Friday, August 21, 2009

7) Dark Matter: The Rigidity of Spacetime

Note that this post makes reference to a scale-model Solar System, which was introduced in a prior post.

What does this have to do with the rigidity of space? Think of a location that is about 40 miles from where you are at this moment. Even if there is interstate highway between you and this location, it would still take quite a drive to get there - 40 miles is a fair distance. Now, imagine that the entire region around you is covered with a layer of insulating foam, which is 50 feet thick (think of something you might find in the cushions of a sofa).

If you were to set a golf ball on the foam in front of you, it would have no reason to roll in any particular direction (for this example, assume that you are somehow hovering above the foam, and that there is nothing else nearby to disrupt its smooth, flat surface).

Now, let's say that 40 miles away there is an enormous floating crane, which is holding a scale model of the sun (a spheroid, 36 feet in diameter) suspended in the air. A sphere this size would have a volume of roughly 24,429 cubic feet.

To stay somewhat true to the model, let's say that the sphere is filled with liquid hydrogen. Even though hydrogen is much lighter than, say, water, a sphere this size would still weigh just under 54 tons on earth.

Now, if the crane were to begin slowly lowering the model sun into the foam, it would sink completely to the bottom and become enveloped within it. It is also safe to say that the depression created by the model sun, which would have the appearance of a gravity well, would not impact our golf ball (40 miles away) in the least. In fact, from this distance there would be no way to know that anything had happened at all. All of the impacts of the presence of the model sun would be absorbed by the surrounding foam, and probably would not produce any observable effects reaching more than a few dozen yards.

Clearly, foam is too soft a medium to transfer the effects of the deformation caused by the model sun for very far at all.

What if the region around us were overlaid with an enormous, perfectly flat steel plate rather than foam (that is, following the curvature of the earth's surface). This would certainly change the analogy some. Even then, it is unlikely that even the highest grade, densest steel could convey the impacts of the resulting depression far enough to reach the golf ball and cause it to roll. We would be closer to doing so, however, since the steel would probably be more than dense enough to transmit the vibrations caused by the event for 40 miles.

Still, if we imagine the plate of steel being 80 miles in diameter, into which we forcefully create a depression of 18' (half the diameter of the model sun), could we expect the golf ball (even one without dimples) to roll towards it? Even if the steel plate were only a few feet thick rather than fifty, it is not likely that the golf ball would roll at all. The steel would bend and absorb the impacts of the depression well before they reached 40 miles - they would simply dissipate.

This leaves us wondering: What material could be so strong that a depression of only 18' in its center could cause a golf ball, 40 miles away, to roll towards it? Surprisingly, there is something.

It is estimated that the spacetime fabric is a billion billion billion times stiffer than steel (Ripples on a Cosmic Sea, David Blair and Geoff McNamara). That's a big number (1043). In the coming posts, we will begin to see that this rigidity is more than only another fascinating cosmic detail. It is a fundamental, pervasive and highly influential factor in the behavior of the Universe, having implications that can help explain some of its more difficult-to-understand characteristics, and move us closer to understanding certain mysteries that only come to light when we appreciate its influence.
Note: Many things in physics have no direct correlation to what we might think of as common reality. Analogies of bowls, rubber sheets, foam and trampolines are rather crude instruments of communication in any discussion about things as abstract as Dark Matter and spacetime.

We should only know that the goal of this discussion is not to painstakingly create perfect illustrations, or to exhaustively point out the flaws in less-than-perfect ones. It is, of course, about the riddle of Dark Matter. These illustrations are only disposable artifacts, created and destroyed along the path to what I hope to be a greater insight.

Thursday, August 20, 2009

6) Dark Matter: Kepler's Third Law

Let us now perform another level-set. So far, we recognize and accept the obvious existence of matter within the Universe. Furthermore, as E=mc2 tells us, whether any unit of matter happens to take the form of energy or mass does not subtract from its overall qualification (or quantification) as matter. In other words, mass and energy are interchangeable; they are only different forms of matter. Of course, this is not to suggest that switching between these two states is a trivial thing - far from it, but that is a topic for another day.

Next, we know that empty space isn't exactly empty. Meaning, in a very real sense, there is a spacetime fabric that can be coerced into forming gravity wells, or producing other observable effects such as gravitational lensing. Gravity wells then, are constructed of spacetime itself; they do not fall within the realms of matter, but have identifiable characteristics nonetheless.
General Relativity actually predicts Embedding Diagrams rather than Gravity Wells, but intimates that gravity is an effect of the curvature of spacetime nonetheless. This distinction is actually quite important, but will not become entirely relevant to this discussion until we reach much finer details later in the series.
If we entertain the notion that galactic Gravity Wells may predate the matter within them, it does not necessarily mean that the two cannot be connected in some way. In fact, it seems likely that the two will prove to be closely related (more on this later), given that they usually seem to occur together (galactic gravity wells are usually filled with stars and other matter). To understand this connection, we must take a moment to consider the rigidity of space.

Given that gravity is the curvature of spacetime caused by the presence of mass, it will be useful for us to understand how much force is required to bend it. How rigid is the spacetime fabric?

This calls for another analogy.

At the Lakeview Museum of Arts and Science in Peoria Illinois, there is a partial model of the sun, which is 36 feet in diameter. Scale models of all the planets of our Solar System are then distributed across the region at distances relative to where they would appear if the sun were actually that size. Together, this model of the sun and planets form an enormous scale-model of the Solar System.

In this model, the earth is roughly the size of a small grapefruit (4 inches in diameter), and 3/4 of a mile away from the sun. Pluto, on the other hand, is only the size of a golf ball, and 40 miles away. Of course, we know that there are many Kuiper Belt objects that are much farther away from the sun than Pluto, but they are not depicted in the model (as far as I know).

This model does a great job of bringing the true size of the Solar System into perspective. Even so, it is amazing for reasons far beyond the simple sizes and distances involved. To see how, we must quickly dispense with a commonly held misconception about gravity.

When we observe videos of astronauts in space, it is easy to get the impression that there is no gravity in space at all; that somehow, once astronauts pass above the atmosphere of the earth, gravity is no longer present. But, that is not true at all. Any satellite in orbit (even living ones like astronauts) stay aloft only by striking a correct balance of orbital velocity and distance from the earth. This relationship between velocity, distance and mass is spelled out in Kepler's Third Law of Planetary Motion.

For example, if we could somehow reach into space and slow the velocity of the International Space Station to zero (relative to the surface of the earth), leaving it hanging momentarily in space with no forward momentum, it would fall like a rock. Interestingly, it wouldn't even burn up in the atmosphere on its way to earth, it would simply fall (although it may pick up enough speed before encountering the atmosphere to heat up quite a bit once it did).

Amazingly, this same principle applies even to the earth's orbit around the sun. If the earth's velocity around the sun could somehow be stopped, the earth would plunge into the sun like a meteor. The same goes for any other planet in our Solar System - even one as far away from the sun as Pluto.

Returning to the earlier illustration of rolling a marble around the inner surface of a bowl, this would be like simply setting the marble on the edge of the bowl and letting it roll directly towards the center.

Saturday, August 1, 2009

5) Dark Matter: The Big Bang

Once we begin considering the possibility that galactic gravity wells could somehow be independent of the matter within them, a few more questions immediately surface.
1. Could gravity wells predate the matter within them?
2. Why does matter seem to always live in these gravity wells rather than more evenly cover the emptiness of intergalactic space?
3. Why do they rotate?
4. And of course, what causes them?
Surprisingly, none of these questions are difficult to answer within the context of our current line of reasoning. There are in fact, agreeable, and what seem to be quite plausible answers to all of them. Note that I will not get to all of these questions within this particular post, but will eventually address each of them within this Dark Matter series.

In terms of the Big Bang, all the matter in the Universe is nothing more than a debris field. On first glance, this debris appears to be remarkably evenly distributed. But on closer inspection we find that although the galaxies that constitute the observable Universe are somewhat evenly distributed, matter on the whole is not. Matter seems to coalesce into galaxies, it does not evenly blanket the emptiness of space.

This seems odd. Without enough matter to account for the gravity within galaxies, why would matter coalesce at all? If all matter did indeed originate from the Big Bang, then it seems that the Universe should appear to be more splotchy that it is; that we should expect to see vast intergalactic regions of space filled with matter (probably hydrogen), interrupted by the presence of an occasional galaxy, which will have swept the immediately-surrounding area clear of debris during its own formation. But we don't; intergalactic space appears to be quite clean.

Perhaps we should take a step back.

If we accept the notion that all matter in the Universe could have begun as a single theoretical point, a singularity (as Big Bang theory suggests), and that everything we see today, at one time existed in this condensed, ethereal state, then we have demonstrated a tremendous ability to accept the extraordinary.

I call hypotheses and theories such as this, Cold Water Theories; meaning, on first exposure to them they are somewhat shocking, but after a while we adjust to them and begin to feel as though they are far less extraordinary than they actually are. This is like diving into a pool of cool water. At first, the experience is quite shocking, but in a matter of only a few minutes we adjust to the temperature and feel quite comfortable.

The notion that all of the matter in the Universe originated from a singularity is an extraordinary concept, to say the very least. It is a Cold Water Theory. It is probably the best explanation so far for how the Universe could have evolved to its current state, especially in light of its phenomenal rate of expansion. And, there certainly are more than a few observations that appear to substantiate the notion of a Big Bang. Things such as the Cosmic Microwave Background Radiation (CMB), the CMB Dipole Anisotropy, the blackbody Spectral Energy Distribution (SED), and so on (I will eventually address each of these and a few others). The question is, is there any value in refuting such a firmly entrenched theory? And if so, what motivation could there be for doing so?

Indeed, there is only one. If Big Bang theory were correct, then I would be perfectly willing to accept it. But the Big Bang is not some random theory, chosen as an arbitrary target from a field of candidate theories to attack; any more than any reasonable person would attack the theories of Gravitation or the Germ Theory of Disease. The problem is that the Big Bang explains some things quite well, but completely misses on many other things - too many things to ignore.

My assertion is that there may be a better explanation; one that raises fewer exceptions than the Big Bang. The Big Bang was a good start, and although it does answer certain questions quite well, there are too many others that it cannot, which cannot be ignored.

Could there be another explanation that plausibly answers these same questions, but also moves us further down the road towards answering some of the questions that Big Bang theory cannot?

I believe there is.