Edwin Hubble's first great discovery was the extragalactic nature of some of the spiral nebulae. The fact that these fuzzy patches of light were entire galaxies or systems of stars remote from our own Milky Way. By the end of his career, he'd expanded the size of the known universe by a factor of thousands compared to the size of the Milky Way. His second great discovery was equally profound and had great implications for the history of the universe. When he measured the distances and velocities of the galaxies he could observe with large telescopes, initially the Mount Wilson 100 inch, later the Palomar 200 inch. He observed a striking correlation, the more distant a galaxy was the faster it was moving away from us. The recession velocities he observed were hundreds of thousands or even millions of miles an hour. And virtually every galaxy he observed had a red shift not a blue shift, meaning it was receding rather than approaching. In this situation, a linear relationship between red shift and distance, we can invert the logic and imagine a time when all galaxies were closer together. Indeed, all galaxies were on top of one another. So, the Hubble relationship or Hubble Law points to an origin for the universe, tracing time backwards. The constant in this linear relationship is called H with a subscript 0. The Hubble Constant, named after Edwin Hubble, and the current expansion rate of the universe. The steeper this relationship, the faster the current expansion rate. The shallower this relationship, the slower the current expansion rate. Using the Hubble Space Telescope in its key project, the expansion rate is measured to be roughly 72 kilometers per second per megaparsec. Which means for every 3 million light years going out from the Earth, the recession velocity increases by about 70 kilometers per second. Hubble didn't make the connection but we understand Hubble's observations now in terms of expanding space. Hubble spoke simply about recession velocities. But in the Theory of General Relativity, which was devised before Hubble made his observations. Expanding space-time is something that the universe participates in and causes every galaxy to move away from every other galaxy. The analogy often used is the expanding fabric of a balloon. Where the fabric of the balloon is space-time itself. Objects on the surface of the balloon are carried away from one another. The best analogy would be tiny beads glued to the surface of the balloon since galaxies individually are held together by their own gravity. So as the distance between them increases, the galaxies themselves do not grow in size. What does the linear expansion imply? And in particular, does the fact that all galaxies are moving away from us imply that we're at the center of the universe? The answer is no. If we look at a two dimensional linear analogy, we imagine ourselves on the red galaxy measuring the distances and speeds of galaxies near us, the green and the blue. We can see that the more distant galaxies move away faster, that's the linear relationship Hubble observed. But if we change our perspective, and imagine we're located on the blue, or the green galaxy, or any other galaxy in the view. And make the same measurements, we would see the same thing. All galaxies are still moving away from us, and their motions are described by Hubble's Law. There's no special place in this distribution which we can imagine continuing infinitely in space. Therefore, either we are the center of the expansion, or all galaxies are the center of expansion. In fact, both are wrong. There is no privileged position in expanding space. Every observer on a galaxy separated in space will see the same thing. There is a very important distinction between the expansion of space in modern cosmology and the Doppler shift familiar from everyday life. In the Doppler shift, the changing wavelength of light or any other wave caused by relative motion. It's based on a reference frame where we can define motion relative to an external environment. For example, when an ambulance or a fire engine approaches, the sound waves are compressed in the direction of motion. And as it goes away from you, the sound waves are stretched out. So the pitch rises and then falls, as the fire engine or ambulance moves toward you and then away from you. But the reference for this motion is the road itself. This is relative motion in what's called an inertial frame in physics, and this is the Doppler effect. The cosmological redshift is conceptually quite different. What's happening is that space-time itself is expanding. The galaxies are hapless victims of this expansion, riding the expansion and therefore moving away from each other. There is no external reference frame because the space-time defines the entire universe. The second situation is called the cosmological redshift and it's quite distinct from the Doppler effect. Analogies are useful as long as we don't overuse them. The expanding balloon analogy is relevant to the universe, but it doesn't capture everything about the cosmological redshift. However, if you drew a small wavy line on a balloon and then inflated it, the distance between the crests and the troughs on the wavy line would increase. And that quite closely mirrors the behavior of radiation in expanding space-time. The cosmological expansion actually has a consequence for radiation traveling through the universe. Where the wavelength of that radiation stretches according to the stretching of space-time. It's remarkable that the cosmic expansion that affects tens of billions of light years propagates down to the waves of light and a tiny fraction of an inch. Light is still traveling through the universe at 300,000 kilometers per second. But it's traveling through a context of expanding space-time where the wavelength continuously increases. The cosmological redshift is just the fact that more distant objects have had their light traveling for longer times and larger distances. And so have been stretched by the intervening expansion. The three dimensional commonplace analogy for expanding space might be a raisin loaf where the raisins represent galaxies. As the loaf is baked, the distance between each of the raisins and every other raisin increases and this is what we would see in the universe of galaxies. With the three dimensional distance between each galaxy and its neighbors continues to increase. Remember that not all galaxies are moving away from every other galaxy, because some galaxies in close proximity are bound by mutual gravity, in pairs, or groups, or even clusters. In the cosmic situation, the answer to the question where is the center or is there a center is that no, there is no discernible center, every galaxy sees the same expansion. It's a democracy of viewpoints. The answer to the question is there an edge? Is that astronomers have not been able to determine an edge of space. Rather we see an edge in time corresponding to the time before which galaxies existed. The universe therefore might be infinite. Hubble observed a linear relationship between the distance of a galaxy and its recession velocity or redshift. The modern interpretation of his data is in terms of an expanding universe. Where space-time itself is expanding, and the galaxies are being carried apart in three dimensional space. This expansion applies to radiation traveling through the universe as well. The waves are stretched out, and the light reddens as it travels through expanding space-time. Cosmological expansion is quite distinct from the Doppler effect.
