Extract a finite length of space; divide it into halves, then into quarters, then into eighths…… After infinite number of divisions, what will remain? A tiny “space atom” that has an infinitesimal, albeit finite length? Absurd, for an infinite number of finite lengths adds up to an infinite length. A “space point” that has no extension nor length? Absurd, for an infinite number of zero lengths still adds to zero length!

The above “paradox of plurality” which starts as a philosophical debate has extended to the twentieth century and continued gnawing on Physicists’ mind. For as long as it remains unsolved, the assumption that space or time composes of single points and that mathematics correlates seamlessly with physical facts are, startlingly, unfounded. A seemingly easy resolution is to say, well, space is after all composed of small “atoms” and not infinitely divisible. But this would turn the whole foundation of modern science topsy-turvy. We have to rest our mind, uneasily, on the recourse of set theory which dismisses the number of “space points” as super-denumerable in number and hence, undefined in their summation.

However, recent strides in Physics has concluded, to our utter amazement, that there is indeed a “rock bottom” to everything, be it space or time. “We’ve long suspected that space-time had to be quantized,” said Dr. Steven B. Giddings, a theorist at the University of California at Santa Barbara. “Recent developments have led to some exciting new proposals about how to make these ideas more concrete1.” Strong evidences of granularity of space and time are seen from recent attempts to unify general relativity, Einstein’s theory of gravity and quantum mechanics into a single, harmonious theory named superstring theory. Modern atomic theory has determined the quantization of energy since Planck’s time, yet the nature of space-time (which is in fact, linked with each other through gravity) continues in its dangling status. It is interestingly, also Planck who suspects that there is in fact a fundamental length in everything and he could prove it if he could somehow manipulate and combine gravitational constant, Planck’s constant and the speed of light in a way that their dimensions cancel each other. But mathematics alone surely does not suffice.

Physicists who believe in super-string theory2 have then sought to achieve the unification by coupling them mathematically and testing them experimentally to achieve a state at which different couplings have the same strength. Sadly, the mass scale required for this “experimental” unifications is way too high than existing particle accelerators. Yet, physicists are now taking a new detour: “Proton decay,” another hypothetical phenomenon which if experimentally observed, would corroborate superstring theory has been actively tested. Besides these thwarted experimental attempts, strong implications of minimal length could also be derived from Heisenberg uncertainty principle, the “non-commutative’ property of which would be adequately explained by granularity of space-time.

The theory of granularity of everything is by no means conclusive. Indeed, it would seem incredibly odd if our universe is in the force of a giant computer screen! But this is not to dismiss the idea as simply false since it does not accommodate our aesthetic and intuitive sense. Modern science is still continuing its quest to reach the heart of this ancient paradox of, “everything”.

References:

1 “How is the Universe Built? Grain by grain” –GEORGE JOHNSON, The New York Times

2 The Official Superstring Theory Web Site - www.superstringtheory.com