 Nikolaus
Copernicus |
Cosmological Principle |
 Three Views of the CMBR |
We do not occupy a preferred place in the Universe (Copernican belief)
and further, that at a given time, the Universe
appears homogeneous and isotropic to all
observers
Homogeneity and Isotropy of the Universe
 |
Homogeneous
means that in some average sense, the Universe appears
the same to all observers regardless of location. This is true for the left
hand figure (the brick wall) but not for the right figure.
Isotropic means that the Universe appears in all
directions which one looks. If one is at the center of the figure on the right,
this is true and so the Universe appears isotropic for an observer at the
center of this Universe. The figure on the left does not appear isotropic for
any observer! |
The question of the homogeneity and isotropy of the Universe
cannot be answered until one
specifies the size of the region which should be averaged over. For
example, the Solar System is clearly inhomogeneous; there is a star at
the center of the system which is surrounded by objects. The Solar System
looks differently depending upon where you look. The
scale upon
which the Universe should appear homogeneous and isotropic is not
well-defined, outside of the requirement that it is large (
(e.g., see Hubble Deep Field Photograph
Great
Wall),
The homogeneous and isotropic assumptions are tough. Recall that the
CMBR is homogeneous and isotropic but that regions in the
Universe which are in opposite directions are
not causally connected and so really have no
reason why they should have the same properties.
Why?
 |
Speed of Light and Communication
Galileo performed an experiment to measure the speed of light (the
maximum speed at which information can travel). The simple experiment was
shown to the left. Because of the great speed at which light traveled, he
could not measure the speed of light. Later, Roemer was able to measure the
speed of light. Roemer determined the orbital periods of the Galilean moons of
Jupiter (say Io). Consequently, he was able to predict when Io would
come out of eclipse. He found that at points L and G, his predictions
matched observation. However, at K and F, discrepancies arose.
Were the observations early or late compared to the
predicted times? From this observation, Roemer was able to determine
the speed of light. Today, the accpeted value for the speed of light is
c
= 300,000 kilometers
per second. |  |
Heat Flow and the CMBR
Because the fastest that information can travel through
the Universe is limited by the speed of light, information does not
propagate instantaneously from one point to another. For heat is generated
by the fire, but it takes a finite amount of time to travel one point to
another. The heat travels because it is trying to make everything have the
same temperature. If everything had the same temperature, no heat would
flow! This make the Homogeneity and Isotropy
of the CMBR perplexing. How could the entire Universe have the same
temperature. If, as we would have expected, the birth of the Universe was
messy in that different parts of the Universe started to expand at different
times and different parts of the Universe had different temperatures.
Is this a problem? Yes, it in fact is a large
problem because of the size of the Universe. The Universe is so large that
pieces of the Universe which are on opposite sides of us have not had a
chance to communicate and so to erase any differences by heat flow.
|
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So, Why is the CMBR homogeneous and isotropic?
This problem is known as the Horizon Problem.
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