8) Dark Matter: The Expansion of Space

So we see that space (the actual spacetime fabric itself) is enormously stiff (or enormously fluid, but that discussion will come later), but that's not all that's strange about it. It is also expanding. This seems a rather odd coupling of characteristics. Anything that is rigid resists bending or flexing in any way, yet the Universe is clearly expanding at an enormous rate.

This forces us to wonder about the nature of that expansion. When we look to the heavens and see that all of the visible galaxies appear to be moving away from us (regardless of where in the sky we look), it begs the question of how they are moving. This may seem to be yet another odd question. If something is moving away from us, does it really matter how it is moving?

In fact, it does. The question boils down to this: Are galaxies moving through space like cars on an interstate, or are they being carried away like suitcases on an enormous, invisible conveyor belt?

This difference is actually quite important. For example, some large airports provide conveyors that people can step onto to be carried forward rather than walking as normal. These conveyors are usually positioned alongside regular thoroughfares where people can choose to walk as well.

If you take a moment to watch the people moving through such an area, it is clear to see that there is a very simple difference between how the people travel forward. Those on the conveyor belt do not have to move at all - they are simply carried forward; whereas the people walking normally on the floor beside them are passing over the surface of the floor beneath them.

It turns out that this analogy works very well when attempting to understand the nature of how the Universe expands. We still do not know why it is expanding, but we do know a little about how it is expanding. The galaxies are not so much moving through space, they are instead being carried along by space. In fact, Hubble's Law talks about structured Spacetime as being the expanding agent upon which matter is resting. Indeed, it is the very Universe itself that is expanding - the matter within it is not simply moving outward into an empty void of nothingness.

With this, we have finally covered enough points to begin constructing a coherent picture of the question we began with: What is Dark Matter? Over the next few posts, we will begin to put these pieces together. As we do, my hope is that the many enigmas surrounding this hard question of science will begin to come into focus.

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.

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.

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.

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.

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.

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!