Multiple Higher Dimensions

Heroic & Dark Fantasy and Science Fiction Character created by Kevin L. O'Brien

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Untitled, © by Don Marquez

Multiple Higher Dimensionslternate universes have long been a popular subject for speculation, but a serious problem for those who believe they exist was why no one could see them. Usually, this was explained by invoking multiple higher dimensions. It went Multiple Higher Dimensionssomething like this. All dimensions begin with a mathematical point, which has no dimensions. However, string an infinite number of them side by side and you get a line, which has the first dimension of length. Lay an infinite number of lines beside each other and you get a plane, which has the second dimension of width. Stack an infinite number of planes on top of each other and you get a space, which has the third dimension of depth. Finally, arrange an infinite number of spaces around each other and get a hyperspace, which has a fourth dimension.

While each dimension may be finite in size, it contains an infinite number of lower dimensions. Hence, if we assume each three-dimensional space is a separate universe, a hyperspace would contain an infinite number of independent universes. These universes would be The Calabi-Yau model of a hyperspaceseparated from each other across the fourth dimension, which we cannot travel or see through, hence they are invisible to us. For many years, it was thought that the fourth dimension was time, since Albert Einstein had used time as a dimension in his theory of relativity. String theory, however, predicts that our universe has eleven dimensions, ten spatial and one temporal. Time is considered to be the eleventh and highest dimension, so the fourth dimension of a hyperspace would now be an uncharacterized spatial dimension like length, width, and depth.

However, string theory also predicts that only four of the dimensions form the kind of nested hierarchy described above. These are the three spatial dimensions of length, width, and depth, plus the dimension of time. The other seven spatial dimensions are subatomic and are bound up with the strings, so they do not form String Theory (Get serious!)"higher" dimensions containing infinite numbers of lower dimensions. The idea is that, before the Big Bang, all eleven dimensions were equal in size, strength, and character; in other words, they were symmetrical. During the Big Bang, however, the universe underwent what is called a symmetry breaking event. Seven of the dimensions collapsed in size and shed most of their energy, which was absorbed by the remaining four, causing them to expand to infinite size and turning three into spatial dimensions and one into a temporal dimension. Each Level 1 multiverse that forms in a Level 2 multiverse undergoes a similar symmetry breaking event, but quantum fluctuations cause the number of dimensions to collapse and the kind to emerge to be random.

Parallel universes are now the primary way to explain where the alternative universes exist and why we cannot see them. However, higher dimensions still play an important role in understanding how universes are ordered and arranged into larger structures.

The Strength of Gravity

One of the enduring mysteries of the universe is why gravity is so weak. The four fundamental forces — electromagnetism, the strong and weak nuclear forces, and gravitation — all have different strengths. The strong nuclear force is the most powerful; it can hold protons together in a nucleus despite the electromagnetic repulsive force they feel. Gravitation, on the other hand, is the weakest, being 10^43 (ten raised to the power 43) times weaker than electromagnetism. Yet, there also seems to be an inverse relationship between the strength of a force and the distance over which it can act: the strong and weak nuclear forces can only act over the diameter of a nucleus, but electromagnetism and gravity can act over billions of light years.

Relativistic GravityYet modern cosmological theory assumes that there was a time shortly after the Big Bang when the four forces were combined into a single force. We have already been able to combine the electromagnetic and the weak nuclear force into a single electroweak force. We do this by colliding particles together in a particle accelerator in such a way as to produce short-lived particles that carry the electroweak force. In order to be combined, the forces have to have equal strength, and this can be simulated by calculating the distance two particles have to be apart for two forces to balance. For electromagnetism and the weak nuclear force, such a distance would be 10^-19 meters. The distance needed to combine gravity with the other three forces would by 10^-35 meters, which is known as the Planck length.

Now, that may not seem all that earth-shattering, but in fact the monstrously huge gap between these two distances is a major problem in physics. The reason is the Standard Model, the otherwise extremely successful theory that explains particle physics, cannot explain this huge gap. This is because, in order to stabilize the electroweak force at 10^-19 meters, the theory has to be carefully adjusted to fit the observed scale of the combined force. This requires fine-tuning the theory to a tolerance of one part in 10^32, otherwise quantum instabilities would reduce the scale for the electroweak force down to the Planck length, which would contradict experimental observations. This kind of delicate balancing act is equivalent to walking into a room and finding a pencil standing upright on its pointed end. While not impossible, it is so unstable that any perturbation, no matter how small, would cause it to collapse. So the $64 trillion question is, what keeps the universe from collapsing?

It turns out that if you assume the cosmos has more than the three familiar spatial dimensions, then the point at which gravity would merge with the other forces would be very close to 10^-19 meters. The reason is the generally accepted value for the Planck length may by derived from a false assumption. Based on his observations, Newton calculated that the force of gravity diminishes as the square of the increase in the distance between two bodies; this is known as the inverse square law. Conversely, the force of gravity increases at the same rate as two objects get closer together. Because gravity is so weak, we can currently only test the law down to a distance of one millimeter. If we then extrapolate beyond this point, we find that the distance at which gravity becomes as strong as the other three forces — which defines the Planck length — is 10^-35 meters. Yet if there was just one extra dimension, gravity would increase by an inverse cube law, and the Planck length would be larger, and the more dimensions you have, the faster gravity would increase, and the larger the Planck length would become.

Extra Dimensions

String Theory (for real this time!)So the gap problem can be solved by simply adding more spatial dimensions onto the cosmos until the unification of gravity with the other forces occurs near 10^-19 meters. How many are needed depends upon how big they are; conversely, we can calculate the size they must be for any given number of extra dimensions. If, for example, there was only one extra dimension, it would have to be as big as the Earth's orbit around the sun. If there were two extra dimensions, however, they would only need to be as big as a millimeter. The more there are, the smaller they can be. Current string theories assume the cosmos has ten spatial dimensions; that means the extra seven can be no bigger than 10^-14 meters, which is about the size of a uranium nucleus.

Of course, an object the size of a millimeter would be visible under a microscope, and we can "see" objects much smaller than a uranium nucleus with particle accelerators, so why haven't we seen these extra dimensions? Well, this is where it gets weird. Some scientists have speculated that our three dimensional universe in a larger multidimensional space would resemble a poster attached to a wall. Everything that happens in our universe is confined to the poster and cannot go beyond it. Put another way, all particles, including photons, are stuck to the poster and cannot leave it. As such, there could be another poster on the either side of the room and we would never see it, because none of its particles could break away and cross the room to encounter our poster.

In other words, cosmologically speaking there could be another universe just one millimeter away from us across a fourth dimension, but we could never see it because none of its particles could cross the dimension to reach us. This idea is "confirmed" by string theory, which predicts that space-time would form sheets called D-branes. It also predicts that particles, including photons, would be represented by lengths of open string with endpoints that would anchor themselves to the D-brane. Being stuck, they could not detach themselves and cross the multidimensional space to other D-branes.

String theory does, however, predict one exception to this. Gravitons, the hypothetical particles that carry gravitational force, are represented as closed loops of string. Without free ends, they are not stuck to the D-branes, and so they can wander off one D-brane and cross multidimensional space to other D-branes. As such, we may not be able to see other universes, but we should be able to feel their gravitational affects.

But How Many?

Multiple D-branes in interdimensional spaceWe can, in fact, use the force of gravity to constrain the size of these extra dimensions. We can do this by measuring the rate at which the strength of gravity changes as the distance between two objects changes. For example, we know the extra dimensions cannot be as large as the Earth's solar orbit, because otherwise we would observe gravity obeying an inverse cube law at such scales instead of the inverse square law Newton observed. There might still be only two extra dimensions, since their maximum size of one millimeter sits right at the threshold of our current ability to measure. Experiments using new detectors that can measure gravitational interactions over distances as short as tens of microns can be conducted. If such experiments did detect a change from an inverse square law to an inverse fourth power law, that would be confirmation of multiple dimensions. More than likely, however, if string theory has any validity, such experiments would yield negative results. We may therefore have to wait until more powerful particle accelerators are built before we can adequately test this theory.

This speculation is also born out by observations of Supernova 1987A. If gravitons can escape our universe D-brane and cross multidimensional space, they would carry away energy with them. Yet we know that most of the energy of a supernova explosion is carried away by the initial neutrino burst. As such, if too many gravitons escaped our universe into multidimensional space, they would carry away too much energy and a supernova would fizzle instead of explode, which we know doesn't happen. Two extra dimensions seem to be the threshold for this effect: two dimensions would cause fizzling, whereas a minimum of three would allow explosions. So if there are no dimension beyond the three we know, we have to explain how supernovas explode dispite this.

Folded Sheets

A folded D-braneThe exciting thing about this theory is that, if true, it gives us a fighting chance to test string theory, because instead of being only 10^-35 meters in size, strings created in particle collisions would be closer to 10^-19 meters in size, and so could be detected. Also, we could create and study micro black holes with particle accelerators as well. We might also be able to create gravitons. We could not detect them directly, but we would know they were there by detecting missing energy that they carried away into multidimensional space. It might even explain why neutrinos have mass and provide an answer for what constitutes dark matter. From the perspective of multiple dimensions, a D-brane is nothing more than a sheet of paper floating in three-dimensional space. Like a sheet of paper, a D-brane can be folded back onto itself any number of times, creating a small, compact structure that, on its own dimensional scale, could still be nearly infinite in size. A fold of our own universe could only be a micron away from us in multidimensional space. There could also be other independent D-branes lying right next to us at the same distance. Regardless, a galaxy in that spot might still be trillions of light years away at our dimensional scale. The universe is not yet old enough for light from that galaxy to have reached us (if it even resides on our D-brane), but its gravitational force can affect us from across multidimensional space. To us, such an affect would be coming from something invisible, hence dark. So what we call dark matter could in fact be normal matter that is just too far away to see but sitting right next door, multidimensionally speaking.

The point should now be obvious. If we assume that alternative universes exist as separate D-branes with their own set of physical laws, they could lie right beside our own D-brane, with barely a micron of separation between us. Yet the multidimensional space that separates us acts as a mostly impenetrable barrier, preventing us from detecting and crossing over to these other branes. Yet the close proximity of these branes could mean that the prodigious amount of energy we might assume would be needed to pierce the dimensional barrier could be considerably String Theory (Oh, stop it!)reduced. And if the branes could be induced to touch each other, gravity could be used to create a wormhole between them, thereby opening a gate.

Similarly, a heavily convoluted Level 1 multiverse that has folded against itself inside its bubble of space-time in a Level 2 multiverse could touch at enough places to allow a being to move from one Hubble volume to another using gates. And even a Level 2 multiverse might fold around itself, allowing gate travel between the various Level 1s.

Sources / Further Reading

"The Universe's Unseen Dimensions" by Nima Arkani-Hamed, Savas Dimopoulos and Georgi Dvali, Scientific American, Vol. 283, No. 2, August 2000, pp. 62-69

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