Wednesday, March 30, 2011

Approaching the Cosmology Question

Cosmology is a tricky subject.  If mathematics is to physics as logic is to philosophy, cosmology is to physics as metaphysics is to philosophy.  At least as early as Kant it was realized that there were statements about the universe as a whole where the thesis and the antithesis seemed equally plausible.  For instance, it seems equally plausible to say of the composition of reality that "Everything in the world consists of the simple," as to say that "There is nothing simple; rather, everything is composite."  Or about the nature of causality, that "In the serious of causes in the world there is some necessary being," seems as fair to say as "There is nothing necessary in it; rather, in this series everything is contingent."  In his set of theses and antitheses, Kant also included the following: "The world has a beginning (boundary) with respect to time and space," and, "The world is infinite with respect to time and space."

The mutual plausibility of claims like these stems from the fact that it seems nigh impossible to come up with a way to affirm one of the claims and refute the other.  For instance, we can accept the standard model and say that everything is composed of quarks, leptons, and bosons, but we cannot deny that saying "it's got electrons" does not tell us much at all about the properties of water as a solvent.  In recent decades the notion of holarchy has provided a way of getting past petty arguments between simplicity and composition by synthesizing the two views.

The second example, pertaining to necessity and contingency, has two equally plausible opposites for a different reason - we cannot have done otherwise than we did, if we did not do so in the first place.  In terms of a previous article, we cannot see whether there is something of necessity or complete contingency because we cannot travel through the sixth dimension.  Again, we have approached something resembling a synthesis of these viewpoints in the postmodern age with the anthropic principle.  We needn't say that a universe must have observers in it in order to exist, but we can surely say the universes with observers in them are a lot more likely to get noticed.  While this doesn't entirely solve the problem of counterfactuals, this type of compromise, to me, is a sign we're getting closer.

On the issue of whether the universe has a beginning, we've made far less progress toward synthesis as a culture.  Rather than integrating with one another, it seems that the beginning view and the ageless view have dissociated with one another.  In the West, we have Creationism, and if you don't buy that, we have Big Bang theory.  Both state roughly that, at one point in time (and possibly all points before it) there was Nothing, and then Something came to exist.  In the East the notion of cyclic existence is far more dominant in religious thinking.  It will be interesting to see what happens as the scientific culture comes to be more influenced by scientists versed in Eastern ways of thinking, but most points of view on whether the universe had a beginning that integrate our current knowledge of physics have a decidedly Western bent.

One interesting attempt to synthesize the two ideas is the Big Bang/Big Crunch hypothesis.  The idea is that the Big Bang posited at the start of this universe was the explosion of the previous universe after it had collapsed in on itself.  An extension of this hypothesis states that eventually our current universe will reverse its expansion and start condensing into another Big Crunch, which will result in the Big Bang of another universe still, and so on.  Amongst subscribers of this idea, it's often held that gravity exactly cancels out entropy over long periods of time in order to bring the universe back together for its next explosion.

This idea is interesting, surely, and it would certainly be quite popular for believers in eternal recurrence, and it also provides a timescale over which every different possible reality can play out, which makes it a candidate support the idea of a multiverse.  But before we get too carried away speculating how many angels can dance on a pin's head, let's take a closer look at Big Bang theory.  Does it even make sense?

Big Bang theory, as a scientific theory, is not the idea that first there was nothing and then it exploded.  It implies that idea, but the essence of Big Bang theory is that the universe is expanding and cooling as vast stretches of time pass.  What does it mean for a universe to be expanding, and why do scientists think ours is expanding?

If space is expanding uniformly, then any two points in space become more distant at a rate proportionate to the distance already between them.  As an example, if the surface of the Earth were to expand uniformly, then the distance between Los Angeles and Detroit and between Los Angeles and Chicago would grow a lot more than the distance between Detroit and Chicago.  For instance, if the Earth expanded by factor of 1.5d, the distance between Detroit and Chicago would grow from 237 miles to 355.5 miles, while the distance between Detroit and L.A. would grow from 2,300 miles to 3,450 miles.

Currently, Big Bang cosmologists do not believe the universe is expanding at a linear rate.  Instead, they think that further objects are moving away faster than nearby ones, which is what they mean when they say that expansion is accelerating.  To go back to the Los Angeles, Detroit, and Chicago example, if the Earth expanded by factor of 0.005(d^2), the distance between Detroit and Chicago would go from 237 miles to 281 miles, while the distance from L.A to Detroit would go from 2,300 miles to 26,450 miles.

Cosmologists often use the example of an inflating balloon as an analogy to explain what it means for the universe to expand.  If you take an uninflated balloon and put one pair of marks near each other and another pair at a greater distance from one another, as you blow the balloon up the first pair of marks will remain relatively close together while the more distant marks will get further and further apart.  The analogy to an actual balloon breaks down when you think about the fact that balloons can only be filled so much.  In fact, if we were to have a balloon that would make a perfect analogy for accelerating expansion, it would have to be a balloon that became easier to blow air into with each bit more air there was already inside of it.

If that's what expansion is, why do scientists think our universe is expanding?  In a word, redshift.  Though the Doppler effect isn't a perfect analogue for expansion redshift, it's a good way of introducing it.  The Doppler effect is most obvious for us Earth-bound observers in sound.  Consider the sound of a car passing you as you walk next to the road.  As long as the car is approaching you, it makes a higher-pitched sound, but as it starts moving away from you, the sound shifts to a lower pitch.  This happens when the car is moving a significant portion of the speed of sound, because the source of the peaks of the sound waves is moving.  So the peaks of the wave are closer together (higher frequency) as it moves towards you and further apart (lower frequency) as it moves away.

Redshift form constant expansion differs from the Doppler shift in that it isn't said that one or the other points is moving; rather, the space between them expands, stretching the light that travels from one to the other.  This effect was postulated to explain the fact that distant stars appear more red than closer stars with the same properties appear.  According to the expansion explanation, the expansion of space itself is the reason that we see lower frequencies in the light from distant stars than from similar near stars.

The accelerating expansion idea was introduced to explain the fact that, the further you look, the more redshift increases relative to distance.  For instance, if we were looking at the distances from Detroit to L.A. (roughly 2,300 miles) and from Detroit to San Diego (roughly 2,400 miles) after an accelerating expansion of 0.05(d^2), we'd see a distance of 264,500 miles to L.A. and one of 288,000 miles to San Diego, a difference of 20,000 miles when seen from Detroit.

Strangely, when we look at the distance between the two California cities (roughly 125 miles) after factoring in the same expansion rate, we'd find a distance of only 781 miles.  Where did the extra 19,000 miles come from?  Well, there is an explanation cosmologists can offer to partially defend the idea of expansion from this criticism.  Light takes millions of years to arrive to us from these distant stars.  So, the further away they are, the longer the light takes to get here, and the longer the universe's expansion has to stretch the light waves.

While this would certainly resolve such an issue with continuous expansion, it doesn't solve the problem of accelerating expansion.  When cosmologists say that further stars increase in their distance at a higher rate (with distance factored out) than nearer stars do, the question on everyone's mind should be, "Further from where?"  You can try any non-linear function for expansion and you will always find that the distances do not add up (and really, this should be obvious to anyone who knows the definition of a linear function).  So it makes sense to suppose that the apparent acceleration of expansion is just that - apparent.  If the stars are not literally expanding away from each other at a rate that's increasing in a way that doesn't make sense, how else can we explain the fact that the further away we look, the faster stars begin to appear more red?

We'll have to save that for next time.


  1. deep stuff, y like all of this cosmos talk but now i realize that my intellect isnt enough to comprehend all of this.

  2. Michio Kaku's Parallel Universes is a good introduction to this sort of stuff for the layman - really good read that explains all the concepts used in it.

  3. you have put a lot of thought into space and time. well thought post