Thursday, July 30, 2009

4) Dark Matter: Another Catalyst

To this point we have not discussed anything new; only clarified the importance of thinking of gravity in the correct context. Rather than visualizing gravity as the attraction of two bodies, we are now thinking of bodies such as stars and planets traveling along the inside of Gravity Wells - a well-known concept. This means, we have only restated the problem in less abstract, less obscure terms.

It turns out that this analogy holds up remarkably well; like rolling a marble along the inner surface of a physical bowl, it will travel around the bowl until it eventually loses momentum and settles to the bottom, or if it is tossed too hard, roll over the edge of the bowl and escape it altogether. If the marble could somehow be rolled with just the right force (momentarily overlooking friction), it could settle into a point of equilibrium, having just the right amount of angular velocity to maintain a constant distance from the bottom of the bowl and its outer edge.

This perfect velocity, of course, is entirely dependent on the mass of the marble, the slope of the inner surface of the bowl (and, in this analogy, the force of gravity acting upon the marble). If we took the same marble, for example, and tossed it with the same velocity around the inside of a much shallower saucer, that same momentum would cause the marble to escape.

Returning to stars within galaxies, the problem boils down to not being able to explain why the gravity wells underlying them are so deep. In other words, the matter within galaxies does not actually behave strangely at all, we are only struggling to understand the shape of the bowls beneath them. This is very much like finding a deep depression in the center of a trampoline, around which we can roll a tennis ball, but with no bowling ball to account for it. Such an anomaly would hardly be any less mystifying on the scales of trampolines than it is at galactic scales - it would compel us to begin investigating possible causes. Is the trampoline sagging because it is not taut enough, or is some other force acting on it?

So, we must now begin questioning whether the depth of these gravity wells has anything to do with the matter within them. For instance, if we sprinkled tiny bits of Styrofoam on the surface of water draining from a kitchen sink, there would come a point where the water would begin to take the form of a whirlpool. When this happened, the Styrofoam bits would then reflect that underlying structure. If we were to attempt to understand the behavior of the Styrofoam without first understanding the nature and behavior of the water upon which it was floating, we would be eternally mystified.

This analogy seems to hold true for the stars and spiral arms within galaxies as well. If we view them as floating debris upon an underlying, and somewhat independent structure (gravity wells), then suddenly the question of Dark Matter begins to dim even more. If another force, besides mass, can bend space into something akin to gravity wells, what could it be? Have we overlooked something?

We may have, and maybe only because it is too obvious to notice.

Wednesday, July 29, 2009

3) Dark Matter: Gravity Wells

These depressions in space (gravity wells) express the classical understanding of gravitation (Relativistic, not Newtonian), which suggests that gravity is not a measure of the force of attraction between two bodies, it is instead a measure of the force with which two bodies fall into the larger gravity well produced by the overlapping of their two individual gravity wells. This means that we could essentially describe the riddle of Dark Matter in another way, by simply saying that we cannot explain how the gravity depressions in which galaxies exist can be deep enough to prevent the spinning matter within them from over-spilling their boundaries.

So, before tackling the question of how these depressions can exist at all, we should first ask an even more basic question. If we concede that such depressions do exist, then perhaps we can first attempt to understand whether the matter within galaxies behaves according to our understanding of gravitation. In other words, start with the simple acknowledgment that sufficient gravity must be present within these galaxies for them to hold their shapes, even though we do not know why or how. Once we have made this leap, we can then ask ourselves whether the behavior of these galaxies then falls in line with the predictions of Gravitation.

Fortunately, the answer to this question appears to be a rather straightforward, yes. Indications are that once we acknowledge that there is indeed sufficient gravity to hold galaxies together, meaning the gravity wells they are in are in fact, deep enough to contain them, some of the mysteries that have given rise to the theories of Dark Matter already begin to dissipate. Once we clear this hurtle, galaxy rotation and structure is no longer mysterious; we are left only with the need to explain why these wells are deeper than it seems they should be.

The very acknowledgment that gravity wells exist is also acknowledgment that spacetime can bend. Space is far from empty. Hubble's Law postulates the notion of structured Spacetime as the expanding agent upon which matter is resting. And, as we have seen, General Relativity describes gravitation as the curvature of spacetime caused by the presence of mass. This means that the next leap we must take is to begin considering whether spacetime is always flat in the absence of mass. Is matter the only thing that can bend it?

As we continue deconstructing the problem of Dark Matter we find that one of the underlying premises upon which it is based is the assumption that only matter can bend spacetime; that in the absence of matter, spacetime is always perfectly flat. But we must ask, is this a well-founded assumption or an accidental one? If we concede the possibility that the spacetime fabric, which we know to be bendable by matter, could possibly bend for other reasons, then we have already begun to dismantle the need for Dark Matter.

From here we can view the entire problem of galactic structure in terms of that curvature. The only remaining question is what other influences could be bending space? Why are galactic gravity wells so deep?

2) Dark Matter: From the Beginning

The paradox of Dark Matter leads unavoidably to a few questions. The first and most obvious has to do with galaxy structure. How can galaxies behave as though they contain 70% more mass than they appear to have? What keeps them from simply flying apart? But these questions quickly lead to the even more intriguing question of how they ever formed at all.

Understanding the riddle of Dark Matter requires rewinding the clock all the way back to the Big Bang. Like so many other questions in physics, it can seem odd that two seemingly disconnected topics can end up having such direct bearing on one another. But in the end, unexpected connections like this often end up being a good thing; they are signals, hints that we may have tapped into a fundamental aspect of the Universe that once understood, could help resolve other mysteries as well.

First, what of galaxy structure and rotation? Here the problem is that we cannot detect enough matter to account for the gravity that we know must be present. So, we speculate that something else, something undetectable to us (at least, directly), is producing it.

Perhaps at this point we should quickly address the question of whether some other binding agent, something besides gravity, could be holding galaxies together. Although we are taught never to say never very early in life, it is unlikely to say the least that there could be another force in the Universe grand enough to have these tremendous effects without having been detected before. So, the most reasonable hypothesis seems to be that it is indeed gravity that is holding the galaxies in shape. We'll proceed on this assumption.

The next question then, is where this gravity comes from. In fact, this is the primary question underlying Dark Matter. In the end, the answer to this question may be simple enough to seem almost anticlimactic. Given how perplexing this question has proven to be over the years, it seems that an explanation should be more difficult than it may turn out to be.

First, we must simply understand that according to General Relativity, gravity is not really a force at all; it is a depression in spacetime (more specifically, gravity is a consequence of the curvature of spacetime). To visualize this, we can imagine a tennis ball rolling around a depression in a trampoline, which is caused by the presence of a heavy bowling ball at its center. Remove the bowling ball and the trampoline springs back into shape (the depression disappears) and the tennis ball drifts away.

In this analogy, the depression represents a Gravity Well. The earth and other planets circle the sun by following the path of least resistance, so to speak (a Geodesic), around the gravity well produced by the sun at the center of the Solar System.

So, if we blow this imagery up to galactic scales, we must know that the stars and spiral arms of those galaxies are moving along the inside of a gravity well too, which is like an enormous invisible bowl in space. (Of course, it's not quite that simple, but we'll get into more detail later in this series)
In fact, the trampoline analogy above is taken from the well-known Rubber Sheet example, which is commonly used to illustrate the phenomenon of gravity. Some take issue with the example, first recognizing it as a somewhat effective aid in visualizing gravitation, but then criticize the fact that it does not fully and accurately portray it.

The problem being, of course, that the analogy employs gravity itself as an actor upon the tennis ball. Furthermore, it does not account for the dimension of time (hence, spacetime).

Yes, we know, ...that's why we call it an analogy.

My stance on the issue is that the analogy is a good one, despite clearly falling short of fully demonstrating the true complexities of General Relativity and gravity wells.

Tuesday, July 28, 2009

1) Dark Matter

Dark Matter is a special form of matter that is hypothesized to explain certain anomalies in the formation and behavior of galaxies, which has been the subject of a great deal of attention and debate in the areas of physics and astronomy over recent years. Over the next few weeks I plan to publish a series of posts on the subject, and along the way, propose a possible alternative to current, and prevailing thinking on the matter.

The concept of Dark Matter was first put forward as a possible explanation for some of the odd characteristics of galaxies that cannot be fully explained based on current notions of gravitation. In a nutshell, it is presumed that gravity is the only binding agent that holds galaxies together. Based on this simple and reasonable assumption, it seems obvious that there must then be enough matter in any given galaxy to account for the fact that it is able to hold its shape.

The problem is that given the rotation of most galaxies (maybe all), there does not seem to be enough matter within them to account for the fact that they do not simply fly apart. If we imagine rotating galaxies as enormous carousels, there is simply not enough detectable matter to create the amount of gravity required to hold them together. This simple fact is intriguing enough, but even more remarkable when we realize that this discrepancy is anything but small. Estimates vary, but overall it seems that a typical galaxy contains only 30% or less of the matter required to hold its shape.

Enter Dark Matter. Dark Matter is a type of matter that has been hypothesized to explain this discrepancy. Dark Matter particles are thought to be virtually undetectable in all respects except for the obvious effects of their gravitational influence on normal matter, yet constitute 70% or more of a typical galaxy's total mass.

Astronomers and physicists have been trying to detect, and otherwise prove or disprove the existence of Dark Matter particles for years. Certainly, no one can say for sure that they don’t exist, especially since their existence would conveniently explain what seems, in all other ways, to be inexplicable. But, drawing for a moment upon the sensibilities of Occam’s Razor, this explanation seems a little too tidy somehow.

Indeed, this is a common pitfall in all research-related disciplines; that the solution to a given problem is often envisioned as a mere reflection of that problem. In this case, the need for something in the Universe to account for the apparent lack of visible matter gives rise to speculation about exotic particles that precisely fit the needed description: invisible matter that produces gravitational effects.

There may be a more reasonable and feasible explanation; one that does not require the existence of hopelessly exotic Dark Matter particles. I have written a full article describing this alternative (actually, several years ago), but would like to publish a series of introductory blogs (which I am calling the Dark Matter Series) to help explain a few simple concepts before publishing a link to it here.

And by the way, thanks for reading!