# Minkowski’s Four–dimensional Space

##### 3 minutes • 478 words

Space is a 3D continuum wherein:

- an object exists in 3 co-ordinates
`x, y, z`

as Point 1 - there are infinite points around Point 1
- These are designated as
`x1, y1, z1`

,`x2, y2, z2`

,`x3, y3, z3`

, etc. - These points create a “continuum”

- These are designated as

Our universe is a 4D space-time continuum, as described by Minkowski. It has the additional coordinate of time-value `t`

.

Every event has infinite “neighbouring” events (realised or imaginary). The leads to co-ordinates `x1, y1, z1, t1`

.

Before my theory of Relativity, time played a different and more independent rôle to the space co-ordinates. This is why we usually treat time as an independent continuum*.

## Superphysics Note

Time is absolute* in classical mechanics – it is independent of the position and the condition of motion of the system of coordinates. This is expressed in the last equation of the Galileian transformation as `t' = t`

.

## Superphysics Note

The 4D spacetime is natural to the theory of relativity which robs time of its independence*.

## Superphysics Note

Time is absolute in classical mechanics because classical movement happened within the observable space that is within human cognitive limitations.

This is shown by the 4th equation of the Lorentz transformation:

```
t' = (t - (v/c2) x) / √ 1-(v2/c2)
```

The time difference `∆ t'`

of two events with respect to `K'`

does not vanish in general, even when the time difference `∆ t`

of the same events with reference to non-moving `K`

vanishes. Pure “space-distance” of two events with respect to non-moving `K`

results in “time-distance” of the same events with respect to the moving `K'`

.

Minkowski’s discovery was important for the development of my theory of relativity.

The 4D space-time continuum of the theory of relativity has a pronounced relationship with the 3D continuum of Euclidean geometrical space. To emphasize this relationship, we must replace the usual time coordinate `t`

by an imaginary magnitude `√ −1ct`

proportional to it. This allows the natural laws that satisfy the demands of Special Relativity to assume mathematical forms wherein the time coordinate plays exactly the same rôle as the `x, y, z`

coordinates.

These 4 coordinates correspond exactly to the 3 space coordinates in Euclidean geometry.

Without Minkowski’s 4D spacetime, General Relativity could not be developed.