Article from ToI, dated 9th April, 2007.


The Fifth Dimension

Apart from length, breadth, height and time, is there anything else through which we can move? Why is it that our mind cannot perceive something that maths says is possible


Sunil Mukhi




There is a fifth dimension beyond that which is known to man. It is a dimension as vast as space and as timeless as infinity. It is the middle ground between light and shadow, between science and superstition, and it lies between the pit of man’s fears and the summit of his knowledge. This is the dimension of imagination.” Thus runs Rod Serling’s introduction to the science-fiction programme The Twilight Zone that played for five seasons on American TV in the early 1960s.
Is there a fifth dimension? We are familiar with three independent spatial dimensions. Einstein’s Special Theory of Relativity tells us that time must also be counted as a dimension, and together with space it forms a fourdimensional “space-time”. These are dimensions the human mind can perceive. The question is whether there are any additional dimensions beyond these four, and the short answer is that there is no evidence as of today. But let us entertain this possibility and see where it leads us.
Rod Serling’s poetic fifth dimension “of imagination” is hardly on the right track - no more than a metaphor at best. Similar literary conceptions of dimensionality appear in older literature, including the scriptures. A more serious occurrence of this idea is in ‘Flatland, A romance of many dimensions’ by British author Edwin Abbott. This mid-nineteenth-century novel poses the question: what if we were condemned to live in a two-dimensional world, like insects on a table- top, in complete ignorance of the three-dimensional world outside? How would we react if some creature from that world tried to show us the way out of Flatland? By analogy, it is rendered plausible that there could be spatial dimensions beyond the three we know, which have somehow remained hidden from us.
For all its mathematical sophistication, the novel is unable to provide a convincing reason why we might have failed to notice additional dimensions. The presence of even a single extra spatial dimension would change virtually every formula of contemporary physics. Yet there are powerful motivations to consider extra dimensions, and good reasons why we may not yet have seen them. At the dawn of the twentieth century, when the only known forces were electromagnetism and gravitation (nuclear interactions had not yet been discovered), Theodore Kaluza and Oskar Klein considered a hypothetical world with four rather than three spatial dimensions, in which the only force is gravitation. They showed that if one of these dimensions is tightly curled up into a circle, their world effectively reduces to a three-dimensional one with both gravitational and electromagnetic forces, the latter originating in the circular dimension. For those, like Einstein, who puzzled over why there are two distinct fundamental forces in nature, this theoretical discovery offered a deeply satisfying solution.
The Kaluza-Klein idea went into obscurity despite Einstein’s strong support for it. The problem was that the very artifice which caused a circular extra dimension to be hidden from our daily lives - the smallness of the circle - made it impossible to observe even in the most sophisticated experiments to date. So we could not judge experimentally whether the idea was right or wrong, and that is still the case today. The idea was nonetheless resurrected in the 1980s with the emergence of “string theory”, a newer theory that potentially unifies all particles and forces. String theory requires the existence of six extra dimensions, and though the theory itself is speculative, its emergence caused the old speculation of Kaluza and Klein to be subsumed into something much more powerful and grand.

Nevertheless, until recently, it was thought that the extra dimensions if any would be too small to be detected by any conceivable experiment. The last decade has seen this paradigm overturned in more ways than one.

Theoreticians have shown that one cannot rule out “large” extra dimensions, curled up in circles large enough to be probed by the energetic high-energy particles that a future accelerator would produce, though still small on an absolute scale. Another theoretical possibility is that of “warped” extra dimensions, in which the extra dimension is truly large in its extent, but our scales of measurement vary as we traverse this dimension. In such a scenario, different members of the particle zoo can be localised at different places in the fifth dimension, which holds the promise of explaining the hierarchy of energy scales seen in nature.

A simple analogy has been proposed to explain how extra dimensions could be observed. Consider the balls on a billiard table, which collide and transfer energy back and forth amongst themselves. Energy is conserved overall, but a tiny fraction of it leaves the table-top in the form of sound waves produced when the balls collide. From the point of view of creatures confined to the table, this phenomenon would lead to a small “missing energy”. Our real world might be just like this. Future accelerators are geared to test whether there is “missing energy” in certain reactions, which would signal the presence of a fifth dimension. If it was found, Rod Serling’s idea would, in his own poetic words, be elevated from the “pit of man’s fears” to the “summit of his knowledge”. (The writer is a theoretical physicist)