String Theory IV- Exploring Hidden Dimensions

Introduction

Though the notion that the Universe has more dimensions than just 3 seems very counter-intuitive, physicists are convinced that they really exist.

Theodor Kaluza was the first to introduce the concept of hidden dimensions. in 1919, he attempted to solve Einstein’s Field Equations in 5 dimensional space-time (he added another space dimension) . He made a startling discovery. By adding another dimension, he was able to derive the equations for General Relativity as well as Maxwell’s equations for electromagnetism. He had unified these two theories.

His discovery was well ahead of its time but, was initially ignored as scientific focus was shifting to quantum mechanics. The unification of fundamental forces due to addition of extra spatial dimensions is what all of String Theory is based on.

Visualizing Curled Up Dimensions

Intuitively, we are aware that we can move in three dimensions. These are: up-down, front-back and left-right. In 1919, Theodor Kaluza added another “direction” in which matter can access by adding another dimension of space. But where are these extra dimensions? Some argue that they are extremely small. Far smaller than what our current technology can measure.

To understand curled up or hidden dimensions, we can take the common example of an ant on a wire.

Suppose, you look at a wire suspended between two poles situated a kilometre (0.6 mi) from your place. The wire seems to be a 1 dimensional line. To locate a point on this line, you only need to calculate its distance from either the left or right pole. Now, suppose you are an ant on that wire. You see that the wire has a thickness as well. You can move around the thickness of the wire. You can access another dimension in addition to just left and right, the circular one.

The circular dimension was hidden to the human you. This is what Physicists think is the case in our Universe. The extra dimensions are so small that they are hidden from us.

Introduction to Hidden dimensions in String Theory

We learnt earlier that extra dimensions of space are required to unify the fundamental forces. We saw that Theodor Kaluza was able to unit Gravity and Electromagnetism – two completely different forces- just by adding another dimension to space. This is also the case in String Theory.

In String Theory, you don’t have 4,5 or 6 but 9 dimensions of space. Out of these, 3 are the everyday dimensions and 6 are the curled up (hidden) dimensions. These curled up dimensions are everywhere, at every point in space.

Unlike Theodor’s speculation, String Theory requires 10 dimensions of space to make any sense. Without 10 dimensional space, mathematical results in String theory make no sense at all.

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