Sunday, June 28, 2009

The Cosmological Principle

The definition of cosmology is the study of the structure and evolution of the universe. In modern physics, cosmology begins with the application of Einstein's theory of gravity, or General Relativity (recall this post), to the universe. This is a difficult task and would probably not be possible without a basic assumption about the universe - that it is spatially homogeneous and isotropic on large scales. Isotropy is a statement that the universe is the same in all directions (the universe looks the same whether you are looking directly outward from the North Pole or the South Pole). Homogeneity contends that the universe is the same at all points. These two hypotheses are together known as the "cosmological principle," without which much of our presumed understanding of the workings of the universe would be invalid.

Over short scales, this is obviously not true. Looking at the Milky Way is clearly different from looking at other parts of the sky. This makes it hard to test the hypotheses, as we need to go to larger and larger length scales to really see this principle in action, by averaging large volumes (using painting again as an example, imagine a canvas entirely of one color. Up close, you can see individual brush strokes with a great variation from place to place. From far away, though, one section of the canvas looks much like any other section, as they are all one color. Our universe is like that, if you believe the cosmological principle) .

Viewed in that context (I originally wrote "viewed in that light" but didn't want anyone to think I was making a pun), this rather boring picture of the CMB (taken from the COBE satellite in the early 1990s) becomes much more exciting - as already discussed, the CMB photons are coming from all corners of the universe. And they all look exactly alike (to 1 part in 100,000)! The first measurement of the very smooth spectrum of the CMB provided strong supporting evidence to the foundational hypothesis of cosmology, as the universe truly does look the same in all directions (it's slightly harder to convince yourself of homogeneity, that the universe looks the same at every point, but Copernicus can help here - if we proceed under the conservative assumption [although perhaps contentious from a religious point of view] that we do not live in a particularly special place in the universe [the "Copernican principle"], we can conclude that since the universe is isotropic around us, it should be isotropic everywhere. This implies homogeneity).

The Horizon Problem
Of course, that is not the entire story. I will briefly discuss the "horizon problem" here, before talking about the "anisotropies" in the CMB in later posts (these are the 1 part in 100,000 fluctuations that you can't see in the above picture because they are too small). We've decided the universe looks the same in all directions (the left side of the picture is the same color pink as the right side of the picture). But is the entire universe in causal contact?

My mom might ask, "what does causal contact mean?" If two events in space and time can be caused by the same preceding event, they are in causal contact. Here on earth, this is generally understood in terms of time. If something happens after something else (say, for example, I get a book out of the library because my mother recommended it), there can be a causal relationship (I got the book because my mom recommended it). On the other hand, if things are happening at the same time, they can't be causal (if my mom's recommendation comes at the exact moment I'm getting the book [or after I do so], she clearly can't be the cause of my literary enjoyment).

On universal scales, things are slightly complicated by the finite speed of light which adds a dimension of distance to the picture. We all know that the speed of light is constant, but for most of us, this doesn't really mean anything. We turn on a light switch, and the light turns on immediately. That is because the speed of light is so fast that we don't notice the time it took for the information to travel down the wire to the light bulb and back to our eyes. In space, however, this is not the case. For example, it takes about 8 minutes for light from the Sun to reach us. That means that an event in the Sun can only cause a response on Earth 8 minutes later. Suppose there were explosion in the Sun followed by an explosion on Earth 4 minutes later. The Sun's explosion cannot be the cause of the one on Earth, because any information from the Sun cannot reach us in less than 8 minutes (of course, both explosions could have been caused by some event happening in between, but hopefully the idea is clear).

This gives rise to the horizon problem. We know roughly how old the universe is and we know the speed of light. That means we know how far light can have traveled since the "epoch of last scattering." The problem is that the far right side of the pink ellipse is too far away from the far left side of the pink ellipse to have been in causal contact. Imagine running time backwards and following a photon emitted from both edges directed towards the center. At the time of last scattering, those photons would not have reached the center yet. In other words, what is happening on the left side and what is happening on the right side could not possibly have been caused by the same thing. Yet, they clearly look the same. How is this possible, when they could not have been influenced by the same initial conditions? This is the horizon problem, because the two extremes are outside of each other's causality horizon.

There are some theories on how to solve the horizon problem (with the leading candidate being "inflation") but they are probably beyond the scope of this blog (an argument can be made that the CMB is beyond the scope of this blog, but I hope my loyal reader(s) ignores that argument).


  1. Good article. Question though about "we do not live in a particularly special place in the universe [the "Copernican principle"]". What do you think of James Trefil and Robert Rood and their book "Are We Alone?" At the end of the book James Trefil concludes "If I were a religious man I would say that everything we have learned about life in the past twenty years shows that we are unique, and therefore special in God's sight." Does that square with the Copernican principle ? - Dave Johnson in Granada Hills, CA

  2. "special in God's sight" doesn't necessarily have to mean a special place in the universe, we don't even know if such a place exists. On a more philosophical view, why do we have to be in a special place in the universe to be special?

  3. Why has God to enter in all these pictures?
    He is not part of the theories, because if He is, it is no longer theories.
    Each piece of knowledge we get it pushes Him far away.
    Why dont we leave Him quiet in his corner, instead to play His similar?

  4. in relation to copernicus, do you think he would have accepted the cosmological principle?? why????????