String Theory: Proposals for Why Dimensions Sometimes Uncurl
Most string theory proposals have been based on the concept that the extra dimensions required by the theory are curled up so small that they can’t be observed. With M-theory and brane worlds, it may be possible to overcome this restriction.
A few scenarios have been proposed to try to describe a mathematically coherent version of M-theory, which would allow the extra dimensions to be extended. If any of these scenarios hold true, they have profound implications for how (and where) physicists should be looking for the extra dimensions of string theory.
One model that has gotten quite a bit of attention was proposed in 1998 by Savas Dimopoulos, Nima Arkani-Hamed, and Gia Dvali. In this theory, some of the extra dimensions could be as large as a millimeter without contradicting known experiments, which means that it may be possible to observe their effects in experiments conducted at CERN’s Large Hadron Collider (LHC).
When Dimopoulos introduced MDM at a 1998 supersymmetry conference, it was actually something of a subversive act. He was making a bold statement: Extra dimensions were as important, if not more so, than supersymmetry.
Many physicists believe that supersymmetry is the key physical principle that will prove to be the foundation of M-theory. Dimopoulos proposed that the extra dimensions — previously viewed as an unfortunate mathematical complication to be ignored as much as possible — could be the fundamental physical principle M-theory was looking for.
In MDM, a pair of extra dimensions could extend as far as a millimeter away from the 3-dimensional brane that we reside on. If they extend much more than a millimeter, someone would have noticed by now, but at a millimeter, the deviation from Newton’s law of gravity would be so slight that no one would be any the wiser. So because gravity is radiating out into extra dimensions, it would explain why gravity is so much weaker than the brane-bound forces.
The way this works is everything in our universe is trapped on our 3-dimensional brane except gravity, which can extend off of our brane to affect the other dimensions. Unlike in string theory, the extra dimensions wouldn’t be noticeable in experiments except for gravity probes, and in 1998, gravity hadn’t been tested at distances shorter than a millimeter.
Infinite dimensions: Randall-Sundrum models
If a millimeter-sized dimension turned heads, the 1999 proposal by Lisa Randall and Raman Sundrum was even more spectacular. In these Randall-Sundrum models, gravity behaves differently in different dimensions, depending on the geometry of the branes.
In the original Randall-Sundrum model, called RS1, they propose a brane that sets the strength of gravity. In this gravitybrane, the strength of gravity is extremely large. As you move in a fifth dimension away from the gravitybrane, the strength of gravity drops exponentially.
An important aspect of the RS1 model is that the strength of gravity depends only on the position within the fifth dimension. Because our entire 3-brane (this is a brane world scenario, where we’re trapped on a 3-brane of space) is at the same fifth-dimensional position, gravity is consistent everywhere in the 3-brane.
In a second scenario, called RS2 or localized gravity, Randall and Sundrum realized that the 3-brane that we’re stuck in could have its own gravitational influence. Though gravitons can drift away from the 3-brane into other dimensions, they can’t get very far because of the pull of our 3-brane. Even with large dimensions, the effects of gravity leaking into other dimensions would be incredibly small.
In both of these models, the key feature is that gravity on our own 3-brane is essentially always the same. If this weren’t the case, we’d have noticed the extra dimensions before now.
In 2000, Lisa Randall proposed another model with Andreas Karch called locally localized gravity. In this model, the extra dimension contained some negative vacuum energy. It goes beyond the earlier models, because it allows gravity to be localized in different ways in different regions. Our local area looks 4-dimensional and has 4-dimensional gravity, but other regions of the universe might follow different laws.