spacetime - Do we live in a world with 4 or more dimension?

A NOVA show have told the audience that we are live in 3 dimensional world, the world we lived in is compose by 3 element: the energy, matter, space. By the time Einstein have invented the 4-dimensional model including the time element, why no one claim that we actually live in 4-dimensional world

Answer

Victor, This is a good question. Probably one of the greatest tragedies surrounding modern science in popular literature is the portrayal of dimensions and our understanding of them.

Many popular shows are inconsistent in when they talk about dimensions, in some cases they refer to the 3 spatial and 1 time dimension that we commonly observe as separate things, and in some cases they talk about the 4-dimensional spacetime that is used in modern physics on a routine basis without any real discussion about what they mean.

Spacetime is a combination of the 3 space dimensions and 1 time dimension, e.g. 3+1 dimensions which equals 4 dimensions.

In the early days of relativistic mechanics, in order to represent the 3 spatial dimensions and 1 time dimension as one entity, they would give the time dimension an imaginary value. So the 4 dimensional spacetime would be represented as:

$$x + y + z + it$$

This covenient, because when one takes the inner product (sometimes called the dot product) of the representation of space time one gets:

$$x^2 + y^2 + z^2 - t^2$$

This sort of representation is convenient because one can begin to understand the relationship between space and time in terms of the Pythagorean theorem.

This is the simplest example of how one can begin to relate the nature of spacetime to geometry. The broader theory of how geometry of spacetime changes as you move in spacetime is Einstein's Theory of General Relativity.

General Relativity assumes that there are 3 dimensions of space and 1 dimension of time that make up the 4-dimensional spacetime that programs sometimes reference.

There are other theories that propose there are more than 3 space dimensions of space and 1 dimension of time. However, these are very speculative still.