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# 16.2 The Expanding Universe

How should the observation of galaxy red shifts be interpreted? There are two basic facts: almost all galaxies are red shifted, and the size of the red shift increases with increasing distance. In other words, galaxies are moving away from us, and the more distant galaxies are moving away faster. We are assuming that red shift is a measure of the Doppler velocity of a galaxy with respect to the Milky Way. At first glance, this seems to indicate that we are at the center of an expanding situation, which goes against the Copernican principle that we have no special location in the universe.

To help explain the red shift of galaxies, consider two different possibilities. First imagine a static universe. A static universe has a fixed size but can contain galaxies that are in motion (if galaxies are not moving at all, no red shifts are measured). Suppose that galaxies are milling around randomly in space, separated by large distances. They change position over time, but their typical separations are constant. In this type of universe, half the galaxies would have a component of motion away from us and half of the galaxies would have a component of motion toward us. This scenario translates into equal numbers of red shifts and blue shifts. Also, galaxies in every region of space have the same random motions, so the results of the measurement do not depend on distance. At every distance, the average size of the red shifts and blue shifts is the same, and the numbers of red shifts and blueshifts are about equal. A plot of velocity against distance would have points (each representing an entire galaxy) scattered around the line of zero velocity. This result is not what Hubble observed.

Determining the Hubble constant using supernova type 1a. Click here for original source URL.

Now imagine an expanding universe. In an expanding universe, the distance between galaxies increases with time. If every galaxy is moving away from the Milky Way, then every galaxy is red shifted. More distant galaxies move away from us faster. To see why this is true, let us consider the analogy of an expanding Earth. Suppose that the Earth is expanding at a rate such that it will double in size in an hour. The distance between any two cities must also double in an hour. For example, Tucson is about 100 miles from Phoenix. After an hour, Tucson will be 200 miles from Phoenix, so the two cities are moving apart at a rate of 100 mph. Tucson is about 500 miles from Los Angeles. After an hour, Tucson will be 1000 miles from Los Angeles, so the two cities are moving apart at a rate of 500 mph. There is a linear relation between distance and recession velocity. A plot of the two quantities will show a correlation, as observed by Hubble for galaxies.

Doppler Shift. Click here for original source URL.

Remember that the most common illustrations and analogies are two-dimensional. Galaxies are actually moving apart in the three dimensions of space. Remember also that Doppler shifts can only measure the component of a galaxy's motion along the line of sight. Galaxies will also have transverse, or sideways, components of their motion that astronomers cannot measure. Galaxies are so far away that their sideways motion is imperceptible even with observations over many decades. Hubble was an observer and he was very cautious about making interpretations about his data. He stuck to a description of the recession velocities of galaxies, which is what he actually observed, and did not talk about an expanding universe. That concept required a theoretical framework, one that would be provided by Einstein's theory of general relativity.