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10 January 2007 @ 05:43 am
Another Go at Everything, Pt. 3 (Quantum Foam, and the Limits of Metaphor)  
Thus far, I have tried to show how the structure of our world can be imagined by the use of metaphorical models and how those models are forced to change with the introduction of new theories and experimental observation, but there are limits to any models of nature where they break down, and our multi-dimensional cosmic balloon is no exception. One of the most strongly held convictions in science is that no known theory that describes natural processes is the final theory, because we can never know all information necessary for such a theory nor predict every outcome in experiments. At best, the mathematical models physicists use are approximations natural phenomena, and so our metaphorical analogies are only simplifications of those models meant to illustrate general ideas. The balloon is meant to show how all parts of space can expand equally over a finite, yet unbounded, area; my 'hoola hoop' addition to it helps to visualize how some dimensions may expand while others contract. Beyond these concepts, the balloon analogy breaks down, however, and for a deeper explanation of how the universe began we must go beyond it.

Part of the reason for this should be obvious to anyone who understands the differences between the Four Fundamental Forces of nature. The rubber in a balloon is held together by electromagnetic forces between atoms and molecules, but the universe as a whole is not. Furthermore, the tension in the skin of the balloon is caused by this same force and becomes greater as the balloon is inflated, in direct relation to the length of its radius. However, there is no such general tension in the fabric of space beyond its tiny overall curvature; the only force attracting the galaxies to one another is gravity, which becomes less as they move apart. This means that, unlike the skin of our balloon, the universe has less overall 'tension' in it as time passes.

Another failing of the balloon analogy can be shown by imagining that, instead of having ants walk over its skin, we instead draw pictures of them on its surface with a pen. As one might expect, when the balloon grows, these pictures grow also. In fact, these two dimensional ants would not be aware of the enlargement of the balloon because they would be growing at the same rate as the distances between them! Yet it is clear to astronomers and physicists alike that this is not what is occuring in our universe. Neither the galaxies, nor the atoms and stars of which they are made, are expanding at the same rate as the universe, if at all. Also, and this leads back to the 'bomb' misrepresentation of the Big Bang, there is no evidence that the galaxies were actually pushed apart, nor that they are being pulled away from each other in the same sense as are the ants on the balloon. Besides their growth through mutual predation, the galaxies have maintained their scale throughout much of the history of the visible universe, and each acts as if it were born in place and the only pulling forces acting on it are the gravitational attractions of its neighbors.

This makes sense when we see that space has no material 'fabric' to be pulled taut like the balloon. As the matter within it becomes less dense on average, its curvature evens out, and it is this curvature which is the tension that would work to make it shrink again. What is expanding in the universe is space itself, and this does not hold onto matter like rubber holds onto ink or the feet of ants. So, we can use the balloon analogy to illustrate the expansion of space, but not accurately how it does, nor how it might have in the past or continue to do so in the future. Except for its use as an overall picture, the balloon analogy must be discarded.

There is another reason the balloon model fails which will lead us much closer to the Beginning itself; the idea of Cosmic Inflation, brought about because of the otherworldly implications of Quantum Mechanics. While Albert Einstein's theories and equations mostly dealt with space and time as being a continuous field of forces, certain experiments done at the same time repeatedly showed matter as being of a pointlike nature. Others, in seeming contradiction, showed it to have a wavelike one. As particle 'waves' might be fitted more easily into his conception, Einstein preferred this view, but throughout the twentieth century, a discrete, or quantum, explanation of matter and energy at the subatomic level persisted and eventually became so well grounded as to have an equal validity as Einstein's General Relativity. Because Relativity dealt with large scale gravitational interactions and Quantum Mechanics dealt with small scale nuclear ones, the two theories rarely overlapped and were allowed to become the twin foundations of the Standard Model of physics.

In the era of massive particle colliders and radio and microwave telescopes, however, this dualistic nature has begun to cause problems, even embarassing ones. Physicists working from both ends of the size and energy scales now see that the Standard Model is doomed. The predictions of Relativity in large part have been confirmed for many amazing things, including black holes and time dilation, leading many scientists to believe the true nature of the universe is one based in a Unified Field Theory, as Einstein searched for in his last years, but until the end of the twentieth century, none had been found which might account for the apparent pointlike properties of matter. Likewise, no formulation of Quantum Electrodynamics or Chromodynamics was at first believed to account for large scale structure or the effects of gravity. Many new theories have been proposed to account for both, but they have thus far been hard to confirm experimentally or have been difficult to formulate mathematically. In a sense, the last few decades have become in scientific circles something of a contest to see which view of the underlying structure of the universe would win out, or whether a new one would have to be invented to replace both Relativity and Quantum Mechanics. Before I get to what a new theory might look like, and how investigations into it have uncovered such weirdness as extra dimensions, I will show what may be the last great overlap between the two former theories of the Standard Model, because it happened very soon after the Beginning and its evidence is literally painted on the sky.

In an earlier section, I said that the overall Homogeneity in mass density of the universe confirmed that all visible parts of it had evolved alike, but there was no special reason why this should be so. As the apparent age of the universe became understood to be at least ten billion yearsand maybe as many as twenty, this proved to be a problem. Although the density of matter overall is very close to a constant, 'clumps' of galaxies, called clusters and superclusters, do exist. Given these departures from uniformity, gradual expansion over that time should have allowed the gravitational attraction between the galaxies to exaggerate the size of these clusters until all matter was concentrated in only a few mega-clusters. In other words, because of the universe's great age, it should have lost its Homogeneity long ago. To look more deeply into this problem, three dimensional surveys encompassing millions of galaxies and large portions of the sky were undertaken, and, even though they have shown larger and larger structures in galaxy clustering, they have yet to disagree with the average Homogeneity. In particular, structures have been found that resemble bubbles where few galaxies reside, with the majority near the outer edges, but no solitary mega-clusters of billions of galaxies. In fact, the latest of such surveys are showing a general trend in universal structure which implies that all galactic clusters conform, more or less, to this bubble shape. It seems that, rather than evolving into a few mega-galaxies or clusters, the universe has become more like a kind of foam, with the galactic clusters taking the part of the walls between bubbles.

Worse, gravitation and its General Theory could not account for the initial emergence of large scale structure at all. If the universe began in a uniform singularity, an idea that was a cornerstone of the Standard Model, the mutual cancelling-out of gravity between particles should have ensured that matter would remain in a kind of gaseous state, never forming stars and galaxies. Until telescopes became strong enough to see into the time immediately following the Beginning, this troubling oversight had been ignored or left for future scientists to understand, as most thought something in Relativity would eventually be found to account for it. When powerful enough telescopes were developed, these problems could no longer be ignored. Since, in that time, no explanatary theory in General Relativity had been found, Cosmologists and astrophysicists were forced to look at Quantum Mechanics for the answer.

Here, I must backtrack a little and show you how it could be that a group of theories about matter at subatomic levels could account for structures millions of light years across comprising billions of galaxies. For this, we must look once again at our ants walking about on the surface of a balloon. Let's imagine one such ant dragging a pen which continuously draws a line thin enough not to widen as the balloon grows, although the distances between any changes in direction it makes would. Now, anyone who has watched ants in a garden knows that they do not walk in straight lines. From afar, they seem to follow well-marked trails, but up close, one sees that they actually turn left and right and move quickly, then slowly, as if constantly checking which direction they should be moving in. At this scale, their paths have curves and kinks, and the line drawn by the ant on our balloon would reflect this. Many processes in nature show this 'kinky' sort of movement. In the jostling of molecules of gases, it is called Brownian Motion, and this has been shown for the particles that make up atoms as well. In researching this seemingly fundamental property of matter, scientists found what is now called the Heisenburg Uncertainty Principle, an idea as profound as Relativity. I hope to show how this Uncertainty created the large scale structure of the universe.

In particle experiments, scientists try to look more and more closely at the activity and interactions of matter. The closer one looks at a particle, however, the more chaotic its path appears, because each kink in it has smaller kinks, down to the limits of our ability to see. If we let loose a particle at one end of a chamber one meter long and detect its exit at the other one second later, we say that it moved at an average of one meter per second, but we do not know exactly where it was at any point in the journey. If we find a way to see when it passed through barriers at one/tenth meter intervals along the way, we see that, in general, it traversed each smaller length close to one meter per second, but any greater time spent in one means less spent in others. We therefore know the moments when it passed through the barriers (where it was at given moments in time), but less about how fast it was moving at those times. Divide the chamber further by ten, and the same thing happens. The better we know where the particle is at a given moment, the less we know about its velocity. Put simply, this is the gist of the Uncertainty Principle. It works for all particles everywhere, and puts ultimate limits on what we can know or see with scientific instruments.

As formulated, this is an indirect relation between the ability to gauge the position of a particle and its velocity, or speed, at the same moment. At the smallest distance scales, this becomes strange in the extreme. At the scale of atoms, this means that the paths of particles like electrons cannot be predicted accurately. Although we can detect them any number of times, where they happen to show up is largely a matter of chance. Because of this, a new way to picture atoms had to be used. The electrons, formerly believed to orbit atoms in clearly defined shells, now are seen to exist within regions of probable position known as electron clouds, which generally are 'thicker' close to atomic nuclei and 'thinner' farther away from them. Each orbit in the old sense translates to a differently shaped cloud in the new, so that clouds might intermingle, allowing electrons going at different speeds to actually appear to be in the same place or for one to be able to change speeds at will (though it must return to its original speed soon or emit a photon). It even proved to be possible for particles to seem to disappear in one place and reappear in another without moving the distance between, a process called tunneling.

As far from ordinary this tiny, quantum world may sound, it is how things really are, as proven through countless experiments. How this comes to relate to our ant and the structure of the universe is that, regardless of its chaotic properties at such small scales, matter still conforms to the Theories of Relativity. Especially the fact that every particle bends space around it, creating the same kind of curvature as large objects like the earth and sun. The appearance of particles as existing in clouds of probability, comes very close to Einstein's dream of a unified field, but the Uncertainty Principle turns this into a frighteningly unmanageable nightmare. At scales below that of atoms, when we again begin to see the separate particles as more pointlike, we find that the speeds they may be traveling at go up considerably. Below the smallest possible measure of distance whereat we can pinpoint their position, called the Planck Length, the upper limit for their possible speed becomes greater than that of light, a feat that should be impossible in a Relativistic universe. Moreover, because the chaotic nature of their movements is translated to the curvature of the space around them, the very shape of space at this level also becomes chaotic. We have reached what physicists call the Quantum Foam. Everything rides along in this Foam like boats tossed in a raging sea, only looking stable when many particles come together like a pontoon bridge or a mat of kelp that takes up an area much larger than the waves themselves.

Now, we can finally understand how the large scale structure of the universe came about. Our ant walks a crooked path over the metaphorical balloon. When the balloon was small, his path was just as crooked as it is now, but as it expanded, the line he drew lengthened, smoothing out the older kinks. In that way, the older portions of his path grew so that, to him, the oldest kinks look as if they cover the entire balloon. By analogy, if we were able to look back long enough in time to when the whole visible portion of our universe was smaller than the size of an atom, it should look just as chaotic as the quantum foam. In fact, thanks to telescopes powerful enough to see the moment when light first became free to travel apart from other matter, a moment which translates to a kind of visible shell greater than twelve billion light years away via the speed of that first light, this is exactly what we see. This virtual shell, called the Cosmic Microwave Background, is the end of what cosmologists believe was a very different stage in the universe's expansion, when it grew so fast that the original quantum chaos was stretched out across the known universe in perhaps only a few thousands or millions of years. This period they call Cosmic Inflation, and the fluctuations in the shape of space it left behind, although stretched so thinly that they amount to less than the energy equivalent of one Kelvin degree of heat over hundreds of millions of light years, were enough to concentrate the initial gassy matter into the shapes that reflect what we see in the universe today. The widely varying density of the gas allowed it to form great clouds surrounding bubblelike areas of lower concentration, then stars, galaxies, and galactic clusters which are still coallescing and engulfing one another.

So, while our balloon analogy is still useful for imagining how the universe has grown, the details of that growth cannot be so easily explained, hence the momentary use of bubbles and Foam. And though we have now come very close, in cosmic terms, to the Beginning, there is now Inflation to get through. Unfortunately, it may never be possible for Mankind to see beyond the Cosmic Microwave Background into the Inflationary Period, because then there wasn't light of any wavelength to see by. Still, theories go ever forward and may yet give us new ways to see. But that's for next time.
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