DEVIL PHYSICSTHE BADDEST CLASS ON

CAMPUS

IB PHYSICS

LSN E-4: COSMOLOGY

Questions From Reading Activity?

IB Assessment Statements

Olbers’ ParadoxE.4.1. Describe Newton’s model of

the universe.E.4.2. Explain Olbers’paradox.

IB Assessment Statements

The Big Bang ModelE.4.3. Suggest that the red-shift of

light from galaxies indicates that the universe is expanding.

E.4.4. Describe both space and time as originating with the Big Bang.

E.4.5. Describe the discovery of cosmic microwave background (CMB) radiation by Penzias and Wilson.

IB Assessment Statements

The Big Bang ModelE.4.6. Explain how cosmic

radiation in the microwave region is consistent with the Big Bang model.

E.4.7. Suggest how the Big Bang model provides a resolution to Olbers’ Paradox.

IB Assessment Statements

The Development of the UniverseE.4.8. Distinguish between the terms

open, flat and closed when used to describe the development of the universe.

E.4.9. Define the term critical density by reference to a flat model of the development of the universe.

E.4.10. Discuss how the density of the universe determines the development of the universe.

E.4.11. Discuss problems associated with determining the density of the universe.

IB Assessment Statements

The Development of the UniverseE.4.12. State that the current

scientific evidence suggests that the universe is open.

E.4.13. Discuss an example of the international nature of recent astrophysics research.

E.4.14. Evaluate arguments related to investing significant resources into researching the nature of the universe.

Olber’s Paradox

Cosmological Principle – uniformity of the universe Near view - Appearance of hierarchy

and structure Planets in a solar system Stars in a galaxy Galaxy in a cluster of galaxies which

is part of a larger super-cluster of galaxies

Olber’s Paradox

Cosmological Principle – uniformity of the universe Beyond that, however, the universe

looks uniform Homogeneity principle – on a large

scale, the universe looks uniform Like comparing a serving spoon of

vegetable soup to the whole pot Isotropy principle – uniform in all

directions

Olber’s Paradox

Cosmological Principle – uniformity of the universe Implication that the universe has no

edges and no center – infinite in extent

Newton proposed that it was infinite and static – it has been uniform and isotropic at all times

This led to Olbers’ Paradox

Olber’s Paradox

Why is the night sky dark? Consider that the universe contains

an infinite number of stars, basically evenly distributed

Olber’s Paradox

Why is the night sky dark? Place an observer somewhere in the

universe The observer is at a distance, d, from a star

which has some luminosity L The apparent brightness (energy received

per area per second) of that star is

Now consider that the one star is in a shell of some thickness, t, that encircles the observer

24 dLb

Olber’s Paradox Why is the night sky

dark? Place an observer somewhere

in the universe The volume of that ring is

equal to the surface area of a sphere times the thickness of the shell, 4πd2t , that contains a number density (i.e., number of stars per unit volume) n

The number of the stars in the ring would be density times volume or, 4πd2t

Olber’s Paradox Why is the night sky dark?

Place an observer somewhere in the universe The energy received by the

observer per second per area from all the stars in the shell would be

This is a constant, if you consider an average number density of stars, that doesn’t depend on distance from the shell

LntntdxdL

22 4

4

Olber’s Paradox Why is the night sky

dark? Place an observer

somewhere in the universe If there are an infinite

number of shells containing stars that emit a constant amount of energy, the total energy received would be infinite which would make the night sky infinitely bright – This is Olbers’ Paradox

Olber’s Paradox

What happens to the energy? Is it absorbed by intervening stars

and other media? In an infinite timeline, this does not

hold up because eventually the media would heat up from the radiation to a point where it was emitting as much as it was receiving

Olber’s Paradox What happens to the energy?

The only explanation is that the universe is finite and expanding Stars are finite in number and have a

finite lifetime They have not been radiating forever and

won’t continue to radiate forever – finite radiation

If the age of the universe is finite, light from stars that are extremely far away haven’t even reached us

If the universe is expanding, radiation from stars is redshifted, the “Doppler effect for light”, so it contains less energy

Expanding universe

When analyzing the absorption spectra of distant galaxies, the dark lines are longer as compared to the same chemicals on earth

This means that they have a longer than expected wavelength

Expanding universe This can be explained by the star

moving away from the earth which causes the radiation to be redshifted – i.e. shifted toward the red end – similar to the Doppler effect

Hubble suggested that the redshift was evidence that the galaxies were moving away from us and away from each other

Expanding universe

Suggests that the universe was originally much smaller and was much more compact

Expansion must have been caused by some type of explosion –

Big Bang Theory

Cosmic Background Radiation In 1964, two radio astronomers from

Bell Laboratories set up an antenna to study radio signals from our galaxy

They kept picking up a microwave signal no matter where they pointed the antenna

Spectral analysis of the signal showed it to be a blackbody radiation corresponding to a temperature of 2.7 K

Cosmic Background Radiation The theory is that the

radiation is the remnant of a hot explosion that occurred at the beginning of time As the universe expanded, the

temperature dropped until it reached its current value of 2.7K

Big Bang Theory

The answer to Olbers’ Paradox combined with the discovery of cosmic background radiation and an abundance of helium in the universe led to the Big Bang Theory

At the beginning of time, about 14 billion years ago, the universe consisted of a single solid mass

Big Bang Theory

The mass exploded with matter flying outwards in all directions, creating space as it went along

The aftermath of the explosion continues as the universe continues to expand

Big Bang Theory

The explosion created tremendous heat with the residual radiation still observed

The theory predicts that about 25% of the mass in the universe would be helium Measurements in nearby galaxies

have shown that the values are never less than 25%

Development of the Universe – What’s Next?

The universe is expanding right now, but what happens next

Development of the Universe – What’s Next?

Consider two galaxies that are some distance apart, x0 At some future time, t, the separation

can be represented by,

R(t) is called the scale factor of the universe or sometimes just the radius of the universe

R(t) describes what the eventual size of the universe will be

0xtRtx

Development of the Universe – What’s Next?

Three possibilities: It will continue to expand forever at

an increasing rate, open universe It will continue to expand forever,

but at a rate that approaches zero, flat universe

Expansion will eventually stop, followed by a collapse, closed universe

Development of the Universe – What’s Next? What will happen next is

dependent on the density of the universe relative to its critical density Consider a mass that is expanding

outward It has kinetic energy due to its

expansion

Development of the Universe – What’s Next? What will happen next is dependent on

the density of the universe relative to its critical density But it has gravitational attraction that

opposes the expansion If kinetic energy is greater than gravitational

attraction, the universe will expand forever If kinetic energy is equal to gravitational

attraction, the universe will expand forever, but at a rate that approaches zero

If kinetic energy is less than the gravitational attraction, the universe will eventually stop expanding and then start to collapse in on itself

Development of the Universe – What’s Next? What will happen next is dependent

on the density of the universe relative to its critical density The equation for total energy of the

expanding universe is

H is the Hubble constant G is the gravitational constant

38

21 22 GHmrE

Development of the Universe – What’s Next? What will happen next is

dependent on the density of the universe relative to its critical density

The key variable here is density, ρ Critical density causes E=0 and is

estimated to be,

38

21 22 GHmrE

326

2

1083

mkg

GH

c

Development of the Universe – What’s Next? What will happen next is

dependent on the density of the universe relative to its critical density

ρ < ρc , the universe is open, the universe will expand forever

326

2

1083

mkg

GH

c

Development of the Universe – What’s Next? What will happen next is dependent

on the density of the universe relative to its critical density

ρ = ρc , the universe is flat, the universe will expand forever, but at a rate that approaches zero

326

2

1083

mkg

GH

c

Development of the Universe – What’s Next? What will happen next is dependent

on the density of the universe relative to its critical density

ρ > ρc , the universe is closed, the universe will eventually stop expanding and then start to collapse in on itself

326

2

1083

mkg

GH

c

Development of the Universe – What’s Next? Problems in determining the mass

density of the universe Dark matter – matter that we can’t see

because it is too cold to radiate (brown dwarfs)

Two hypotheses: WIMPS – weakly interacting massive

particles Neutrino masses are not yet determined so

contribution is unknown MACHOS – massive compact halo objects

Development of the Universe – What’s Next? Dark energy

Previous discussion on Big Bang Theory is the classic perspective that has been outdated since 1998 when it was discovered that distant supernovas are moving away from us at speeds much greater than expected

Theory that the universe is filled with an all-permeating vacuum energy called Dark Energy

Development of the Universe – What’s Next? Dark energy

Creates a repulsive force that opposes the force of gravity

Appears that dark energy started to dominate gravity about 5 billion years ago

Development of the Universe – What’s Next? Dark energy

Belief is that the density of the universe is equal to critical density, but instead of the rate of expansion approaching zero, dark energy is causing the expansion to accelerate????

Development of the Universe – What’s Next? Dark energy

Universe is now thought to be made of 73% dark energy and 27% matter Of the 27% matter, 85% is thought to be dark

matter and 15% (only 4% of the universe) to be ordinary matter

SO WHAT HAPPENS NEXT???

SO WHAT HAPPENS NEXT??? IB Exams

College Job Family Retirement Ashes to ashes, dust to dust

IB Assessment Statements

Olbers’ ParadoxE.4.1. Describe Newton’s model of

the universe.E.4.2. Explain Olbers’paradox.

IB Assessment Statements

The Big Bang ModelE.4.3. Suggest that the red-shift of

light from galaxies indicates that the universe is expanding.

E.4.4. Describe both space and time as originating with the Big Bang.

E.4.5. Describe the discovery of cosmic microwave background (CMB) radiation by Penzias and Wilson.

IB Assessment Statements

The Big Bang ModelE.4.6. Explain how cosmic

radiation in the microwave region is consistent with the Big Bang model.

E.4.7. Suggest how the Big Bang model provides a resolution to Olbers’ Paradox.

IB Assessment Statements

The Development of the UniverseE.4.8. Distinguish between the terms

open, flat and closed when used to describe the development of the universe.

E.4.9. Define the term critical density by reference to a flat model of the development of the universe.

E.4.10. Discuss how the density of the universe determines the development of the universe.

E.4.11. Discuss problems associated with determining the density of the universe.

IB Assessment Statements

The Development of the UniverseE.4.12. State that the current

scientific evidence suggests that the universe is open.

E.4.13. Discuss an example of the international nature of recent astrophysics research.

E.4.14. Evaluate arguments related to investing significant resources into researching the nature of the universe.

QUESTIONS?

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