing can escape

Black Hole

2GM

Rs

c2

Event Horizon Rs distance where escape speed

equals speed of light!

A black hole a big as the solar system, e.g. Rs

40 AU, has a mass M 2 Billion Mo

Singularity

Singularity Mathematical point at center,

where the point of the funnel comes to a head

Anything that falls into a black hole disappears

form the observable universe.

The center of the Blackhole

- Could a black hole somehow be connected to

another part of spacetime, or even some other

universe? - General relativity predicts that such

connections, called wormholes, might exist for

black holes

THE FUTURE? Travel

through a black hole and wormhole to Vega!

Gravitational waves

- GR predicts that ripples in spacetime propagate

at the speed of light gravitational waves - Mergers of compact objects (e.g. black holes)

produce immense amounts of gravitational

radiation - Note that the universe is not dim in terms of

gravitational radiation all mass produces it - Exceptionally difficult to detect because of the

weak coupling to matter Fgrav/Felec10-36

Laser Interferometer Gravitational Wave

Observatory LIGO (Livingston, Louisiana)

(No Transcript)

General Relativity and the Universe on Large

Scales-------Cosmology

Historical Time Line

- 1823 Olbers Paradox
- Cosmological Assumptions
- 1916 Einsteins static universe and the

cosmological constant (Force) - 1929 Hubbles Law---the universe is expanding
- 1930 Einsteins biggest mistake ---the

cosmological constant is zero. - 1921-1935 FRW models--- A Friedmann H. P.

Robertson, - and A. G. Walker

Olberss Paradox Why is the

night sky dark?

1823 - Heinrich Olbers Paradox The sky should

be uniformly bright. Assume universe is

infinite and stars are randomly scattered. Then

in every direction you will eventually come to a

star and the sky will be glowing!

Resolution Stars are moving away so light is

red-shift and not as bright. The universe is not

infinitely old - so some light hasn't had time to

reach us.

Cosmological

Assumptions

1. Universality of Physical Law 2. The

Cosmological Principle (or Copernican view) The

place we occupy in the Universe is not special.

The matter in the universe is homogeneous and

isotropic when averaged over very large scales

greater than about 300 Mpc. a. Homogeneity

b. Isotropic

Consequences 1. Laws of Physics are the same

through out the universe 2. No center 3. No

edge, 4. All observers see the same

(No Transcript)

Time Line for the beginnings of Cosmology

1916 Einsteins static universe and the

cosmological constant (Force) 1922 Three models

of the Universe by A Friedmann

1929 Hubbles Law---the universe is expanding

1930 Einsteins biggest mistake ---the

cosmological constant is zero.

1935 H. P. Robertson, A. G. Walker--- Three

Models

Geoffrey Walker

H.P. Robertson

In 1917 Einstein constructed a static model of

the Universe. Models of the Universe were a

natural out come of Einstein's General Relativity

as applied to a homogeneous universe.

Static Universe

The idea that the universe was expanding was

thought to be absurd so Einstein invented the

Cosmological constant as a term in his General

Relativity theory that allowed for a static

universe

Repulsive force Cosmological Constant

Attractive Gravity

1930 Hubble Expansion

- 1930 Einstein learns the Universe is Expanding
- Einstein was unhappy with the cosmological

constant and dropped it. - Einsteins biggest mistake
- ---the cosmological constant is zero

Hubbles Law Galaxies are receding with

velocities directly proportional to the distance

away

1921-1935 FRW models

The Russian mathematician Friedmann realized in

1921 that Einstein equations could describe an

expanding universe.

Alexander Friedmann

The joint work of Walker and colleague H P

Robertson in the late 1930s put Friedmann's

theories of an expanding universe on a sound

mathematical foundation. This theory is called

the FRW model and still forms the basis for

models of the universe in modern cosmology.

Geoffrey Walker

H.P. Robertson

The British astronomer Fred Hoyle dismissively

called it the "Big Bang'', and the name stuck.

This model implied that the Universe was born at

one moment, about ten billion years ago All the

matter, indeed the Universe itself, was created

at just one instant.

Time

The Space continued to expand after the

initial burst.

The End of Chapter 26a