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Evolution of the Universe,
Radiation Laws and
Cosmic Background
Radiation
"In the beginning, there was nothing at all. Earth was not
found, nor Heaven above, a Yawning-Gap there was, but
grass nowhere."
The Edda -- collection of Norse Myths dating to 1200
In this lecture period, we wish to learn:
What
What
What
What
can we know about the origin of the Universe?
is the evidence for the Big Bang ?
role does radiation play ?
are some of the fundamental laws ?
Format for printing
The Origin of the Universe
"In the beginning".... The question of how and why the world
around us came into being is perhaps the most fundamental
question of all. It is the root of faith and fantasy, dogma and
bewilderment, poetry and intensive scientific inquiry. While we
cannot hope to resolve these questions completely, we can use the
modern scientific approach to describe and discuss possible
timelines, scenarios, and outcomes. Such a discussion can help to
illuminate our fledgling understanding of today's universe. The
activity below explores the main steps in its evolution (requires free
Macromedia plug-in; http://www.macromedia.com/downloads/ ).
Load Macromedia browser plug-ins (Flash and Shockwave);
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from NOVAonline
We live in an amazing time. For the first time in human history, we
can rationally speculate on the origin of the Universe and make
tangible progress in reaching a description, and even perhaps a
rudimentary understanding. We will try in this lecture to sketch out
the modern scientific view of the origin of the Universe.
The scientific evidence is now overwhelming that the Universe
began with a "Big Bang" ~15 billion (15,000,000,000 or 15E9)
years ago. We review the major supporting pieces of evidence for
this assertion and discuss some of the consequences. First, let's
look at our place in the Universe and introduce some terms, with
images.
Earth
A planet with a rocky composition and a
temperate climate at an intermediate distance
from an average star. The Earth is unique in
many ways. For example, it is the only body we
know of where water can exist in all three
phases: vapor, liquid and solid forms. Click on
the image for a general tour that is offered
through Windows to the Universe.
Sun

A medium-sized, moderately bright,
middle aged star, born ~5 billion years
ago from a gaseous nebula, with
perhaps another 4-5 billion years to
live before expanding to a "red-giant",
engulfing the Earth and finally cooling
to become a fading "white dwarf" star. This image of
today's Sun, as seen in hydrogen emissions that show the
turbulent solar atmosphere, is the most recent available
from NASA.
Nebulae
The birthplace of stars. Our own sun
formed in just such a nebula. The
example shown here is the Great
Orion Nebula, one of the youngest
objects in the sky - thought to be less
than 20,000 years old. Orion is very
hot (about 20,000 K). Other
spectacular examples are the Cat's
Eye Nebula, and the Trifid Nebula.
Star clusters are recently-born families of stars that form in such
nebula and then gradually drift apart. Click on Orion and see the
Horsehead Nebula, which is 1500 light years away. A "light year"
is a unit of distance which represents the distance traveled by
light in one year.
Galaxy
A collection of billions of stars, held
together by gravity. Our own galaxy is
known as the "Milky-Way" Galaxy and is
100,000 light years across. Galaxies are
in many ways "Island Universes". Each
galaxy contains billions of stars, with
some having more than 1000 billion
stars. This Hubble Space Telescope true-color image is the
Cartwheel Galaxy, located 500 million light-years away in the
constellation Sculptor. Click on it to see our nearest neighbor
galaxy, Andromeda.
Visible Universe
The visible universe contains at least 100
billion galaxies - these are incredible
numbers. This image is of very young
galaxies observed by the Hubble Space
Telescope at the very limit of its range. The
sky is full of such strange looking galaxies in
all directions (except where masked by
intervening dust clouds). The universe is
home to a variety of exotic objects. For
example, quasars, which were first
discovered in 1960, are still baffling objects.
Incredibly energetic, they are found at great distances near what
is thought to be the edge of the known universe (the most distant
one has been estimated to be 10 billion light years away). Some
quasars produce more energy than 100 large galaxies. Some
scientists think that quasars may represent holes to other
universes.
Radiation Laws
The Universe is an enormously vast system. How did all this come
into being?
To address this question, we first discuss radiation as it offer the
means by which we perceive the universe. We start with basic
concepts of radiation, since our ability to sense radiation is
responsible for what little we know of the early Universe.
What is radiation?
Electromagnetic Radiation includes visible light, radio waves,
microwaves, x-rays, gamma rays, and infra-red (heat) rays. All
these forms of radiation are characterized by traveling oscillations
of a combined electric and magnetic field. These electromagnetic
waves differ by the wavelength of the oscillation, with shorter
wavelength radiation carrying more energy than longer wavelength
radiation, as we shall see.
Scientists usually think of light as consisting either of innumerable
"wave packets" (characterized by specific wavelengths or colors) or
"photons", particles of energy that carry no mass, but travel at the
speed of light (300,000 kilometers per second). Our eyes perceive
just a tiny fraction of the possible wavelengths of light, centered on
the wavelengths that the Sun happens to emit. All possible
wavelengths make up the electromagnetic spectrum.
The
electromagnetic
spectrum can be
expressed in
terms of energy,
wavelength, or
frequency.
(from NASA)
To understand radiation we need to discuss a few important
physical laws (laws that no Congress can repeal!). You will find that
these radiation laws will reappear throughout this course.
Everything emits
Let's start with the statement that everything (including you, me
and the chair you are sitting on) emits radiation. The type and
amount of radiation emitted depends on the temperature of the
object. The hotter the object the more radiation is emitted. (Our
hot Sun emits lots of light). Also, the hotter the object, the more
energetic (i.e. the bluer) the radiation. To see how this works, let's
state (not derive) the following important physical laws.
Planck's Law
Planck's Law is sometimes called the "black-body" formula. It works
perfectly for objects that are perfect black bodies (i.e., objects that
absorb and emit radiation uniformly and with 100% efficiency).
Planck's Law works very well for celestial bodies.
Where E (lambda) is the amount of radiant energy emitted at a
given wavelength, lambda. T is the temperature of the object, and
a and b are constants.
This strange-looking
mathematical formula
has a quite simple
meaning. The
spectrum of
wavelengths emitted
by a body at a
temperature, T, has a
characteristic shape
that is strongly
dependent on the
wavelength (to the
inverse fifth power).
This law describes the
spectral distribution of
radiation emitted by a
black body. We can
best understand what
this means with a
picture. The figure
shows the shapes of the wavelength-dependent radiation emitted
from so-called "black-bodies" (objects that agree perfectly with
Planck's law).
Black-body radiation curves, showing the
wavelength distribution of emitted photons
at different temperatures, on a logarithmic
scale. Note the different regions of the
electromagnetic spectrum
Very hot bodies (3000 - 20,000 K) like our Sun emit a lot of light at
visible wavelengths. This is why our eyes have evolved to be
sensitive to the visible wavelength range.
The Sun acts like a black body near 6000K, whereas the Earth acts
like a black body near 300 K (can you guess where its curve would
lie?).
Stefan-Boltzmann Law ("E equals sigma T to the fourth")
This one is just as important as E = mc2, and as easy to
remember:
where E is the total energy emitted (calculated by adding up the
areas under the curves of Figure 1), sigma is a constant, and T is
temperature.
The Stefan-Boltzmann law tells us that the amount of energy
emitted by an object increases as the fourth power of its
temperature. This means that a small increase in temperature
results in a much bigger increase in radiation. To see how this
works, take another look at the figure, and mentally add up (or
integrate) the areas under the curves (remember that it is a
logarithmic plot).
Wein's Law
Wein's Law is really just a consequence of Planck's Law. Wein's Law
states that the wavelength of the peak radiance [lambda (max)]
decreases linearly as the temperature increases, where c is a
constant:
This means that as objects get hotter, the
wavelengths emitted become shorter (bluer). You can see how this
works by looking at the Figure above. Notice how the peak
wavelength shifts to the left as the temperature increases.
Radiation laws in action
The figure shows how the radiation laws work for the two celestial
bodies of greatest interest to us: the Sun and the Earth. While the
Sun emits in the visible end of the spectrum, the much cooler
Earth emits longer infra-red wavelengths back out to space. The
temperature of the Earth is controlled by the balance between the
incoming visible light and the outgoing infra-red light. We will
discuss this in greater detail later. Click here to see how the S-B
law is used to calculate planetary temperatures.
Radiation emitted
from the Sun and
from the Earth have
different
wavelengths, as
predicted by the
radiation laws.
Is summary:



Planck's law gives us the shape of the curves.
Stefan-Boltzmann's Law tells us that much more energy
comes from the Sun than from the Earth.
Wein's law tells us that the hot Sun is much bluer than the
cooler Earth.
One last principle, the Doppler Effect, and we're ready to talk about
the origin of the Universe in more detail.
The Doppler Effect
Although you may not know it, you are already familiar with the
Doppler Effect. This is the phenomenon that occurs when the wail
of an ambulance seems to get faster as it gets closer. But this
phenomenon can occur with more than sound; an equivalent effect
occurs for light, due to the wave-like property of radiation. When
we observe a sound or light wave from a source at rest, the time
between the arrival of wave crests at our instruments is the same
as the time between crests as they leave the source. However,
when the source is moving away from us, the time between arrivals
of successive wave crests is increased over the time, because each
crest has a little farther to go on its journey to us than the crest
before. Click here to see how the speed of an object affects
wavelength.
The Doppler effect shifts the light to
longer wavelengths (red shift) for a
receding object, and to shorter
wavelengths (blue shift) for an
approaching object.
Similarly, if the source is moving towards us, the time between
arrival of wave crests is decreased because each successive wave
crest has a shorter distance to go, and the wave appears to have a
shorter wavelength.
Think of the traveling salesman who writes a letter home each week
at the same time, but as he gets farther and farther away from
home, the letters are received more than once a week apart. Then,
when he turns back towards home, the letters arrive at shorter
intervals.
The Doppler Effect for Light is calculated by:
Change of wavelength
Speed of source
=
Normal wavelength
Speed of light
The Doppler Shift turns out to be the most useful of all astronomical
tools, since it gives us the ability to determine the velocity of
celestial bodies by comparing the wavelengths of known emission
features with stationary sources.
Big Bang Theory
The Big Bang hypothesis is the most widely accepted theory of the
origin of the universe. The Big Bang theory states that the Universe
began when primordial mass exploded in titanic holocaust. This
fireball gradually cooled as it expanded outward, and giant clouds
of swirling gas formed the celestial bodies. Entire galaxies took
shape as they were propelled outward by the initial cataclysm. The
universe created by the Big Bang may expand forever or it may
gradually slow and eventually collapse in on itself.
The Big Bang theory does not explain why the bang occurred, but
predicts (with surprising accuracy) what the consequences of such
an event would be. Several key pieces of evidence have been
assembled that support the Big Bang theory and have laid to rest
many of the competing theories. We will summarize the three most
important "smoking guns" for the Big Bang theory.
Smoking Gun #1
The first smoking gun is from the field of atomic physics. If the big
bang occurred, the initial temperatures must have been so
unimaginably high that matter could only have existed in exotic and
unstable forms. As the temperature cooled in the first second, free
hydrogen nuclei (atomic mass 1) were formed that could undergo
fusion reactions to give heavier forms of hydrogen (atomic mass 2,
3) and helium (atomic mass 3 and 4). The lack of stable nuclei of
atomic mass 5 and rapidly dropping temperatures limited the fusion
reactions at this point. Thus, the theory predicts a early universe
with only a mixture of ~75% hydrogen and 25% helium (by
weight) and no heavier species. This ratio is exactly what is
observed in stars - a major piece of evidence supporting the big
bang.
Smoking Gun #2
Measurements of low energy microwave radiation (see Figure) have
shown that the visible universe is permeated by "cosmic
background" microwave radiation, coming uniformly (or nearuniformly) from all directions and similar to what is expected from a
black body at 3K. The Big Bang theory predicts that such radiation
is the red-shifted remnant of the radiation released when matter
and light became decoupled about 1 million years after the Big
Bang. The American scientists who first made this measurement in
1965 (Penzias and Wilson) obtained the Nobel Prize. They were not
looking for the cosmic background, and were at first irritated by the
unexpected source of noise in their measurements.
A timeline for
the Big Bang
model of the
Universe. At ~1
million years
after the Big
Bang,
temperatures
cool sufficiently
to allow
hydrogen- and
helium-neutral
atoms to form
from the plasma
(charged
particles). This
event freed up
radiation that
was previously
contained in
thermal
equilibrium with
matter. Since
then, radiation
and matter have
gone their own
ways. When
astronomers
observe the
cosmic ray
background,
they are looking
at photons
released from
the big bang
when radiation
and matter
became
uncoupled.
Smoking Gun #3
Measurements of the red shifts of virtually all galaxies (except a
few in our immediate vicinity) show that the visible universe is
expanding in all directions. Everything is moving away from
everything else, much as painted spots on a balloon will all move
away from each other as the balloon is blown up. The further away
the galaxy, the faster it recedes. The constant of proportionality
between the distance and velocity of recession is known as Hubble's
constant.
These measurements support the Big Bang theory, which states
that the Universe must continually expand away from the
"singularity" of the Big Bang. The theory leaves open the possibility
that matter might at some point collapse inwards again; this will
depend on exactly how much mass there is and whether
gravitational attraction is strong enough to overcome the effects of
the explosion.
Smoking Gun #4 discovered in 1992?
Measurements from the NASA Cosmic Ray Background Explorer
(COBE) mission have provided additional supporting evidence for
the big bang.
Briefly, the COBE satellite results are showing that the cosmic ray
background is not completely uniform in direction (see Figure), but
that there is some clumping in preferred directions with differences
in effective temperature of only one hundred millionth of a degree.
This clumpiness would have been necessary for the big bang to
produce galaxies, since a perfectly uniform explosion would not
produce localized high densities.
Summary
The Radiation Laws mathematically describe the manner in which
all objects emit radiation according to their temperature.
The Big Bang theory is the most widely accepted theory of the
creation of the Universe. Several predictions made by the theory
have been verified by experiment. These include:



the observed solar system hydrogen to helium ratio
the cosmic background radiation
the expansion determined by measurements of red shifts
Suggested Readings
Weinberg, S., The First Three Minutes, Basic Books, 1988
Cox, P. A., The Elements: Their Origin, Abundance, and Distribution
Oxford Scientific Publications, 1989.
Self Test
Take the Self-Test for this lecture.
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