Under
construction...now, where have you heard that before ?
The following notes are intended for our students following A-Level Modular Physics, Cosmology, UCLES. They are intended as notes to clarify certain aspects of the course. They are not intended to be a replacement for their own notes,or to take the place of standard textbooks.
HTML is not a nice medium for using Greek symbols, so I have substituted
some of the standard symbols with appropriate English letters.
3.1 Line spectrum
When gases are heated they absorb energy. Electrons move to higher energy
levels (greater potential energy) Electromagnetic radiation is emitted when
an electron returns to a lower energy level. The energy emitted is equal
to the difference in energy levels between the two states. This is the photon
energy given by E = hf , and the corresponding wavelength is given
by w = c/f .
When light from a heated gas is analysed using a spectrometer the different
wavelengths are clearly visible as a set of distinct lines. This is the
emission spectrum of that gas. Each gas is characterised by a unique
set distinct lines (wavelengths) . This is a result of the differences in
the atomic structure of each element. No single wavelength can identify an
element , but the overall pattern clearly identifies the element (or compound)
This is of immense importance in studying spectra from distant star.
All stars emit a continuous spectrum of all wavelengths through the
electromagnetic spectrum. The relative intensity of these wavelengths is
given by the black body distribution. Gases in the surrounding 'atmosphere'
absorb amounts of electromagnetic energy which correspond to the differences
between energy levels for the electrons . As electrons return to the lower
state the wavelengths are emitted in all directions. Therefore very
little of the original electromagnetic energy at these wavelengths actually
reaches the observer. The continuous spectrum of a star appears to be missing
these wavelengths . This pattern of missing wavelengths in a continuous spectrum
is called an absorption spectrum. For a given gas the position of
these absorption lines coincides exactly with the wavelengths of the emission
spectrum for that gas. Therefore , the study of the spectra from distant
stars can be used to identify gases surrounding the star, by looking for
characteristic 'fingerprint' pattern of gases and elements
The absorption spectrum of a distant galaxy can be used to determine the
velocity v at which the galaxy is moving relative to our galaxy. This is
because each distinct pattern of wavelengths will have been 'red shifted'...a
consequence of the Doppler effect.The degree of red shift is directly
proportional to the recessional velocity.
The change of wavelength due to the relative motion between the source and
observer is known as the Doppler Effect.
We will make the assumption that v is much smaller than c .
Let w be the wavelength when there is no relative velocity between
source and observer, The change of wavelength is directly proportional to
the relative velocity v between the source and the observer.
The change of wavelength, = (v x w)/c
and the fractional change of wavelength = v/c
As v becomes larger this approximation is no longer valid, due to
the greater influence of relativity.
One of the most important discoveries occured in 1929, when Edwin Hubble
discovered that the Universe is expanding. He found that the red-shifts of
a set of local galaxies were directly proportional to the distance
of these galaxies from our galaxy. This has became known as Hubble's
Law, and is given by
v = Hd
where H is known as Hubble's constant.
The value of H is measured in km/s per Megaparsec.
A value of 50 km/s per Mpc would mean that a galaxy 1Mpc away would be receding
at 50km/s. A galaxy 10 Mpc away would be receding at 500 km/s.
This equation does not take account of the effect of gravity on the outward
expansion. The presence of gravity will oppose the outward expansion,so the
velocity of expansion reduces with time. The value of H is the value of H
as measured today. It is sometimes called the Hubble Parameter...since
its value is not constant with time. ( A graph of distance between two
galaxies against time is not a straight line)
The value of H will always give a calculated value of the age of the Universe
(1/H) which is higher than the actual value. An accurate determination
of H depends on the accuracy to which we can determine distances to distant
galaxies.Unfortunately, the greater the distance of a galaxy the greater
the uncertainty in measurements of that distance.Most estimates give values
between 40 and 80 km/s per Megapasec.
The gravitational attraction between masses slows down the outward expansion
of the Universe. If we knew the mass of the Universe with a high degree of
accuracy , we would be able to predict confidently just what the future of
the Universe will be. Unfortunately much of the mass of the Universe appears
missing...or at least it hasn't been found yet. This missing mass, which
would enable the density of the Universe to be calculated , is difficult
to observe, unlike stars which emit their own light. Yet an accurate
determination is absolutely essential if we are to predict with some accuracy
the fate of the Universe.
According to the Cosmological Principle there are no preferred places in
the Universe. Measurements of the Universe made from Earth, disregarding
local irregularities, can be considered to be identical to those made in
any other part of the Universe. A classic illustration of this is in the
way in which the expansion of the Universe, according to Hubble's Law, occurs.
Take a length of elastic.Mark dots at even intervals to indicate galaxies.
Gradually pull the elastic apart.At any time the distances from a galaxy
will vary according with Hubble's Law, irrespective of which galaxy (dot)
is chosen as the reference point. A similar pattern can be observed by using
a series of dots on a balloon which is gradually inflated.
Therefore, irrespective of where we are in the Universe, we should observe
the same expansion properties , and the same laws of physics in operation.
Earth has therefore no special significance, other than to humans, on a
cosmic scale !
The early Universe,according to the Big Bang, involved extremely high
temperatures. So high are these temperatures, that it is extremely difficult
to reach them in scientific experiments. Fundamental investigations into
particles involve accelerating particles at very high speeds, which would
normally be associated with particles at very high temperatures. It is possible
to reach speeds in particle accelerators which correspond to 10^15 K , which
would occur about 10^-15 s after the Big Bang. For times earlier than this,
we need to rely on theoretical models,used to explain our present observations
,and 'extrapolate' these backwards to predict the mechanisms which occur
in the very early stages of the Big-Bang. This is an incredible difficult
task, because a number of complex interactions which take place . Protons
and neutrons are thought to consist of smaller particles, called quarks At
temperatures above 10^7 these quarks cannot be held together as protons and
neutrons. At higher temperature the four fundamental forces become almost
indistinguishable from one another . Different 'messenger' particles are
believed to be responsible for these four different forces. Above 10^5 K
photons, massless particles, are being converted into particles,and their
anti-particles.The reverse process is also happening . The theories are therefore
very different to theories involving everday experiences of forces,and the
synthesis of the four fundamental forces makes them extraordinarily complex
theories. These are known as Grand Unified Theories (GUTs). These attempt
to explain the physical behaviour of particles and forces during the very
early stages of the Universe, in a single set of equations.The more recent
theories which try to reach the goal of TOE (Theory of Everything) are called
String Theories. These have gained some success in providing a desription
of gravity, but the theory itself appears to some scientists as a mathematical
instrument or 'toy', with very little foundation based on physics (as most
of us know it !)
At time t=0 a singularity is predicted, where all laws as we know
them break down.Space and time are infinitely distorted. The uncertainty
principle of quantum mechanics prevents any accurate predictions to be
made for times less than 10^-45 s.
In 1965 , Arno Penzias and Robert Wilson discovered , quite accidently, the existence of a low level microwave radiation. This was found to be virtually of the same intensity no matter which way they looked with their radio telescope. This was one of the greatest discoveries for the support of the Big Bang Theory. After billions of years the great fireball would have cooled to give a black-body peak temperature of approximately 2.7 K. Furthermore, this temperature would be associated with a peak wavelength of 1.07mm . Analysis of the radiation supported this prediction. Until recently, the uniformity of the background radiation was of some concern to many cosmologists.The apparent uniformity of the background radiation was not consistent with the requirements for the formation of galaxies. Small variations in the density are required in order that galaxies can be formed. This is due to the effect of gravitational attraction between particles of gases in these higher density regions. Therefore, this should be reflected in slight variations in the background radiation. The measurement of such variations was performed by Cosmic Background Explorer (COBE) in 1992.These measurements amounted to variations of just 30 millionths of a degree Kelvin.
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