The Universe, “Branes,” and the Science of Multiple Dimensions
By Maria Popova
“The mystery of being is a permanent mystery,” John Updike once observed in pondering why the universe exists, and yet of equal permanence is the allure this mystery exerts upon the scientists, philosophers, and artists of any given era. The Universe: Leading Scientists Explore the Origin, Mysteries, and Future of the Cosmos (public library) collects twenty-one illuminating, mind-expanding meditations on various aspects of that mystery, from multiple dimensions to quantum monkeys to why the universe looks the way it does, by some of the greatest scientific thinkers of our time. It is the fourth installment in an ongoing series by Edge editor John Brockman, following Thinking (2013), Culture (2011), and The Mind (2011).
In one of the essays, theoretical physicist Leonard Suskind marvels at the unique precipice we’re fortunate to witness:
The beginning of the 21st century is a watershed in modern science, a time that will forever change our understanding of the universe. Something is happening which is far more than the discovery of new facts or new equations. This is one of those rare moments when our entire outlook, our framework for thinking, and the whole epistemology of physics and cosmology are suddenly undergoing real upheaval. The narrow 20th-century view of a unique universe, about 10 billion years old and 10 billion light years across with a unique set of physical laws, is giving way to something far bigger and pregnant with new possibilities.
Gradually physicists and cosmologists are coming to see our ten billion light years as an infinitesimal pocket of a stupendous megaverse.
Here, an inevitable note on a different kind of human narrowness: I am not one to advocate for a blind quota-filling approach, where there must be equal representation on all levels at all cost. And yet it’s rather disappointing to see only one female scientist alongside her twenty-two male peers. (One of the twenty-one essays has three authors.) To be sure, Edge itself is far from gender-balanced — one could rationalize that this is simply the state of science still — but the site’s vast archive, spanning fifteen years of conversations and essays, does feature a number of female scientists, which renders the 5% female representation in this collection editorially lamentable.
This gender gap lends double meaning to Susskind’s reflections on the progress of science in the twenty-first century as he notes: “Man’s place in the universe is also being reexamined and challenged.” Woman’s, evidently, is not.
And yet, it’s perhaps not coincidental that the sole female contributor is none other than Harvard’s Lisa Randall, one of the most influential theoretical physicists of our time, and her essay is the most intensely interesting in the entire collection. (Perchance Brockman considered its weighted quotient equal to several of the male essays combined. No, not really, but when the skies of equality get particularly cloudy, what is one to do but squint for silver linings?)
Randall’s essay explores her work on the physics of extra dimensions of space, particularly the concept of “branes” — membrane-like two-dimensional objects that exist in a higher-dimensional space. (Randall illustrates this with the visual metaphor of a shower curtain, “virtually a two-dimensional object in a three-dimensional space.”) To understand why branes matter — more than that, why they are so infinitely interesting — we first need a primer on the physics of what is known as the “TeV scale.” Randall explains:
Particle physicists measure energy in units of electron volts. “TeV” means “a trillion electron volts.” This is a very high energy and challenges the limits of current technology, but it’s low from the perspective of quantum gravity, whose consequences are likely to show up only at energies 16 orders of magnitude higher. This energy scale is interesting, because we know that the as-yet-undiscovered part of the theory associated with giving elementary particles their masses should be found there… Back at the very beginning, the entire universe could have been squeezed to the size of an elementary particle. Quantum fluctuations could shake the entire universe, and there would be an essential link between cosmology and the microworld.
This ghostly playground of particles raises the question of whether “space and time are so complicated and screwed up that we can’t really talk about a beginning in time” — which brings us to string theory and its peculiar predicament. Randall writes:
The one thing that’s rather unusual about string theory from the viewpoint of the sociology and history of science is that it’s one of the few instances where physics has been held up by a lack of the relevant mathematics. In the past, physicists have generally taken fairly old-fashioned mathematics off the shelf. Einstein used 19th-century non-Euclidean geometry, and the pioneers in quantum theory used group theory and differential equations that had essentially been worked out long beforehand. But string theory poses mathematical problems that aren’t yet solved, and has actually brought math and physics closer together.
String theory is the dominant approach right now, and it has some successes already, but the question is whether it will develop to the stage where we can actually solve problems that can be tested observationally. If we can’t bridge the gap between this ten-dimensional theory and anything that we can observe, it will grind to a halt. In most versions of string theory, the extra dimensions above the normal three are all wrapped up very tightly, so that each point in our ordinary space is like a tightly wrapped origami in six dimensions. We see just three dimensions; the rest are invisible to us because they are wrapped up very tightly. If you look at a needle, it looks like a one-dimensional line from a long distance, but really it’s three-dimensional. Likewise, the extra dimensions could be seen if you looked at things very closely. Space on a very tiny scale is grainy and complicated — its smoothness is an illusion of the large scale. That’s the conventional view in these string theories.
This is where Randall’s work on branes comes in as a promising contender for a better solution. She writes:
According to this theory, there could be other universes, perhaps separated from ours by just a microscopic distance; however, that distance is measured in some fourth spatial dimension, of which we are not aware. Because we are imprisoned in our three dimensions, we can’t directly detect these other universes. It’s rather like a whole lot of bugs crawling around on a big two-dimensional sheet of paper, who would be unaware of another set of bugs that might be crawling around on another sheet of paper that could be only a short distance away in the third dimension.
Of course, the concepts of multiple dimensions and parallel universes are far from new and can be traced as far back as another trailblazing woman in scientific thought, Margaret Cavendish, Duchess of Newcastle — her 1666 book The Blazing World features a heroine who passes into a world with different stars through a space-time portal near the North Pole.
Randall takes us into her own time machine to trace the history of multiple dimensions in contextualizing what makes branes so special:
People entertained the idea of extra dimensions before string theory came along, although such speculations were soon forgotten or ignored. It’s natural to ask what would happen if there were different dimensions of space; after all, the fact that we see only three spatial dimensions doesn’t necessarily mean that only three exist, and Einstein’s general relativity doesn’t treat a three-dimensional universe preferentially. There could be many unseen ingredients to the universe. However, it was first believed that if additional dimensions existed they would have to be very small in order to have escaped our notice. The standard supposition in string theory was that the extra dimensions were curled up into incredibly tiny scales — 1033 centimeters, the so-called Planck length and the scale associated with quantum effects becoming relevant. In that sense, this scale is the obvious candidate: If there are extra dimensions, which are obviously important to gravitational structure, they’d be characterized by this particular distance scale. But if so, there would be very few implications for our world. Such dimensions would have no impact whatsoever on anything we see or experience.
Branes are special, particularly in the context of string theory, because there’s a natural mechanism to confine particles to the brane; thus not everything need travel in the extra dimensions, even if those dimensions exist. Particles confined to the brane would have momentum and motion only along the brane, like water spots on the surface of your shower curtain. Branes allow for an entirely new set of possibilities in the physics of extra dimensions, because particles confined to the brane would look more or less as they would in a three-plus-one-dimension world; they never venture beyond it. Protons, electrons, quarks, all sorts of fundamental particles could be stuck on the brane. In that case, you may wonder why we should care about extra dimensions at all, since despite their existence the particles that make up our world do not traverse them. However, although all known standard-model particles stick to the brane, this is not true of gravity. The mechanisms for confining particles and forces mediated by the photon or electrogauge proton to the brane do not apply to gravity. Gravity, according to the theory of general relativity, must necessarily exist in the full geometry of space. Furthermore, a consistent gravitational theory requires that the graviton, the particle that mediates gravity, has to couple to any source of energy, whether that source is confined to the brane or not. Therefore, the graviton would also have to be out there in the region encompassing the full geometry of higher dimensions—a region known as the bulk—because there might be sources of energy there. Finally, there’s a string-theory explanation of why the graviton is not stuck to any brane: The graviton is associated with the closed string, and only open strings can be anchored to a brane.
Meanwhile, scientists haven’t studied gravity as intensely as they have other particles, largely because gravity is an extremely weak force. (It might not seem so every time you trip and fall, but as Randall points out, that’s because the entire Earth is pulling you down at that moment, whereas “the result of coupling an individual graviton to an individual particle is quite small.”) What makes branes especially intriguing is that including them into string theory allows us to contemplate, to use Randall’s technical term, “crazily large extra dimensions.” These, in turn, might explain why gravity is so weak — if its force is spread out across these gigantic dimensions, no wonder it would be this diluted on any one brane.
But it gets even more interesting — citing her work with Johns Hopkins scientist Raman Sundrum, Randall writes:
A more natural explanation for the weakness of gravity could be the direct result of the gravitational attraction associated with the brane itself. In addition to trapping particles, branes carry energy. We showed that from the perspective of general relativity this means that the brane curves the space around it, changing gravity in its vicinity. When the energy in space is correlated with the energy on the brane so that a large flat three-dimensional brane sits in the higher-dimensional space, the graviton — the particle communicating the gravitational force — is highly attracted to the brane. Rather than spreading uniformly in an extra dimension, gravity stays localized, very close to the brane.
Randall’s discoveries get even more mind-bending. Outlining a finding that calls to mind the legendary Victorian allegory Flatland: A Romance of Many Dimensions (which in turn inspired Norton Juster’s brilliant 1963 book and film The Dot and the Line: A Romance in Lower Mathematics, she writes:
Conventionally, it was thought that extra dimensions must be curled up or bounded between two branes, or else we would observe higher-dimensional gravity. The aforementioned second brane appeared to serve two purposes: It explained the hierarchy problem because of the small probability for the graviton to be there, and it was also responsible for bounding the extra dimension so that at long distances, bigger than the dimension’s size, only three dimensions are seen.
The concentration of the graviton near the Planck brane can, however, have an entirely different implication. If we forget the hierarchy problem for the moment, the second brane is unnecessary. That is, even if there’s an infinite extra dimension and we live on the Planck brane in this infinite dimension, we wouldn’t know about it. In this “warped geometry,” as the space with exponentially decreasing graviton amplitude is known, we would see things as if this dimension did not exist and the world were only three-dimensional.
Because the graviton makes only infrequent excursions into the bulk, a second brane or a curled-up dimension isn’t necessary to get a theory that describes our three-dimensional world, as had previously been thought. We might live on the Planck brane and address the hierarchy problem in some other manner—or we might live on a second brane out in the bulk, but this brane would not be the boundary of the now infinite space. It doesn’t matter that the graviton occasionally leaks away from the Planck brane; it’s so highly localized there that the Planck brane essentially mimics a world of three dimensions, as though an extra dimension didn’t exist at all. A four-spatial-dimensions world, say, would look almost identical to one with three spatial dimensions. Thus all the evidence we have for three spatial dimensions could equally well be evidence for a theory in which there are four spatial dimensions of infinite extent.
So why does any of this matter, this “exciting but frustrating game” of speculation, as Randall elegantly puts it? For one thing, there might be subtle but important differences between these different dimensions and different worlds — for instance, black holes may not behave the same way in each of them. If energy leaks off a brane, a black hole might spit out particles into an extra dimension as it perishes. (If you’ve ever steamed a New England clam, you may have noticed it “spitting” water at you in its final moments — perhaps this is somewhat akin to what Randall describes.) Most importantly, multiple dimensions offer endless possibilities for the very structure of space. Randall writes:
There can be different numbers of dimensions and there might be arbitrary numbers of branes contained within. Branes don’t even all have to be three-plus-one-dimensional; maybe there are other dimensions of branes in addition to those that look like ours and are parallel to ours. This presents an interesting question about the global structure of space, since how space evolves with time would be different in the context of the presence of many branes. It’s possible that there are all sorts of forces and particles we don’t know about that are concentrated on branes and can affect cosmology.
So where does this leave us? Randall echoes Marie Curie’s famous words upon receiving her second graduate degree — a sentiment no doubt common to any great scientist who understands that not-knowing is the currency of meaningful work — and concludes:
In general, the problems that get solved, although they seem very complicated, are in many ways simple problems. There’s much more work to be done; exciting discoveries await, and they will have implications for other fields… It’s my hope that time and experiments will distinguish among the possibilities.
Randall’s essay is a spectacular, mind-bending read in its entirety, as are the rest of the contributions in The Universe. Complement it with Brockman’s compendium of leading scientists’ selections of the most elegant theory of how the world works and the single most important concept to make you smarter.
Published July 23, 2014