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 hand figure. Isotropic means that the Universe appears the same in whatever direction 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! This remarkable suggestion is consistent with the smoothness of the CMBR, but more on this later.

The question of the homogeneity and isotropy of the Universe cannot be answered until one specifies the size of the region over which the Universe should be averaged. For example, the Solar System is clearly inhomogeneous, there is a star at the center of the system surrounded by planets. The Solar System looks differently depending upon where you are and where you look. The scale over which the Universe should appear homogeneous and isotropic is not well-defined, outside of the requirement that it is large (e.g., see Abell 2218 , Hubble Deep Field Photograph Great Wall),

There is structure in the Universe, but the argument is that it is small compared to the overall size of the Universe and so, in a sense, it can be averaged over ===> the Cosmologoical Principle is apparently valid.


The homogeneous and isotropic requirements 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 the picture shown to the right, heat is produced by the fire, but it takes a finite amount of time to travel from one point to another. The person's hands do not warm instantaneously. Heat flows because it is trying to make everything come to the same temperature. This takes time and makes the observation that the CMBR is Homogeneous and Isotropic perplexing.


Why is the CMBR homogeneous and isotropic? When I look in one direction on the sky and observe the CMBR, I see light that has traveled over the lifetime of the Universe to reach me. When I look behind me, in the opposite direction, I see light that has also traveled over the lifetime of the Universe to reach me. That is, the part of the Universe in front of me and the part behind me are so far apart that they have never been in thermal contact (and, in fact, in principle do not even know of the other's existence). Given this, how can they have the same temperature?

This problem is known as the Horizon Problem.


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