Only a few years ago, the idea of extra dimensions inhabited a nebulous region somewhere between physics and science fiction. We are all aware of the three dimensions of space and the extra fourth dimension of time. It is odd to treat time as a dimension. In terms of vectors time is not a dimension – neither is it in Euclidian geometry. But we use the word ‘dimension’ to describe the position of an object. To do this we need not only the three dimensions of space but also the fourth dimension of time. The same object can be perceived as being at two different locations by two separate observers if the dimension of time is not stipulated. This is absolutely beyond contest and has to do with the finite speed of light. Bizarre, but such are the ramifications of Einstein’s theory of relativity. So if we can have four dimensions, can we not consider the possibility of higher dimensions?
Plato in his book Republic, asks us to imagine a cave with a ‘shadow gallery’ in which people are chained so that they may only look forward at their own shadows cast on the cave wall. Forced to live their whole lives in this fashion, the viewers come to believe that their two-dimensional shadows reflected on the wall are accurate representations of themselves. The lesson is that we may be similarly restricted in our world-view of three spatial dimensions and one time dimension. It is hard, practically impossible, to envisage these higher dimensions as entities accustomed to only three dimensions.
In his book, Flatland, Edwin Abbott presents both a cutting satire on the society of the time, and a wonderful introduction to higher-dimensional thinking. He describes a character called A Square, a two-dimensional creature who lives in flat plane among a society of two-dimensional creatures. The inhabitants of this flat-land have no inkling that their entire world is merely a ghostly, infinitely-thin, slice of a higher-dimensional space.
A Square is visited by A Sphere, a three-dimensional creature from a space of the kind we are familiar with. The sphere is visible to A Square as a circular cross-section, which changes in size as the sphere passes through the plane of the flat world.
By using the analogy of how a two-dimensional creature might appear to creatures living in a one-dimension line-land, the sphere attempts to explain to A Square the concept of higher-dimensional spaces. The square is at first incredulous about the sphere’s ideas and asks the sphere to demonstrate in which direction this mysterious `third’ dimension lies. Eventually, through the use of analogy, the square is convinced that the third dimension exists (and is, unfortunately, imprisoned for these heretical ideas).
When we attempt to conceive of what living in a higher number of spatial dimensions might be like, we can readily sympathise with A Square’s difficulties and scepticism. But it is just this kind of higher-dimensional sense that might help us to more fully appreciate abstract structures, which may exist in higher-dimensions.
Just a millimetre away from us there could be another universe. We may not see it, smell it or touch it but it could be there. We could only get to it by travelling in a direction that is forbidden. – Because we are trapped in our dimensions, forming what physicists call the ‘braneworld’.
According to their theories, the familiar three dimensions that contain all the stars and galaxies we see could actually be a membrane—a brane for short—floating in a space of five, six or more dimensions, like a soap bubble. There could be other branes out there in the higher dimensions, other universes we can never see.
So it could turn out that our world is ‘pinned’ to a 3-dimensional sheet (or braneworld) that is located in a higher dimensional space. To illustrate this, imagine an ant crawling on a sheet of paper in your hand. For the ant, the ‘universe’ is pretty much two-dimensional, as it cannot leave the surface of the paper. It only knows North from South and East from West, but up and down don’t make any sense as long as it has to stay on the sheet of paper. In pretty much the same way, we could be restrained to a three-dimensional world, which is in fact a part of a more complicated multi-dimensional universe!
These extra spatial dimensions, if they really exist, are thought to be curled-up, or “compactified”. In the example with the ant, let’s roll the sheet of paper so that it forms a cylinder. In this case, if the ant starts crawling in the direction of curvature, it will eventually come back to the same point it started from. This is an example of a compactified dimension. If the ant crawls in a direction parallel to the length of the cylinder, it would never come back to the same point (we are assuming that the paper cylinder is so long so that it never reaches the edge). This is an example of a “flat” dimension.
Unseen dimensions are nothing new. The idea of additional spatial dimensions comes from string theory, the only self-consistent quantum theory of gravity so far. It turns out that for a consistent description of gravity, one needs more than 3+1 dimensions, and the world around us could have up to 11 spatial dimensions! These extra dimensions are usually thought to be curled into tight circles only 10 to the power -35 metres around—far smaller than the radius of a proton. No wonder they are invisible.
But could some of these extra dimensions be a lot larger—or even infinite, like our familiar space and time? If so, then shouldn’t we be able to see these extra dimensions or walk through into them? This might not be possible if we stick to the idea of braneworlds. Matter or light stuck in our brane leave us blind to anything outside. It is theorized only gravity is free to escape and roam in the higher dimensions of hyperspace. This could explain why gravity appears to be so weak compared to the electromagnetic and nuclear forces. This weakness may be only an illusion. On a fundamental level, gravity might be as strong as the other forces, but appears to be weaker because it leaks out into higher dimensions.
The basic idea of braneworlds and higher dimensions is that our universe is folded over many times. Light from distant objects has to travel along the brane and so would take billions of years to reach us, but gravity could take a short cut through a higher dimension and trick us into thinking that there’s unseen matter around us. The existence of brane worlds would this solve the problem of ‘dark matter’.
If all this were true then it would lead to fascinating consequences; – for example, could we somehow manipulate gravity to allow us to pass ourselves through these higher dimensions; or, if not, could we influence gravity in such a way as to send information to distant regions of the universe in fractions of seconds that would otherwise have taken billions of years? The mind boggles at the infinite possibilities that the existence of higher dimensions would engender.
